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Product Name: Envision 2.0 grades 6-8 grade 6
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Curriculum Standards:

Convert between customary and metric units. - 6.P.5.10
Find and position pairs of rational numbers on a coordinate plane. - NC.6.NS.6.b.3
Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - NC.6.NS.6.b.2
Understand signs of numbers in ordered pairs as indicating locations in quadrants. - NC.6.NS.6.b.1
Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. - 6.2.3.2
Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. - 6.2.3.1
Summarize numerical data sets in relation to their context, such as by: - MAFS.6.SP.2.5
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. - MAFS.6.SP.2.4
Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems. - 6.A.2.1
Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm². - 6.3.1.3
Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. - 6.3.1.2
Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. - 6.3.1.1
Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. - MAFS.K12.MP.3.1
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. - NC.6.NS.7.a
Write, interpret, and explain statements of order for rational numbers in real-world contexts. - NC.6.NS.7.b
Find and position rational numbers on a horizontal or vertical number line. - NC.6.NS.6.a.2
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. - NC.6.NS.6.a.1
Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. - NC.6.NS.5.c.1
Distinguish comparisons of absolute value from statements about order. - NC.6.NS.5.c.2
Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false. - 6.A.1.3
Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations. - 6.A.1.2
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. - MAFS.6.SP.1.2
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. - MAFS.6.SP.1.1
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. - MAFS.6.SP.1.3
Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact. - 6.3.2.2
Solve problems using the relationships between the angles formed by intersecting lines. - 6.3.2.1
Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. - MAFS.K12.MP.2.1
Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. - 6.A.1.1
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi? - MAFS.6.NS.1.1
Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles. - 6.3.2.3
The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. - 6.1
The student will recognize and represent patterns with whole number exponents and perfect squares. - 6.4
Create and evaluate expressions involving variables and whole number exponents. - 6.EEI.A.2
Identify and generate equivalent algebraic expressions using mathematical properties. - 6.EEI.A.3
Describe the difference between an expression and an equation. - 6.EEI.A.1
Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations. - 6.N.3.3
Use multiplicative reasoning and representations to solve ratio and unit rate problems. - 6.N.3.4
Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. - 6.N.3.1
Determine the unit rate for ratios. - 6.N.3.2
Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. - 6.3.3.1
Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. - MAFS.K12.MP.5.1
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). - MAFS.6.NS.2.4
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation. - MAFS.6.NS.2.3
Fluently divide multi-digit numbers using the standard algorithm. - MAFS.6.NS.2.2
Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. - 6.3.3.2
Solve problems involving division of fractions by fractions. - 6.NS.A.1a
Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units. - 6.GM.3.1
Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units. - 6.GM.3.2
Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. - 6.EEI.B.5
Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. - 6.EEI.B.6
Solve one-step linear equations in one variable involving non-negative rational numbers. - 6.EEI.B.7
Understand additive inverses when adding and subtracting integers. - NC.6.NS.9.a
Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. - 6.EEI.B.4
Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. - NC.6.SP.3.a.1
Understand the median as a measure of center that is the numerical middle of an ordered data set. - NC.6.SP.3.a.2
Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships. - 6.N.4.2
Multiply and divide fractions and decimals using efficient and generalizable procedures. - 6.N.4.3
Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers. - 6.N.4.4
Use dot plots, histograms, and box plots to represent data. - NC.6.SP.4.a
Compare the attributes of different representations of the same data. - NC.6.SP.4.b
Analyze and describe the properties of prisms and pyramids. - 5.GM.A.3
Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers. - 6.A.3.1
Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution. - 6.A.3.2
Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem. - 6.N.4.1
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - MAFS.6.NS.3.5
Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. - 6.GM.4.3
Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. - MAFS.K12.MP.4.1
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. - MAFS.6.NS.3.8
Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. - NC.6.G.1.b
Find the area of triangles by composing into rectangles and decomposing into right triangles. - NC.6.G.1.a
Solve multistep problems with fractions and decimals. - 6.NC.1.7
Divide with mixed numbers. - 6.NC.1.6
Display numerical data in plots on a number line. - NC.6.SP.4
Use models and equations to multiply fractions and mixed numbers. - 6.NC.1.3
Summarize numerical data sets in relation to their context. - NC.6.SP.5
Divide whole numbers and decimals. - 6.NC.1.2
Divide a fraction by another fraction. - 6.NC.1.5
Use models and equations to represent fraction division. - 6.NC.1.4
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. - NC.6.SP.1
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. - NC.6.SP.2
Add, subtract, and multiply decimals. - 6.NC.1.1
Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. - NC.6.SP.3
Evaluate an algebraic expression with whole numbers, decimals, and fractions. - 6.AF.3.5
Use variables to write algebraic expressions. - 6.AF.3.4
Combine like terms in algebraic expressions. - 6.AF.3.7
Identify and write equivalent algebraic expressions. - 6.AF.3.6
Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. - NC.6.SP.3.a
Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. - NC.6.SP.3.b
Write and evaluate numbers with exponents. - 6.AF.3.1
Use the order of operations to evaluate numerical expressions. - 6.AF.3.3
Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. - 6.AF.3.2
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2). - M.6.13c
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.) - M.6.13b
Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.) - M.6.13a
Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. - 6.GM.A.1
Mathematical Modeling: Use Positive Rational Numbers - 6.NC.1MM
Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. - MAFS.K12.MP.7.1
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. - MAFS.6.EE.3.9
Mathematical Modeling: Solve Area, Surface Area, and Volume Problems - 6.G.7MM
Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. - 6.GM.1.1
Develop and use formulas to determine the area of triangles. - 6.GM.1.2
Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems. - 6.GM.1.3
Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.) - M.6.10d
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.) - M.6.10a
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars). - M.6.10c
Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C). - M.6.10b
Find areas of trapezoids and kites. - 6.G.7.3
Find the areas of triangles. - 6.G.7.2
Represent solid figures using nets. - 6.G.7.5
Find the areas of polygons. - 6.G.7.4
Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. - 6.G.7.1
Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. - NC.6.RP.2
Draw a net of a pyramid and use it to find the pyramid's surface area. - 6.G.7.7
Draw a net of a prism and use it to find the prism's surface area. - 6.G.7.6
Find the volume of a rectangular prism with fractional edge lengths. - 6.G.7.8
Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. - MAFS.K12.MP.6.1
Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. - NC.6.G.2
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers. - MAFS.6.EE.2.7
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. - MAFS.6.EE.2.8
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. - MAFS.6.EE.2.5
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set. - MAFS.6.EE.2.6
Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. - NC.6.G.4
Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines. - 6.GM.2.1
Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. - NC.6.G.3.b
Drawing polygons in the coordinate plane given coordinates for the vertices. - NC.6.G.3.a
Understand a ratio as a comparison of two quantities and represent these comparisons. - 6.RP.A.1
Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. - 6.RP.A.2
Solve problems involving ratios and rates. - 6.RP.A.3
Mathematical Modeling: Understand and Use Percent - 6.P.6MM
Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. - NC.6.EE.2.b
Write expressions that record operations with numbers and with letters standing for numbers. - NC.6.EE.2.a
Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. - NC.6.EE.2.c
Find the whole amount when given a part and the percent. - 6.P.6.6
Write equivalent values as fractions, decimals, and percents. - 6.P.6.2
Write percents that are greater than 100 or less than 1. - 6.P.6.3
Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. - 6.P.6.4
Reporting the number of observations in dot plots and histograms. - NC.6.SP.5.a.1
Solve problems involving percents. - 6.P.6.5
Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. - NC.6.SP.5.a.2
Represent and find the whole percent of a whole. - 6.P.6.1
Mathematical Modeling: Numeric and Algebraic Expressions - 6.NC.3MM
Mathematical Modeling: Understand and Use Ratio and Rate - 6.P.5MM
Find side lengths of polygons on a coordinate plane. - 6.NC.2.6
Use absolute value to find distance on a coordinate plane. - 6.NC.2.5
Represent rational numbers using a number line. - 6.NC.2.2
Use positive and negative integers. - 6.NC.2.1
Graph points with rational coordinates on a coordinate plane. - 6.NC.2.4
Find and interpret absolute value. - 6.NC.2.3
Write and solve a multiplication or division equation. - 6.AF.4.4
Write and solve an addition or subtraction equation. - 6.AF.4.3
Understand and write an inequality that describes a real-world situation. - 6.AF.4.6
Write and solve equations that involve rational numbers. - 6.AF.4.5
Identify dependent and independent variables. - 6.AF.4.8
Write and represent solutions of inequalities. - 6.AF.4.7
Use patterns to write and solve equations with variables. - 6.AF.4.9
Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true. - M.6.16
Identify parts of an expression using mathematical terminology. - 6.EEI.A.2a
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set. - M.6.17
Evaluate non-negative rational number expressions. - 6.EEI.A.2c
Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y). - M.6.14
Evaluate expressions at specific values of the variables. - 6.EEI.A.2b
Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.) - M.6.15
Understand the meaning of the variable in the context of the situation. - 6.EEI.A.2e
Write and evaluate numerical expressions involving whole-number exponents. - M.6.12
Write and evaluate algebraic expressions. - 6.EEI.A.2d
Use the properties of equality to write equivalent equations. - 6.AF.4.2
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. - M.6.11
Determine if a value for a variable makes an equation true. - 6.AF.4.1
Use unit rates to solve problems. - 6.P.5.7
Analyze the relationship between dependent and independent variables in tables, graphs, and equations. - 6.AF.4.10
Use ratio reasoning to convert customary measurements. - 6.P.5.8
Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers. - M.6.18
Use unit rates to convert metric measurements. - 6.P.5.9
Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. - M.6.19
Compare ratios to solve problems. - 6.P.5.3
Solve ratio problems by using tables and graphs to show equivalent ratios. - 6.P.5.4
Solve problems involving rates. - 6.P.5.5
Compare unit rates to solve problems. - 6.P.5.6
Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. - NC.6.SP.5.b.1
Mathematical Modeling: Integers and Rational Numbers - 6.NC.2MM
Justifying the appropriate choice of measures of center using the shape of the data distribution. - NC.6.SP.5.b.2
Use a ratio to describe the relationship between two quantities. - 6.P.5.1
Use multiplication and division to find equivalent ratios. - 6.P.5.2
Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) - M.6.20
Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. - MAFS.K12.MP.8.1
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. - M.6.27
Display numerical data in plots on a number line, including dot plots, histograms and box plots. - M.6.28
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.) - M.6.25
Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape. - M.6.26
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. - M.6.23
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. - M.6.24
Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - M.6.21
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. - M.6.22
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. - MAFS.6.G.1.1
Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. - MAFS.6.G.1.2
Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. - MAFS.6.G.1.3
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. - MAFS.6.G.1.4
Demonstrate fluency with addition, subtraction, multiplication and division of decimals. - 6.NS.B.3
Demonstrate fluency with division of multi-digit whole numbers. - 6.NS.B.2
Locate rational numbers on a horizontal or vertical number line. - 6.NS.C.6a
Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. - 6.DSP.A.1
Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. - 6.NS.C.6c
Write, interpret and explain problems of ordering of rational numbers. - 6.NS.C.6b
Summarize numerical data sets in relation to the context. - 6.DSP.B.5
Display and interpret data. - 6.DSP.B.4
Finding the whole, given a part and the percent. - NC.6.RP.4.c
Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. - NC.6.RP.4.b
Understanding and finding a percent of a quantity as a ratio per 100. - NC.6.RP.4.a
Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - M.6.3a
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. - M.6.3d
Compute and interpret quotients of positive fractions. - 6.NS.A.1
Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?) - M.6.3b
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - M.6.3c
Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. - 6.DSP.A.2
Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. - 6.DSP.A.3
Mathematical Modeling: Represent and Solve Equations and Inequalities - 6.NC.4MM
Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. - 6.EEI.C.9a
Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. - 6.EEI.C.9b
Make sense of problems and persevere in solving them. - MP.1
Reason abstractly and quantitatively. - MP.2
Look for and make use of structure. - MP.7
Look for and express regularity in repeated reasoning. - MP.8
Construct viable arguments and critique the reasoning of others. - MP.3
Model with mathematics. - MP.4
Use appropriate tools strategically. - MP.5
Attend to precision. - MP.6
Describe situations in which opposite quantities combine to make 0. - NC.6.NS.9.a.1
Convert measurement units within and between two systems of measurement. - 6.RP.A.3d
Solve unit rate problems. - 6.RP.A.3b
Solve percent problems. - 6.RP.A.3c
Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. - NC.6.NS.9.a.3
Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. - 6.RP.A.3a
Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. - NC.6.NS.9.a.2
Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. - NC.6.NS.9.a.4
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. - MAFS.6.EE.1.4
Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. - M.6.29d
Write, read, and evaluate expressions in which letters stand for numbers. - MAFS.6.EE.1.2
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. - MAFS.6.EE.1.3
Reporting the number of observations. - M.6.29a
Write and evaluate numerical expressions involving whole-number exponents. - MAFS.6.EE.1.1
Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. - M.6.29c
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. - M.6.29b
Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). - 6.NS.C.8
The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. - 6.13
Understand that the absolute value of a rational number is its distance from 0 on the number line. - 6.NS.C.7
Use positive and negative numbers to represent quantities. - 6.NS.C.5
Interpret and compute quotients of fractions. - NC.6.NS.1.a
Solve real-world and mathematical problems involving division of fractions. - NC.6.NS.1.b
Plotting the pairs of values on the coordinate plane. - NC.6.RP.3.e
Converting and manipulating measurements using given ratios. - NC.6.RP.3.d
Using a unit ratio. - NC.6.RP.3.c
Graph the solution set of an inequality. - 6.EEI.B.8b
Finding missing values in the tables. - NC.6.RP.3.b
Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. - 6.EEI.B.8a
Creating and using a table to compare ratios. - NC.6.RP.3.a
Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. - 6.GM.A.4b
Representing solutions of inequalities on number line diagrams. - NC.6.EE.8.d
Represent three-dimensional figures using nets made up of rectangles and triangles. - 6.GM.A.4a
Recognizing that inequalities of the form x > c or x < c have infinitely many solutions. - NC.6.EE.8.c
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - M.6.9b
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - M.6.9c
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. - M.6.9a
Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?) - M.6.4
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”) - M.6.1
Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions. - M.6.2
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). - M.6.7
Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - M.6.8
Fluently divide multi-digit numbers using the standard algorithm. - M.6.5
Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation. - M.6.6
Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. - 6.N.1.5
Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property. - 6.N.1.6
Convert between equivalent representations of positive rational numbers. - 6.1.1.7
Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. - 6.1.1.6
Factor whole numbers; express a whole number as a product of prime factors with exponents. - 6.1.1.5
Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. - 6.1.1.4
Understand that percent represents parts out of 100 and ratios to 100. - 6.1.1.3
Compare positive rational numbers represented in various forms. Use the symbols <, = and >. - 6.1.1.2
Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. - MAFS.6.NS.3.7c
Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC. - MAFS.6.NS.3.7b
Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. - MAFS.6.NS.3.7a
Writing an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. - NC.6.EE.8.b
Using substitution to determine whether a given number in a specified set makes an inequality true. - NC.6.EE.8.a
Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. - MAFS.6.NS.3.7d
Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation. - 6.N.1.1
Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =. - 6.N.1.2
Explain that a percent represents parts “out of 100” and ratios “to 100.” - 6.N.1.3
Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems. - 6.N.1.4
Make and analyze frequency tables and histograms. - 6.DP.8.4
Use measures of variability to describe a data set. - 6.DP.8.5
The student will compare and order positive rational numbers. - 6.2b
Select and use appropriate statistical measures. - 6.DP.8.6
Summarize numerical data sets. - 6.DP.8.7
Identify and write statistical questions. - 6.DP.8.1
Identify the mean, median, mode, and range of a data set. - 6.DP.8.2
Make and interpret box plots. - 6.DP.8.3
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - MAFS.6.NS.3.6b
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. - MAFS.6.NS.3.6a
The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. - 6.2a
Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. - MAFS.6.NS.3.6c
Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood. - 6.4.1.2
for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial represent - 6.4.1.1
Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. - 6.4.1.4
Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences. - 6.4.1.3
Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. - 6.GM.A.2b
Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. - 6.GM.A.2a
Mathematical Modeling: Display, Describe, and Summarize Data - 6.DP.8MM
The student will identify and describe absolute value of integers. - 6.3c
Use reasoning about multiplication and division to solve ratio and rate problems. - 6.1.2.4
Determine the rate for ratios of quantities with different units. - 6.1.2.3
Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. - 6.1.2.2
Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. - 6.1.2.1
x + p = q in which p, q and x are all nonnegative rational numbers; and, - NC.6.EE.7.a
The student will compare and order integers. - 6.3b
The student will identify and represent integers. - 6.3a
p · x = q for cases in which p, q and x are all nonnegative rational numbers. - NC.6.EE.7.b
Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. - 6.GM.A.3a
Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. - MAFS.6.SP.2.5d
Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered. - MAFS.6.SP.2.5c
Construct polygons in the Cartesian coordinate plane. - 6.GM.A.3d
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. - MAFS.6.SP.2.5b
Find distances between points with the same first coordinate or the same second coordinate. - 6.GM.A.3c
Reporting the number of observations. - MAFS.6.SP.2.5a
Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. - 6.GM.A.3b
Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. - 6.1.1.1
Model a ratio relationship using a variety of representations. - NC.6.RP.1.b
Describe a ratio as a multiplicative relationship between two quantities. - NC.6.RP.1.a
Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. - NC.6.NS.4.d
Write, read, and evaluate algebraic expressions. - NC.6.EE.2
Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. - NC.6.EE.1
Identify when two expressions are equivalent and justify with mathematical reasoning. - NC.6.EE.4
Find the greatest common factor of two whole numbers less than or equal to 100. - NC.6.NS.4.b
Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. - NC.6.NS.4.c
Apply the properties of operations to generate equivalent expressions without exponents. - NC.6.EE.3
The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. - 6.11b
Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. - 6.DSP.B.5d
Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. - NC.6.EE.6
Make sense of problems and persevere in solving them. - 6.MP.1
Use substitution to determine whether a given number in a specified set makes an equation true. - NC.6.EE.5
Reason abstractly and quantitatively. - 6.MP.2
Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. - 6.1.3.5
Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. - 6.1.3.4
Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. - 6.1.3.3
Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. - 6.1.3.2
Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. - 6.1.3.1
Apply and extend previous understandings of addition and subtraction. - NC.6.NS.9
Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. - NC.6.NS.8
The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. - 6.5b
The student will multiply and divide fractions and mixed numbers. - 6.5a
Find the unique prime factorization for a whole number. - NC.6.NS.4.a
The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals. - 6.5c
Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. - NC.6.NS.3
Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. - NC.6.NS.2
Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. - 6.2.1.2
Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. - 6.2.1.1
The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. - 6.12d
The student will represent a proportional relationship between two quantities, including those arising from practical situations. - 6.12a
The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. - 6.12b
Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data. - 6.D.1.2
Use appropriate tools strategically. - 6.MP.5
Calculate the mean, median, and mode for a set of real-world data. - 6.D.1.1
Attend to precision. - 6.MP.6
Construct viable arguments and critique the reasoning of others. - 6.MP.3
Model with mathematics. - 6.MP.4
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. - MAFS.6.RP.1.3d
Report the number of observations. - 6.DSP.B.5a
Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. - MAFS.K12.MP.1.1
Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent. - MAFS.6.RP.1.3c
Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. - 6.DSP.B.5c
Look for and make use of structure. - 6.MP.7
Create and analyze box and whisker plots observing how each segment contains one quarter of the data. - 6.D.1.3
Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. - MAFS.6.RP.1.3e
Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. - 6.DSP.B.5b
Look for and express regularity in repeated reasoning. - 6.MP.8
Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? - MAFS.6.RP.1.3b
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios. - MAFS.6.RP.1.3a
The student will simplify numerical expressions involving integers. - 6.6c
Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). - NC.6.EE.9.b
Describe quantities having opposite directions or values. - NC.6.NS.5.a
Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. - NC.6.NS.5.b
Create and interpret circle graphs. - 6.DSP.B.4b
Use dot plots, histograms and box plots to display and interpret numerical data. - 6.DSP.B.4a
Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” - MAFS.6.RP.1.1
Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” - MAFS.6.RP.1.2
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. - MAFS.6.RP.1.3
The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. - 6.7c
Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. - NC.6.EE.9.a
Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. - 7.EEI.B.4a
Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. - MAFS.6.EE.1.2b
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. - MAFS.6.EE.1.2c
Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. - MAFS.6.EE.1.2a
Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. - 6.2.2.1
The student will represent a practical situation with a linear inequality in one variable. - 6.14a
The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. - 6.14b
Represent possible outcomes using a probability continuum from impossible to certain. - 6.D.2.1
Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results. - 6.D.2.3
The student will identify the components of the coordinate plane. - 6.8a
The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. - 6.8b
Find the greatest common factor (GCF) and the least common multiple (LCM). - 6.NS.B.4a
Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. - 6.NS.B.4b


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Title: enVisionmath2.0 Grades 6-8 Grade 6 2017

Description: enVisionmath2.0 Grades 6-8 Grade 6 2017


         Beginning-of-Year Assessment

         Math Practices Animations

            Math Practice 1 Animation

            Math Practice 2 Animation

            Math Practice 3 Animation

            Math Practice 4 Animation

            Math Practice 5 Animation

            Math Practice 6 Animation

            Math Practice 7 Animation

            Math Practice 8 Animation

         Topic 1: Use Positive Rational Numbers

            i1-2 Part 1

            i10-3 Part 1

            i10-4 Part 2

            i11-1 Part 1

            i11-4 Part 1

            i18-2 Part 1

            i3-3 Part 1

            i3-5 Part 1

            i5-2 Part 1

            i6-1 Part 1

            i7-1 Part 2

            i8-2 Part 1

            i1-2 Part 2

            i10-3 Part 2

            i10-4 Part 3

            i11-1 Part 3

            i11-4 Part 2

            i18-2 Part 2

            i3-3 Part 2

            i3-5 Part 2

            i5-2 Part 2

            i6-1 Part 2

            i7-1 Part 1

            i8-2 Part 3

            i1-2 Part 3

            i10-3 Part 3

            i10-4 Part 1

            i11-1 Part 2

            i11-4 Part 3

            i18-2 Part 3

            i3-3 Part 3

            i3-5 Part 3

            i5-2 Part 3

            i6-1 Part 3

            i7-1 Part 3

            i8-2 Part 2

            i1-2 Lesson Check

            i10-3 Lesson Check

            i10-4 Lesson Check

            i11-1 Lesson Check

            i11-4 Lesson Check

            i18-2 Lesson Check

            i3-3 Lesson Check

            i3-5 Lesson Check

            i5-2 Lesson Check

            i6-1 Lesson Check

            i7-1 Lesson Check

            i8-2 Lesson Check

            i1-2 Practice

            i10-3 Practice

            i10-4 Practice

            i11-1 Practice

            i11-4 Practice

            i18-2 Practice

            i3-3 Practice

            i3-5 Practice

            i5-2 Practice

            i6-1 Practice

            i7-1 Practice

            i8-2 Practice

            Topic 1 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 1

            Topic 1 STEM Project

               Topic 1: STEM Project

               Topic 1 STEM Video

            Topic 1: Today's Challenge

            1-1: Fluently Add, Subtract, and Multiply Decimals

               Interactive Student Edition: Grade 6 Lesson 1-1

               Student's Edition eText: Grade 6 Lesson 1-1

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-1: Solve & Discuss It!
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Develop: Visual Learning

                  1-1: Example 1 & Try It!
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Example 2 & Try It!
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Example 3 & Try It!
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Additional Example 1
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Additional Example 3 with Try Another One
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Key Concept
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Assess & Differentiate

                  1-1: Lesson Quiz
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Virtual Nerd™: How Do You Multiply Decimals?
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Virtual Nerd™: How Do You Subtract Decimals?
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: MathXL for School: Additional Practice
                    Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-1: Additional Practice

            1-2: Fluently Divide Whole Numbers and Decimals

               Interactive Student Edition: Grade 6 Lesson 1-2

               Student's Edition eText: Grade 6 Lesson 1-2

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-2: Solve & Discuss It!
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Develop: Visual Learning

                  1-2: Example 1 & Try It!
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

                  1-2: Example 2
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

                  1-2: Example 3 & Try It!
                    Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Additional Example 3
                    Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Additional Example 3B with Try Another One
                    Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Key Concept
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Assess & Differentiate

                  1-2: Lesson Quiz
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Virtual Nerd™: How Do You Divide Whole Numbers?
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Virtual Nerd™: How Do You Divide a Decimal by a Decimal?
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: MathXL for School: Additional Practice
                    Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-2: Additional Practice

            1-3: Multiply Fractions

               Interactive Student Edition: Grade 6 Lesson 1-3

               Student's Edition eText: Grade 6 Lesson 1-3

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-3: Solve & Discuss It!
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Develop: Visual Learning

                  1-3: Example 1 & Try It!
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Example 2 & Try It!
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Example 3 & Try It!
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Additional Example 2
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Additional Example 3 with Try Another One
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Key Concept
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Assess & Differentiate

                  1-3: Lesson Quiz
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Virtual Nerd™: How do you Multiply Fractions?
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Virtual Nerd™: How Do You Multiply Mixed Numbers?
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: MathXL for School: Additional Practice
                    Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-3: Additional Practice

            1-1: Example 3 & Try It!
              Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

            1-1: Virtual Nerd™: How Do You Multiply Decimals?
              Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

            1-2: Example 2
              Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

            1-2: Example 3 & Try It!
              Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

            1-2: Key Concept
              Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

            1-2: Virtual Nerd™: How Do You Divide a Decimal by a Decimal?
              Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

            1-3: Example 3 & Try It!
              Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

            1-3: Virtual Nerd™: How Do You Multiply Mixed Numbers?
              Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

            Topic 1 Mid-Topic Assessment
              Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. Fluently divide multi-digit numbers using the standard algorithm. Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

            3-Act Mathematical Modeling: Stocking Up

               Student's Edition eText: Grade 6 Topic 1 3-Act Mathematical Modeling

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 1 Math Modeling: Act 1
                    Curriculum Standards: Mathematical Modeling: Use Positive Rational Numbers Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Demonstrate fluency with division of multi-digit whole numbers. Reason abstractly and quantitatively. Model with mathematics. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Reason abstractly and quantitatively. Model with mathematics. 

