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Product Name: enVisionmath 2.0 Custom Grades 6-8 Grade 6 West Virginia
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Curriculum Standards:


Divide rational numbers. - 7.NC.1.9
Find and position pairs of rational numbers on a coordinate plane. - NC.6.NS.6.b.3
Convert between customary and metric units. - 6.P.5.10
Recognize rational numbers and write them in decimal form. - 7.NC.1.2
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
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
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
The student will solve practical problems involving operations with rational numbers. - 7.2
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
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
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
Understand that every quotient of integers (with non-zero divisor) is a rational number. - 7.NS.A.2c
Given two congruent figures, describe a sequence that exhibits the congruence between them. - NC.8.G.2.c
Convert a rational number to a decimal. - 7.NS.A.2d
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations. - NC.8.G.2.b
Understand that all rational numbers can be written as fractions or decimal numbers that terminate or repeat. - 7.NS.A.2e
Describe the difference between an expression and an equation. - 6.EEI.A.1
Interpret products and quotients of rational numbers by describing real-world contexts. - 7.NS.A.2f
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
Multiply and divide rational numbers. - 7.NS.A.2a
Verify experimentally the properties of rotations, reflections, and translations that create congruent figures. - NC.8.G.2.a
Determine that a number and its reciprocal have a product of 1 (multiplicative inverse). - 7.NS.A.2b
Describe a possible sequence of transformations between two similar figures. - 8.GM.A.4a
Use transformations to define congruence. - NC.8.G.2
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - MAFS.7.NS.1.2d
Apply properties of operations as strategies to multiply and divide rational numbers. - MAFS.7.NS.1.2c
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts. - MAFS.7.NS.1.2b
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
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
Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. - 7.1.1.5
Solve problems involving division of fractions by fractions. - 6.NS.A.1a
Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. - 7.1.1.2
Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that π is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14. - 7.1.1.1
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
Describe a possible sequence of rigid transformations between two congruent figures. - 8.GM.A.2a
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
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
Divide whole numbers and decimals. - 6.NC.1.2
Summarize numerical data sets in relation to their context. - NC.6.SP.5
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
Add, subtract, and multiply decimals. - 6.NC.1.1
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
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
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
Solve real-world and mathematical problems involving the four operations with rational numbers. - MAFS.7.NS.1.3
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
Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations. - NC.7.NS.3
Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. - 6.G.7.1
Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers, using the properties of operations, and describing real-world contexts using sums and differences. - NC.7.NS.1
Apply properties of operations to calculate with positive and negative numbers in any form. - NC.7.EE.3.a
Convert between different forms of a number and equivalent forms of the expression as appropriate. - NC.7.EE.3.b
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
Interpret sums and differences of rational numbers. - 7.NS.A.1f
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
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
Add and subtract rational numbers. - 7.NS.A.1a
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
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
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
Identify parts of an expression using mathematical terminology. - 6.EEI.A.2a
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
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
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 non-negative rational number expressions. - 6.EEI.A.2c
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
Evaluate expressions at specific values of the variables. - 6.EEI.A.2b
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
Analyze the relationship between dependent and independent variables in tables, graphs, and equations. - 6.AF.4.10
Use unit rates to solve problems. - 6.P.5.7
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
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
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
Use a sequence of translations, reflections, and rotations to show that figures are congruent. - 8.G.6.5
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
Use division and previous understandings of fractions and decimals. - NC.7.NS.2.c
Write, interpret and explain problems of ordering of rational numbers. - 6.NS.C.6b
Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts. - NC.7.NS.2.b
Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor. - NC.7.NS.2.a
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation. - MAFS.7.EE.2.3
Summarize numerical data sets in relation to the context. - 6.DSP.B.5
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
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
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
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - M.8.17
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
Solve problems with rational numbers. - 7.NC.1.10
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
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
Solve multi-step real-world and mathematical problems posed with rational numbers in algebraic expressions. - NC.7.EE.3
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
Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. - MAFS.8.G.1.3
Convert a fraction to a decimal using long division. - NC.7.NS.2.c.1
Interpret and compute quotients of fractions. - NC.6.NS.1.a
Understand that the decimal form of a rational number terminates in 0s or eventually repeats. - NC.7.NS.2.c.2
Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. - MAFS.8.G.1.2
Solve real-world and mathematical problems involving division of fractions. - NC.6.NS.1.b
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats. - M.7.5d
Apply properties of operations as strategies to multiply and divide rational numbers. - M.7.5c
Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real world contexts. - M.7.5b
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
Representing solutions of inequalities on number line diagrams. - NC.6.EE.8.d
Use nets to find the surface area of threedimensional figures whose sides are made up of rectangles and triangles. - 6.GM.A.4b
Recognizing that inequalities of the form x > c or x < c have infinitely many solutions. - NC.6.EE.8.c
Represent three-dimensional figures using nets made up of rectangles and triangles. - 6.GM.A.4a
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
Understand that two-dimensional figures are congruent if a series of rigid transformations can be performed to map the preimage to the image. - 8.GM.A.2
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
Solve problems involving the four arithmetic operations with rational numbers. - 7.NS.A.3
Identify and write statistical questions. - 6.DP.8.1
Identify the mean, median, mode, and range of a data set. - 6.DP.8.2
Solve real-world and mathematical problems involving addition, subtraction, multiplication and division of rational numbers; use efficient and generalizable procedures including but not limited to standard algorithms. - 7.N.2.3
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
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
Solve real-world and mathematical problems involving the four operations with rational numbers. Instructional Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions. - M.7.6
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
Construct polygons in the Cartesian coordinate plane. - 6.GM.A.3d
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
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
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
Reporting the number of observations. - MAFS.6.SP.2.5a
Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid. - 6.1.1.1
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. (e.g., If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.) - M.7.9
Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest. - 7.1.2.4
Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. - 7.1.2.1
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
Understand that calculators and other computing technologies often truncate or round numbers. - 7.1.2.3
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 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
Apply the properties of operations to generate equivalent expressions without exponents. - NC.6.EE.3
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
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
Use substitution to determine whether a given number in a specified set makes an equation true. - NC.6.EE.5
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
Find the unique prime factorization for a whole number. - NC.6.NS.4.a
The student will multiply and divide fractions and mixed numbers. - 6.5a
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
Calculate the mean, median, and mode for a set of real-world data. - 6.D.1.1
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
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
Understand the concept of Pi as the ratio of the circumference of a circle to its diameter. - MAFS.6.RP.1.3e
Create and analyze box and whisker plots observing how each segment contains one quarter of the data. - 6.D.1.3
Describe the nature of the attribute under investigation, including how it was measured and its units of measurement. - 6.DSP.B.5b
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
Assess the reasonableness of answers using mental computation and estimation strategies. - 7.EEI.B.3b
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
Recognize and generate equivalent representations of rational numbers, including equivalent fractions. - 7.N.1.3
Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. - 7.N.1.1
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
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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