**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 |
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Test 44 | 48 |

Test 45 | 49 |

Test 46 | 50 |

**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 |
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Test 47 | 51 |

Test 76 | 80 |

Test 89 | 93 |

**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 |
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Test 23 | 27 |

Test 30 | 34 |

**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 |
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Test 2 | 6 |

Test 6 | 10 |

Test 7 | 11 |

Test 30 | 34 |

Test 32 | 36 |

Test 34 | 38 |

Test 35 | 39 |

Test 36 | 40 |

Test 37 | 41 |

Test 39 | 43 |

Test 40 | 44 |

Test 41 | 45 |

Test 43 | 47 |

Test 47 | 51 |

Test 49 | 53 |

Test 50 | 54 |

Test 52 | 56 |

Test 74 | 79 |

**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 |
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Test 15 | 19 |

Test 17 | 21 |

Test 18 | 22 |

Test 19 | 23 |

Test 21 | 25 |

Test 38 | 42 |

Test 48 | 52 |

Test 51 | 55 |

Test 55 | 59 |

**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 |
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Test 11 | 15 |

Test 12 | 16 |

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

*Math.6.NS.C.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.

Activity | Page |
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Test 11 | 15 |

**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 |
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Test 56 | 60 |

Test 57 | 61 |

**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 |
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Test 99 | 103 |

Test 100 | 104 |

**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 |
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Test 12 | 16 |

**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 |
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Test 8 | 12 |

Test 55 | 59 |

**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 |
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Test 53 | 57 |

Test 54 | 58 |

Test 95 | 99 |

Test 96 | 100 |

Test 97 | 101 |

Test 98 | 102 |

**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 |
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Test 98 | 102 |

**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.

Activity | Page |
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Test 1 | 5 |

Test 7 | 11 |

Test 51 | 55 |

Test 92 | 96 |

Test 93 | 97 |

Test 94 | 98 |

**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.

Activity | Page |
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Test 64 | 68 |

Test 65 | 69 |

**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 |
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Test 66 | 70 |

Test 67 | 71 |

**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 |
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Test 68 | 72 |

Test 69 | 73 |

Test 70 | 74 |

**Develop understanding of statistical variability.**

*Math.6.SP.A.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.

Activity | Page |
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Test 78 | 82 |

Test 85 | 89 |

Test 87 | 91 |

Test 88 | 92 |

**Develop understanding of statistical variability.**

*Math.6.SP.A.1*: 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*.

Activity | Page |
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Test 79 | 83 |

Test 80 | 84 |

Test 81 | 85 |

Test 82 | 86 |

Test 87 | 91 |

Test 88 | 92 |

Test 90 | 94 |

**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 |
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Test 75 | 79 |

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

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

Activity | Page |
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Test 75 | 79 |

Test 81 | 85 |

**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 |
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Test 77 | 81 |

Test 84 | 88 |

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

*Math.6.SP.B.5b*: Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.

Activity | Page |
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Test 85 | 89 |

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.