                  Topic 1 Math Modeling: Act 2
                    Curriculum Standards: Mathematical Modeling: Use Positive Rational Numbers Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Demonstrate fluency with division of multi-digit whole numbers. Reason abstractly and quantitatively. Model with mathematics. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Reason abstractly and quantitatively. Model with mathematics. 

                  Topic 1 Math Modeling: Act 3
                    Curriculum Standards: Mathematical Modeling: Use Positive Rational Numbers Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Demonstrate fluency with division of multi-digit whole numbers. Reason abstractly and quantitatively. Model with mathematics. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Reason abstractly and quantitatively. Model with mathematics. 

            1-4: Understand Division with Fractions

               Interactive Student Edition: Grade 6 Lesson 1-4

               Student's Edition eText: Grade 6 Lesson 1-4

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-4: Explore It!
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Develop: Visual Learning

                  1-4: Example 1 & Try It!
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Example 2 & Try It!
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Example 3 & Try It!
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Additional Example 1
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Additional Example 3 with Try Another One
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Key Concept
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Assess & Differentiate

                  1-4: Lesson Quiz
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Virtual Nerd™: How Do You Divide Fractions?
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: MathXL for School: Additional Practice
                    Curriculum Standards: Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-4: Additional Practice

            1-5: Divide Fractions by Fractions

               Interactive Student Edition: Grade 6 Lesson 1-5

               Student's Edition eText: Grade 6 Lesson 1-5

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-5: Solve & Discuss It!
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Develop: Visual Learning

                  1-5: Example 1 & Try It!
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Example 2 & Try It!
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Example 3 & Try It!
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Additional Example 1
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Additional Example 3 with Try Another One
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Key Concept
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Assess & Differentiate

                  1-5: Lesson Quiz
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Virtual Nerd™: How Do You Divide Fractions?
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: MathXL for School: Additional Practice
                    Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-5: Additional Practice

            1-6: Divide Mixed Numbers

               Interactive Student Edition: Grade 6 Lesson 1-6

               Student's Edition eText: Grade 6 Lesson 1-6

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-6: Solve & Discuss It!
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Develop: Visual Learning

                  1-6: Example 1 & Try It!
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Example 2
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Example 3 & Try It!
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Additional Example 1
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Additional Example 3 with Try Another One
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Key Concept
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

               Assess & Differentiate

                  1-6: Lesson Quiz
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Virtual Nerd™: How Do You Divide Mixed Numbers?
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: MathXL for School: Additional Practice
                    Curriculum Standards: Divide with mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-6: Additional Practice

            1-7: Solve Problems with Rational Numbers

               Interactive Student Edition: Grade 6 Lesson 1-7

               Student's Edition eText: Grade 6 Lesson 1-7

               Math Anytime

                  Topic 1: Today's Challenge

               Develop: Problem-Based Learning

                  1-7: Explain It!
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Develop: Visual Learning

                  1-7: Example 1 & Try It!
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-7: Example 2 & Try It!
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Additional Example 1
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

                  1-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Divide whole numbers and decimals. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Key Concept
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

               Assess & Differentiate

                  1-7: Lesson Quiz
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Virtual Nerd™: How Do You Multiply Mixed Numbers?
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Virtual Nerd™: How Do You Divide a Decimal by a Decimal?
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: MathXL for School: Additional Practice
                    Curriculum Standards: Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

                  1-7: Additional Practice

            Interactive Student Edition: End of Topic 1

            Topic 1 Performance Task
              Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Solve multistep problems with fractions and decimals. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Demonstrate fluency with division of multi-digit whole numbers. 

            Topic 1 Assessment
              Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. Fluently divide multi-digit numbers using the standard algorithm. Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Use models and equations to represent fraction division. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Divide a fraction by another fraction. Divide with mixed numbers. Solve multistep problems with fractions and decimals. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. 

         Topic 2:  Integers and Rational Numbers

            i9-5 Part 1

            i9-3 Part 1

            i6-2 Part 1

            i7-2 Part 1

            i20-1 Part 2

            i20-2 Part 2

            i22-1 Part 3

            i22-4 Part 1

            i22-2 Part 1

            i9-5 Part 2

            i9-3 Part 2

            i6-2 Part 2

            i7-2 Part 2

            i20-1 Part 3

            i20-2 Part 3

            i22-1 Part 1

            i22-4 Part 3

            i22-2 Part 2

            i9-5 Lesson Check

            i6-2 Part 3

            i7-2 Part 3

            i20-1 Part 1

            i20-2 Part 1

            i22-1 Part 2

            i22-4 Part 2

            i22-2 Part 3

            i9-5 Part 3

            i9-3 Lesson Check

            i6-2 Lesson Check

            i7-2 Lesson Check

            i20-1 Lesson Check

            i20-2 Lesson Check

            i22-1 Lesson Check

            i22-4 Lesson Check

            i22-2 Lesson Check

            i9-3 Part 3

            i7-2 Practice

            i20-1 Practice

            i22-1 Practice

            i22-4 Practice

            i9-5 Practice

            i9-3 Practice

            i6-2 Practice

            i22-2 Practice

            i20-2 Practice

            Topic 2 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 2

            Topic 2 STEM Project

               Topic 2: STEM Project

               Topic 2 STEM Video

            Topic 2: Today's Challenge

            2-1: Understand Integers

               Interactive Student Edition: Grade 6 Lesson 2-1

               Student's Edition eText: Grade 6 Lesson 2-1

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-1: Explain It!
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

               Develop: Visual Learning

                  2-1: Example 1 & Try It!
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

                  2-1: Example 2 & Try It!
                    Curriculum Standards: Use positive and negative integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Example 3 & Try It!
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

                  2-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

                  2-1: Additional Example 2
                    Curriculum Standards: Use positive and negative integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Key Concept
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

               Assess & Differentiate

                  2-1: Enrichment
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Lesson Quiz
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Virtual Nerd™: How Do You Represent Real World Situations Using Integers?
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Virtual Nerd™: How Do You Compare Integers Using a Number Line?
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: MathXL for School: Additional Practice
                    Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-1: Additional Practice

            2-2: Represent Rational Numbers on the Number Line

               Interactive Student Edition: Grade 6 Lesson 2-2

               Student's Edition eText: Grade 6 Lesson 2-2

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-2: Explore It!
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

               Develop: Visual Learning

                  2-2: Example 1 & Try It!
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-2: Example 2 & Try It!
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-2: Example 3 & Try It!
                    Curriculum Standards: Represent rational numbers using a number line. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret and explain problems of ordering of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 

                  2-2: Additional Example 2
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-2: Additional Example 3 with Try Another One
                    Curriculum Standards: Represent rational numbers using a number line. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret and explain problems of ordering of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 

                  2-2: Key Concept
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

               Assess & Differentiate

                  2-2: Lesson Quiz
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: Virtual Nerd™: What's a Rational Number?
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: Virtual Nerd™: How Do You Order Fractions and Decimals From Greatest to Least?
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: MathXL for School: Additional Practice
                    Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

                  2-2: Additional Practice

            2-3: Absolute Values of Rational Numbers

               Interactive Student Edition: Grade 6 Lesson 2-3

               Student's Edition eText: Grade 6 Lesson 2-3

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-3: Solve & Discuss It!
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

               Develop: Visual Learning

                  2-3: Example 1 & Try It!
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

                  2-3: Example 2 & Try It!
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

                  2-3: Example 3 & Try It!
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Distinguish comparisons of absolute value from statements about order. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

                  2-3: Additional Example 2 with Try Another One
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

                  2-3: Additional Examples for 2 & 3
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: Key Concept
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

               Assess & Differentiate

                  2-3: Lesson Quiz
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: Virtual Nerd™: What Does Absolute Value Mean?
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: Virtual Nerd™: How Do You Find the Absolute Value of Positive and Negative Numbers?
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: MathXL for School: Additional Practice
                    Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

                  2-3: Additional Practice

            2-1: Example 1 & Try It!
              Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

            2-2: Example 1 & Try It!
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

            2-2: Example 2 & Try It!
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

            2-2: Virtual Nerd™: How Do You Order Fractions and Decimals From Greatest to Least?
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

            2-3: Example 2 & Try It!
              Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

            2-3: Example 3 & Try It!
              Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Distinguish comparisons of absolute value from statements about order. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

            2-3: Virtual Nerd™: How Do You Find the Absolute Value of Positive and Negative Numbers?
              Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

            2-2: Virtual Nerd™: What's a Rational Number?
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

            2-3: Virtual Nerd™: What Does Absolute Value Mean?
              Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

            2-1: Key Concept
              Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

            2-2: Key Concept
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. 

            2-3: Key Concept
              Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

            Topic 2 Mid-Topic Assessment
              Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Convert between equivalent representations of positive rational numbers. Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Distinguish comparisons of absolute value from statements about order. 

            2-4: Represent Rational Numbers on the Coordinate Plane

               Interactive Student Edition: Grade 6 Lesson 2-4

               Student's Edition eText: Grade 6 Lesson 2-4

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-4: Solve & Discuss It!
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

               Develop: Visual Learning

                  2-4: Example 1 & Try It!
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Example 2 & Try It!
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Example 3 & Try It!
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

                  2-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Additional Example 3
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

                  2-4: Key Concept
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

               Assess & Differentiate

                  2-4: Lesson Quiz
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Virtual Nerd™: How Do You Graph Ordered Pairs in Each Quadrant?
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Virtual Nerd™: How Do You Identify Points on a Graph?
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: MathXL for School: Additional Practice
                    Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

                  2-4: Additional Practice

            3-Act Mathematical Modeling: The Ultimate Throw

               Student's Edition eText: Grade 6 Topic 2 3-Act Mathematical Modeling

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 2 Math Modeling: Act 1
                    Curriculum Standards: Mathematical Modeling: Integers and Rational Numbers Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and represent integers. The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Make sense of problems and persevere in solving them.  Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Use positive and negative numbers to represent quantities. Understand that the absolute value of a rational number is its distance from 0 on the number line. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Distinguish comparisons of absolute value from statements about order. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. 

                  Topic 2 Math Modeling: Act 2
                    Curriculum Standards: Mathematical Modeling: Integers and Rational Numbers Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and represent integers. The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Make sense of problems and persevere in solving them.  Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Use positive and negative numbers to represent quantities. Understand that the absolute value of a rational number is its distance from 0 on the number line. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Distinguish comparisons of absolute value from statements about order. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. 

                  Topic 2 Math Modeling: Act 3
                    Curriculum Standards: Mathematical Modeling: Integers and Rational Numbers Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and represent integers. The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Make sense of problems and persevere in solving them.  Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Use positive and negative numbers to represent quantities. Understand that the absolute value of a rational number is its distance from 0 on the number line. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Distinguish comparisons of absolute value from statements about order. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Model with mathematics. 

            2-5: Find Distances on the Coordinate Plane

               Interactive Student Edition: Grade 6 Lesson 2-5

               Student's Edition eText: Grade 6 Lesson 2-5

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-5: Solve & Discuss It!
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

               Develop: Visual Learning

                  2-5: Example 1 & Try It!
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Example 2 & Try It!
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Example 3 & Try It!
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Additional Example 2
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Key Concept
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

               Assess & Differentiate

                  2-5: Lesson Quiz
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Virtual Nerd™: How Can You Find Horizontal and Vertical Distance in the Coordinate Plane?

                  2-5: MathXL for School: Additional Practice
                    Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

                  2-5: Additional Practice

            2-6: Represent Polygons on the Coordinate Plane

               Interactive Student Edition: Grade 6 Lesson 2-6

               Student's Edition eText: Grade 6 Lesson 2-6

               Math Anytime

                  Topic 2: Today's Challenge

               Develop: Problem-Based Learning

                  2-6: Solve & Discuss It!
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

               Develop: Visual Learning

                  2-6: Example 1 & Try It!
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Example 2 & Try It!
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Example 3 & Try It!
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Additional Example 1
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Additional Example 2 with Try Another One
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Key Concept
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

               Assess & Differentiate

                  2-6: Lesson Quiz
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Virtual Nerd™: How Do You Find the Perimeter of a Rectangle in the Coordinate Plane?
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Virtual Nerd™: How Do You Find the Perimeter of a Shape?
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: MathXL for School: Additional Practice
                    Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  2-6: Virtual Nerd™: How Can You Find Horizontal and Vertical Distance in the Coordinate Plane?

                  2-6: Additional Practice

            Interactive Student Edition: End of Topic 2

            Topic 2 Performance Task
              Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  Distinguish comparisons of absolute value from statements about order. (e.g., recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.)  The student will identify and describe absolute value of integers. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Distinguish comparisons of absolute value from statements about order. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

            Topic 2 Assessment
              Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Convert between equivalent representations of positive rational numbers. Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find side lengths of polygons on a coordinate plane. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

         1-1: Example 2 & Try It!
           Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

         1-1: Example 3 & Try It!
           Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

         1-2: Example 1 & Try It!
           Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

         1-2: Example 3 & Try It!
           Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. 

         1-3: Example 1 & Try It!
           Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

         1-3: Example 2 & Try It!
           Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

         1-3: Example 3 & Try It!
           Curriculum Standards: Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

         1-5: Example 1 & Try It!
           Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

         2-2: Example 1 & Try It!
           Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

         2-2: Example 2 & Try It!
           Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

         2-2: Example 3 & Try It!
           Curriculum Standards: Represent rational numbers using a number line. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret and explain problems of ordering of rational numbers. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 

         2-3: Example 1 & Try It!
           Curriculum Standards: Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. 

         2-4: Example 2 & Try It!
           Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position rational numbers on a horizontal or vertical number line. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

         2-4: Example 3 & Try It!
           Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

         2-6: Example 2 & Try It!
           Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

         Topics 1-2: Cumulative/Benchmark Assessment
           Curriculum Standards: Add, subtract, and multiply decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. Fluently divide multi-digit numbers using the standard algorithm. Use models and equations to multiply fractions and mixed numbers. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Convert between equivalent representations of positive rational numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Divide a fraction by another fraction. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. (e.g., interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.)  Find and interpret absolute value. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. (e.g., for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars).  The student will identify and describe absolute value of integers. Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars. Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars. Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. Understand that the absolute value of a rational number is its distance from 0 on the number line. Interpret absolute value as magnitude for a positive or negative quantity in a real-world context. Understand p + q as the number located a distance q from p, in the positive or negative direction depending on the sign of q. Show that a number and its additive inverse create a zero pair. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

         Topic 3: Numeric and Algebraic Expressions

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            i9-4 Part 2

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            i25-1 Lesson Check

            i9-4 Lesson Check

            i10-3 Lesson Check

            i11-2 Lesson Check

            i11-3 Lesson Check

            i2-2 Lesson Check

            i2-1 Lesson Check

            i3-1 Lesson Check

            i7-2 Lesson Check

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            i25-1 Practice

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            Topic 3 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 3

            Topic 3 STEM Project

               Topic 3: STEM Project

               Topic 3 STEM Video

            Topic 3: Today's Challenge

            3-1: Understand  and Represent Exponents

               Interactive Student Edition: Grade 6 Lesson 3-1

               Student's Edition eText: Grade 6 Lesson 3-1

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-1: Solve & Discuss It!
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

               Develop: Visual Learning

                  3-1: Example 1 & Try It!
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Example 2 & Try It!
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Example 3 & Try It!
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Additional Example 2
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Additional Example 3 with Try Another One
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Key Concept
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

               Assess & Differentiate

                  3-1: Lesson Quiz
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Virtual Nerd™: What is an Exponent?
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Virtual Nerd™: What Do You Do With a Zero Exponent?
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: MathXL for School: Additional Practice
                    Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

                  3-1: Additional Practice

            3-2: Find Greatest Common Factor and Least Common Multiple

               Interactive Student Edition: Grade 6 Lesson 3-2

               Student's Edition eText: Grade 6 Lesson 3-2

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-2: Solve & Discuss It!
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

               Develop: Visual Learning

                  3-2: Example 1 & Try It!
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. 

                  3-2: Example 2 & Try It!
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. 

                  3-2: Example 3 & Try It!
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. 

                  3-2: Example 4 & Try It!
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: Additional Example 2
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. 

                  3-2: Additional Example 3 with Try Another One
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. 

                  3-2: Key Concept
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

               Assess & Differentiate

                  3-2: Lesson Quiz
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: Virtual Nerd™: How Do You Find the Greatest Common Factor of Two Numbers Using Prime Factorization?
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: Virtual Nerd™: How Do You Find the Least Common Multiple by Multiplying Common Factors?
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: MathXL for School: Additional Practice
                    Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

                  3-2: Additional Practice

            3-3: Write and Evaluate Numerical Expressions

               Interactive Student Edition: Grade 6 Lesson 3-3

               Student's Edition eText: Grade 6 Lesson 3-3

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-3: Solve & Discuss It!
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

               Develop: Visual Learning

                  3-3: Example 1 & Try It!
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Example 2
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Example 3 & Try It!
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Additional Example 2
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Additional Example 3 with Try Another One
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Key Concept
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

               Assess & Differentiate

                  3-3: Lesson Quiz
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Virtual Nerd™: What's the Order of Operations?
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Virtual Nerd™: How Do You Use the Order of Operations?
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: MathXL for School: Additional Practice
                    Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-3: Additional Practice

            3-2: Key Concept
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

            3-2: Virtual Nerd™: How Do You Find the Greatest Common Factor of Two Numbers Using Prime Factorization?
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

            3-2: Virtual Nerd™: How Do You Find the Least Common Multiple by Multiplying Common Factors?
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

            3-3: Virtual Nerd™: How Do You Use the Order of Operations?
              Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

            3-3: Key Concept
              Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

            3-2: Example 1 & Try It!
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. 

            3-2: Example 2 & Try It!
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. 

            3-2: Example 4 & Try It!
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

            3-3: Example 1 & Try It!
              Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

            3-3: Example 2
              Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

            Topic 3 Mid-Topic Assessment
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

            3-4: Write Algebraic Expressions

               Interactive Student Edition: Grade 6 Lesson 3-4

               Student's Edition eText: Grade 6 Lesson 3-4

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-4: Explore It!
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

               Develop: Visual Learning

                  3-4: Example 1 & Try It!
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-4: Example 2 & Try It!
                    Curriculum Standards: Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-4: Example 3 & Try It!
                    Curriculum Standards: Use variables to write algebraic expressions. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: Additional Example 1
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-4: Key Concept
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

               Assess & Differentiate

                  3-4: Lesson Quiz
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: Virtual Nerd™: How Do You Turn a Simple Verbal Phrase into an Algebraic Expression?
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: Virtual Nerd™: What's a Term?
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: MathXL for School: Additional Practice
                    Curriculum Standards: Use variables to write algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

                  3-4: Additional Practice

            3-5: Evaluate Algebraic Expressions

               Interactive Student Edition: Grade 6 Lesson 3-5

               Student's Edition eText: Grade 6 Lesson 3-5

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-5: Explore It!
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

               Develop: Visual Learning

                  3-5: Example 1 & Try It!
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Example 2 & Try It!
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Example 3 & Try It!
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Additional Example 2 with Try Another One
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Additional Example 3
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Key Concept
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

               Assess & Differentiate

                  3-5: Lesson Quiz
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Virtual Nerd™: How Do You Evaluate an Algebraic Expression with One Variable?
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Virtual Nerd™: How Do You Evaluate an Algebraic Expression with Two Variables?
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: MathXL for School: Additional Practice
                    Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

                  3-5: Additional Practice

            3-Act Mathematical Modeling: The Field Trip

               Student's Edition eText: Grade 6 Topic 3 3-Act Mathematical Modeling

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 3 Math Modeling: Act 1
                    Curriculum Standards: Mathematical Modeling: Numeric and Algebraic Expressions Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write, read, and evaluate expressions in which letters stand for numbers.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision. Write, read, and evaluate algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and express regularity in repeated reasoning. 

                  Topic 3 Math Modeling: Act 2
                    Curriculum Standards: Mathematical Modeling: Numeric and Algebraic Expressions Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write, read, and evaluate expressions in which letters stand for numbers.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision. Write, read, and evaluate algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and express regularity in repeated reasoning. 

