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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. - 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
Convert between customary and metric units. - 6.P.5.10
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
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
Display numerical data in plots on a number line, including dot plots, histograms, and box plots. - MAFS.6.SP.2.4
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
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
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
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
The student will determine congruence of segments, angles, and polygons. - 6.9
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 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
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
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. - M.6.29b
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
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
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
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
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
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
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
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
Solve multistep problems with fractions and decimals. - 6.NC.1.7
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
Divide with mixed numbers. - 6.NC.1.6
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
Use models and equations to multiply fractions and mixed numbers. - 6.NC.1.3
Divide whole numbers and decimals. - 6.NC.1.2
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
Divide a fraction by another fraction. - 6.NC.1.5
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
Use models and equations to represent fraction division. - 6.NC.1.4
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
Add, subtract, and multiply decimals. - 6.NC.1.1
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
Evaluate an algebraic expression with whole numbers, decimals, and fractions. - 6.AF.3.5
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
Use variables to write algebraic expressions. - 6.AF.3.4
Convert between equivalent representations of positive rational numbers. - 6.1.1.7
Combine like terms in algebraic expressions. - 6.AF.3.7
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
Identify and write equivalent algebraic expressions. - 6.AF.3.6
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
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
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
Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic 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
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
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
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
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
The student will represent and determine equivalencies among fractions, mixed numbers, decimals, and percents. - 6.2a
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
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
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
The student will identify and describe absolute value of integers. - 6.3c
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 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
Use what I know about areas of rectangles to find the areas of parallelograms and rhombuses. - 6.G.7.1
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
The student will compare and order integers. - 6.3b
The student will identify and represent integers. - 6.3a
The student, given a practical situation, will compare circle graphs with the same data represented in bar graphs, pictographs, and line plots. - 6.10c
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
The student, given a practical situation, will represent data in a circle graph. - 6.10a
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
The student, given a practical situation, will make observations and inferences about data represented in a circle graph. - 6.10b
Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. - MAFS.6.SP.2.5b
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
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
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
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
The student will represent the mean of a data set graphically as the balance point. - 6.11a
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
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
The student will solve multistep practical problems involving addition, subtraction, multiplication, and division of decimals. - 6.5c
The student will determine whether a proportional relationship exists between two quantities. - 6.12c
Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. - 6.2.1.2
Find the whole amount when given a part and the percent. - 6.P.6.6
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
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
Solve problems involving percents. - 6.P.6.5
Represent and find the whole percent of a whole. - 6.P.6.1
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
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
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
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
The student will add, subtract, multiply, and divide integers. - 6.6a
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
The student will solve practical problems involving operations with integers. - 6.6b
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
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
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
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
The student will solve problems, including practical problems, involving circumference and area of a circle. - 6.7b
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
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
The student will derive π (pi). - 6.7a
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
Write and evaluate numerical expressions involving whole-number exponents. - M.6.12
The student will solve problems, including practical problems, involving area and perimeter of triangles and rectangles. - 6.7c
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
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
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
The student will represent a practical situation with a linear inequality in one variable. - 6.14a
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
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
Solve problems involving rates. - 6.P.5.5
Compare unit rates to solve problems. - 6.P.5.6
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
The student will identify the components of the coordinate plane. - 6.8a
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
The student will identify the coordinates of a point and graph ordered pairs in a coordinate plane. - 6.8b
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




List of all Files Validated:


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