**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.

Problem | Page |
---|---|

Problem 14 | 15 |

Problem 13 | 15 |

Problem 16 | 16 |

Problem 17 | 17 |

Problem 18 | 17 |

Problem 19 | 18 |

Problem 26 | 21 |

Problem 27 | 22 |

Problem 39 | 28 |

Problem 41 | 29 |

Problem 42 | 29 |

Problem 43 | 30 |

Problem 44 | 30 |

Problem 52 | 34 |

Problem 51 | 34 |

Problem 54 | 35 |

Problem 53 | 35 |

Problem 55 | 36 |

Problem 56 | 36 |

Problem 60 | 38 |

Problem 63 | 40 |

Problem 71 | 44 |

Problem 75 | 46 |

Problem 77 | 47 |

Problem 84 | 50 |

Problem 88 | 52 |

Problem 89 | 53 |

Problem 92 | 54 |

Problem 93 | 55 |

Problem 94 | 55 |

**Understand ratio concepts and use ratio reasoning to solve problems.**

*Math.6.RP.A.2*: 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.”*

Problem | Page |
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Problem 28 | 22 |

Problem 29 | 23 |

Problem 30 | 23 |

Problem 31 | 24 |

Problem 82 | 49 |

Problem 89 | 53 |

Problem 91 | 54 |

Problem 92 | 54 |

Problem 94 | 55 |

Problem 93 | 55 |

**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.”*

Problem | Page |
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Problem 87 | 52 |

Problem 88 | 52 |

Problem 90 | 53 |

Problem 91 | 54 |

Problem 92 | 54 |

Problem 93 | 55 |

Problem 94 | 55 |

**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?*.

Problem | Page |
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Problem 22 | 19 |

Problem 34 | 25 |

Problem 35 | 26 |

Problem 36 | 26 |

Problem 38 | 27 |

Problem 46 | 31 |

**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.

Problem | Page |
---|---|

Problem 1 | 9 |

Problem 3 | 10 |

Problem 10 | 13 |

Problem 14 | 15 |

Problem 13 | 15 |

Problem 18 | 17 |

Problem 17 | 17 |

Problem 19 | 18 |

Problem 24 | 20 |

Problem 23 | 20 |

Problem 25 | 21 |

Problem 28 | 22 |

Problem 31 | 24 |

Problem 37 | 27 |

Problem 46 | 31 |

Problem 49 | 33 |

Problem 54 | 35 |

Problem 57 | 37 |

Problem 60 | 38 |

Problem 65 | 41 |

Problem 66 | 41 |

Problem 67 | 42 |

Problem 72 | 44 |

Problem 71 | 44 |

Problem 73 | 45 |

Problem 77 | 47 |

Problem 84 | 50 |

Problem 83 | 50 |

Problem 95 | 56 |

Problem 96 | 56 |

Problem 97 | 57 |

Problem 99 | 58 |

Problem 100 | 58 |

**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.

Problem | Page |
---|---|

Problem 15 | 16 |

Problem 20 | 18 |

Problem 32 | 24 |

Problem 33 | 25 |

Problem 45 | 31 |

Problem 47 | 32 |

Problem 61 | 39 |

Problem 79 | 48 |

Problem 81 | 49 |

Problem 86 | 51 |

Problem 85 | 51 |

**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.

Problem | Page |
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Problem 11 | 14 |

**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.

Problem | Page |
---|---|

Problem 110 | 63 |

**Reason about and solve one-variable equations and inequalities.**

*Math.6.EE.B.6*: 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.

Problem | Page |
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Problem 9 | 13 |

Problem 29 | 23 |

Problem 30 | 23 |

Problem 32 | 24 |

Problem 40 | 28 |

Problem 44 | 30 |

Problem 48 | 32 |

Problem 50 | 33 |

Problem 49 | 33 |

Problem 53 | 35 |

Problem 56 | 36 |

Problem 55 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 59 | 38 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 63 | 40 |

Problem 64 | 40 |

Problem 66 | 41 |

Problem 68 | 42 |

Problem 67 | 42 |

Problem 74 | 45 |

Problem 75 | 46 |

Problem 76 | 46 |

Problem 77 | 47 |

Problem 78 | 47 |

Problem 80 | 48 |

Problem 81 | 49 |

Problem 84 | 50 |

Problem 83 | 50 |

**Reason about and solve one-variable equations and inequalities.**

*Math.6.EE.B.7*: 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.

Problem | Page |
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Problem 30 | 23 |

Problem 29 | 23 |

Problem 32 | 24 |

Problem 40 | 28 |

Problem 44 | 30 |

Problem 48 | 32 |

Problem 50 | 33 |

Problem 49 | 33 |

Problem 53 | 35 |

Problem 55 | 36 |

Problem 56 | 36 |

Problem 58 | 37 |

Problem 57 | 37 |

Problem 59 | 38 |

Problem 60 | 38 |

Problem 61 | 39 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 63 | 40 |

Problem 66 | 41 |

Problem 68 | 42 |

Problem 67 | 42 |

Problem 74 | 45 |

Problem 75 | 46 |

Problem 76 | 46 |

Problem 77 | 47 |

Problem 78 | 47 |

Problem 80 | 48 |

Problem 81 | 49 |

Problem 83 | 50 |

Problem 84 | 50 |

**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.

Problem | Page |
---|---|

Problem 38 | 27 |

Problem 40 | 28 |

Problem 48 | 32 |

Problem 62 | 39 |

Problem 64 | 40 |

Problem 76 | 46 |

Problem 80 | 48 |

**Represent and analyze quantitative relationships between dependent and independent variables.**

*Math.6.EE.C.9*: 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.

Problem | Page |
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Problem 51 | 34 |

Problem 65 | 41 |

Problem 70 | 43 |

Problem 72 | 44 |

Problem 71 | 44 |

Problem 73 | 45 |

**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.

Problem | Page |
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Problem 97 | 57 |

**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.

Problem | Page |
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Problem 98 | 57 |

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

*Math.6.G.A.3*: 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.

Problem | Page |
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Problem 99 | 58 |

**Summarize and describe distributions.**

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

Problem | Page |
---|---|

Problem 69 | 43 |

Problem 79 | 48 |

Problem 85 | 51 |

Problem 86 | 51 |

Problem 107 | 62 |

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.