                  Topic 3 Math Modeling: Act 3
                    Curriculum Standards: Mathematical Modeling: Numeric and Algebraic Expressions Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write, read, and evaluate expressions in which letters stand for numbers.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Construct viable arguments and critique the reasoning of others. Model with mathematics. Attend to precision. Write, read, and evaluate algebraic expressions. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and express regularity in repeated reasoning. 

            3-6: Generate Equivalent Expressions

               Interactive Student Edition: Grade 6 Lesson 3-6

               Student's Edition eText: Grade 6 Lesson 3-6

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-6: Explain It!
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Develop: Visual Learning

                  3-6: Example 1 & Try It!
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

                  3-6: Example 2 & Try It!
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Example 3 & Try It!
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Additional Example 2
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use models and equations to represent fraction division. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Divide a fraction by another fraction. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Use the order of operations to evaluate numerical expressions. The student will simplify numerical expressions involving integers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Additional Example 3 with Try Another One
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Key Concept
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Assess & Differentiate

                  3-6: Lesson Quiz
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Virtual Nerd™: What's the Distributive Property?
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Virtual Nerd™: What are the Associative Properties of Addition and Multiplication?
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: MathXL for School: Additional Practice
                    Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-6: Additional Practice

            3-7: Simplify Algebraic Expressions

               Interactive Student Edition: Grade 6 Lesson 3-7

               Student's Edition eText: Grade 6 Lesson 3-7

               Math Anytime

                  Topic 3: Today's Challenge

               Develop: Problem-Based Learning

                  3-7: Solve & Discuss It!
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Develop: Visual Learning

                  3-7: Example 1 & Try It!
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Example 2 & Try It!
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Example 3 & Try It!
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Additional Example 1
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Key Concept
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Assess & Differentiate

                  3-7: Lesson Quiz
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Virtual Nerd™: What are the Identity Properties of Addition and Multiplication?
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Virtual Nerd™: What's the Distributive Property?
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: MathXL for School: Additional Practice
                    Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  3-7: Additional Practice

            Interactive Student Edition: End of Topic 3

            Topic 3 Performance Task
              Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

            Topic 3 Assessment
              Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

         Topic 4: Represent and Solve Equations and Inequalities

            i12-5 Part 1

            i8-2 Part 1

            i22-1 Part 3

            i22-4 Part 1

            i23-2 Part 3

            i23-4 Part 2

            i12-5 Part 2

            i8-2 Part 3

            i22-1 Part 1

            i22-4 Part 3

            i23-2 Part 2

            i23-4 Part 1

            i12-5 Part 3

            i8-2 Part 2

            i22-1 Part 2

            i22-4 Part 2

            i23-2 Part 1

            i23-4 Part 3

            i12-5 Lesson Check

            i8-2 Lesson Check

            i22-1 Lesson Check

            i22-4 Lesson Check

            i23-2 Lesson Check

            i23-4 Lesson Check

            i23-2 Practice

            i22-4 Practice

            i23-4 Practice

            i25-4 Practice

            i22-1 Practice

            i12-3 Practice

            i11-2 Practice

            i12-5 Practice

            i2-2 Practice

            i8-2 Practice

            i7-2 Practice

            i25-4 Part 1

            i12-3 Part 1

            i12-3 Part 2

            i25-4 Part 2

            i12-3 Part 3

            i25-4 Part 3

            i12-3 Lesson Check

            i25-4 Lesson Check

            i11-2 Part 2

            i2-2 Part 1

            i7-2 Part 1

            i11-2 Part 3

            i2-2 Part 2

            i7-2 Part 2

            i11-2 Part 1

            i2-2 Part 3

            i7-2 Part 3

            i11-2 Lesson Check

            i2-2 Lesson Check

            i7-2 Lesson Check

            Topic 4 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 4

            Topic 4 STEM Project

               Topic 4: STEM Project

               Topic 4 STEM Video

            Topic 4: Today's Challenge

            4-1: Understand Equations and Solutions

               Interactive Student Edition: Grade 6 Lesson 4-1

               Student's Edition eText: Grade 6 Lesson 4-1

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-1: Solve & Discuss It!
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

               Develop: Visual Learning

                  4-1: Example 1 & Try It!
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Example 2 & Try It!
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Additional Example 1
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Additional Example 2 with Try Another One
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Key Concept
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

               Assess & Differentiate

                  4-1: Lesson Quiz
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Virtual Nerd™: How do you solve an equation by guessing and checking?
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: MathXL for School: Additional Practice
                    Curriculum Standards: Determine if a value for a variable makes an equation true. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-1: Additional Practice

            4-2: Apply Properties of Equality

               Interactive Student Edition: Grade 6 Lesson 4-2

               Student's Edition eText: Grade 6 Lesson 4-2

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-2: Solve & Discuss It!
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Develop: Visual Learning

                  4-2: Example 1 & Try It!
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Example 2
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Example 3 & Try It!
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Additional Example 3
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Key Concept
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

               Assess & Differentiate

                  4-2: Lesson Quiz
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Virtual Nerd™: What's the Addition Property of Equality?
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Virtual Nerd™: What's the Multiplication Property of Equality?
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: MathXL for School: Additional Practice
                    Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

                  4-2: Additional Practice

            4-3: Write and Solve Addition and Subtraction Equations

               Interactive Student Edition: Grade 6 Lesson 4-3

               Student's Edition eText: Grade 6 Lesson 4-3

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-3: Solve & Discuss It!
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

               Develop: Visual Learning

                  4-3: Example 1 & Try It!
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Example 2
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Example 3 & Try It!
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Additional Example 2
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-3: Additional Example 3 with Try Another One
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Key Concept
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

               Assess & Differentiate

                  4-3: Lesson Quiz
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Subtraction?
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Addition?
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: MathXL for School: Additional Practice
                    Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-3: Additional Practice

            4-4: Write and Solve Multiplication and Division Equations

               Interactive Student Edition: Grade 6 Lesson 4-4

               Student's Edition eText: Grade 6 Lesson 4-4

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-4: Solve & Discuss It!
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

               Develop: Visual Learning

                  4-4: Example 1 & Try It!
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-4: Example 2
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-4: Example 3 & Try It!
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: Additional Example 1
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-4: Key Concept
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

               Assess & Differentiate

                  4-4: Lesson Quiz
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Division?
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Multiplication?
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: MathXL for School: Additional Practice
                    Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-4: Additional Practice

            4-5: Write and Solve Equations with Rational Numbers

               Interactive Student Edition: Grade 6 Lesson 4-5

               Student's Edition eText: Grade 6 Lesson 4-5

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-5: Explore It!
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

               Develop: Visual Learning

                  4-5: Example 1 & Try It!
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-5: Example 2 & Try It!
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Example 3 & Try It!
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Example 4 & Try It!
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-5: Additional Example 2 with Try Another One
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-5: Additional Example 4
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

                  4-5: Key Concept
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

               Assess & Differentiate

                  4-5: Lesson Quiz
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Virtual Nerd™: How Do You Solve an Equation Where You're Multiplying Fractions?
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Subtraction?
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: MathXL for School: Additional Practice
                    Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

                  4-5: Additional Practice

            4-2: Virtual Nerd™: What's the Addition Property of Equality?
              Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

            4-3: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Subtraction?
              Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-3: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Addition?
              Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-4: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Division?
              Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-5: Virtual Nerd™: How Do You Solve an Equation Where You're Multiplying Fractions?
              Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-4: Virtual Nerd™: How Do You Solve a Word Problem with an Equation Using Multiplication?
              Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-2: Example 1 & Try It!
              Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

            4-3: Example 1 & Try It!
              Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-3: Example 2
              Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-4: Example 3 & Try It!
              Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-5: Example 3 & Try It!
              Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-5: Example 2 & Try It!
              Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            Topic 4 Mid-Topic Assessment
              Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and solve a multiplication or division equation. Write and solve equations that involve rational numbers. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. Write and evaluate algebraic expressions. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. 

            4-6: Understand and Write Inequalitites

               Interactive Student Edition: Grade 6 Lesson 4-6

               Student's Edition eText: Grade 6 Lesson 4-6

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-6: Solve & Discuss It!
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

               Develop: Visual Learning

                  4-6: Example 1 & Try It!
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-6: Example 2 & Try It!
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-6: Additional Example 1
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-6: Additional Example 2 with Try Another One
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-6: Key Concept
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

               Assess & Differentiate

                  4-6: Lesson Quiz
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: Virtual Nerd™: What's an Inequality?
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: MathXL for School: Additional Practice
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: Virtual Nerd™: How Do You Write an Inequality from a Number Line Graph?
                    Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. 

                  4-6: Additional Practice

            4-7: Solve Inequalities

               Interactive Student Edition: Grade 6 Lesson 4-7

               Student's Edition eText: Grade 6 Lesson 4-7

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-7: Solve & Discuss It!
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

               Develop: Visual Learning

                  4-7: Example 1 & Try It!
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-7: Example 2 & Try It!
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-7: Example 3 & Try It!
                    Curriculum Standards: Write and represent solutions of inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

                  4-7: Additional Example 3
                    Curriculum Standards: Write and represent solutions of inequalities. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: Key Concept
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

               Assess & Differentiate

                  4-7: Lesson Quiz
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: Virtual Nerd™: How Do You Graph an Inequality or an Infinite Set on a Number Line?
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: MathXL for School: Additional Practice
                    Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. 

                  4-7: Additional Practice

            3-Act Mathematical Modeling: Checking a Bag

               Student's Edition eText: Grade 6 Topic 4 3-Act Mathematical Modeling

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 4 Math Modeling: Act 1
                    Curriculum Standards: Mathematical Modeling: Represent and Solve Equations and Inequalities Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Model with mathematics. Use appropriate tools strategically. Attend to precision. Use substitution to determine whether a given number in a specified set makes an equation true. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Using substitution to determine whether a given number in a specified set makes an inequality true. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Topic 4 Math Modeling: Act 2
                    Curriculum Standards: Mathematical Modeling: Represent and Solve Equations and Inequalities Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Model with mathematics. Use appropriate tools strategically. Attend to precision. Use substitution to determine whether a given number in a specified set makes an equation true. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Using substitution to determine whether a given number in a specified set makes an inequality true. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Topic 4 Math Modeling: Act 3
                    Curriculum Standards: Mathematical Modeling: Represent and Solve Equations and Inequalities Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Model with mathematics. Use appropriate tools strategically. Attend to precision. Use substitution to determine whether a given number in a specified set makes an equation true. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Using substitution to determine whether a given number in a specified set makes an inequality true. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

            4-8: Understand Dependent and Independent Variables

               Interactive Student Edition: Grade 6 Lesson 4-8

               Student's Edition eText: Grade 6 Lesson 4-8

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-8: Explain It!
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Develop: Visual Learning

                  4-8: Example 1 & Try It!
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Example 2 & Try It!
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Additional Example 2
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Key Concept
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Do You Understand?/Do You Know How?
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Assess & Differentiate

                  4-8: Lesson Quiz
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Virtual Nerd™: What Are Dependent and Independent Variables?
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: MathXL for School: Additional Practice
                    Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-8: Additional Practice

            4-9: Use Patterns to Write and Solve Equations

               Interactive Student Edition: Grade 6 Lesson 4-9

               Student's Edition eText: Grade 6 Lesson 4-9

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-9: Solve & Discuss It!
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Develop: Visual Learning

                  4-9: Example 1 & Try It!
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Example 2 & Try It!
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Additional Example 1 with Try Another One
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Additional Example 2
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Key Concept
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Assess & Differentiate

                  4-9: Lesson Quiz
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Virtual Nerd™: How Do You Write a Linear Equation From a Table?
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: MathXL for School: Additional Practice
                    Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-9: Additional Practice

            4-10: Relate Tables, Graphs, and Equations

               Interactive Student Edition: Grade 6 Lesson 4-10

               Student's Edition eText: Grade 6 Lesson 4-10

               Math Anytime

                  Topic 4: Today's Challenge

               Develop: Problem-Based Learning

                  4-10: Solve & Discuss It!
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Develop: Visual Learning

                  4-10: Example 1 & Try It!
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Example 2 & Try It!
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Additional Example 1
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Additional Example 2 with Try Another One
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Key Concept
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Do You Understand?/Do You Know How?
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

               Assess & Differentiate

                  4-10: Lesson Quiz
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Virtual Nerd™: How Do You Graph a Linear Equation From a Table?
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: MathXL for School: Additional Practice
                    Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

                  4-10: Additional Practice

            Interactive Student Edition: End of Topic 4

            Topic 4 Performance Task
              Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

            Topic 4 Assessment
              Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

         1-2: Example 1 & Try It!
           Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

         1-5: Example 3 & Try It!
           Curriculum Standards: Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Multiply and divide fractions and decimals using efficient and generalizable procedures. Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. 

         2-1: Example 1 & Try It!
           Curriculum Standards: Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. 

         2-1: Example 2 & Try It!
           Curriculum Standards: Use positive and negative integers. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

         2-2: Example 2 & Try It!
           Curriculum Standards: Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. 

         2-4: Example 3 & Try It!
           Curriculum Standards: Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. 

         2-5: Example 3 & Try It!
           Curriculum Standards: Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find distances between points with the same first coordinate or the same second coordinate. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. 

         2-6: Example 3 & Try It!
           Curriculum Standards: Find side lengths of polygons on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find distances between points with the same first coordinate or the same second coordinate. Construct polygons in the Cartesian coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

         3-1: Example 2 & Try It!
           Curriculum Standards: Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. 

         3-2: Example 2 & Try It!
           Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. 

         3-2: Example 4 & Try It!
           Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

         3-3: Example 1 & Try It!
           Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

         3-4: Example 2 & Try It!
           Curriculum Standards: Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

         3-4: Example 3 & Try It!
           Curriculum Standards: Use variables to write algebraic expressions. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. 

         3-5: Example 1 & Try It!
           Curriculum Standards: Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

         3-6: Example 2 & Try It!
           Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

         3-7: Example 1 & Try It!
           Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

         4-10: Example 1 & Try It!
           Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

         4-2: Example 1 & Try It!
           Curriculum Standards: Use the properties of equality to write equivalent equations. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Identify when two expressions are equivalent and justify with mathematical reasoning. 

         4-3: Example 1 & Try It!
           Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         4-4: Example 1 & Try It!
           Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         4-5: Example 1 & Try It!
           Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         4-5: Example 4 & Try It!
           Curriculum Standards: Write and solve equations that involve rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         4-6: Example 1 & Try It!
           Curriculum Standards: Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

         4-7: Example 1 & Try It!
           Curriculum Standards: Write and represent solutions of inequalities. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

         4-8: Example 1 & Try It!
           Curriculum Standards: Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

         4-9: Example 1 & Try It!
           Curriculum Standards: Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

         Topics 1-4: Cumulative/Benchmark Assessment
           Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Divide a fraction by another fraction. Interpret and compute quotients of fractions and solve word problems involving division of fractions by fractions by using visual fraction models and equations to represent the problem. (e.g., Create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?)  The student will multiply and divide fractions and mixed numbers. The student will solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division of fractions and mixed numbers. Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Multiply and divide fractions and decimals using efficient and generalizable procedures. Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?  Use positive and negative integers. Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.  Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite.  The student will identify and represent integers. The student will compare and order integers. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., –(–3) = 3, and that 0 is its own opposite. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Represent rational numbers using a number line. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Convert between equivalent representations of positive rational numbers. Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Find side lengths of polygons on a coordinate plane. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Write and evaluate numbers with exponents. Write and evaluate numerical expressions involving whole-number exponents. The student will recognize and represent patterns with whole number exponents and perfect squares. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Write and evaluate numerical expressions involving whole-number exponents. Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use the order of operations to evaluate numerical expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. (e.g., Describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.)  Evaluate an algebraic expression with whole numbers, decimals, and fractions. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Identify and write equivalent algebraic expressions. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Combine like terms in algebraic expressions. Use the properties of equality to write equivalent equations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve an addition or subtraction equation. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Write and solve a multiplication or division equation. Write and solve equations that involve rational numbers. Understand and write an inequality that describes a real-world situation. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write and represent solutions of inequalities. The student will solve one-step linear inequalities in one variable, involving addition or subtraction, and graph the solution on a number line. Identify dependent and independent variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Use patterns to write and solve equations with variables. Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Compute and interpret quotients of positive fractions. Solve problems involving division of fractions by fractions. Interpret and compute quotients of fractions. Solve real-world and mathematical problems involving division of fractions. Use positive and negative numbers to represent quantities. Understand that a number and its opposite (additive inverse) are located on opposite sides of zero on the number line. Describe quantities having opposite directions or values. Represent quantities in real-world contexts, explaining the meaning of 0 in each situation. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 and that the opposite of the opposite of a number is the number itself. Apply and extend previous understandings of addition and subtraction. Understand additive inverses when adding and subtracting integers. Describe situations in which opposite quantities combine to make 0. Use models to add and subtract integers from -20 to 20 and describe real-world contexts using sums and differences. Locate rational numbers on a horizontal or vertical number line. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write, interpret and explain problems of ordering of rational numbers. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Create and evaluate expressions involving variables and whole number exponents. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Describe the difference between an expression and an equation. Identify parts of an expression using mathematical terminology. Identify parts of an expression using mathematical terms and view one or more of those parts as a single entity. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Identify when two expressions are equivalent and justify with mathematical reasoning. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Use substitution to determine whether a given number in a specified set makes a one-variable equation or inequality true. Understand that if any solutions exist, the solution set for an equation or inequality consists of values that make the equation or inequality true. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Use substitution to determine whether a given number in a specified set makes an equation true. Using substitution to determine whether a given number in a specified set makes an inequality true. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

         Topic 5: Understand and Use Ratio and Rate

            i25-6 Part 1

            i25-6 Part 2

            i25-6 Part 3

            i25-6 Lesson Check

            i25-6 Practice

            i14-1 Part 1

            i14-1 Part 2

            i14-1 Part 3

            i14-1 Lesson Check

            i14-1 Practice

            i14-2 Practice

            i14-3 Practice

            i6-3 Practice

            i21-1 Part 1

            i21-1 Part 2

            i21-1 Practice

            i21-1 Part 3

            i21-1 Lesson Check

            i22-1 Part 3

            i22-1 Practice

            i22-1 Part 1

            i22-1 Part 2

            i22-1 Lesson Check

            i23-3 Part 2

            i23-3 Practice

            i23-3 Part 1

            i23-3 Part 3

            i23-3 Lesson Check

            i25-4 Practice

            i25-4 Part 1

            i14-2 Part 1

            i14-2 Part 2

            i14-2 Part 3

            i14-2 Lesson Check

            i14-3 Part 3

            i14-3 Part 1

            i14-3 Part 2

            i14-3 Lesson Check

            i6-3 Part 3

            i6-3 Part 1

            i6-3 Part 2

            i6-3 Lesson Check

            i25-4 Part 2

            i25-4 Part 3

            i25-4 Lesson Check

            Topic 5 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 5

            Topic 5 STEM Project

               Topic 5 STEM Video

            Topic 5: Today's Challenge

            5-1: Understand Ratios

               Interactive Student Edition: Grade 6 Lesson 5-1

               Student's Edition eText: Grade 6 Lesson 5-1

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-1: Explore It!
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

               Develop: Visual Learning

                  5-1: Example 1 & Try It!
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

                  5-1 Example 2
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

                  5-1: Example 3 & Try It!
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

                  5-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

                  5-1: Additional Example 2
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

                  5-1: Key Concept
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

               Assess & Differentiate

                  5-1: Lesson Quiz
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: Virtual Nerd™: What's a Ratio?
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: Virtual Nerd™: How Do You Solve a Word Problem Using Ratios?
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: MathXL for School: Additional Practice
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Solve problems involving ratios and rates. 

                  5-1: Additional Practice
                    Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

            5-2: Generate Equivalent Ratios

               Student's Edition eText: Grade 6 Lesson 5-2

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-2: Solve & Discuss It!
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Develop: Visual Learning

                  5-2: Example 1 & Try It!
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Example 2 & Try It!
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Example 3 & Try It!
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Additional Example 1
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Key Concept
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Assess & Differentiate

                  5-2: Lesson Quiz
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Virtual Nerd™: What are Equivalent Ratios?
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Virtual Nerd™: How Do You Find Equivalent Ratios?
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: MathXL for School: Additional Practice
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-2: Additional Practice
                    Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-3: Compare Ratios

               Interactive Student Edition: Grade 6 Lesson 5-3

               Student's Edition eText: Grade 6 Lesson 5-3

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-3: Solve & Discuss It!
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Develop: Visual Learning

                  5-3: Example 1 & Try It!
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Example 2  &  Try It!
                  5-3: Example 2 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Additional Example 1
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Key Concept
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Assess & Differentiate

                  5-3: Lesson Quiz
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Virtual Nerd™: How Do You Find Equivalent Ratios by Making a Table?
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Virtual Nerd™: How Do You Use a Table of Equivalent Ratios to Predict a Value?
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: MathXL for School: Additional Practice
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-3: Additional Practice
                    Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-4: Represent and Graph Ratios

               Interactive Student Edition: Grade 6 Lesson 5-4

               Student's Edition eText: Grade 6 Lesson 5-4

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-4: Solve & Discuss It!
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Develop: Visual Learning

                  5-4: Example 1 & Try It!
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Example 2
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Example 3 & Try It!
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Additional Example 1
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Key Concept
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

               Assess & Differentiate

                  5-4: Lesson Quiz
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Virtual Nerd™: How Do You Find Equivalent Ratios by Making a Table?
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: MathXL for School: Additional Practice
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

                  5-4: Additional Practice
                    Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-2: Virtual Nerd™: What are Equivalent Ratios?
              Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-3: Virtual Nerd™: How Do You Find Equivalent Ratios by Making a Table?
              Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-3: Virtual Nerd™: How Do You Use a Table of Equivalent Ratios to Predict a Value?
              Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-5: Virtual Nerd™: What are Rates and Unit Rates?
              Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

            5-1: Example 1 & Try It!
              Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

            5-2: Example 1 & Try It!
              Curriculum Standards: Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-3: Example 2 & Try It!
              Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-4: Example 2
              Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-5: Example 1 & Try It!
              Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

            Topic 5 Mid-Topic Assessment
              Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Compare ratios to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve ratio problems by using tables and graphs to show equivalent ratios. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Determine the rate for ratios of quantities with different units. Determine the unit rate for ratios. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

            5-5: Understand Rates and Unit Rates

               Interactive Student Edition: Grade 6 Lesson 5-5

               Student's Edition eText: Grade 6 Lesson 5-5

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-5: Solve & Discuss It!
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

               Develop: Visual Learning

                  5-5: Example 1 & Try It!
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: Example 2 & Try It!
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

                  5-5: Example 3 & Try It!
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

                  5-5: Additional Example 2 with Try Another One
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

                  5-5: Additional Example 3
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

                  5-5: Key Concept
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

               Assess & Differentiate

                  5-5: Lesson Quiz
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: Virtual Nerd™: What are Rates and Unit Rates?
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: Virtual Nerd™: How Do You Convert a Rate to a Unit Rate?
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: MathXL for School: Additional Practice
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

                  5-5: Additional Practice
                    Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

            5-6: Compare Unit Rates

               Interactive Student Edition: Grade 6 Lesson 5-6

               Student's Edition eText: Grade 6 Lesson 5-6

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-6: Solve &  Discuss It!
                  5-6: Solve & Discuss It!This interactive component provides the Problem-Based Learning from the student edition in an interactive format. It is designed for whole-class instruction.
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

               Develop: Visual Learning

                  5-6: Example 1 & Try It!
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Example 2  &  Try It!
                  5-6: Example 2 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Additional Example 1
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Additional Example 2 with Try Another One
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Key Concept
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

               Assess & Differentiate

                  5-6: Lesson Quiz
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Virtual Nerd™: How Do You Use Unit Rates to Compare Rates?
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Virtual Nerd™: How Do You Solve a Word Problem Using Unit Rates?
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: MathXL for School: Additional Practice
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-6: Additional Practice
                    Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

            5-7: Solve Unit Rate Problems

               Interactive Student Edition: Grade 6 Lesson 5-7

               Student's Edition eText: Grade 6 Lesson 5-7

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-7: Solve & Discuss It!
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

               Develop: Visual Learning

                  5-7: Example 1 & Try It!
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Example 2  &  Try It!
                  5-7: Example 2 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Example 3 & Try It!
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Additional Example 1
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Key Concept
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

               Assess & Differentiate

                  5-7: Lesson Quiz
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Virtual Nerd™: How Do You Solve a Word Problem Using Unit Rates?
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Virtual Nerd™: How Do You Find Equivalent Ratios by Making a Table?
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: MathXL for School: Additional Practice
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

                  5-7: Additional Practice
                    Curriculum Standards: Use unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

            3-Act Mathematical Modeling: Get In Line

               Student's Edition eText: Grade 6 Topic 5 3-Act Mathematical Modeling

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 5 Math Modeling: Act 1
                    Curriculum Standards: Mathematical Modeling: Understand and Use Ratio and Rate Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. 

