**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.”*

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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.

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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.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.

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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?*

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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.

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Percent | 13 |

Percent | 38 |

Percent | 63 |

**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?*.

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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.

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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.

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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).*.

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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.

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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.

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Ordering Rational Numbers | 24 |

Ordering Rational Numbers | 49 |

Ordering Rational Numbers | 74 |

**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.

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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.

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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.

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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*.

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Absolute Value of Rational Numbers | 25 |

Absolute Value of Rational Numbers | 50 |

Absolute Value of Rational Numbers | 75 |

**Apply and extend previous understandings of arithmetic to algebraic expressions.**

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

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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.

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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*.

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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.

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One-variable Equations and Inequalities | 30 |

One-variable Equations and Inequalities | 55 |

One-variable Equations and Inequalities | 80 |

**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*.

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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 = s ^{3} and A = 6 s^{2} to find the volume and surface area of a cube with sides of length s = 1/2*.

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Evaluating Expressions | 28 |

Evaluating Expressions | 53 |

Evaluating Expressions | 78 |

**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.

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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.

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Volume of Rectangular Prisms with Fractional Sides | 32 |

Volume of Rectangular Prisms with Fractional Sides | 57 |

Volume of Rectangular Prisms with Fractional Sides | 82 |

**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.

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

Activity | Page |
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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 numerical data sets in relation to their context, such as by:**

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

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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.

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Histograms and Box Plots | 34 |

Histograms and Box Plots | 59 |

Histograms and Box Plots | 84 |

Common Core State Standards and Expectations© Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.