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

*Math.4.OA.A.1*: Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations.

Activity | Page |
---|---|

Doubling and Halving | 13 |

Multiplication with Modeling and Mental Strategies | 30 |

Reasoning with Numbers | 31 |

Multiplication (×2, ×4, and ×8) | 32 |

Multiplication (×5 and ×10) | 33 |

Multiplication (×3, ×6, and ×9) | 34 |

Multiplication (×7, ×8, and ×9) | 35 |

Multiplication | 36 |

Number Lines | 51 |

Multiplication and Division Practice | 126 |

**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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Subtracting 2-Digit Numbers without Regrouping | 23 |

Subtracting with Regrouping | 24 |

Division with Remainders | 47 |

Division Practice | 48 |

Multiplication and Division | 49 |

Multiplication and Division Practice | 126 |

**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 |
---|---|

Multiplication with Modeling and Mental Strategies | 30 |

Multiplication by Tens | 41 |

Extended Multiplication | 42 |

Division | 43 |

Division Problems and Remainders | 44 |

Division with Multiplication Grid | 45 |

Estimation with Division | 46 |

Division with Remainders | 47 |

Division Practice | 48 |

Multiplication and Division | 49 |

Inverse Operations | 50 |

**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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Multiples | 38 |

Factors | 39 |

Multiplication Strategies | 40 |

Division with Multiplication Grid | 45 |

Multiplication and Division | 49 |

Inverse Operations | 50 |

Prime and Composite Numbers | 52 |

**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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Ordering Numbers | 9 |

Less Than and Greater Than | 14 |

Number Patterns | 15 |

Reasoning with Numbers | 31 |

Multiplication (×2, ×4, and ×8) | 32 |

Multiplication (×5 and ×10) | 33 |

Multiplication (×3, ×6, and ×9) | 34 |

Multiplication (×7, ×8, and ×9) | 35 |

Multiplication | 36 |

Square and Triangular Numbers | 37 |

Multiples | 38 |

1-Step and 2-Step Rules | 53 |

**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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Numbers to 9,999 | 7 |

Place Value 0 – 9,999 | 8 |

Ordering Numbers | 9 |

Counting by Thousands | 10 |

Expanding 4-Digit Numbers | 11 |

Less Than and Greater Than | 14 |

Mixed Practice | 123 |

Place Value Practice | 124 |

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

*Math.4.NBT.A.1*: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.* For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division*.

Activity | Page |
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Place Value 0 – 9,999 | 8 |

Ordering Numbers | 9 |

Counting by Thousands | 10 |

Expanding 4-Digit Numbers | 11 |

Multiplication by Tens | 41 |

Extended Multiplication | 42 |

**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 |
---|---|

Counting by Thousands | 10 |

Rounding Numbers | 22 |

Rounding Numbers and Estimating | 29 |

**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 |
---|---|

Adding to 99 | 16 |

Adding to 999 | 17 |

Adding to 9,999 | 18 |

Adding with Regrouping to 999 | 19 |

Adding Three Numbers | 20 |

Adding Three or More Numbers | 21 |

Subtracting 2-Digit Numbers without Regrouping | 23 |

Subtracting with Regrouping | 24 |

Subtracting 3-Digit Numbers without Regrouping | 25 |

Subtracting 3-Digit Numbers with Regrouping | 26 |

Subtracting without Regrouping to 9,999 | 27 |

Subtracting with Regrouping to 9,999 | 28 |

Inverse Operations | 50 |

Number Lines | 51 |

Problem Solving | 122 |

Mixed Practice | 123 |

Place Value Practice | 124 |

Addition and Subtraction Practice | 125 |

**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 |
---|---|

Multiplication with Modeling and Mental Strategies | 30 |

Reasoning with Numbers | 31 |

Multiplication (×2, ×4, and ×8) | 32 |

Multiplication (×5 and ×10) | 33 |

Multiplication (×3, ×6, and ×9) | 34 |

Multiplication (×7, ×8, and ×9) | 35 |

Multiplication | 36 |

Square and Triangular Numbers | 37 |

Multiples | 38 |

Multiplication and Division | 49 |

Inverse Operations | 50 |

Problem Solving | 122 |

Mixed Practice | 123 |

Multiplication and Division Practice | 126 |

**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 |
---|---|

Reasoning with Numbers | 31 |

Division | 43 |

Division Problems and Remainders | 44 |

Division with Multiplication Grid | 45 |

Estimation with Division | 46 |

Division with Remainders | 47 |

Division Practice | 48 |

Multiplication and Division | 49 |

Multiplication and Division Practice | 126 |

**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 |
---|---|

Number Lines | 51 |

Fraction Names | 56 |

Fractions | 57 |

Comparing Fractions | 58 |

Equivalent Fractions | 59 |

Mixed Numbers | 60 |

Hundredths | 61 |

Tenths | 62 |

Percentages | 73 |

Fractions Practice | 127 |

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

*Math.4.NF.A.1*: Explain why a fraction *a*/*b* is equivalent to a fraction (*n* × *a*)/(*n* × *b*) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Activity | Page |
---|---|