                  Topic 5 Math Modeling: Act 2
                    Curriculum Standards: Mathematical Modeling: Understand and Use Ratio and Rate Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. 

                  Topic 5 Math Modeling: Act 3
                    Curriculum Standards: Mathematical Modeling: Understand and Use Ratio and Rate Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Look for and express regularity in repeated reasoning.  Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Model with mathematics. Look for and make use of structure. Look for and express regularity in repeated reasoning. 

            5-8: Ratio Reasoning: Convert Customary Units

               Interactive Student Edition: Grade 6 Lesson 5-8

               Student's Edition eText: Grade 6 Lesson 5-8

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-8: Solve & Discuss It!
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Develop: Visual Learning

                  5-8: Example 1 & Try It!
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Example 2 & Try It!
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Example 3 & Try It!
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Additional Example 1 with Try Another One
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Additional Example 2
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Key Concept
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Assess & Differentiate

                  5-8: Lesson Quiz
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Virtual Nerd™: How Do You Convert Feet to Inches?
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Virtual Nerd™: How Do You Convert Gallons to Quarts?
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: MathXL for School: Additional Practice
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-8: Additional Practice
                    Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

            5-9: Ratio Reasoning: Convert Metric Units

               Interactive Student Edition: Grade 6 Lesson 5-9

               Student's Edition eText: Grade 6 Lesson 5-9

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-9: Solve & Discuss It!
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Develop: Visual Learning

                  5-9: Example 1 & Try It!
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Example 2
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Example 3 & Try It!
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Additional Example 1 with Try Another One
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Additional Example 2
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Key Concept
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Do You Understand?/Do You Know How?
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Assess & Differentiate

                  5-9: Lesson Quiz
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Virtual Nerd™: What are the Metric Units of Length?
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Virtual Nerd™: What are the Metric Units of Capacity?
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: MathXL for School: Additional Practice
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-9: Additional Practice
                    Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

            5-10: Relate Customary and Metric Units

               Interactive Student Edition: Grade 6 Lesson 5-10

               Student's Edition eText: Grade 6 Lesson 5-10

               Math Anytime

                  Topic 5: Today's Challenge

               Develop: Problem-Based Learning

                  5-10: Explain It!
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Develop: Visual Learning

                  5-10: Example 1 & Try It!
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Example 2
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Example 3 & Try It!
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Additional Example 1 with Try Another One
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Additional Example 3
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Key Concept
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Do You Understand?/Do You Know How?
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

               Assess & Differentiate

                  5-10: Lesson Quiz
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Virtual Nerd™: What are the Metric Units of Capacity?
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: MathXL for School: Additional Practice
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

                  5-10: Additional Practice
                    Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

            Interactive Student Edition: End of Topic 5

            Topic 5 Performance Task
              Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Determine the rate for ratios of quantities with different units. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

            Topic 5 Assessment
              Curriculum Standards: Use a ratio to describe the relationship between two quantities. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Use multiplication and division to find equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Solve ratio problems by using tables and graphs to show equivalent ratios. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Determine the rate for ratios of quantities with different units. Determine the unit rate for ratios. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Compare unit rates to solve problems. Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Use unit rates to convert metric measurements. Understand a ratio as a comparison of two quantities and represent these comparisons. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

         Topic 6: Understand and Use Percent

            i25-6 Part 1

            i25-6 Part 2

            i25-6 Part 3

            i25-6 Lesson Check

            i25-6 Practice

            i9-1 Practice

            i9-5 Part 2

            i9-5 Part 1

            i9-5 Lesson Check

            i9-5 Part 3

            i9-5 Practice

            i11-5 Practice

            i15-3 Part 1

            i15-3 Part 2

            i15-3 Practice

            i15-3 Part 3

            i15-3 Lesson Check

            i3-3 Practice

            i3-3 Journal

            i6-3 Practice

            i8-2 Part 1

            i8-2 Practice

            i8-2 Part 3

            i8-2 Part 2

            i8-2 Lesson Check

            i8-4 Practice

            i25-4 Practice

            i25-4 Part 1

            i9-1 Part 1

            i9-1 Lesson Check

            i9-1 Part 2

            i9-1 Part 3

            i11-5 Part 1

            i11-5 Part 2

            i11-5 Part 3

            i11-5 Lesson Check

            i3-3 Part 2

            i3-3 Part 3

            i3-3 Part 1

            i3-3 Lesson Check

            i6-3 Part 3

            i6-3 Part 1

            i6-3 Part 2

            i6-3 Lesson Check

            i8-4 Part 1

            i8-4 Part 2

            i8-4 Part 3

            i8-4 Lesson Check

            i25-4 Part 2

            i25-4 Part 3

            i25-4 Lesson Check

            Topic 6 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 6

            Topic 6 STEM Project

               Topic 6 STEM Video

            Topic 6: Today's Challenge

            6-1: Understand Percent

               Interactive Student Edition: Grade 6 Lesson 6-1

               Student's Edition eText: Grade 6 Lesson 6-1

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-1: Explain It!
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-1: Example 1 & Try It!
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Example 2 & Try it!
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Example 3 & Try It!
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Additional Example 1
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Additional Example 3 with Try Another One
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Key Concept
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-1: Lesson Quiz
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Virtual Nerd™: What's a Percent?
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Virtual Nerd™: How Do You Use a Proportion to Find What Percent a Part is of a Whole?
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: MathXL for School: Additional Practice
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-1: Additional Practice
                    Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-2: Relate Fractions, Decimals, and Percents

               Interactive Student Edition: Grade 6 Lesson 6-2

               Student's Edition eText: Grade 6 Lesson 6-2

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-2: Solve & Discuss It!
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-2: Example 1 & Try It!
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Example 2
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Example 3 & Try It!
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Additional Example 1
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Additional Example 2 with Try Another One
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Key Concept
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-2: Lesson Quiz
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Virtual Nerd™: How Do You Turn a Decimal Into a Percent?
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Virtual Nerd™: How Do You Turn a Fraction Into a Percent?
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: MathXL for School: Additional Practice
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-2: Additional Practice
                    Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-3: Represent Percents Greater Than 100 or Less Than 1

               Interactive Student Edition: Grade 6 Lesson 6-3

               Student's Edition eText: Grade 6 Lesson 6-3

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-3: Solve & Discuss It!
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-3: Example 1 & Try It!
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Example 2
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Example 3  &  Try It!
                  6-3: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Additional Example 1
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Additional Example 2 with Try Another One
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Key Concept
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-3: Lesson Quiz
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Virtual Nerd™: How Do You Turn a Percent Into a Decimal?
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Virtual Nerd™: How Do You Turn a Percent Into a Fraction?
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: MathXL for School: Additional Practice
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-3: Additional Practice
                    Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-1: Virtual Nerd™: What's a Percent?
              Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-2: Virtual Nerd™: How Do You Turn a Decimal Into a Percent?
              Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-2: Virtual Nerd™: How Do You Turn a Fraction Into a Percent?
              Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-3: Virtual Nerd™: How Do You Turn a Percent Into a Decimal?
              Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-1: Example 1 & Try It!
              Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-2: Example 1 & Try It!
              Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-2: Example 2
              Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-3: Example 1 & Try It!
              Curriculum Standards: Write percents that are greater than 100 or less than 1. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            Topic 6 Mid-Topic Assessment
              Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Write equivalent values as fractions, decimals, and percents. Convert between equivalent representations of positive rational numbers. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Write percents that are greater than 100 or less than 1. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-4: Estimate to Find Percent

               Interactive Student Edition: Grade 6 Lesson 6-4

               Student's Edition eText: Grade 6 Lesson 6-4

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-4: Explore It!
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-4: Example 1 & Try It!
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Example 2 & Try It!
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Additional Example 1
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Key Concept
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-4: Lesson Quiz
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Virtual Nerd™: How Do You Use Compatible Numbers to Estimate a Part of a Whole?
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Virtual Nerd™: How Do You Turn a Percent Into a Fraction?
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: MathXL for School: Additional Practice
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-4: Additional Practice
                    Curriculum Standards: Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Explain that a percent represents parts “out of 100” and ratios “to 100.” Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-5: Find the Percent of a Number

               Interactive Student Edition: Grade 6 Lesson 6-5

               Student's Edition eText: Grade 6 Lesson 6-5

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-5: Solve & Discuss It!
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-5: Example 1 & Try It!
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Example 2 & Try It!
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Example 3 & Try It!
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Additional Example 2
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Additional Example 3 with Try Another One
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Key Concept
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-5: Lesson Quiz
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Virtual Nerd™: How Do You Use an Equation to Find a Part of a Whole?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Virtual Nerd™: How Do You Use a Proportion to Find What Percent a Part is of a Whole?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: MathXL for School: Additional Practice
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-5: Additional Practice
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            6-6: Find the Whole Given a Part and the Percent

               Interactive Student Edition: Grade 6 Lesson 6-6

               Student's Edition eText: Grade 6 Lesson 6-6

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Problem-Based Learning

                  6-6: Solve &  Discuss It!
                  6-6: Solve & Discuss It!This interactive component provides the Problem-Based Learning from the student edition in an interactive format. It is designed for whole-class instruction.
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Develop: Visual Learning

                  6-6: Example 1 & Try It!
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Example 2
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Example 3  &  Try It!
                  6-6: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Additional Example 1
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Additional Example 2 with Try Another One
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Key Concept
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

               Assess & Differentiate

                  6-6: Lesson Quiz
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Virtual Nerd™: How Do You Use an Equation to Find a Whole?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Virtual Nerd™: How Do You Solve a Word Problem Using a Percent Proportion?
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: MathXL for School: Additional Practice
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

                  6-6: Additional Practice
                    Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            3-Act Mathematical Modeling: Ace the Test

               Student's Edition eText: Grade 6 Topic 6 3-Act Mathematical Modeling

               Math Anytime

                  Topic 6: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 6 Math Modeling: Act 1
                    Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Mathematical Modeling: Understand and Use Percent Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand a ratio as a comparison of two quantities and represent these comparisons. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Reason abstractly and quantitatively. Model with mathematics. Attend to precision. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

                  Topic 6 Math Modeling: Act 2
                    Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Mathematical Modeling: Understand and Use Percent Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand a ratio as a comparison of two quantities and represent these comparisons. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Reason abstractly and quantitatively. Model with mathematics. Attend to precision. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

                  Topic 6 Math Modeling: Act 3
                    Curriculum Standards: Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. (e.g., “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”)  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Mathematical Modeling: Understand and Use Percent Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Reason abstractly and quantitatively.  Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand a ratio as a comparison of two quantities and represent these comparisons. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Reason abstractly and quantitatively. Model with mathematics. Attend to precision. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. Reason abstractly and quantitatively. Model with mathematics. Attend to precision. 

            Interactive Student Edition: End of Topic 6

            Topic 6 Performance Task
              Curriculum Standards: Write equivalent values as fractions, decimals, and percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Convert between equivalent representations of positive rational numbers. Explain that a percent represents parts “out of 100” and ratios “to 100.” Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve problems involving percents. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

            Topic 6 Assessment
              Curriculum Standards: Represent and find the whole percent of a whole. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Explain that a percent represents parts “out of 100” and ratios “to 100.” Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Write equivalent values as fractions, decimals, and percents. Convert between equivalent representations of positive rational numbers. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Write percents that are greater than 100 or less than 1. Estimate the percent of a number using equivalent fractions, rounding, or compatible numbers. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve problems involving percents. Find the whole amount when given a part and the percent. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

         4-3: Example 1 & Try It!
           Curriculum Standards: Write and solve an addition or subtraction equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         4-6: Example 2 & Try It!
           Curriculum Standards: Understand and write an inequality that describes a real-world situation. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. 

         4-4: Example 1 & Try It!
           Curriculum Standards: Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. 

         5-10: Example 1 & Try It!
           Curriculum Standards: Convert between customary and metric units. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

         5-3: Example 1 & Try It!
           Curriculum Standards: Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

         5-4: Example 1 & Try It!
           Curriculum Standards: Solve ratio problems by using tables and graphs to show equivalent ratios. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. 

         5-5: Example 1 & Try It!
           Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Creating and using a table to compare ratios. Finding missing values in the tables. Using a unit ratio. Plotting the pairs of values on the coordinate plane. 

         5-5: Example 2 & Try It!
           Curriculum Standards: Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. 

         5-6: Example 1 & Try It!
           Curriculum Standards: Compare unit rates to solve problems. Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Solve unit rate problems. Using a unit ratio. 

         5-8: Example 2 & Try It!
           Curriculum Standards: Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

         5-9: Example 1 & Try It!
           Curriculum Standards: Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use multiplicative reasoning and representations to solve ratio and unit rate problems. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. 

         6-5: Example 1 & Try It!
           Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

         6-5: Example 2 & Try It!
           Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

         6-6: Example 1 & Try It!
           Curriculum Standards: Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

         1-2: Example 1 & Try It!
           Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. 

         3-2: Example 2 & Try It!
           Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. 

         3-2: Example 4 & Try It!
           Curriculum Standards: Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. 

         3-3: Example 1 & Try It!
           Curriculum Standards: Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. 

         3-3: Example 3 & Try It!
           Curriculum Standards: Use the order of operations to evaluate numerical expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

         3-4: Example 2 & Try It!
           Curriculum Standards: Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. 

         3-6: Example 1 & Try It!
           Curriculum Standards: Identify and write equivalent algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. 

         3-7: Example 2 & Try It!
           Curriculum Standards: Combine like terms in algebraic expressions. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Identify and generate equivalent algebraic expressions using mathematical properties. Apply the properties of operations to generate equivalent expressions without exponents. Identify when two expressions are equivalent and justify with mathematical reasoning. 

         4-10: Example 1 & Try It!
           Curriculum Standards: Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). 

         5-1 Example 2
           Curriculum Standards: Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. 

         Topics 1-6: Cumulative/Benchmark Assessment
           Curriculum Standards: Divide whole numbers and decimals. Fluently divide multi-digit numbers using the standard algorithm. The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Use variables to write algebraic expressions. Write expressions that record operations with numbers and with letters standing for numbers. (e.g., Express the calculation, “Subtract y from 5” as 5 – y.)  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Identify and write equivalent algebraic expressions. Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Combine like terms in algebraic expressions. Identify when two expressions are equivalent; i.e., when the two expressions name the same number regardless of which value is substituted into them. (e.g., The expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.)  Write and solve an addition or subtraction equation. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve a multiplication or division equation. Understand and write an inequality that describes a real-world situation. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Compare ratios to solve problems. Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  The student will represent a proportional relationship between two quantities, including those arising from practical situations. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Use reasoning about multiplication and division to solve ratio and rate problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve ratio problems by using tables and graphs to show equivalent ratios. The student will make connections between and among representations of a proportional relationship between two quantities using verbal descriptions, ratio tables, and graphs. Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Determine the rate for ratios of quantities with different units. Determine the unit rate for ratios. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Compare unit rates to solve problems. Use ratio reasoning to convert customary measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Use unit rates to convert metric measurements. Convert between customary and metric units. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Solve problems involving percents. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Find the whole amount when given a part and the percent. Demonstrate fluency with division of multi-digit whole numbers. Fluently divide using long division with a minimum of a four-digit dividend and interpret the quotient and remainder in context. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. Write and evaluate algebraic expressions. Understand the meaning of the variable in the context of the situation. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Write expressions that record operations with numbers and with letters standing for numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. Identify when two expressions are equivalent and justify with mathematical reasoning. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Create tables of equivalent ratios, find missing values in the tables and plot the pairs of values on the Cartesian coordinate plane. Creating and using a table to compare ratios. Finding missing values in the tables. Plotting the pairs of values on the coordinate plane. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. 

         Topic 7: Solve Area, Surface Area, and Volume Problems

            i11-2 Practice

            i12-3 Practice

            i14-3 Practice

            i8-2 Part 1

            i8-2 Part 3

            i8-2 Part 2

            i8-2 Practice

            i8-2 Lesson Check

            i19-1 Practice

            i20-1 Practice

            i20-5 Part 2

            i20-5 Practice

            i20-5 Part 3

            i20-5 Part 1

            i20-5 Lesson Check

            i24-3 Part 1

            i24-3 Practice

            i24-3 Part 2

            i24-3 Part 3

            i24-3 Lesson Check

            i24-1 Practice

            i24-1 Part 3

            i24-1 Part 2

            i24-1 Part 1

            i24-1 Lesson Check

            i11-2 Part 2

            i11-2 Part 3

            i11-2 Part 1

            i11-2 Lesson Check

            i12-3 Part 1

            i12-3 Part 2

            i12-3 Part 3

            i12-3 Lesson Check

            i14-3 Part 3

            i14-3 Part 1

            i14-3 Part 2

            i14-3 Lesson Check

            i19-1 Part 1

            i19-1 Part 2

            i19-1 Part 3

            i19-1 Lesson Check

            i20-1 Part 2

            i20-1 Part 3

            i20-1 Part 1

            i20-1 Lesson Check

            Topic 7 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 7

            Topic 7 STEM Project

               Topic 7 STEM Video

            Topic 7: Today's Challenge

            7-1: Find Areas of Parallelograms and Rhombuses

               Interactive Student Edition: Grade 6 Lesson 7-1

               Student's Edition eText: Grade 6 Lesson 7-1

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-1: Solve & Discuss It!
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Develop: Visual Learning

                  7-1: Example 1 & Try It!
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-1: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-1: Example 3 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-1: Additional Example 1
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-1: Additional Example 3 with Try Another One
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-1: Key Concept
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Assess & Differentiate

                  7-1: Lesson Quiz
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: Virtual Nerd™: What is the Formula for the Area of a Parallelogram?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: Virtual Nerd™: How Do You Find the Area of a Parallelogram?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: MathXL for School: Additional Practice
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-1: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-2: Solve Triangle Area Problems

               Interactive Student Edition: Grade 6 Lesson 7-2

               Student's Edition eText: Grade 6 Lesson 7-2

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-2: Solve & Discuss It!
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Develop: Visual Learning

                  7-2: Example 1 & Try It!
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-2: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-2: Example 3 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-2: Additional Example 2
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-2: Additional Example 3 with Try Another One
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-2: Key Concept
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Assess & Differentiate

                  7-2: Lesson Quiz
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: Virtual Nerd™: What is the Formula for the Area of a Triangle?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: Virtual Nerd™: How Do You Find the Area of a Triangle?
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: MathXL for School: Additional Practice
                    Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-2: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-3: Find Areas of Trapezoids and Kites

               Interactive Student Edition: Grade 6 Lesson 7-3

               Student's Edition eText: Grade 6 Lesson 7-3

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-3: Explain It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

               Develop: Visual Learning

                  7-3: Example 1 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Example 3  &  Try It!
                  7-3: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Additional Example 1 with Try Another One
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Additional Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Key Concept
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

               Assess & Differentiate

                  7-3: Lesson Quiz
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Virtual Nerd™: What is the Formula for the Area of a Trapezoid?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Virtual Nerd™: How Do You Find the Area of a Trapezoid?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: MathXL for School: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-3: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-4: Find Areas of Polygons

               Interactive Student Edition: Grade 6 Lesson 7-4

               Student's Edition eText: Grade 6 Lesson 7-4

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-4: Solve & Discuss It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

               Develop: Visual Learning

                  7-4: Example 1 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-4: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-4: Example 3 &  Try It!
                  7-4: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Construct polygons in the Cartesian coordinate plane. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: Additional Example 1 with Try Another One
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-4: Additional Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

                  7-4: Key Concept
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

               Assess & Differentiate

                  7-4: Lesson Quiz
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: Virtual Nerd™: How Do You Find the Area of a Composite Figure?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: Virtual Nerd™: How Do You Find the Area of an Irregular Figure in the Coordinate Plane?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: MathXL for School: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

                  7-4: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Construct polygons in the Cartesian coordinate plane. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

            7-1: Key Concept
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-1: Virtual Nerd™: What is the Formula for the Area of a Parallelogram?
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-2: Virtual Nerd™: What is the Formula for the Area of a Triangle?
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-3: Key Concept
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-3: Virtual Nerd™: How Do You Find the Area of a Trapezoid?
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-1: Example 1 & Try It!
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-1: Example 2
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-2: Example 1 & Try It!
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Develop and use formulas to determine the area of triangles. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-3: Example 2
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-3: Example 3  &  Try It!
            7-3: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find areas of trapezoids and kites. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            7-4: Example 2
              Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. 

            Topic 7 Mid-Topic Assessment
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Develop and use formulas to determine the area of triangles. Find the areas of triangles. Find areas of trapezoids and kites. Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

            7-5: Represent Solid Figures Using Nets

               Interactive Student Edition: Grade 6 Lesson 7-5

               Student's Edition eText: Grade 6 Lesson 7-5

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-5: Explore It!
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Develop: Visual Learning

                  7-5: Example 1 & Try It!
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Example 2
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Example 3 & Try It!
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Additional Example 2
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Additional Example 3 with Try Another One
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Key Concept
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Assess & Differentiate

                  7-5: Lesson Quiz
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Virtual Nerd™: How Do You Identify a Three-Dimensional Figure from a Net?
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Virtual Nerd™: What is a Net?
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: MathXL for School: Additional Practice
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-5: Additional Practice
                    Curriculum Standards: Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

            3-Act Mathematical Modeling: That's a Wrap

               Student's Edition eText: Grade 6 Topic 7 3-Act Mathematical Modeling

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 7 Math Modeling: Act 1
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Mathematical Modeling: Solve Area, Surface Area, and Volume Problems Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. 

