## 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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Test 9 13
Test 26 30
Test 27 31
Test 30 34

Analyze patterns and relationships.

Math.5.OA.B.3: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

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Test 6 10
Test 28 32
Test 29 33
Test 45 49

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

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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Test 1 5
Test 2 6
Test 3 7
Test 4 8
Test 5 9
Test 32 36
Test 33 37
Test 40 44
Test 41 45

Understand the place value system.

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

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Test 44 48

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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Test 9 13
Test 10 14
Test 13 17
Test 45 49
Test 46 50
Test 48 52
Test 49 53
Test 50 54
Test 51 55
Test 52 56
Test 53 57
Test 81 85
Test 82 86
Test 83 87
Test 87 91

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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Test 14 18
Test 15 19
Test 16 20
Test 17 21
Test 18 22
Test 19 23
Test 26 30
Test 30 34
Test 31 35
Test 84 88
Test 85 89
Test 86 90
Test 99 103
Test 100 104

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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Test 20 24
Test 21 25
Test 22 26
Test 23 27
Test 24 28
Test 25 29
Test 26 30
Test 43 47
Test 87 91
Test 98 102
Test 100 104

### 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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Test 39 43

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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Test 34 38

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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Test 36 40

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

Math.5.NF.B.3: Interpret a fraction as division of the numerator by the denominator (a/b = a : b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

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Test 47 51

### 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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Test 10 14
Test 79 83
Test 80 84
Test 88 92
Test 89 93

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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Test 48 52
Test 93 97
Test 96 99

### 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.5b: Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

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Test 90 94

### Domain - Geometry, Grade 5

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

Math.5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

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Test 70 74
Test 71 75
Test 73 77

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

Math.5.G.B.4: Classify two-dimensional figures in a hierarchy based on properties.

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Test 54 58
Test 62 66
Test 69 73