## Mathematics

### Domain - Operations and Algebraic Thinking, Grade 3

Represent and solve problems involving multiplication and division.

Math.3.OA.A.1: Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7.

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Represent and solve problems involving multiplication and division.

Math.3.OA.A.2: Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of  shares or a number of groups can be expressed as 56 ÷ 8.

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Represent and solve problems involving multiplication and division.

Math.3.OA.A.4: Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = _ ÷ 3, 6 × 6 = ?

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Represent and solve problems involving multiplication and division.

Math.3.OA.A.3: Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

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Understand properties of multiplication and the relationship between multiplication and division.

Math.3.OA.B.6: Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8.

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Understand properties of multiplication and the relationship between multiplication and division.

Math.3.OA.B.5: Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

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Multiply and divide within 100.

Math.3.OA.C.7: Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.

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Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Math.3.OA.D.8: Solve two-step word problems using the four operations. 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.(This standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order).

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Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Math.3.OA.D.9: Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

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### Domain - Number and Operations in Base Ten, Grade 3

Use place value understanding and properties of operations to perform multi-digit arithmetic.4

Math.3.NBT.A.2: Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

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Use place value understanding and properties of operations to perform multi-digit arithmetic.4

Math.3.NBT.A.3: Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations.

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### Domain - Number and Operations-Fractions, Grade 3

Develop understanding of fractions as numbers.

Math.3.NF.A.2: Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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Develop understanding of fractions as numbers.

Math.3.NF.A.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

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Develop understanding of fractions as numbers.

Math.3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

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### Domain - Measurement and Data, Grade 3

Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Math.3.MD.A.1: Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

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Represent and interpret data.

Math.3.MD.B.4: Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

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Represent and interpret data.

Math.3.MD.B.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.

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

Math.3.MD.C.6: Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

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

Math.3.MD.C.7: Relate area to the operations of multiplication and addition.

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

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

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Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Math.3.MD.D.8: Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.

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### Domain - Geometry, Grade 3

Reason with shapes and their attributes.

Math.3.G.A.2: Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

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Reason with shapes and their attributes.

Math.3.G.A.1: Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

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