                  Topic 7 Math Modeling: Act 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Mathematical Modeling: Solve Area, Surface Area, and Volume Problems Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. 

                  Topic 7 Math Modeling: Act 3
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Mathematical Modeling: Solve Area, Surface Area, and Volume Problems Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Construct viable arguments and critique the reasoning of others.  Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Look for and make use of structure.  Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Construct viable arguments and critique the reasoning of others. Model with mathematics. Look for and make use of structure. 

            7-6: Find Surface Areas of Prisms

               Interactive Student Edition: Grade 6 Lesson 7-6

               Student's Edition eText: Grade 6 Lesson 7-6

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-6: Solve &  Discuss It!
                  7-6: Solve & Discuss It!This interactive component provides the Problem-Based Learning from the student edition in an interactive format. It is designed for whole-class instruction.
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Develop: Visual Learning

                  7-6: Example 1 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Example 3  &  Try It!
                  7-6: Example 3 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Additional Example 1 with Try Another One
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Additional Example 3
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Key Concept
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Assess & Differentiate

                  7-6: Lesson Quiz
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Virtual Nerd™: What is the Formula for the Surface Area of a Prism?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Virtual Nerd™: How Do You Find the Surface Area of a Triangular Prism Using a Net?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: MathXL for School: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-6: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

            7-7: Find Surface Areas of Pyramids

               Interactive Student Edition: Grade 6 Lesson 7-7

               Student's Edition eText: Grade 6 Lesson 7-7

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-7: Solve & Discuss It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Develop: Visual Learning

                  7-7: Example 1 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Example 2  &  Try It!
                  7-7: Example 2 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Additional Example 1 with Try Another One
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Additional Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Key Concept
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

               Assess & Differentiate

                  7-7: Lesson Quiz
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Virtual Nerd™: How Do You Find the Lateral and Surface Areas of a Regular Pyramid?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Virtual Nerd™: What is the Formula for the Surface Area of a Regular Pyramid?
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: MathXL for School: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

                  7-7: Additional Practice
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Draw a net of a pyramid and use it to find the pyramid's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. 

            7-8: Find Volume with Fractional Edge Lengths

               Interactive Student Edition: Grade 6 Lesson 7-8

               Student's Edition eText: Grade 6 Lesson 7-8

               Math Anytime

                  Topic 7: Today's Challenge

               Develop: Problem-Based Learning

                  7-8: Solve & Discuss It!
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Develop: Visual Learning

                  7-8: Example 1 & Try It!
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

                  7-8: Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

                  7-8: Example 3 & Try It!
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

                  7-8: Additional Example 1 with Try Another One
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

                  7-8: Additional Example 2
                    Curriculum Standards: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

                  7-8: Key Concept
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: Do You Understand?/Do You Know How?
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

               Assess & Differentiate

                  7-8: Lesson Quiz
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: Virtual Nerd™: What is the Formula for the Volume of a Rectangular Prism?
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: Virtual Nerd™: How Do You Find the Volume of a Rectangular Prism?
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: MathXL for School: Additional Practice
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

                  7-8: Additional Practice
                    Curriculum Standards: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. 

            Interactive Student Edition: End of Topic 7

            Topic 7 Performance Task
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Develop and use formulas to determine the area of triangles. Find the areas of triangles. Find the areas of polygons. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Construct polygons in the Cartesian coordinate plane. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Drawing polygons in the coordinate plane given coordinates for the vertices. Using coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. 

            Topic 7 Assessment
              Curriculum Standards: Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Develop and use formulas to determine the area of triangles. Find the areas of triangles. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find areas of trapezoids and kites. Find the areas of polygons. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Draw a net of a prism and use it to find the prism's surface area. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Draw a net of a pyramid and use it to find the pyramid's surface area. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Find the volume of a rectangular prism with fractional edge lengths. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Write and evaluate algebraic expressions. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. 

         Topic 8: Display, Describe, and Summarize Data

            i21-2 Practice

            i25-1 Part 3

            i25-1 Part 2

            i25-1 Part 1

            i25-1 Lesson Check

            i25-1 Practice

            i9-1 Practice

            i11-3 Practice

            i11-4 Practice

            i7-2 Practice

            i8-3 Practice

            i21-1 Part 1

            i21-1 Part 2

            i21-1 Part 3

            i21-1 Lesson Check

            i21-1 Practice

            i21-2 Part 2

            i21-2 Part 1

            i21-2 Part 3

            i21-2 Lesson Check

            i22-4 Part 1

            i22-4 Part 3

            i22-4 Part 2

            i22-4 Lesson Check

            i22-4 Practice

            i9-1 Part 1

            i9-1 Lesson Check

            i9-1 Part 2

            i9-1 Part 3

            i11-3 Part 1

            i11-3 Part 2

            i11-3 Part 3

            i11-3 Lesson Check

            i11-4 Part 1

            i11-4 Part 2

            i11-4 Part 3

            i11-4 Lesson Check

            i7-2 Part 1

            i7-2 Part 2

            i7-2 Part 3

            i7-2 Lesson Check

            i8-3 Part 1

            i8-3 Part 3

            i8-3 Part 2

            i8-3 Lesson Check

            Topic 8 Readiness Assessment

            Interactive Student Edition: Beginning of Topic 8

            Topic 8 STEM Project

               Topic 8 STEM Video

            Topic 8: Today's Challenge

            8-1: Recognize Statistical Questions

               Interactive Student Edition: Grade 6 Lesson 8-1

               Student's Edition eText: Grade 6 Lesson 8-1

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-1: Solve & Discuss It!
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

               Develop: Visual Learning

                  8-1: Example 1 & Try It!
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1 Example 2 & Try It!
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Example 3 & Try It!
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. 

                  8-1: Additional Example 1 with Try Another One
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Additional Example 2
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Key Concept
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Do You Understand?/Do You Know How?
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

               Assess & Differentiate

                  8-1: Lesson Quiz
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Virtual Nerd™: What is a Line Plot?
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: MathXL for School: Additional Practice
                    Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-1: Additional Practice

            8-2: Summarize Data Using Mean, Median, and Mode

               Interactive Student Edition: Grade 6 Lesson 8-2

               Student's Edition eText: Grade 6 Lesson 8-2

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-2: Solve & Discuss It!
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

               Develop: Visual Learning

                  8-2: Example 1 & Try It!
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Example 2
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Example 3 & Try It!
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Example 4
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Example 5 & Try It!
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Additional Example 2
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Additional Example 5 with Try Another One
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-2: Key Concept
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: Do You Understand?/Do You Know How?
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

               Assess & Differentiate

                  8-2: Lesson Quiz
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: Virtual Nerd™: How Do You Find an Average?
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: Virtual Nerd™: What is the Median of a Data Set?
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: MathXL for School: Additional Practice
                    Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. 

                  8-2: Additional Practice

            8-3: Display Data in Box Plots

               Interactive Student Edition: Grade 6 Lesson 8-3

               Student's Edition eText: Grade 6 Lesson 8-3

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-3: Solve & Discuss It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

               Develop: Visual Learning

                  8-3: Example 1 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3 Example 2
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3 Example 3 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Additional Example 2
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Additional Example 3 with Try Another One
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Key Concept
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Do You Understand?/Do You Know How?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

               Assess & Differentiate

                  8-3: Lesson Quiz
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Virtual Nerd™: How Do You Make a Box-and-Whisker Plot?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Virtual Nerd™: What is a Box-and-Whisker Plot?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: MathXL for School: Additional Practice
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-3: Additional Practice

            8-4: Display Data in Frequency Tables and Histograms

               Interactive Student Edition: Grade 6 Lesson 8-4

               Student's Edition eText: Grade 6 Lesson 8-4

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-4: Explore It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

               Develop: Visual Learning

                  8-4: Example 1 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-4: Example 2 & Try It!
                    Curriculum Standards: Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Summarize numerical data sets in relation to the context. Report the number of observations. Summarize numerical data sets in relation to their context. 

                  8-4: Example 3 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-4: Additional Example 2 with Try Another One
                    Curriculum Standards: Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Summarize numerical data sets in relation to the context. Report the number of observations. Summarize numerical data sets in relation to their context. 

                  8-4: Additional Example 3
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

                  8-4: Key Concept
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: Do You Understand?/Do You Know How?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

               Assess & Differentiate

                  8-4: Lesson Quiz
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: Virtual Nerd™: How Do You Make a Histogram?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: Virtual Nerd™: What is a Frequency Table?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: MathXL for School: Additional Practice
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Summarize numerical data sets in relation to their context. 

                  8-4: Additional Practice

            8-2: Example 3 & Try It!
              Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

            8-3: Example 1 & Try It!
              Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            8-4: Example 1 & Try It!
              Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            8-4: Example 3 & Try It!
              Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            8-3: Virtual Nerd™: How Do You Make a Box-and-Whisker Plot?
              Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            8-4: Virtual Nerd™: How Do You Make a Histogram?
              Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Reporting the number of observations. Make and analyze frequency tables and histograms. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Reporting the number of observations. Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Report the number of observations. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            8-4: Virtual Nerd™: What is a Frequency Table?
              Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. 

            Topic 8 Mid-Topic Assessment
              Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Reporting the number of observations. Make and analyze frequency tables and histograms. Reporting the number of observations. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Report the number of observations. 

            8-5: Summarize Data Using Measures of Variability

               Interactive Student Edition: Grade 6 Lesson 8-5

               Student's Edition eText: Grade 6 Lesson 8-5

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-5: Solve & Discuss It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

               Develop: Visual Learning

                  8-5: Example 1 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Example 2 & Try It!
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Example 3 & Try It!
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Additional Example 1 with Try Another One
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Additional Example 2
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Key Concept
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Do You Understand?/Do You Know How?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

               Assess & Differentiate

                  8-5: Lesson Quiz
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Virtual Nerd™: How do You Summarize Data Using Measures of Variability?

                  8-5: MathXL for School: Additional Practice
                    Curriculum Standards: Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use measures of variability to describe a data set. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Use dot plots, histograms and box plots to display and interpret numerical data. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-5: Additional Practice

            8-6: Choose Appropriate Statistical Measures

               Interactive Student Edition: Grade 6 Lesson 8-6

               Student's Edition eText: Grade 6 Lesson 8-6

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-6: Solve &  Discuss It!
                  8-6: Solve & Discuss It!This interactive component provides the Problem-Based Learning from the student edition in an interactive format. It is designed for whole-class instruction.
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

               Develop: Visual Learning

                  8-6: Example 1 & Try It!
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Example 2  &  Try It!
                  8-6: Example 2 & Try It!This component continues the Visual Learning Bridge from the student edition. Some use interactivity or animation to illustrate math ideas. It is designed for whole-class instruction.
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Additional Example 1 with Try Another One
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Additional Example 2
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Key Concept
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Do You Understand?/Do You Know How?
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

               Assess & Differentiate

                  8-6: Lesson Quiz
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Virtual Nerd™: How Do You Find the Interquartile Range of a Data Set?
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Virtual Nerd™: How Do You Figure Out Whether the Mean, Median, or Mode Best Describes a Data Set?
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: MathXL for School: Additional Practice
                    Curriculum Standards: Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Select and use appropriate statistical measures. Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

                  8-6: Additional Practice

            8-7: Summarize Data Distributions

               Interactive Student Edition: Grade 6 Lesson 8-7

               Student's Edition eText: Grade 6 Lesson 8-7

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Problem-Based Learning

                  8-7: Explain It!
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

               Develop: Visual Learning

                  8-7: Example 1 & Try It!
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Example 2
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Example 3 & Try It!
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Additional Example 2 with Try Another One
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Additional Example 3
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Key Concept
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Do You Understand?/Do You Know How?
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: MathXL for School: Practice & Problem Solving
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

               Assess & Differentiate

                  8-7: Lesson Quiz
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Virtual Nerd™: How Do You Figure Out Whether the Mean, Median, or Mode Best Describes a Data Set?
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Virtual Nerd™: What is the Interquartile Range?
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: MathXL for School: Additional Practice
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Use dot plots, histograms and box plots to display and interpret numerical data. Create and interpret circle graphs. Summarize numerical data sets in relation to the context. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Compare the attributes of different representations of the same data. Summarize numerical data sets in relation to their context. Reporting the number of observations in dot plots and histograms. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

                  8-7: Additional Practice

            3-Act Mathematical Modeling: Vocal Range

               Student's Edition eText: Grade 6 Topic 8 3-Act Mathematical Modeling

               Math Anytime

                  Topic 8: Today's Challenge

               Develop: Mathematical Modeling

                  Topic 8 Math Modeling: Act 1
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Mathematical Modeling: Display, Describe, and Summarize Data Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Summarize numerical data sets in relation to their context, such as by: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Display and interpret data. Model with mathematics. Use appropriate tools strategically. Attend to precision. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Topic 8 Math Modeling: Act 2
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Mathematical Modeling: Display, Describe, and Summarize Data Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Summarize numerical data sets in relation to their context, such as by: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Display and interpret data. Model with mathematics. Use appropriate tools strategically. Attend to precision. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

                  Topic 8 Math Modeling: Act 3
                    Curriculum Standards: Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Mathematical Modeling: Display, Describe, and Summarize Data Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Summarize numerical data sets in relation to their context, such as by: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Use appropriate tools strategically.  Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Attend to precision.  Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Display and interpret data. Model with mathematics. Use appropriate tools strategically. Attend to precision. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Model with mathematics. Use appropriate tools strategically. Attend to precision. 

            Interactive Student Edition: End of Topic 8

            Topic 8 Performance Task
              Curriculum Standards: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Select and use appropriate statistical measures. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Use dot plots, histograms and box plots to display and interpret numerical data. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand the median as a measure of center that is the numerical middle of an ordered data set. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Justifying the appropriate choice of measures of center using the shape of the data distribution. 

            Topic 8 Assessment
              Curriculum Standards: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Make and analyze frequency tables and histograms. Reporting the number of observations. Use measures of variability to describe a data set. Relating the choice of measures of center to the shape of the data distribution and the context in which the data were gathered. Select and use appropriate statistical measures. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered. Through informal observation, understand that a set of data collected to answer a statistical question has a distribution which can be described by its center (mean/ median), spread (range), and overall shape.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Summarize numerical data sets. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.  Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. Understand the median as a measure of center that is the numerical middle of an ordered data set. Analyze the choice of measures of center and variability based on the shape of the data distribution and/or the context of the data. Understand that describing the variability of a data set is needed to distinguish between data sets in the same scale, by comparing graphical representations of different data sets in the same scale that have similar measures of center, but different spreads. Justifying the appropriate choice of measures of center using the shape of the data distribution. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread and overall shape. Create and interpret circle graphs. Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. Understand that both a measure of center and a description of variability should be considered when describing a numerical data set. Compare the attributes of different representations of the same data. Communicating the nature of the attribute under investigation, how it was measured, and the units of measurement. 

         End-of-Year Assessment
           Curriculum Standards: Divide whole numbers and decimals. Fluently add, subtract, multiply and divide multi-digit decimals using the standard algorithm for each operation.  The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals.  Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms. Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers. Estimate solutions to problems with whole numbers, fractions and decimals and use the estimates to assess the reasonableness of results in the context of the problem. Estimate solutions to problems with whole numbers, decimals, fractions, and mixed numbers and use the estimates to assess the reasonableness of results in the context of the problem.  Illustrate multiplication and division of fractions and decimals to show connections to fractions, whole number multiplication, and inverse relationships.  Solve and interpret real-world and mathematical problems including those involving money, measurement, geometry, and data requiring arithmetic with decimals, fractions and mixed numbers.  Fluently divide multi-digit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.  Represent rational numbers using a number line. Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts (e.g., write –3o C > –7o C to express the fact that –3o C is warmer than –7o C).  The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. The student will compare and order positive rational numbers. The student will identify and represent integers. The student will compare and order integers. Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. Compare positive rational numbers represented in various forms. Use the symbols <, = and >. Convert between equivalent representations of positive rational numbers. Represent integers with counters and on a number line and rational numbers on a number line, recognizing the concepts of opposites, direction, and magnitude; use integers and rational numbers in real-world and mathematical situations, explaining the meaning of 0 in each situation.  Compare and order positive rational numbers, represented in various forms, or integers using the symbols <, >, and =.  Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane. Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right. Write, interpret, and explain statements of order for rational numbers in real-world contexts. 
For example, write –3 ºC > –7 ºC to express the fact that –3 ºC is warmer than –7 ºC.  Graph points with rational coordinates on a coordinate plane. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.  The student will identify the components of the coordinate plane. The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. Plot integer- and rational-valued (limited to halves and fourths) ordered-pairs as coordinates in all four quadrants and recognize the reflective relationships among coordinates that differ only by their signs. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Use absolute value to find distance on a coordinate plane. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Use distances between two points that are either vertical or horizontal to each other (not requiring the distance formula) to solve real-world and mathematical problems about congruent two-dimensional figures. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Write the prime factorization and find the greatest common factor and the least common multiple of two numbers. Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor (e.g., express 36 + 8 as 4 (9 + 2)). Factor whole numbers; express a whole number as a product of prime factors with exponents. Determine greatest common factors and least common multiples. Use common factors and common multiples to calculate with fractions and find equivalent fractions. Factor whole numbers and express prime and composite numbers as a product of prime factors with exponents. Determine the greatest common factors and least common multiples. Use common factors and multiples to calculate with fractions, find equivalent fractions, and express the sum of two-digit numbers with a common factor using the distributive property.  Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2). Use the order of operations to evaluate numerical expressions. Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions (e.g., apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y).  The student will simplify numerical expressions involving integers. Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Generate equivalent expressions and evaluate expressions involving positive rational numbers by applying the commutative, associative, and distributive properties and order of operations to solve real-world and mathematical problems.  Represent real-world or mathematical situations using expressions, equations and inequalities involving variables and rational numbers.  Write and evaluate numerical expressions involving whole-number exponents. Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. Identify and write equivalent algebraic expressions. Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Use and evaluate variables in expressions, equations, and inequalities that arise from various contexts, including determining when or if, for a given value of the variable, an equation or inequality involving a variable is true or false.  Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for. Write and solve a multiplication or division equation. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number or depending on the purpose at hand, any number in a specified set.  The student will solve one-step linear equations in one variable, including practical problems that require the solution of a one-step linear equation in one variable. Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Use number sense and properties of operations and equality to solve real-world and mathematical problems involving equations in the form x + p = ! and px = q, where x, p, and q are nonnegative rational numbers. Graph the solution on a number line, interpret the solution in the original context, and assess the reasonableness of the solution.  Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.  Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.  Write and solve equations that involve rational numbers. Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.  Understand and write an inequality that describes a real-world situation. Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. The student will represent a practical situation with a linear inequality in one variable. Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.  Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Use patterns to write and solve equations with variables. Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. (e.g., In a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.) Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Represent relationships between two varying quantities involving no more than two operations with rules, graphs, and tables; translate between any two of these representations.  Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time. Analyze the relationship between dependent and independent variables in tables, graphs, and equations. Use a ratio to describe the relationship between two quantities. The student will represent relationships between quantities using ratios, and will use appropriate notations, such as a/b, a to b, and a:b. Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Identify and use ratios to compare quantities. Recognize that multiplicative comparison and additive comparison are different. Use multiplicative reasoning and representations to solve ratio and unit rate problems. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.  Solve problems involving rates. Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. (e.g., “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”) Instructional Note: Expectations for unit rates in this grade are limited to non-complex fractions.  Solve unit rate problems including those involving unit pricing and constant speed. (e.g., If it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed?)  The student will determine the unit rate of a proportional relationship and use it to find a missing value in a ratio table. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Determine the rate for ratios of quantities with different units. Use reasoning about multiplication and division to solve ratio and rate problems. Determine the unit rate for ratios. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixture and concentrations.  Understand the concept of a unit rate a/b associated with a ratio a:b with b ? 0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations. Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.  Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns could be mowed in 35 hours? At what rate were lawns being mowed? Use unit rates to convert metric measurements. Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. The student will represent a proportional relationship between two quantities, including those arising from practical situations. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units. Solve problems in various real-world and mathematical contexts that require the conversion of weights, capacities, geometric measurements, and time within the same measurement systems using appropriate units.  Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities. Convert between customary and metric units. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Understand that percent represents parts out of 100 and ratios to 100. Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Explain that a percent represents parts “out of 100” and ratios “to 100.” Determine equivalencies among fractions, decimals, and percents. Select among these representations to solve problems.  Find the whole amount when given a part and the percent. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.  Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole number exponents, in the conventional order when there are no parentheses to specify a particular order: Order of Operations (e.g., use the formulas V = s3 and A = 6s2 to find the volume and surface area of a cube with sides of length s = 1/2).  Find the area of right triangles, other triangles, special quadrilaterals and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Develop and use formulas for the area of squares and parallelograms using a variety of methods including but not limited to the standard algorithm. Find the area of right triangles, other triangles, special quadrilaterals, and polygons that can be decomposed into triangles and other shapes to solve real-world and mathematical problems.  Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).  For example, use the formulas V = s³ and A = 6s² to find the volume and surface area of a cube with sides of length s = 1/2. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.  Find areas of trapezoids and kites. Find the areas of polygons. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Represent solid figures using nets. Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.  Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = B h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Find the volume of a rectangular prism with fractional edge lengths. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5 – y. Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.  Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. (e.g., “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.)  Display numerical data in plots on a number line, including dot plots, histograms and box plots.  Identify and write statistical questions. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.  Recognize that a measure of center for a numerical data set summarizes all of its values with a single number. Giving quantitative measures of center (median and/or mean), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  The student will determine the effect on measures of center when a single value of a data set is added, removed, or changed. Calculate the mean, median, and mode for a set of real-world data.  Explain and justify which measure of central tendency (mean, median, or mode) would provide the most descriptive information for a given set of data.  Identify the mean, median, mode, and range of a data set. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.  Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.  Create and analyze box and whisker plots observing how each segment contains one quarter of the data. Make and interpret box plots. Demonstrate fluency with addition, subtraction, multiplication and division of decimals. Apply and extend previous understandings of decimals to develop and fluently use the standard algorithms for addition, subtraction, multiplication and division of decimals. Locate rational numbers on a horizontal or vertical number line. Write, interpret and explain problems of ordering of rational numbers. Find and position rational numbers on a horizontal or vertical number line. Find and position pairs of rational numbers on a coordinate plane. Write, interpret, and explain statements of order for rational numbers in real-world contexts. Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate. Understand signs of numbers in ordered pairs as indicating locations in quadrants of the Cartesian coordinate plane. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Understand signs of numbers in ordered pairs as indicating locations in quadrants. Recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. Find distances between points with the same first coordinate or the same second coordinate. Understand subtraction of integers as adding the additive inverse, p – q = p + (– q). Show that the distance between two integers on the number line is the absolute value of their difference. Find the greatest common factor (GCF) and the least common multiple (LCM). Use the distributive property to express a sum of two whole numbers with a common factor as a multiple of a sum of two whole numbers. Find the unique prime factorization for a whole number. Find the greatest common factor of two whole numbers less than or equal to 100. Create and evaluate expressions involving variables and whole number exponents. Identify and generate equivalent algebraic expressions using mathematical properties. Write and evaluate numerical expressions, with and without grouping symbols, involving whole-number exponents. Apply the properties of operations to generate equivalent expressions without exponents. Write and evaluate algebraic expressions. Write and solve equations using variables to represent quantities, and understand the meaning of the variable in the context of the situation. Solve one-step linear equations in one variable involving non-negative rational numbers. Write and/or solve equations of the form x+p = q and px = q in which p and q are rational numbers. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem. x + p = q in which p, q and x are all nonnegative rational numbers; and, p · x = q for cases in which p, q and x are all nonnegative rational numbers. Write an inequality of the form x > c, x < c, x = c, or x = c to represent a constraint or condition. Graph the solution set of an inequality. Writing an inequality of the form  x > c or x < c  to represent a constraint or condition in a real-world or mathematical problem. Recognizing that inequalities of the form  x > c or x < c  have infinitely many solutions. Representing solutions of inequalities on number line diagrams. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. Analyze the relationship between the dependent and independent variables using graphs, tables and equations and relate these representations to each other. Using variables to represent two quantities in a real-world or mathematical context that change in relationship to one another. Analyze the relationship between quantities in different representations (context, equations, tables, and graphs). Understand a ratio as a comparison of two quantities and represent these comparisons. Solve problems involving ratios and rates. Describe a ratio as a multiplicative relationship between two quantities. Model a ratio relationship using a variety of representations. Understand the concept of a unit rate associated with a ratio, and describe the meaning of unit rate. Solve unit rate problems. Understand that ratios can be expressed as equivalent unit ratios by finding and interpreting both unit ratios in context. Using a unit ratio. Convert measurement units within and between two systems of measurement. Converting and manipulating measurements using given ratios. Solve percent problems. Extend prior knowledge to generate equivalent representations of rational numbers between fractions, decimals and percentages (limited to terminating decimals and/or benchmark fractions of 1/3 and 2/3). Understanding and finding a percent of a quantity as a ratio per 100. Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. Finding the whole, given a part and the percent. Evaluate expressions at specific values of the variables. Evaluate non-negative rational number expressions. Find the area of polygons by composing or decomposing the shapes into rectangles or triangles. Evaluate expressions at specific values of their variables using expressions that arise from formulas used in real-world problems. Find the area of triangles by composing into rectangles and decomposing into right triangles. Find the area of special quadrilaterals and polygons by decomposing into triangles or rectangles. Analyze and describe the properties of prisms and pyramids. Represent three-dimensional figures using nets made up of rectangles and triangles. Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. Represent right prisms and right pyramids using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. Understand that the volume of a right rectangular prism can be found by filling the prism with multiple layers of the base. Apply V = l · w · h and V = Bh to find the volume of right rectangular prisms. Apply and extend previous understandings of the volume of a right rectangular prism to find the volume of right rectangular prisms with fractional edge lengths. Apply this understanding to the context of solving real-world and mathematical problems. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Use dot plots, histograms and box plots to display and interpret numerical data. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. Display numerical data in plots on a number line. Use dot plots, histograms, and box plots to represent data. Reporting the number of observations in dot plots and histograms. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary from a single number. Summarize numerical data sets in relation to the context. Give quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context of the data. Determine the measure of center of a data set and understand that it is a single number that summarizes all the values of that data set. Understand that a mean is a measure of center that represents a balance point or fair share of a data set and can be influenced by the presence of extreme values within the data set. Understand the median as a measure of center that is the numerical middle of an ordered data set. Summarize numerical data sets in relation to their context. Giving quantitative measures of center, describing variability, and any overall pattern, and noting any striking deviations. 