Number Lines | 51 |

Fraction Names | 56 |

Fractions | 57 |

Comparing Fractions | 58 |

Equivalent Fractions | 59 |

Mixed Numbers | 60 |

Hundredths | 61 |

Tenths | 62 |

Simple Percentages | 72 |

Percentages | 73 |

Fractions Practice | 127 |

**Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.**

*Math.4.NF.B.3*: Understand a fraction *a*/*b* with *a* > 1 as a sum of fractions 1/*b*.

Activity | Page |
---|---|

Mixed Numbers | 60 |

Hundredths | 61 |

Fractions Practice | 127 |

**Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.**

*Math.4.NF.B.4*: Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

Activity | Page |
---|---|

Problem Solving | 122 |

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

*Math.4.NF.C.6*: Use decimal notation for fractions with denominators 10 or 100. *For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram*.

Activity | Page |
---|---|

Hundredths | 61 |

Tenths | 62 |

Decimals – Place Value | 63 |

Decimals | 64 |

Decimals with Whole Numbers | 66 |

Fractions and Decimals | 67 |

Simple Percentages | 72 |

Percentages | 73 |

Fractions, Decimals, and Percentages | 74 |

Decimals Practice | 128 |

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

*Math.4.NF.C.5*: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.^{2} *For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100*.

Activity | Page |
---|---|

Hundredths | 61 |

Tenths | 62 |

Decimals – Place Value | 63 |

Decimals | 64 |

Decimals with Whole Numbers | 66 |

Fractions and Decimals | 67 |

Simple Percentages | 72 |

Percentages | 73 |

Decimals Practice | 128 |

**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 |
---|---|

Tenths | 62 |

Comparing Decimals | 65 |

Decimals with Whole Numbers | 66 |

Fractions and Decimals | 67 |

Simple Percentages | 72 |

Percentages | 73 |

Fractions, Decimals, and Percentages | 74 |

Decimals Practice | 128 |

**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 |
---|---|

Use of Money | 75 |

Money Addition and Subtraction | 76 |

Money Multiplication and Division | 77 |

Money Rounding and Estimation | 78 |

Analog Time | 104 |

Digital and Analog Time | 105 |

Calendars | 106 |

Time Lines and Timetables | 107 |

Weight in Ounces and Pounds | 113 |

Problem Solving | 122 |

Mixed Practice | 123 |

Decimals Practice | 128 |

**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 |
---|---|

Length | 108 |

Length with Decimals | 109 |

**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 |
---|---|

Perimeter | 110 |

Area | 111 |

Area and Perimeter | 112 |

**Represent and interpret data.**

*Math.4.MD.B.4*: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. *For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection*.

Activity | Page |
---|---|

Picture Graphs | 116 |

Tally Marks and Tables | 117 |

Reading Graphs and Tables | 118 |

Working with Tables | 119 |

Bar Graphs | 120 |

Surveys and Collecting Data | 121 |

Problem Solving | 122 |

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

*Math.4.MD.C.5*: Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:

Activity | Page |
---|---|

Angles in Real Life | 83 |

Comparing Angles | 84 |

Angles – Right, Obtuse, and Acute | 85 |

Drawing Angles | 86 |

**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 |
---|---|

Comparing Angles | 84 |

Angles – Right, Obtuse, and Acute | 85 |

Drawing Angles | 86 |

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

*Math.4.G.A.3*: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

Activity | Page |
---|---|

Symmetry | 79 |

Paper Folding and Shapes | 103 |

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

*Math.4.G.A.2*: Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

Activity | Page |
---|---|

Shapes | 80 |

Plane Shapes | 81 |

Regular and Irregular Shapes | 82 |

Angles – Right, Obtuse, and Acute | 85 |

Drawing Angles | 86 |

Triangles and Quadrilaterals | 90 |

Polygons | 91 |

**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 |
---|---|

Shapes | 80 |

Plane Shapes | 81 |

Regular and Irregular Shapes | 82 |

Angles in Real Life | 83 |

Comparing Angles | 84 |

Angles – Right, Obtuse, and Acute | 85 |

Drawing Angles | 86 |

Parallel and Perpendicular Lines | 87 |

Triangles and Quadrilaterals | 90 |

Polygons | 91 |

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.