 ## Common Core State Standards (CCSS) Correlations ## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 5

Write and interpret numerical expressions.

Math.5.OA.A.1: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

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Simplifying Expressions 19
Using Parenthesis and Brackets 20
Simplifying Expressions 44
Using Parenthesis and Brackets 45
Simplifying Expressions 69
Using Parenthesis and Brackets 70

### Domain - Number and Operations in Base Ten, Grade 5

Understand the place value system.

Math.5.NBT.A.3: Read, write, and compare decimals to thousandths.

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Interpreting Place Value 13
Interpreting Place Value 38
Interpreting Place Value 63

Understand the place value system.

Math.5.NBT.A.1: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

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Interpreting Place Value 13
Interpreting Place Value 38
Interpreting Place Value 63

Understand the place value system.

Math.5.NBT.A.4: Use place value understanding to round decimals to any place.

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Rounding Decimals 15
Rounding Decimals 40
Rounding Decimals 65

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.5: Fluently multiply multi-digit whole numbers using the standard algorithm.

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Multiplying Multi-digit Numbers 10
Multiplying Multi-digit Numbers 35
Multiplying Multi-digit Numbers 60

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.6: Find whole-number quotients of whole numbers with up to four-digit dividends and two-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.

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Dividing by Two-digit Divisors 11
Dividing by Two-digit Divisors 36
Dividing by Two-digit Divisors 61

Perform operations with multi-digit whole numbers and with decimals to hundredths.

Math.5.NBT.B.7: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Multiplying and Dividing Decimals 17
Multiple-step Problems with Decimals 18
Multiplying and Dividing Decimals 42
Multiple-step Problems with Decimals 43
Multiplying and Dividing Decimals 67
Multiple-step Problems with Decimals 68

### Domain - Understand the place value system., Grade 5

Read, write, and compare decimals to thousandths.

Math.5.NBT.A.3a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

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Reading and Writing Decimals to Thousandths 12
Reading and Writing Decimals to Thousandths 37
Reading and Writing Decimals to Thousandths 62

Read, write, and compare decimals to thousandths.

Math.5.NBT.A.3b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

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Comparing Decimals to Thousandths 14
Comparing Decimals to Thousandths 39
Comparing Decimals to Thousandths 64

### Domain - Number and Operations-Fractions, Grade 5

Use equivalent fractions as a strategy to add and subtract fractions.

Math.5.NF.A.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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Finding Common Denominators 21
Adding and Subtracting Fractions with Unlike Denominators 22
Adding and Subtracting Mixed Numbers 23
Finding Common Denominators 46
Adding and Subtracting Fractions with Unlike Denominators 47
Adding and Subtracting Mixed Numbers 48
Finding Common Denominators 71
Adding and Subtracting Fractions with Unlike Denominators 72
Adding and Subtracting Mixed Numbers 73

Use equivalent fractions as a strategy to add and subtract fractions.

Math.5.NF.A.2: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

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Adding and Subtracting Fractions with Unlike Denominators 22
Adding and Subtracting Mixed Numbers 23
Adding and Subtracting Fractions with Unlike Denominators 47
Adding and Subtracting Mixed Numbers 48
Adding and Subtracting Fractions with Unlike Denominators 72
Adding and Subtracting Mixed Numbers 73

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.6: Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

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Multiplying Fractions 24
Multiplying Fractions and Whole Numbers 25
Multiplying and Dividing Fractions to Solve Word Problems 27
Multiplying Fractions 49
Multiplying Fractions and Whole Numbers 50
Multiplying and Dividing Fractions to Solve Word Problems 52
Multiplying Fractions 74
Multiplying Fractions and Whole Numbers 75
Multiplying and Dividing Fractions to Solve Word Problems 77

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

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Multiplying Fractions 24
Multiplying Fractions and Whole Numbers 25
Multiplying Fractions 49
Multiplying Fractions and Whole Numbers 50
Multiplying Fractions 74
Multiplying Fractions and Whole Numbers 75

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Math.5.NF.B.7: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

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Dividing Fractions and Whole Numbers 26
Dividing Fractions and Whole Numbers 51
Dividing Fractions and Whole Numbers 76

### Domain - Apply and extend previous understandings of multiplication and division to multiply and divide fractions., Grade 5

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

Math.5.NF.B.4b: Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

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Area of Rectangles with Fractional Sides 33
Area of Rectangles with Fractional Sides 58
Area of Rectangles with Fractional Sides 83

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

Math.5.NF.B.7c: Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

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Dividing Fractions and Whole Numbers 26
Multiplying and Dividing Fractions to Solve Word Problems 27
Dividing Fractions and Whole Numbers 51
Multiplying and Dividing Fractions to Solve Word Problems 52
Dividing Fractions and Whole Numbers 76
Multiplying and Dividing Fractions to Solve Word Problems 77

### Domain - Measurement and Data, Grade 5

Convert like measurement units within a given measurement system.

Math.5.MD.A.1: Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

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Converting Measurement Units 28
Converting Measurement Units 53
Converting Measurement Units 78

Represent and interpret data.

Math.5.MD.B.2: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

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Line Plots 30
Line Plots 55
Line Plots 80

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Math.5.MD.C.4: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

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Volume of Solid Figures 31
Volume of Solid Figures 56
Volume of Solid Figures 81

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Math.5.MD.C.3: Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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Volume of Solid Figures 31
Volume of Solid Figures 56
Volume of Solid Figures 81

### Domain - Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition., Grade 5

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.

Math.5.MD.C.5a: Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.

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Volume of Rectangular Prisms 32
Volume of Rectangular Prisms 57
Volume of Rectangular Prisms 82

### Domain - Geometry, Grade 5

Graph points on the coordinate plane to solve real-world and mathematical problems.

Math.5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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Ordered Pairs 29
Ordered Pairs 54
Ordered Pairs 79

Classify two-dimensional figures into categories based on their properties.

Math.5.G.B.3: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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Classifying Two-dimensional Shapes 34
Classifying Two-dimensional Shapes 59
Classifying Two-dimensional Shapes 84