         Next-Generation Assessment Practice Performance Tasks

            Next-Generation Assessment Performance Task 1

            Next-Generation Assessment Performance Task 2

         Next-Generation Assessment Practice Test

         Intervention Lessons

            Cluster 1: Place Value

               Lesson i1-1: Place Value

                  Interactive Learning

                     i1-1 Part 1

                     i1-1 Part 2

                     i1-1 Part 3

                     i1-1 Lesson Check

                  Journal

                     i1-1 Journal

                  Practice

                     i1-1 Practice

               Lesson i1-2: Comparing and Ordering Whole Numbers

                  Interactive Learning

                     i1-2 Part 1

                     i1-2 Part 2

                     i1-2 Part 3

                     i1-2 Lesson Check

                  Journal

                     i1-2 Journal

                  Practice

                     i1-2 Practice

            Cluster 2: Multiplication Number Sense

               Lesson i2-1: Addition and Multiplication Properties

                  Interactive Learning

                     i2-1 Part 1

                     i2-1 Part 2

                     i2-1 Part 3

                     i2-1 Lesson Check

                  Journal

                     i2-1 Journal

                  Practice

                     i2-1 Practice

               Lesson i2-2: Distributive Property

                  Interactive Learning

                     i2-2 Part 1

                     i2-2 Part 2

                     i2-2 Part 3

                     i2-2 Lesson Check

                  Journal

                     i2-2 Journal

                  Practice

                     i2-2 Practice

               Lesson i2-3: Multiplying by Multiples of 10, 100, and 1,000

                  Interactive Learning

                     i2-3 Part 1

                     i2-3 Part 2

                     i2-3 Part 3

                     i2-3 Lesson Check

                  Journal

                     i2-3 Journal

                  Practice

                     i2-3 Practice

               Lesson i2-4: Using Mental Math to Multiply

                  Interactive Learning

                     i2-4 Part 1

                     i2-4 Part 2

                     i2-4 Part 3

                     i2-4 Lesson Check

                  Journal

                     i2-4 Journal

                  Practice

                     i2-4 Practice

               Lesson i2-5: Estimating Products

                  Interactive Learning

                     i2-5 Part 1

                     i2-5 Part 2

                     i2-5 Part 3

                     i2-5 Lesson Check

                  Journal

                     i2-5 Journal

                  Practice

                     i2-5 Practice

            Cluster 3: Multiplying Whole Numbers

               Lesson i3-1: Multiplying by 1-Digit Numbers: Expanded

                  Interactive Learning

                     i3-1 Part 1

                     i3-1 Part 2

                     i3-1 Part 3

                     i3-1 Lesson Check

                  Journal

                     i3-1 Journal

                  Practice

                     i3-1 Practice

               Lesson i3-2: Multiplying by 1-Digit Numbers

                  Interactive Learning

                     i3-2 Part 1

                     i3-2 Part 2

                     i3-2 Part 3

                     i3-2 Lesson Check

                  Journal

                     i3-2 Journal

                  Practice

                     i3-2 Practice

               Lesson i3-3: Using Patterns to Multiply and Estimate

                  Interactive Learning

                     i3-3 Part 1

                     i3-3 Part 2

                     i3-3 Part 3

                     i3-3 Lesson Check

                  Journal

                     i3-3 Journal

                  Practice

                     i3-3 Practice

               Lesson i3-4: Multiplying by 2-Digit Numbers: Expanded

                  Interactive Learning

                     i3-4 Part 1

                     i3-4 Part 2

                     i3-4 Part 3

                     i3-4 Lesson Check

                  Journal

                     i3-4 Journal

                  Practice

                     i3-4 Practice

               Lesson i3-5: Multiplying by 2-Digit Numbers

                  Interactive Learning

                     i3-5 Part 1

                     i3-5 Part 2

                     i3-5 Part 3

                     i3-5 Lesson Check

                  Journal

                     i3-5 Journal

                  Practice

                     i3-5 Practice

            Cluster 4: Dividing by 1-Digit Numbers

               Lesson i4-1: Dividing Multiples of 10 and 100

                  Interactive Learning

                     i4-1 Part 1

                     i4-1 Part 2

                     i4-1 Part 3

                     i4-1 Lesson Check

                  Journal

                     i4-1 Journal

                  Practice

                     i4-1 Practice

               Lesson i4-2: Estimating Quotients with 1-Digit Divisors

                  Interactive Learning

                     i4-2 Part 1

                     i4-2 Part 2

                     i4-2 Part 3

                     i4-2 Lesson Check

                  Journal

                     i4-2 Journal

                  Practice

                     i4-2 Practice

               Lesson i4-3: Dividing: 1-Digit Divisors, 2-Digit Dividends

                  Interactive Learning

                     i4-3 Part 1

                     i4-3 Part 2

                     i4-3 Part 3

                     i4-3 Lesson Check

                  Journal

                     i4-3 Journal

                  Practice

                     i4-3 Practice

               Lesson i4-4: Dividing: 1-Digit Divisors, 3-Digit Dividends

                  Interactive Learning

                     i4-4 Part 1

                     i4-4 Part 2

                     i4-4 Part 3

                     i4-4 Lesson Check

                  Journal

                     i4-4 Journal

                  Practice

                     i4-4 Practice

               Lesson i4-5: Dividing: 1-Digit Divisors, 4-Digit Dividends

                  Interactive Learning

                     i4-5 Part 1

                     i4-5 Part 2

                     i4-5 Part 3

                     i4-5 Lesson Check

                  Journal

                     i4-5 Journal

                  Practice

                     i4-5 Practice

               Lesson i4-6: Divisibility Rules

                  Interactive Learning

                     i4-6 Part 1

                     i4-6 Part 2

                     i4-6 Part 3

                     i4-6 Lesson Check

                  Journal

                     i4-6 Journal

                  Practice

                     i4-6 Practice

            Cluster 5: Dividing by 2-Digit Numbers

               Lesson i5-1: Using Patterns to Divide

                  Interactive Learning

                     i5-1 Part 1

                     i5-1 Part 2

                     i5-1 Part 3

                     i5-1 Lesson Check

                  Journal

                     i5-1 Journal

                  Practice

                     i5-1 Practice

               Lesson i5-2: Estimating Quotients with 2-Digit Divisors

                  Interactive Learning

                     i5-2 Part 1

                     i5-2 Part 2

                     i5-2 Part 3

                     i5-2 Lesson Check

                  Journal

                     i5-2 Journal

                  Practice

                     i5-2 Practice

               Lesson i5-3: Dividing: 2-Digit Divisors, 1-Digit Quotients

                  Interactive Learning

                     i5-3 Part 1

                     i5-3 Part 2

                     i5-3 Part 3

                     i5-3 Lesson Check

                  Journal

                     i5-3 Journal

                  Practice

                     i5-3 Practice

               Lesson i5-4: Dividing: 2-Digit Divisors, 2-Digit Quotients

                  Interactive Learning

                     i5-4 Part 1

                     i5-4 Part 2

                     i5-4 Part 3

                     i5-4 Lesson Check

                  Journal

                     i5-4 Journal

                  Practice

                     i5-4 Practice

            Cluster 6: Decimal Number Sense

               Lesson i6-1: Understanding Decimals

                  Interactive Learning

                     i6-1 Part 1

                     i6-1 Part 2

                     i6-1 Part 3

                     i6-1 Lesson Check

                  Journal

                     i6-1 Journal

                  Practice

                     i6-1 Practice

               Lesson i6-2: Comparing and Ordering Decimals

                  Interactive Learning

                     i6-2 Part 1

                     i6-2 Part 2

                     i6-2 Part 3

                     i6-2 Lesson Check

                  Journal

                     i6-2 Journal

                  Practice

                     i6-2 Practice

               Lesson i6-3: Rounding Decimals

                  Interactive Learning

                     i6-3 Part 1

                     i6-3 Part 2

                     i6-3 Part 3

                     i6-3 Lesson Check

                  Journal

                     i6-3 Journal

                  Practice

                     i6-3 Practice

            Cluster 7: Adding and Subtracting Decimals

               Lesson i7-1: Estimating Sums and Differences of Decimals

                  Interactive Learning

                     i7-1 Part 1

                     i7-1 Part 2

                     i7-1 Part 3

                     i7-1 Lesson Check

                  Journal

                     i7-1 Journal

                  Practice

                     i7-1 Practice

               Lesson i7-2: Adding and Subtracting Decimals

                  Interactive Learning

                     i7-2 Part 1

                     i7-2 Part 2

                     i7-2 Part 3

                     i7-2 Lesson Check

                  Journal

                     i7-2 Journal

                  Practice

                     i7-2 Practice

            Cluster 8: Multiplying and Dividing Decimals

               Lesson i8-1: Patterns in Multiplying and Dividing Decimals

                  Interactive Learning

                     i8-1 Part 1

                     i8-1 Part 2

                     i8-1 Part 3

                     i8-1 Lesson Check

                  Journal

                     i8-1 Journal

                  Practice

                     i8-1 Practice

               Lesson i8-2: Multiplying Decimals

                  Interactive Learning

                     i8-2 Part 1

                     i8-2 Part 2

                     i8-2 Part 3

                     i8-2 Lesson Check

                  Journal

                     i8-2 Journal

                  Practice

                     i8-2 Practice

               Lesson i8-3: Dividing Decimals by Whole Numbers

                  Interactive Learning

                     i8-3 Part 1

                     i8-3 Part 2

                     i8-3 Part 3

                     i8-3 Lesson Check

                  Journal

                     i8-3 Journal

                  Practice

                     i8-3 Practice

               Lesson i8-4: Estimating Decimal Products and Quotients

                  Interactive Learning

                     i8-4 Part 1

                     i8-4 Part 2

                     i8-4 Part 3

                     i8-4 Lesson Check

                  Journal

                     i8-4 Journal

                  Practice

                     i8-4 Practice

               Lesson i8-5: Dividing Decimals

                  Interactive Learning

                     i8-5 Part 1

                     i8-5 Part 2

                     i8-5 Part 3

                     i8-5 Lesson Check

                  Journal

                     i8-5 Journal

                  Practice

                     i8-5 Practice

            Cluster 9: Fraction Number Sense

               Lesson i9-1: Equivalent Fractions

                  Interactive Learning

                     i9-1 Part 1

                     i9-1 Part 2

                     i9-1 Part 3

                     i9-1 Lesson Check

                  Journal

                     i9-1 Journal

                  Practice

                     i9-1 Practice

               Lesson i9-2: Fractions in Simplest Form

                  Interactive Learning

                     i9-2 Part 1

                     i9-2 Part 2

                     i9-2 Part 3

                     i9-2 Lesson Check

                  Journal

                     i9-2 Journal

                  Practice

                     i9-2 Practice

               Lesson i9-3: Comparing and Ordering Fractions

                  Interactive Learning

                     i9-3 Part 1

                     i9-3 Part 2

                     i9-3 Part 3

                     i9-3 Lesson Check

                  Journal

                     i9-3 Journal

                  Practice

                     i9-3 Practice

               Lesson i9-4: Fractions and Division

                  Interactive Learning

                     i9-4 Part 1

                     i9-4 Part 2

                     i9-4 Part 3

                     i9-4 Lesson Check

                  Journal

                     i9-4 Journal

                  Practice

                     i9-4 Practice

               Lesson i9-5: Fractions and Decimals

                  Interactive Learning

                     i9-5 Part 1

                     i9-5 Part 2

                     i9-5 Part 3

                     i9-5 Lesson Check

                  Journal

                     i9-5 Journal

                  Practice

                     i9-5 Practice

            Cluster 10: Adding and Subtracting Fractions

               Lesson i10-1: Adding Fractions with Like Denominators

                  Interactive Learning

                     i10-1 Part 1

                     i10-1 Part 2

                     i10-1 Part 3

                     i10-1 Lesson Check

                  Journal

                     i10-1 Journal

                  Practice

                     i10-1 Practice

               Lesson i10-2: Subtracting Fractions with Like Denominators

                  Interactive Learning

                     i10-2 Part 1

                     i10-2 Part 2

                     i10-2 Part 3

                     i10-2 Lesson Check

                  Journal

                     i10-2 Journal

                  Practice

                     i10-2 Practice

               Lesson i10-3: Adding Fractions with Unlike Denominators

                  Interactive Learning

                     i10-3 Part 1

                     i10-3 Part 2

                     i10-3 Part 3

                     i10-3 Lesson Check

                  Journal

                     i10-3 Journal

                  Practice

                     i10-3 Practice

               Lesson i10-4: Subtracting with Unlike Denominators

                  Interactive Learning

                     i10-4 Part 1

                     i10-4 Part 2

                     i10-4 Part 3

                     i10-4 Lesson Check

                  Journal

                     i10-4 Journal

                  Practice

                     i10-4 Practice

            Cluster 11: Multiplying and Dividing Fractions

               Lesson i11-1: Multiplying a Whole Number and a Fraction

                  Interactive Learning

                     i11-1 Part 1

                     i11-1 Part 3

                     i11-1 Part 2

                     i11-1 Lesson Check

                  Journal

                     i11-1 Journal

                  Practice

                     i11-1 Practice

               Lesson i11-2: Multiplying Fractions

                  Interactive Learning

                     i11-2 Part 1

                     i11-2 Part 2

                     i11-2 Part 3

                     i11-2 Lesson Check

                  Journal

                     i11-2 Journal

                  Practice

                     i11-2 Practice

               Lesson i11-3: Dividing a Unit Fraction by a Whole Number

                  Interactive Learning

                     i11-3 Part 1

                     i11-3 Part 2

                     i11-3 Part 3

                     i11-3 Lesson Check

                  Practice

                     i11-3 Practice

               Lesson i11-4: Dividing a Whole Number by a Unit Fraction

                  Interactive Learning

                     i11-4 Part 1

                     i11-4 Part 2

                     i11-4 Part 3

                     i11-4 Lesson Check

                  Journal

                     i11-4 Journal

                  Practice

                     i11-4 Practice

               Lesson i11-5: Dividing Fractions

                  Interactive Learning

                     i11-5 Part 1

                     i11-5 Part 2

                     i11-5 Part 3

                     i11-5 Lesson Check

                  Journal

                     i11-5 Journal

                  Practice

                     i11-5 Practice

            Cluster 12: Mixed Numbers

               Lesson i12-1: Mixed Numbers and Improper Fractions

                  Interactive Learning

                     i12-1 Part 1

                     i12-1 Part 2

                     i12-1 Part 3

                     i12-1 Lesson Check

                  Journal

                     i12-1 Journal

                  Practice

                     i12-1 Practice

               Lesson i12-2: Adding Mixed Numbers

                  Interactive Learning

                     i12-2 Part 1

                     i12-2 Part 2

                     i12-2 Part 3

                     i12-2 Lesson Check

                  Journal

                     i12-2 Journal

                  Practice

                     i12-2 Practice

               Lesson i12-3: Subtracting Mixed Numbers

                  Interactive Learning

                     i12-3 Part 1

                     i12-3 Part 2

                     i12-3 Part 3

                     i12-3 Lesson Check

                  Journal

                     i12-3 Journal

                  Practice

                     i12-3 Practice

               Lesson i12-4: Multiplying Mixed Numbers

                  Interactive Learning

                     i12-4 Part 1

                     i12-4 Part 2

                     i12-4 Part 3

                     i12-4 Lesson Check

                  Journal

                     i12-4 Journal

                  Practice

                     i12-4 Practice

               Lesson i12-5: Dividing Mixed Numbers

                  Interactive Learning

                     i12-5 Part 1

                     i12-5 Part 2

                     i12-5 Part 3

                     i12-5 Lesson Check

                  Journal

                     i12-5 Journal

                  Practice

                     i12-5 Practice

            Cluster 13: Ratios

               Lesson i13-1: Ratios

                  Interactive Learning

                     i13-1 Part 1

                     i13-1 Part 2

                     i13-1 Part 3

                     i13-1 Lesson Check

                  Journal

                     i13-1 Journal

                  Practice

                     i13-1 Practice

               Lesson i13-2: Equivalent Ratios

                  Interactive Learning

                     i13-2 Part 1

                     i13-2 Part 2

                     i13-2 Part 3

                     i13-2 Lesson Check

                  Journal

                     i13-2 Journal

                  Practice

                     i13-2 Practice

            Cluster 14: Rates and Measurements

               Lesson i14-1: Unit Rates

                  Interactive Learning

                     i14-1 Part 1

                     i14-1 Part 2

                     i14-1 Part 3

                     i14-1 Lesson Check

                  Journal

                     i14-1 Journal

                  Practice

                     i14-1 Practice

               Lesson i14-2: Converting Customary Measurements

                  Interactive Learning

                     i14-2 Part 1

                     i14-2 Part 2

                     i14-2 Part 3

                     i14-2 Lesson Check

                  Journal

                     i14-2 Journal

                  Practice

                     i14-2 Practice

               Lesson i14-3: Converting Metric Measurements

                  Interactive Learning

                     i14-3 Part 1

                     i14-3 Part 2

                     i14-3 Part 3

                     i14-3 Lesson Check

                  Practice

                     i14-3 Practice

                  Journal

                     i14-3 Journal

            Cluster 15: Proportional Relationships

               Lesson i15-1: Graphing Ratios

                  Interactive Learning

                     i15-1 Part 1

                     i15-1 Part 2

                     i15-1 Part 3

                     i15-1 Lesson Check

                  Journal

                     i15-1 Journal

                  Practice

                     i15-1 Practice

               Lesson i15-2: Recognizing Proportional Relationships

                  Interactive Learning

                     i15-2 Part 1

                     i15-2 Part 2

                     i15-2 Part 3

                     i15-2 Lesson Check

                  Journal

                     i15-2 Journal

                  Practice

                     i15-2 Practice

               Lesson i15-3: Constant of Proportionality

                  Interactive Learning

                     i15-3 Part 1

                     i15-3 Part 2

                     i15-3 Part 3

                     i15-3 Lesson Check

                  Practice

                     i15-3 Practice

                  Journal

                     i15-3 Journal

            Cluster 16: Number Sense with Percents

               Lesson i16-1: Understanding Percent

                  Interactive Learning

                     i16-1 Part 1

                     i16-1 Part 2

                     i16-1 Part 3

                     i16-1 Lesson Check

                  Journal

                     i16-1 Journal

                  Practice

                     i16-1 Practice

               Lesson i16-2: Estimating Percent

                  Interactive Learning

                     i16-2 Part 1

                     i16-2 Part 2

                     i16-2 Part 3

                     i16-2 Lesson Check

                  Practice

                     i16-2 Practice

                  Journal

                     i16-2 Journal

            Cluster 17: Computations with Percents

               Lesson i17-1: Finding a Percent of a Number

                  Interactive Learning

                     i17-1 Part 1

                     i17-1 Part 2

                     i17-1 Part 3

                     i17-1 Lesson Check

                  Journal

                     i17-1 Journal

                  Practice

                     i17-1 Practice

               Lesson i17-2: Finding a Percent

                  Interactive Learning

                     i17-2 Part 1

                     i17-2 Part 2

                     i17-2 Part 3

                     i17-2 Lesson Check

                  Journal

                     i17-2 Journal

                  Practice

                     i17-2 Practice

               Lesson i17-3: Finding the Whole Given a Percent

                  Interactive Learning

                     i17-3 Part 1

                     i17-3 Part 2

                     i17-3 Part 3

                     i17-3 Lesson Check

                  Journal

                     i17-3 Journal

                  Practice

                     i17-3 Practice

               Lesson i17-4: Sales Tax, Tips, and Simple Interest

                  Interactive Learning

                     i17-4 Part 1

                     i17-4 Part 2

                     i17-4 Part 3

                     i17-4 Lesson Check

                  Journal

                     i17-4 Journal

                  Practice

                     i17-4 Practice

               Lesson i17-5: Markdowns

                  Interactive Learning

                     i17-5 Part 1

                     i17-5 Part 2

                     i17-5 Part 3

                     i17-5 Lesson Check

                  Practice

                     i17-5 Practice

                  Journal

                     i17-5 Journal

            Cluster 18: Exponents

               Lesson i18-1: Exponents

                  Interactive Learning

                     i18-1 Part 1

                     i18-1 Part 2

                     i18-1 Part 3

                     i18-1 Lesson Check

                  Journal

                     i18-1 Journal

                  Practice

                     i18-1 Practice

               Lesson i18-2: Multiplying Decimals by Powers of Ten

                  Interactive Learning

                     i18-2 Part 1

                     i18-2 Part 2

                     i18-2 Part 3

                     i18-2 Lesson Check

                  Journal

                     i18-2 Journal

                  Practice

                     i18-2 Practice

            Cluster 19: Geometry

               Lesson i19-1: Classifying Triangles

                  Interactive Learning

                     i19-1 Part 1

                     i19-1 Part 2

                     i19-1 Part 3

                     i19-1 Lesson Check

                  Journal

                     i19-1 Journal

                  Practice

                     i19-1 Practice

               Lesson i19-2: Classifying Quadrilaterals

                  Interactive Learning

                     i19-2 Part 1

                     i19-2 Part 2

                     i19-2 Part 3

                     i19-2 Lesson Check

                  Journal

                     i19-2 Journal

                  Practice

                     i19-2 Practice

            Cluster 20: Measuring 2- and 3-Dimensional Objects

               Lesson i20-1: Perimeter

                  Interactive Learning

                     i20-1 Part 1

                     i20-1 Part 2

                     i20-1 Part 3

                     i20-1 Lesson Check

                  Journal

                     i20-1 Journal

                  Practice

                     i20-1 Practice

               Lesson i20-2: Area of Rectangles and Squares

                  Interactive Learning

                     i20-2 Part 1

                     i20-2 Part 2

                     i20-2 Part 3

                     i20-2 Lesson Check

                  Journal

                     i20-2 Journal

                  Practice

                     i20-2 Practice

               Lesson i20-3: Area of Parallelograms and Triangles

                  Interactive Learning

                     i20-3 Part 1

                     i20-3 Part 2

                     i20-3 Part 3

                     i20-3 Lesson Check

                  Journal

                     i20-3 Journal

                  Practice

                     i20-3 Practice

               Lesson i20-4: Nets and Surface Area

                  Interactive Learning

                     i20-4 Part 1

                     i20-4 Part 2

                     i20-4 Lesson Check

                  Journal

                     i20-4 Journal

                  Practice

                     i20-4 Practice

               Lesson i20-5: Volume of Prisms

                  Interactive Learning

                     i20-5 Part 1

                     i20-5 Part 2

                     i20-5 Part 3

                     i20-5 Lesson Check

                  Journal

                     i20-5 Journal

                  Practice

                     i20-5 Practice

            Cluster 21: Integers

               Lesson i21-1: Understanding Integers

                  Interactive Learning

                     i21-1 Part 1

                     i21-1 Part 2

                     i21-1 Part 3

                     i21-1 Lesson Check

                  Journal

                     i21-1 Journal

                  Practice

                     i21-1 Practice

               Lesson i21-2: Comparing and Ordering Integers

                  Interactive Learning

                     i21-2 Part 1

                     i21-2 Part 2

                     i21-2 Part 3

                     i21-2 Lesson Check

                  Journal

                     i21-2 Journal

                  Practice

                     i21-2 Practice

               Lesson i21-3: Adding Integers

                  Interactive Learning

                     i21-3 Part 1

                     i21-3 Part 2

                     i21-3 Part 3

                     i21-3 Lesson Check

                  Journal

                     i21-3 Journal

                  Practice

                     i21-3 Practice

               Lesson i21-4: Subtracting Integers

                  Interactive Learning

                     i21-4 Part 1

                     i21-4 Part 2

                     i21-4 Part 3

                     i21-4 Lesson Check

                  Journal

                     i21-4 Journal

                  Practice

                     i21-4 Practice

               Lesson i21-5: Multiplying Integers

                  Interactive Learning

                     i21-5 Part 1

                     i21-5 Part 2

                     i21-5 Part 3

                     i21-5 Lesson Check

                  Journal

                     i21-5 Journal

                  Practice

                     i21-5 Practice

               Lesson i21-6: Dividing Integers

                  Interactive Learning

                     i21-6 Part 1

                     i21-6 Part 2

                     i21-6 Part 3

                     i21-6 Lesson Check

                  Journal

                     i21-6 Journal

                  Practice

                     i21-6 Practice

            Cluster 22: Graphing and Rational Numbers

               Lesson i22-1: Graphing in the First Quadrant

                  Interactive Learning

                     i22-1 Part 3

                     i22-1 Part 1

                     i22-1 Part 2

                     i22-1 Lesson Check

                  Journal

                     i22-1 Journal

                  Practice

                     i22-1 Practice

               Lesson i22-2: Graphing in the Coordinate Plane

                  Interactive Learning

                     i22-2 Part 1

                     i22-2 Part 2

                     i22-2 Part 3

                     i22-2 Lesson Check

                  Journal

                     i22-2 Journal

                  Practice

                     i22-2 Practice

               Lesson i22-3: Distance When There's a Common Coordinate

                  Interactive Learning

                     i22-3 Part 1

                     i22-3 Part 2

                     i22-3 Part 3

                     i22-3 Lesson Check

                  Journal

                     i22-3 Journal

                  Practice

                     i22-3 Practice

               Lesson i22-4: Rational Numbers on the Number Line

                  Interactive Learning

                     i22-4 Part 1

                     i22-4 Part 2

                     i22-4 Part 3

                     i22-4 Lesson Check

                  Journal

                     i22-4 Journal

                  Practice

                     i22-4 Practice

