**Use the four operations with whole numbers to solve problems.**

*Math.4.OA.A.3*: Solve multi-step word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.

Activity | Page |
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Problem Solving with Mixed Operations: Missing or Extra Information | 17 |

Multiple-step Problems with Mixed Operations | 18 |

Problem Solving with Mixed Operations: Missing or Extra Information | 42 |

Multiple-step Problems with Mixed Operations | 43 |

Problem Solving with Mixed Operations: Missing or Extra Information | 67 |

Multiple-step Problems with Mixed Operations | 68 |

**Use the four operations with whole numbers to solve problems.**

*Math.4.OA.A.2*: Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.

Activity | Page |
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Problem Solving with Mixed Operations: Missing or Extra Information | 17 |

Problem Solving with Mixed Operations: Missing or Extra Information | 42 |

Problem Solving with Mixed Operations: Missing or Extra Information | 67 |

**Gain familiarity with factors and multiples.**

*Math.4.OA.B.4*: Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Activity | Page |
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Factors and Multiples | 19 |

Prime and Composite Numbers | 20 |

Factors and Multiples | 44 |

Prime and Composite Numbers | 45 |

Factors and Multiples | 69 |

Prime and Composite Numbers | 70 |

**Generate and analyze patterns.**

*Math.4.OA.C.5*: Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. *For example, given the rule “Add 3” and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way*.

Activity | Page |
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Input/Output and Function Tables | 21 |

Input/Output and Function Tables | 46 |

Input/Output and Function Tables | 71 |

**Generalize place value understanding for multi-digit whole numbers.**

*Math.4.NBT.A.3*: Use place value understanding to round multi-digit whole numbers to any place.

Activity | Page |
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Estimating Sums and Differences of Whole Numbers | 11 |

Estimating Products and Quotients | 16 |

Estimating Sums and Differences of Whole Numbers | 36 |

Estimating Products and Quotients | 41 |

Estimating Sums and Differences of Whole Numbers | 61 |

Estimating Products and Quotients | 66 |

**Generalize place value understanding for multi-digit whole numbers.**

*Math.4.NBT.A.2*: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

Activity | Page |
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Comparing Numbers to Hundred Thousands | 12 |

Comparing Numbers to Hundred Thousands | 37 |

Comparing Numbers to Hundred Thousands | 62 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.**

*Math.4.NBT.B.4*: Fluently add and subtract multi-digit whole numbers using the standard algorithm.

Activity | Page |
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Addition and Subtraction to One Million | 10 |

Addition and Subtraction to One Million | 35 |

Addition and Subtraction to One Million | 60 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.**

*Math.4.NBT.B.5*: Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Activity | Page |
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Multiplication and Division Using Basic Facts | 13 |

Multiplying by One-digit and Two-digit Numbers | 14 |

Multiplication and Division Using Basic Facts | 38 |

Multiplying by One-digit and Two-digit Numbers | 39 |

Multiplication and Division Using Basic Facts | 63 |

Multiplying by One-digit and Two-digit Numbers | 64 |

**Use place value understanding and properties of operations to perform multi-digit arithmetic.**

*Math.4.NBT.B.6*: Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Activity | Page |
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Dividing by One-digit Numbers | 15 |

Dividing by One-digit Numbers | 40 |

Dividing by One-digit Numbers | 65 |

**Extend understanding of fraction equivalence and ordering.**

*Math.4.NF.A.2*: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Activity | Page |
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Comparing Fractions | 22 |

Comparing Fractions | 47 |

Comparing Fractions | 72 |

**Understand decimal notation for fractions, and compare decimal fractions.**

*Math.4.NF.C.7*: Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Activity | Page |
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Comparing Decimals | 28 |

Comparing Decimals | 53 |

Comparing Decimals | 78 |

**Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> > 1 as a sum of fractions 1/<i>b</i>.**

*Math.4.NF.B.3a*: Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Activity | Page |
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Adding and Subtracting Fractions with Like and Unlike Denominators | 23 |

Adding and Subtracting Fractions with Like and Unlike Denominators | 48 |

Adding and Subtracting Fractions with Like and Unlike Denominators | 73 |

**Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> > 1 as a sum of fractions 1/<i>b</i>.**

*Math.4.NF.B.3d*: Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

Activity | Page |
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Adding and Subtracting Fractions with Like and Unlike Denominators | 23 |

Adding and Subtracting Fractions with Like and Unlike Denominators | 48 |

Adding and Subtracting Fractions with Like and Unlike Denominators | 73 |

**Understand a fraction <i>a</i>/<i>b</i> with <i>a</i> > 1 as a sum of fractions 1/<i>b</i>.**

*Math.4.NF.B.3c*: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Activity | Page |
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Improper Fractions and Mixed Numbers | 24 |

Adding and Subtracting Mixed Numbers | 25 |

Improper Fractions and Mixed Numbers | 49 |

Adding and Subtracting Mixed Numbers | 50 |

Improper Fractions and Mixed Numbers | 74 |

Adding and Subtracting Mixed Numbers | 75 |

**Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.**

*Math.4.NF.B.4c*: Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem. *For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?*

Activity | Page |
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Multiplying Fractions by Whole Numbers | 26 |

Word Problems with Whole Numbers and Fractions | 27 |

Multiplying Fractions by Whole Numbers | 51 |

Word Problems with Whole Numbers and Fractions | 52 |

Multiplying Fractions by Whole Numbers | 76 |

Word Problems with Whole Numbers and Fractions | 77 |

**Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.**

*Math.4.NF.B.4a*: Understand a fraction *a*/*b* as a multiple of 1/*b*. *For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4)*.

Activity | Page |
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Multiplying Fractions by Whole Numbers | 26 |

Multiplying Fractions by Whole Numbers | 51 |

Multiplying Fractions by Whole Numbers | 76 |

**Solve problems involving measurement and conversion of measurements.**

*Math.4.MD.A.1*: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. *For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...*

Activity | Page |
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Converting Customary and Metric Units | 29 |

Converting Units of Time | 30 |

Converting Customary and Metric Units | 54 |

Converting Units of Time | 55 |

Converting Customary and Metric Units | 79 |

Converting Units of Time | 80 |

**Solve problems involving measurement and conversion of measurements.**

*Math.4.MD.A.2*: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Activity | Page |
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Converting Units of Time | 30 |

Elapsed Time | 31 |

Converting Units of Time | 55 |

Elapsed Time | 56 |

Converting Units of Time | 80 |

Elapsed Time | 81 |

**Solve problems involving measurement and conversion of measurements.**

*Math.4.MD.A.3*: Apply the area and perimeter formulas for rectangles in real world and mathematical problems. *For example, find the width of a rectangular room given the area of the flooring and the length, by viewing the area formula as a multiplication equation with an unknown factor*.

Activity | Page |
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Perimeter and Area | 32 |

Perimeter and Area | 57 |

Perimeter and Area | 82 |

**Geometric measurement: understand concepts of angle and measure angles.**

*Math.4.MD.C.7*: Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

Activity | Page |
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Angles | 34 |

Angles | 59 |

Angles | 84 |

**Draw and identify lines and angles, and classify shapes by properties of their lines and angles.**

*Math.4.G.A.1*: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

Activity | Page |
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Lines and Angles | 33 |

Lines and Angles | 58 |

Lines and Angles | 83 |

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.