 ## Common Core State Standards (CCSS) Correlations ## Mathematics

### Domain - Ratios and Proportional Relationships, Grade 6

Understand ratio concepts and use ratio reasoning to solve problems.

Math.6.RP.A.1: 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.”

Activity Page
Ratios 10
Ratios 35
Ratios 60

Understand ratio concepts and use ratio reasoning to solve problems.

Math.6.RP.A.3: 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.

Activity Page
Ratio Relationships 11
Ratio Relationships 36
Ratio Relationships 61

### Domain - Understand ratio concepts and use ratio reasoning to solve problems., Grade 6

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.

Math.6.RP.A.3a: Make tables of equivalent ratios relating quantities with wholenumber measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.

Activity Page
Ratio Relationships 11
Ratio Relationships 36
Ratio Relationships 61

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.

Math.6.RP.A.3b: 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?

Activity Page
Unit Rate Ratios 12
Unit Rate Ratios 37
Unit Rate Ratios 62

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.

Math.6.RP.A.3c: 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.

Activity Page
Percent 13
Percent 38
Percent 63

### Domain - The Number System, Grade 6

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Math.6.NS.A.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?.

Activity Page
Dividing Fractions 14
Dividing Fractions 39
Dividing Fractions 64

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.2: Fluently divide multi-digit numbers using the standard algorithm.

Activity Page
Dividing Multi-digit Numbers 15
Dividing Multi-digit Numbers 40
Dividing Multi-digit Numbers 65

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.3: Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Activity Page
Adding, Subtracting, Multiplying, and Dividing Decimals 16
Adding, Subtracting, Multiplying, and Dividing Decimals 41
Adding, Subtracting, Multiplying, and Dividing Decimals 66

Compute fluently with multi-digit numbers and find common factors and multiples.

Math.6.NS.B.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. For example, express 36 + 8 as 4 (9 + 2)..

Activity Page
Greatest Common Factor of Two Whole Numbers 17
Least Common Multiple of Two Whole Numbers 18
Distributive Property 19
Greatest Common Factor of Two Whole Numbers 42
Least Common Multiple of Two Whole Numbers 43
Distributive Property 44
Greatest Common Factor of Two Whole Numbers 67
Least Common Multiple of Two Whole Numbers 68
Distributive Property 69

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.5: 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.

Activity Page
Positive and Negative Numbers 20
Positive and Negative Numbers 45
Positive and Negative Numbers 70

Apply and extend previous understandings of numbers to the system of rational numbers.

Math.6.NS.C.7: Understand ordering and absolute value of rational numbers.

Activity Page
Ordering Rational Numbers 24
Ordering Rational Numbers 49
Ordering Rational Numbers 74

### Domain - Apply and extend previous understandings of numbers to the system of rational numbers., Grade 6

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Math.6.NS.C.6a: 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.

Activity Page
Numbers and Their Opposites 21
Numbers and Their Opposites 46
Numbers and Their Opposites 71

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Math.6.NS.C.6b: 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.

Activity Page
Ordered Pairs on a Coordinate Plane 22
Ordered Pairs on a Coordinate Plane 47
Ordered Pairs on a Coordinate Plane 72

Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

Math.6.NS.C.6c: 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.

Activity Page
Identifying Rational Numbers on a Number Line 23
Identifying Rational Numbers on a Number Line 48
Identifying Rational Numbers on a Number Line 73

Understand ordering and absolute value of rational numbers.

Math.6.NS.C.7c: 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.

Activity Page
Absolute Value of Rational Numbers 25
Absolute Value of Rational Numbers 50
Absolute Value of Rational Numbers 75

### Domain - Expressions and Equations, Grade 6

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.1: Write and evaluate numerical expressions involving whole-number exponents.

Activity Page
Expressions with Whole-number Exponents 26
Expressions with Whole-number Exponents 51
Expressions with Whole-number Exponents 76

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.2: Write, read, and evaluate expressions in which letters stand for numbers.

Activity Page
Variable Expressions 27
Evaluating Expressions 28
Variable Expressions 52
Evaluating Expressions 53
Variable Expressions 77
Evaluating Expressions 78

Apply and extend previous understandings of arithmetic to algebraic expressions.

Math.6.EE.A.3: 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.

Activity Page
Equivalent Expressions 29
Equivalent Expressions 54
Equivalent Expressions 79

Reason about and solve one-variable equations and inequalities.

Math.6.EE.B.5: 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.

Activity Page
One-variable Equations and Inequalities 30
One-variable Equations and Inequalities 55
One-variable Equations and Inequalities 80

### Domain - Apply and extend previous understandings of arithmetic to algebraic expressions., Grade 6

Write, read, and evaluate expressions in which letters stand for numbers.

Math.6.EE.A.2a: 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.

Activity Page
Variable Expressions 27
Variable Expressions 52
Variable Expressions 77

Write, read, and evaluate expressions in which letters stand for numbers.

Math.6.EE.A.2c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic 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 = 6 s2 to find the volume and surface area of a cube with sides of length s = 1/2.

Activity Page
Evaluating Expressions 28
Evaluating Expressions 53
Evaluating Expressions 78

### Domain - Geometry, Grade 6

Solve real-world and mathematical problems involving area, surface area, and volume.

Math.6.G.A.1: 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 technique in the context of solving real-world and mathematical problems.

Activity Page
Area 31
Area 56
Area 81

Solve real-world and mathematical problems involving area, surface area, and volume.

Math.6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

Activity Page
Volume of Rectangular Prisms with Fractional Sides 32
Volume of Rectangular Prisms with Fractional Sides 57
Volume of Rectangular Prisms with Fractional Sides 82

### Domain - Statistics and Probability, Grade 6

Summarize and describe distributions.

Math.6.SP.B.5: Summarize numerical data sets in relation to their context, such as by:

Activity Page
Dot Plots 33
Histograms and Box Plots 34
Dot Plots 58
Histograms and Box Plots 59
Dot Plots 83
Histograms and Box Plots 84

Summarize and describe distributions.

Math.6.SP.B.4: Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

Activity Page
Dot Plots 33
Histograms and Box Plots 34
Dot Plots 58
Histograms and Box Plots 59
Dot Plots 83
Histograms and Box Plots 84

### Domain - Summarize and describe distributions., Grade 6

Summarize numerical data sets in relation to their context, such as by:

Math.6.SP.B.5a: Reporting the number of observations.

Activity Page
Dot Plots 33
Dot Plots 58
Dot Plots 83

Summarize numerical data sets in relation to their context, such as by:

Math.6.SP.B.5c: 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.

Activity Page
Histograms and Box Plots 34
Histograms and Box Plots 59
Histograms and Box Plots 84