               Lesson i22-5: Comparing and Ordering Rational Numbers

                  Interactive Learning

                     i22-5 Part 1

                     i22-5 Part 2

                     i22-5 Part 3

                     i22-5 Lesson Check

                  Journal

                     i22-5 Journal

                  Practice

                     i22-5 Practice

            Cluster 23: Numerical and Algebraic Expressions

               Lesson i23-1: Order of Operations

                  Interactive Learning

                     i23-1 Part 1

                     i23-1 Part 2

                     i23-1 Part 3

                     i23-1 Lesson Check

                  Journal

                     i23-1 Journal

                  Practice

                     i23-1 Practice

               Lesson i23-2: Variables and Expressions

                  Interactive Learning

                     i23-2 Part 1

                     i23-2 Part 2

                     i23-2 Part 3

                     i23-2 Lesson Check

                  Journal

                     i23-2 Journal

                  Practice

                     i23-2 Practice

               Lesson i23-3: Patterns and Expressions

                  Interactive Learning

                     i23-3 Part 1

                     i23-3 Part 2

                     i23-3 Part 3

                     i23-3 Lesson Check

                  Journal

                     i23-3 Journal

                  Practice

                     i23-3 Practice

               Lesson i23-4: Evaluating Expressions: Whole Numbers

                  Interactive Learning

                     i23-4 Part 1

                     i23-4 Part 2

                     i23-4 Part 3

                     i23-4 Lesson Check

                  Journal

                     i23-4 Journal

                  Practice

                     i23-4 Practice

            Cluster 24: More Algebraic Expressions

               Lesson i24-1: Evaluating Expressions: Rational Numbers

                  Interactive Learning

                     i24-1 Part 1

                     i24-1 Part 2

                     i24-1 Part 3

                     i24-1 Lesson Check

                  Journal

                     i24-1 Journal

                  Practice

                     i24-1 Practice

               Lesson i24-2: Equivalent Expressions

                  Interactive Learning

                     i24-2 Part 1

                     i24-2 Part 2

                     i24-2 Part 3

                     i24-2 Lesson Check

                  Journal

                     i24-2 Journal

                  Practice

                     i24-2 Practice

               Lesson i24-3: Simplifying Expressions

                  Interactive Learning

                     i24-3 Part 1

                     i24-3 Part 2

                     i24-3 Part 3

                     i24-3 Lesson Check

                  Journal

                     i24-3 Journal

                  Practice

                     i24-3 Practice

            Cluster 25: Equations

               Lesson i25-1: Writing Equations

                  Interactive Learning

                     i25-1 Part 1

                     i25-1 Part 2

                     i25-1 Part 3

                     i25-1 Lesson Check

                  Journal

                     i25-1 Journal

                  Practice

                     i25-1 Practice

               Lesson i25-2: Principles of Solving Equations

                  Interactive Learning

                     i25-2 Part 1

                     i25-2 Part 2

                     i25-2 Part 3

                     i25-2 Lesson Check

                  Journal

                     i25-2 Journal

                  Practice

                     i25-2 Practice

               Lesson i25-3: Solving Addition and Subtraction Equations

                  Interactive Learning

                     i25-3 Part 1

                     i25-3 Part 2

                     i25-3 Part 3

                     i25-3 Lesson Check

                  Journal

                     i25-3 Journal

                  Practice

                     i25-3 Practice

               Lesson i25-4: Solving Multiplication and Division Equations

                  Interactive Learning

                     i25-4 Part 1

                     i25-4 Part 2

                     i25-4 Part 3

                     i25-4 Lesson Check

                  Journal

                     i25-4 Journal

                  Practice

                     i25-4 Practice

               Lesson i25-5: Solving Rational-Number Equations, Part 1

                  Interactive Learning

                     i25-5 Part 1

                     i25-5 Part 2

                     i25-5 Part 3

                     i25-5 Lesson Check

                  Journal

                     i25-5 Journal

                  Practice

                     i25-5 Practice

               Lesson i25-6: Solving Rational-Number Equations, Part 2

                  Interactive Learning

                     i25-6 Part 1

                     i25-6 Part 2

                     i25-6 Part 3

                     i25-6 Lesson Check

                  Journal

                     i25-6 Journal

                  Practice

                     i25-6 Practice

               Lesson i25-7: Solving Two-Step Equations

                  Interactive Learning

                     i25-7 Part 1

                     i25-7 Part 2

                     i25-7 Part 3

                     i25-7 Lesson Check

                  Journal

                     i25-7 Journal

                  Practice

                     i25-7 Practice

         State-Specific Resources

            Minnesota Grade 6

               MN-1: Estimate and Use Customary Units of Length
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-2: Estimate and Use Customary Units of Weight
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-3: Estimate and Use Customary Units of Capacity
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-4: Estimate and Use Metric Units of Length
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-5: Estimate and Use Metric Units of Weight
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-6: Estimate and Use Metric Units of Capacity
                 Curriculum Standards: Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Estimate weights, capacities and geometric measurements using benchmarks in customary and metric measurement systems with appropriate units.  

               MN-7: Solve Problems Using Angle Relationships
                 Curriculum Standards: Solve problems using the relationships between the angles formed by intersecting lines. Solve problems using the relationships between the angles (vertical, complementary, and supplementary) formed by intersecting lines.  

               MN-8: Angles of Triangles
                 Curriculum Standards: Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact. 

               MN-9: Angles of Polygons
                 Curriculum Standards: Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles. 

               MN-10: Estimate Perimeter and Area of Irregular Figures
                 Curriculum Standards: Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm². 

               MN-11: Sample Space
                 Curriculum Standards: for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial represent 

               MN-12: Understand Likelihood and Probability
                 Curriculum Standards: for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial represent Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood. Represent possible outcomes using a probability continuum from impossible to certain. 

               MN-13: Experiments and Relative Frequency
                 Curriculum Standards: Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences. Demonstrate simple experiments in which the probabilities are known and compare the resulting relative frequencies with the known probabilities, recognizing that there may be differences between the two results.  

               MN-14: Use Experimental Probability
                 Curriculum Standards: Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. 

         Teacher Resources Container

            Assessment Sourcebook
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            English Language Learners Toolkit
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            Teaching Tools
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            Today's Challenge Teacher Guide
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            Math Practices and Problem Solving Handbook
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            Teacher's Edition eText: Grade 6
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            Teacher's Edition Program Overview: Grade 6
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            Beginning-of-Year Assessment: Answer Key
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            Topic 1 Readiness Assessment: Answer Key
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            Teacher's Edition eText: Grade 6 Lesson 1-2
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            Teacher's Edition eText: Grade 6 Lesson 1-5
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            1-5: Reteach to Build Understanding
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            Teacher's Edition eText: Grade 6 Lesson 1-6
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            1-6: Reteach to Build Understanding
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            Teacher's Edition eText: Grade 6 Lesson 1-7
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            K26: Solving Equations with Decimals
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            L64: Multiplying Decimals by Decimals
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            L31: Dividing Greater Numbers
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            L46: Multiplying Two Fractions
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            L47: Understanding Division with Fractions
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            L50: Dividing Fractions
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            L51: Estimating Products and Quotients of Mixed Numbers
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            L69: Dividing a Decimal by a Decimal
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            Topic 2 Readiness Assessment: Answer Key
              Intended Role: Instructor

            Printable Topic 2 Readiness Assessment
              Intended Role: Instructor

            Topic 2: Review What You Know!
              Intended Role: Instructor

            Topic 2: Math Literacy Activity
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            Topic 2 STEM Masters
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            Topic 2 STEM Masters Answer Key
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            Topic 2: Today's Challenge Teacher's Guide
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            2-1: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 2-1
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            Topic 2: Today's Challenge Teacher's Guide
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            2-1: Explain It! Solution
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            2-1: Reteach to Build Understanding
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            2-1: Reteach to Build Understanding
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            Teacher's Edition eText: Grade 6 Lesson 2-2
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            2-2: Listen and Look For
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            Topic 2: Today's Challenge Teacher's Guide
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            2-2: Explain It! Solution
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            2-3: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 2-3
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            2-3: Solve & Discuss It! Solution
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            2-3: Additional Practice Answer Key
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            2-4: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 2-4
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            2-4: Solve & Discuss It! Solution
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            2-4: Additional Practice Answer Key
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            Teacher's Edition eText: Grade 6 Topic 2 3-Act Mathematical Modeling
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            Topic 2: Today's Challenge Teacher's Guide
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            2-5: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 2-5
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              Intended Role: Instructor

            2-6: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 2-6
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            2-6: Listen and Look For
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            Topic 2: Today's Challenge Teacher's Guide
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            2-6: Solve & Discuss It! Solution
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            Topic 2: Fluency Practice
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            Topic 2 Performance Task A: Answer Key
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            Printable Topic 2 Performance Task A
              Intended Role: Instructor

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              Intended Role: Instructor

            K47: Lengths of Line Segments
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            K48: Graphing Points in the Coordinate Plane
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            L70: Meaning of Integers
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            L71: Absolute Value
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            L73: Comparing and Ordering Rational Numbers
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            N7: Polygons on the Coordinate Plane
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            N37: Perimeter
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            Topic 2 Assessment A: Answer Key
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            K48: Graphing Points in the Coordinate Plane
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            L31: Dividing Greater Numbers
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            L46: Multiplying Two Fractions
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            L47: Understanding Division with Fractions
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            L50: Dividing Fractions
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            L52: Multiplying Mixed Numbers
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            L57: Subtracting Decimals to Hundredths
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            L59: Adding and Subtracting Decimals to Thousandths
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            L61: Multiplying Decimals by 10, 100, or 1,000
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            L64: Multiplying Decimals by Decimals
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            L71: Absolute Value
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            L72: Comparing and Ordering Integers
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            L73: Comparing and Ordering Rational Numbers
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            M15: Fractions and Mixed Numbers on the Number Line
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            N37: Perimeter
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            Printable Topics 1-2: Cumulative/Benchmark Assessment
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            Topics 1-2: Cumulative/Benchmark Assessment: Answer Key
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            Topic 3: Home-School Connection
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            Topic 3: Home-School Connection (Spanish)
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            Teacher's Edition eText: Grade 6 Topic 3
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            i25-1 Journal
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            Topic 3: Today's Challenge Teacher's Guide
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            3-1: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 3-1
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            3-1: Listen and Look For
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            Teacher's Edition eText: Grade 6 Lesson 3-2
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            Topic 3: Today's Challenge Teacher's Guide
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            3-2: Solve & Discuss It! Solution
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            Teacher's Edition eText: Grade 6 Lesson 3-3
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            3-4: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 3-4
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            3-4: Listen and Look For
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            Topic 3: Today's Challenge Teacher's Guide
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            Teacher's Edition eText: Grade 6 Lesson 3-5
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            3-5: Printable Lesson Quiz
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            3-5: Digital Math Tool Activity
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            3-5: Additional Practice Answer Key
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            Teacher's Edition eText: Grade 6 Topic 3 3-Act Mathematical Modeling
              Intended Role: Instructor

            Topic 3: Today's Challenge Teacher's Guide
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            3-6: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 3-6
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            Teacher's Edition eText: Grade 6 Lesson 3-7
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            Topic 3: Fluency Practice
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            Printable Topic 3 Performance Task A
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            K15: Writing Expressions
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            K17: Write Equivalent Expressions
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            K18: Simplify Algebraic Expressions
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            K45: Patterns and Equations
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            L2: Exponents
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            L4: Greatest Common Factor
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            L5: Least Common Multiple
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            L31: Dividing Greater Numbers
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            Topic 3 Assessment A: Answer Key
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            Topic 4: Home-School Connection
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            Topic 4: Professional Development Video
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            i23-2 Journal
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            Topic 4: Today's Challenge Teacher's Guide
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            4-1: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 4-1
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            Teacher's Edition eText: Grade 6 Lesson 4-2
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            Teacher's Edition eText: Grade 6 Lesson 4-3
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            4-4: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 4-4
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            Teacher's Edition eText: Grade 6 Lesson 4-5
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            4-5: Listen and Look For
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            4-6: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 4-6
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            Teacher's Edition eText: Grade 6 Lesson 4-7
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            4-7: Build Mathematical Literacy
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            Teacher's Edition eText: Grade 6 Topic 4 3-Act Mathematical Modeling
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            Topic 4: Today's Challenge Teacher's Guide
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            4-8: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 4-8
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            Topic 4: Today's Challenge Teacher's Guide
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            Teacher's Edition eText: Grade 6 Lesson 4-9
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            4-9: Solve & Discuss It! Solution
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            Teacher's Edition eText: Grade 6 Lesson 4-10
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            Topic 4: Fluency Practice
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            K7: Equality and Inequality
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            K23: Solving Addition and Subtraction Equations
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            K25: Solving Equations with Whole Numbers
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            K26: Solving Equations with Decimals
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            K37: Writing Inequalities
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            K45: Patterns and Equations
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            K49: Graphing Equations in the Coordinate Plane
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            Topic 4 Assessment A: Answer Key
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            K6: Translating Words to Expressions
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            K8: Expressions with Parentheses
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            K12: Properties of Operations
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            K14: More Variables and Expressions
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            K16: Identify Parts of Expressions
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            K17: Write Equivalent Expressions
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            K22: Properties of Equality
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            K23: Solving Addition and Subtraction Equations
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            K26: Solving Equations with Decimals
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            K27: Writing Addition and Subtraction Equations
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            K29: Solving Equations with Fractions
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            K37: Writing Inequalities
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            K38: Solving Inequalities
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            K42: Dependent and Independent Variables
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            K45: Patterns and Equations
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            K47: Lengths of Line Segments
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            K48: Graphing Points in the Coordinate Plane
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            L2: Exponents
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            L4: Greatest Common Factor
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            L5: Least Common Multiple
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            L31: Dividing Greater Numbers
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            L50: Dividing Fractions
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            L70: Meaning of Integers
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            L72: Comparing and Ordering Integers
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            M15: Fractions and Mixed Numbers on the Number Line
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            N37: Perimeter
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            Printable Topics 1-4: Cumulative/Benchmark Assessment
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            Topic 5: Home-School Connection
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            Topic 5: Home-School Connection (Spanish)
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            Teacher's Edition eText: Grade 6 Topic 5
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            Topic 5: Today's Challenge Teacher's Guide
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            5-1: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 5-1
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            5-3: Lesson Plan
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            5-6: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 5-6
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            Teacher's Edition eText: Grade 6 Lesson 5-7
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            Teacher's Edition eText: Grade 6 Topic 5 3-Act Mathematical Modeling
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            5-8: Lesson Plan
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            M28: Rates and Unit Rates
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            M29: Comparing Rates
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            M31: Equivalent Ratios
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            M27: Understanding Ratios
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            N29: Converting Customary Units of Capacity
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            N32: Converting Between Measurement Systems
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            Topic 5 Assessment A: Answer Key
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            Topic 6: Home-School Connection
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            Topic 6: Review What You Know!
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            Topic 6: STEM Project
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            Topic 6 STEM Masters
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            Topic 6: Today's Challenge Teacher's Guide
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            6-1: Lesson Plan
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            Teacher's Edition eText: Grade 6 Lesson 6-1
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            Teacher's Edition eText: Grade 6 Lesson 6-6
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            Teacher's Edition eText: Grade 6 Topic 6 3-Act Mathematical Modeling
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            M37: Understanding Percent
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            M38: Relating Percents, Decimals, and Fractions
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            M39: Percents Greater Than 100 or Less Than 1
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            M40: Estimating Percent of a Number
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            M41: Finding the Percent of a Whole Number
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            M42: Find the Whole
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            Topic 6 Assessment A: Answer Key
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            K6: Translating Words to Expressions
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            K17: Write Equivalent Expressions
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            K18: Simplify Algebraic Expressions
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            K23: Solving Addition and Subtraction Equations
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            K24: Solving Multiplication and Division Equations
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            K37: Writing Inequalities
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            K49: Graphing Equations in the Coordinate Plane
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            L4: Greatest Common Factor
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            L5: Least Common Multiple
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            L34: Dividing by Two-Digit Divisors
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            M28: Rates and Unit Rates
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            M41: Finding the Percent of a Whole Number
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            M42: Find the Whole
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            Teacher's Edition eText: Grade 6 Lesson 7-3
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            Teacher's Edition eText: Grade 6 Lesson 7-6
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            Printable Topic 7 Performance Task A
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            K15: Writing Expressions
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            N15: Solids and Nets
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            N41: Area of Rectangles and Squares
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            N44: Area of Parallelograms
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            N45: Area of Triangles
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            N48: Surface Area of Rectangular Prisms
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            N49: Surface Area of Cylinders, Pyramids, and Triangular Prisms
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            N52: Volume of Rectangular Prisms
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            Topic 8: Review What You Know!
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            Topic 8 STEM Masters
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            Topic 8 STEM Masters Answer Key
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            Teacher's Edition eText: Grade 6 Topic 8 3-Act Mathematical Modeling
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            N78: Median, Mode, and Range
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              Intended Role: Instructor

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            i5-3 Journal with Answer Key
              Intended Role: Instructor

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            i5-3 Teacher Guide
              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i6-1 Teacher Guide
              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i7-1 Journal with Answer Key
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              Intended Role: Instructor

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              Intended Role: Instructor

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            i7-2 Teacher Guide
              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i10-1 Journal with Answer Key
              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i11-1 Journal with Answer Key
              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i15-1 Journal with Answer Key
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              Intended Role: Instructor

            i15-1 Editable Lesson Plan
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            i15-2 Teacher Guide
              Intended Role: Instructor

            i15-2 Editable Lesson Plan
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            i15-3 Teacher Guide
              Intended Role: Instructor

            i15-3 Editable Lesson Plan
              Intended Role: Instructor

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            i16-1 Journal with Answer Key
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              Intended Role: Instructor

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              Intended Role: Instructor

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              Intended Role: Instructor

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            i21-6 Editable Lesson Plan
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              Intended Role: Instructor

            i25-7 Editable Lesson Plan
              Intended Role: Instructor

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              Intended Role: Instructor

            K1: Repeating Patterns
              Intended Role: Instructor

            K2: Number Patterns
              Intended Role: Instructor

            K3: Geometric Growth Patterns
              Intended Role: Instructor

            K4: Expressions with Addition and Subtraction
              Intended Role: Instructor

            K5: Expressions with Multiplication and Division
              Intended Role: Instructor

            K6: Translating Words to Expressions
              Intended Role: Instructor

            K7: Equality and Inequality
              Intended Role: Instructor

            K8: Expressions with Parentheses
              Intended Role: Instructor

            K9: Order of Operations
              Intended Role: Instructor

            K10: Mental Math: Using Properties
              Intended Role: Instructor

            K11: Using the Distributive Property
              Intended Role: Instructor

            Booklet K: Expressions, Equations, and Functions
              Intended Role: Instructor

            K12: Properties of Operations
              Intended Role: Instructor

            K13: Variables and Expressions
              Intended Role: Instructor

            K14: More Variables and Expressions
              Intended Role: Instructor

            K15: Writing Expressions
              Intended Role: Instructor

            K16: Identify Parts of Expressions
              Intended Role: Instructor

            K17: Write Equivalent Expressions
              Intended Role: Instructor

            K18: Simplify Algebraic Expressions
              Intended Role: Instructor

            K19: Factoring Algebraic Expressions
              Intended Role: Instructor

            K20: Adding and Subtracting Algebraic Expressions
              Intended Role: Instructor

            K21: Formulas and Equations
              Intended Role: Instructor

            K22: Properties of Equality
              Intended Role: Instructor

            K23: Solving Addition and Subtraction Equations
              Intended Role: Instructor

            K24: Solving Multiplication and Division Equations
              Intended Role: Instructor

            K25: Solving Equations with Whole Numbers
              Intended Role: Instructor

            K26: Solving Equations with Decimals
              Intended Role: Instructor

            K27: Writing Addition and Subtraction Equations
              Intended Role: Instructor

            K28: Writing Multiplication and Division Equations
              Intended Role: Instructor

            K29: Solving Equations with Fractions
              Intended Role: Instructor

            K30: Writing Two-Step Equations
              Intended Role: Instructor

            K31: Solving Two-Step Equations
              Intended Role: Instructor

            K32: Solve Multi-Step Equations
              Intended Role: Instructor

            K33: Solving Systems of Equations by Inspection
              Intended Role: Instructor

            K34: Solving Systems of Equations by Graphing
              Intended Role: Instructor

            K35: Solving Systems of Equations by Substitution
              Intended Role: Instructor

            K36: Solving Systems of Equations by Elimination
              Intended Role: Instructor

            K37: Writing Inequalities
              Intended Role: Instructor

            K38: Solving Inequalities
              Intended Role: Instructor

            K39: Writing Two-Step Inequalities
              Intended Role: Instructor

            K40: Solving Two-Step Inequalities
              Intended Role: Instructor

            K41: Solving Multi-Step Inequalities
              Intended Role: Instructor

            K42: Dependent and Independent Variables
              Intended Role: Instructor

            K43: Input/Output Tables
              Intended Role: Instructor

            K44: Find a Rule
              Intended Role: Instructor

            K45: Patterns and Equations
              Intended Role: Instructor

            K46: Graphing Ordered Pairs
              Intended Role: Instructor

            K47: Lengths of Line Segments
              Intended Role: Instructor

            K48: Graphing Points in the Coordinate Plane
              Intended Role: Instructor

            K49: Graphing Equations in the Coordinate Plane
              Intended Role: Instructor

            K51: Relations and Functions
              Intended Role: Instructor

            K52: Linear Functions
              Intended Role: Instructor

            K50: Finding Slope
              Intended Role: Instructor

            K53: Nonlinear Functions
              Intended Role: Instructor

            K54: Sketching Functions
              Intended Role: Instructor

            Booklet L: Numbers and Operations
              Intended Role: Instructor

            L1: Factoring Numbers
              Intended Role: Instructor

            L2: Exponents
              Intended Role: Instructor

            L3: Prime Factorization
              Intended Role: Instructor

            L4: Greatest Common Factor
              Intended Role: Instructor

            L5: Least Common Multiple
              Intended Role: Instructor

            L6: Perfect Squares
              Intended Role: Instructor

            L7: Addition Properties
              Intended Role: Instructor

            L8: Relating Addition and Subtraction
              Intended Role: Instructor

            L9: Estimating Sums
              Intended Role: Instructor

            L10: Estimating Differences
              Intended Role: Instructor

            L11: Adding and Subtracting on a Number Line
              Intended Role: Instructor

            L12: Skip Counting on the Number Line
              Intended Role: Instructor

            L13: Adding Two-Digit Numbers
              Intended Role: Instructor

            L14: Subtracting Two-Digit Numbers
              Intended Role: Instructor

            L15: Mental Math Strategies
              Intended Role: Instructor

            L16: Adding Three-Digit Numbers
              Intended Role: Instructor

            L17: Subtracting Three-Digit Numbers
              Intended Role: Instructor

            L18: Subtracting Four-Digit Numbers
              Intended Role: Instructor

            L19: Adding 4-Digit Numbers
              Intended Role: Instructor

            L20: Multiplication Properties
              Intended Role: Instructor

            L21: Relating Multiplication and Division
              Intended Role: Instructor

            L22: Estimating Products
              Intended Role: Instructor

            L23: Estimating Quotients
              Intended Role: Instructor

            L24: Multiplying by Multiples of 10
              Intended Role: Instructor

            L25: Multiplying Two-Digit Numbers
              Intended Role: Instructor

            L26: Multiplying Three-Digit Numbers
              Intended Role: Instructor

            L27: Multiplying Greater Numbers
              Intended Role: Instructor

            L28: Dividing by Multiples of 10
              Intended Role: Instructor

            L29: Dividing Two-Digit Numbers
              Intended Role: Instructor

            L30: Dividing Three-Digit Numbers
              Intended Role: Instructor

            L31: Dividing Greater Numbers
              Intended Role: Instructor

            L32: Divisibility
              Intended Role: Instructor

            L33: Estimating Quotients with Two-Digit Divisors
              Intended Role: Instructor

            L34: Dividing by Two-Digit Divisors
              Intended Role: Instructor

            L35: One- and Two-Digit Quotients
              Intended Role: Instructor

            L36: Adding Fractions with Like Denominators
              Intended Role: Instructor

            L37: Subtracting Fractions with Like Denominators
              Intended Role: Instructor

            L38: Adding and Subtracting Fractions with Like Denominators
              Intended Role: Instructor

            L39: Adding and Subtracting Fractions on a Number Line
              Intended Role: Instructor

            L40: Adding Fractions with Unlike Denominators
              Intended Role: Instructor

            L41: Subtracting Fractions with Unlike Denominators
              Intended Role: Instructor

            L42: Working with Unit Fractions
              Intended Role: Instructor

            L43: Adding Mixed Numbers
              Intended Role: Instructor

            L44: Subtracting Mixed Numbers
              Intended Role: Instructor

            L45: Multiplying Fractions by Whole Numbers
              Intended Role: Instructor

            L46: Multiplying Two Fractions
              Intended Role: Instructor

            L47: Understanding Division with Fractions
              Intended Role: Instructor

            L48: Divide Whole Numbers by Unit Fractions
              Intended Role: Instructor

            L49: Divide Unit Fractions by Non-Zero Whole Numbers
              Intended Role: Instructor

            L50: Dividing Fractions
              Intended Role: Instructor

            L51: Estimating Products and Quotients of Mixed Numbers
              Intended Role: Instructor

            L52: Multiplying Mixed Numbers
              Intended Role: Instructor

            L53: Dividing Mixed Numbers
              Intended Role: Instructor

            L54: Using Models to Add and Subtract Decimals
              Intended Role: Instructor

            L55: Estimating Decimal Sums and Differences
              Intended Role: Instructor

            L56: Adding Decimals to Hundredths
              Intended Role: Instructor

            L57: Subtracting Decimals to Hundredths
              Intended Role: Instructor

            L58: More Estimation of Decimal Sums and Differences
              Intended Role: Instructor

            L59: Adding and Subtracting Decimals to Thousandths
              Intended Role: Instructor

            L60: Multiplying with Decimals and Whole Numbers
              Intended Role: Instructor

            L61: Multiplying Decimals by 10, 100, or 1,000
              Intended Role: Instructor

            L62: Estimating the Product of a Whole Number and a Decimal
              Intended Role: Instructor

            L63: Multiplying Decimals Using Grids
              Intended Role: Instructor

            L64: Multiplying Decimals by Decimals
              Intended Role: Instructor

            L65: Dividing with Decimals and Whole Numbers
              Intended Role: Instructor

            L66: Dividing Decimals by 10, 100, or 1,000
              Intended Role: Instructor

            L67: Dividing a Decimal by a Whole Number
              Intended Role: Instructor

            L68: Estimating the Quotient of a Decimal and a Whole Number
              Intended Role: Instructor

            L69: Dividing a Decimal by a Decimal
              Intended Role: Instructor

            L70: Meaning of Integers
              Intended Role: Instructor

            L71: Absolute Value
              Intended Role: Instructor

            L72: Comparing and Ordering Integers
              Intended Role: Instructor

            L73: Comparing and Ordering Rational Numbers
              Intended Role: Instructor

            L74: Adding Integers
              Intended Role: Instructor

            L75: Subtracting Integers
              Intended Role: Instructor

            L76: Multiplying and Dividing Integers
              Intended Role: Instructor

            L77: Adding Rational Numbers
              Intended Role: Instructor

            L78: Subtracting Rational Numbers
              Intended Role: Instructor

            L79: Multiplying and Dividing Rational Numbers
              Intended Role: Instructor

            L80: Rational and Irrational Numbers
              Intended Role: Instructor

            L81: Square Roots
              Intended Role: Instructor

            L82: Cube Roots
              Intended Role: Instructor

            L83: Integer Exponents
              Intended Role: Instructor

            L84: Scientific Notation
              Intended Role: Instructor

            L85: Operations with Scientific Notation
              Intended Role: Instructor

            Booklet M: Fractions, Decimals, Ratios, and Proportionality:
              Intended Role: Instructor

            M1: Equal Parts of a Whole
              Intended Role: Instructor

            M2: Parts of a Region
              Intended Role: Instructor

            M3: Fractions and Length
              Intended Role: Instructor

            M4: Fractions on the Number Line
              Intended Role: Instructor

            M5: Using Models to Compare Fractions
              Intended Role: Instructor

            M6: Using Models to Find Equivalent Fractions
              Intended Role: Instructor

            M7: Comparing Fractions on the Number Line
              Intended Role: Instructor

            M8: Comparing Fractions
              Intended Role: Instructor

            M9: Equivalent Fractions
              Intended Role: Instructor

            M10: Equivalent Fractions and the Number Line
              Intended Role: Instructor

            M11: Estimating Fractional Amounts
              Intended Role: Instructor

            M12: Mixed Numbers
              Intended Role: Instructor

            M13: Comparing and Ordering Fractions
              Intended Role: Instructor

            M14: Comparing and Ordering Mixed Numbers
              Intended Role: Instructor

            M15: Fractions and Mixed Numbers on the Number Line
              Intended Role: Instructor

            M16: Fractions and Decimals
              Intended Role: Instructor

            M17: Decimals on the Number Line
              Intended Role: Instructor

            M18: Rounding Decimals Through Hundredths
              Intended Role: Instructor

            M19: Rounding Decimals Through Thousandths
              Intended Role: Instructor

            M20: Comparing and Ordering Decimals Through Hundredths
              Intended Role: Instructor

            M21: Comparing and Ordering Decimals Through Thousandths
              Intended Role: Instructor

            M22: Relating Fractions and Decimals
              Intended Role: Instructor

            M23: Decimals to Fractions
              Intended Role: Instructor

            M24: Fractions to Decimals
              Intended Role: Instructor

            M25: Using Models to Compare Fractions and Decimals
              Intended Role: Instructor

            M26: Fractions, Decimals, and the Number Line
              Intended Role: Instructor

            M27: Understanding Ratios
              Intended Role: Instructor

            M28: Rates and Unit Rates
              Intended Role: Instructor

            M29: Comparing Rates
              Intended Role: Instructor

            M30: Distance, Rate, and Time
              Intended Role: Instructor

            M31: Equivalent Ratios
              Intended Role: Instructor

            M32: Constant of Proportionality
              Intended Role: Instructor

            M33: Recognizing Proportional Relationships
              Intended Role: Instructor

            M34: Comparing Proportional Relationships
              Intended Role: Instructor

            M35: Solving Proportions
              Intended Role: Instructor

            M36: Maps and Scale Drawings
              Intended Role: Instructor

            M37: Understanding Percent
              Intended Role: Instructor

            M38: Relating Percents, Decimals, and Fractions
              Intended Role: Instructor

            M39: Percents Greater Than 100 or Less Than 1
              Intended Role: Instructor

            M40: Estimating Percent of a Number
              Intended Role: Instructor

            M41: Finding the Percent of a Whole Number
              Intended Role: Instructor

            M42: Find the Whole
              Intended Role: Instructor

            M43: The Percent Equation
              Intended Role: Instructor

            M44: Tips and Sales Tax
              Intended Role: Instructor

            M45: Markups and Markdowns
              Intended Role: Instructor

            M46: Percent Change
              Intended Role: Instructor

            M47: Percent Error
              Intended Role: Instructor

            M48: Simple Interest
              Intended Role: Instructor

            Booklet N: Measurement, Geometry, Data Analysis, and Probability:
              Intended Role: Instructor

            N1: Geometric Ideas
              Intended Role: Instructor

            N2: Lines and Line Segments
              Intended Role: Instructor

            N3: Measuring and Classifying Angles
              Intended Role: Instructor

            N4: Angle Pairs
              Intended Role: Instructor

            N5: Parallel Lines and Transversals
              Intended Role: Instructor

            N6: Polygons
              Intended Role: Instructor

            N7: Polygons on the Coordinate Plane
              Intended Role: Instructor

            N8: Classifying Triangles Using Sides and Angles
              Intended Role: Instructor

            N9: Quadrilaterals
              Intended Role: Instructor

            N10: Circles
              Intended Role: Instructor

            N11: Missing Angles in Triangles and Quadrilaterals
              Intended Role: Instructor

            N12: Interior and Exterior Angles of Triangles
              Intended Role: Instructor

            N13: Cutting Shapes Apart
              Intended Role: Instructor

            N14: Solid Figures
              Intended Role: Instructor

            N15: Solids and Nets
              Intended Role: Instructor

            N16: Views of Solid Figures
              Intended Role: Instructor

            N17: Cross Sections
              Intended Role: Instructor

            N18: Line Symmetry
              Intended Role: Instructor

            N19: Rotational Symmetry
              Intended Role: Instructor

            N20: Using Customary Units of Length
              Intended Role: Instructor

            N21: Using Metric Units of Length
              Intended Role: Instructor

            N22: Using Customary Units of Capacity
              Intended Role: Instructor

            N23: Using Metric Units of Capacity
              Intended Role: Instructor

            N24: Using Customary Units of Weight
              Intended Role: Instructor

            N25: Using Metric Units of Mass
              Intended Role: Instructor

            N26: Measuring Capacity or Weight
              Intended Role: Instructor

            N27: Units of Time
              Intended Role: Instructor

            N28: Converting Customary Units of Length
              Intended Role: Instructor

            N29: Converting Customary Units of Capacity
              Intended Role: Instructor

            N30: Converting Customary Units of Weight
              Intended Role: Instructor

            N31: Converting Metric Units
              Intended Role: Instructor

            N32: Converting Between Measurement Systems
              Intended Role: Instructor

            N33: Converting Units
              Intended Role: Instructor

            N34: Units of Measure and Precision
              Intended Role: Instructor

            N35: More Units of Time
              Intended Role: Instructor

            N36: Solving Problems with Units of Time
              Intended Role: Instructor

            N37: Perimeter
              Intended Role: Instructor

            N38: Exploring Area
              Intended Role: Instructor

            N39: Finding Area on a Grid
              Intended Role: Instructor

            N40: More Perimeter
              Intended Role: Instructor

            N41: Area of Rectangles and Squares
              Intended Role: Instructor

            N42: Area of Irregular Figures
              Intended Role: Instructor

            N43: Rectangles with the Same Area or Perimeter
              Intended Role: Instructor

            N44: Area of Parallelograms
              Intended Role: Instructor

            N45: Area of Triangles
              Intended Role: Instructor

            N46: Circumference
              Intended Role: Instructor

            N47: Area of a Circle
              Intended Role: Instructor

            N48: Surface Area of Rectangular Prisms
              Intended Role: Instructor

            N49: Surface Area of Cylinders, Pyramids, and Triangular Prisms
              Intended Role: Instructor

            N50: Surface Area of Cones and Spheres
              Intended Role: Instructor

            N51: Counting Cubes to Find Volume
              Intended Role: Instructor

            N52: Volume of Rectangular Prisms
              Intended Role: Instructor

            N53: Volume of Cylinders
              Intended Role: Instructor

            N54: Volume of Cones
              Intended Role: Instructor

            N55: Volume of Spheres
              Intended Role: Instructor

            N56: Comparing Volume and Surface Area
              Intended Role: Instructor

            N57: Combining Volumes
              Intended Role: Instructor

            N58: Transformations
              Intended Role: Instructor

            N59: Composing Transformations
              Intended Role: Instructor

            N60: Congruent Figures
              Intended Role: Instructor

            N61: Dilations
              Intended Role: Instructor

            N62: Similar Figures
              Intended Role: Instructor

            N63: Angle-Angle Triangle Similarity
              Intended Role: Instructor

            N64: The Pythagorean theorem
              Intended Role: Instructor

            N65: The Converse of the Pythagorean theorem
              Intended Role: Instructor

            N66: Distance on the Coordinate Plane
              Intended Role: Instructor

            N67: Recording Data from a Survey
              Intended Role: Instructor

            N68: Reading and Making a Bar Graph
              Intended Role: Instructor

            N69: Interpreting Graphs
              Intended Role: Instructor

            N70: Stem-and-Leaf Plots
              Intended Role: Instructor

            N71: Histograms
              Intended Role: Instructor

            N72: Scatterplots
              Intended Role: Instructor

            N73: Making Dot Plots
              Intended Role: Instructor

            N74: Line Plots
              Intended Role: Instructor

            N75: Box Plotsterals
              Intended Role: Instructor

            N76: Statistical Questions
              Intended Role: Instructor

            N77: Finding the Mean
              Intended Role: Instructor

            N78: Median, Mode, and Range
              Intended Role: Instructor

            N79: Measures of Variability
              Intended Role: Instructor

            N80: Appropriate Use of Statistical Measures
              Intended Role: Instructor

            N81: Summarize Data Distributions
              Intended Role: Instructor

            N82: Populations and Samples
              Intended Role: Instructor

            N83: Drawing Inferences about Populations
              Intended Role: Instructor

            N84: Comparing Populations
              Intended Role: Instructor

            N85: Sample Spaces
              Intended Role: Instructor

            N86: Probability of Simple Events
              Intended Role: Instructor

            N87: Probability of Compound Events
              Intended Role: Instructor

            N88: Linear Models
              Intended Role: Instructor

            N89: Two-Way Frequency Tables
              Intended Role: Instructor

            N90: Relative Frequency Tables
              Intended Role: Instructor

            N71: Histograms
              Intended Role: Instructor

            N75: Box Plots
              Intended Role: Instructor

            N76: Statistical Questions
              Intended Role: Instructor

            N78: Median, Mode, and Range
              Intended Role: Instructor

            N79: Measures of Variability
              Intended Role: Instructor

            Teacher's Guide, Grades 6-8
              Intended Role: Instructor

            Diagnostic Tests and Answer Keys, Grades 5-8
              Intended Role: Instructor

            Grade 5 Diagnostic Test, Form A
              Intended Role: Instructor

            Grade 5 Diagnostic Test, Form B
              Intended Role: Instructor

            Grade 6 Diagnostic Test, Form A
              Intended Role: Instructor

            Grade 6 Diagnostic Test, Form B
              Intended Role: Instructor

            Grade 7 Diagnostic Test, Form A
              Intended Role: Instructor

            Grade 7 Diagnostic Test, Form B
              Intended Role: Instructor

            Grade 8 Diagnostic Test, Form A
              Intended Role: Instructor

            Grade 8 Diagnostic Test, Form B
              Intended Role: Instructor

            Grade 6: Correlation to Minnesota Academic Standards
              Intended Role: Instructor

            MN-1: Estimate and Use Customary Units of Length Teacher's Guide
              Intended Role: Instructor

            MN-2: Estimate and Use Customary Units of Weight Teacher's Guide
              Intended Role: Instructor

            MN-3: Estimate and Use Customary Units of Capacity Teacher's Guide
              Intended Role: Instructor

            MN-4: Estimate and Use Metric Units of Length Teacher's Guide
              Intended Role: Instructor

            MN-5: Estimate and Use Metric Units of Weight Teacher's Guide
              Intended Role: Instructor

            MN-6: Estimate and Use Metric Units of Capacity Teacher's Guide
              Intended Role: Instructor

            MN-7: Solve Problems Using Angle Relationships Teacher's Guide
              Intended Role: Instructor

            MN-8: Angles of Triangles Teacher's Guide
              Intended Role: Instructor

            MN-9: Angles of Polygons Teacher's Guide
              Intended Role: Instructor

            MN-10: Estimate Perimeter and Area of Irregular Figures Teacher's Guide
              Intended Role: Instructor

            MN-11: Sample Space Teacher's Guide
              Intended Role: Instructor

            MN-12: Understand Likelihood and Probability Teacher's Guide
              Intended Role: Instructor

            MN-13: Experiments and Relative Frequency Teacher's Guide
              Intended Role: Instructor

            MN-14 Use Experimental Probability Teacher's Guide
              Intended Role: Instructor

            Teacher's Edition eText: Grade 6
              Intended Role: Instructor

            Teacher's Edition Program Overview eText: Grade 6
              Intended Role: Instructor

            Interactive Student Edition: Grade 6
              Intended Role: Instructor

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            Grade 6: Accessible Student Edition

            Student's Edition eText: Grade 6

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