# Arizona Mathematics Standards — Grade 3

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#### 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.

#### 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.

#### 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.

#### 3.MD.A.1a

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., representing the problem on a number line diagram).

#### 3.MD.A.1b

Solve word problems involving money through \$20.00, using symbols \$, ".", .

#### 3.MD.A.2

Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). (Excludes compound units such as cm 3 and finding the geometric volume of a container.) Add, subtract, multiply, or divide to solve one? step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem. Excludes multiplicative comparison problems.

#### 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.

#### 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.

#### 3.MD.C.5

Understand area as an attribute of plane figures and understand concepts of area measurement.

#### 3.MD.C.5.a

A square with side length 1 unit, called a unit square, is said to have one square unit of area, and can be used to measure area.

#### 3.MD.C.5.b

A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

#### 3.MD.C.5a

Recognize area as an attribute of plane figures and understand concepts of area measurement.

#### 3.MD.C.6

Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

#### 3.MD.C.7

Relate area to the operations of multiplication and addition.

#### 3.MD.C.7.a

Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.

#### 3.MD.C.7.b

Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real-world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

#### 3.MD.C.7.c

Use tiling to show that the area of a rectangle with whole-number side lengths a and b + c is the sum of a b and a c. Use area models to represent the distributive property in mathematical reasoning.

#### 3.MD.C.7.d

Understand that rectilinear figures can be decomposed into non-overlapping rectangles and that the sum of the areas of these rectangles is identical to the area of the original rectilinear figure. Apply this technique to solve problems in real-world contexts.

#### 3.MD.C.7a

Relate area to the operations of multiplication and addition.

#### 3.MD.C.8

Solve real-world and mathematical problems involving perimeters of plane figures and areas of rectangles, including finding the perimeter given the side lengths, finding an unknown side length. Represent rectangles with the same perimeter and different areas or with the same area and different perimeters.

#### 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.

#### 3.NBT.A.1

Use place value understanding to round whole numbers to the nearest 10 or 100.

#### 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.

#### 3.NBT.A.3

Multiply one?digit whole numbers by multiples of 10 in the range 1090 (e.g., 9 80, 5 60) using strategies based on place value and properties of operations.

#### 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

#### 3.NF.A.2

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

#### 3.NF.A.2.a

Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Understand that each part has size 1/b and that the end point of the part based at 0 locates the number 1/b on the number line.

#### 3.NF.A.2.b

Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Understand that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line including values greater than 1.

#### 3.NF.A.2.c

Understand a fraction 1/b as a special type of fraction that can be referred to as a unit fraction (e.g. 1/2, 1/4).

#### 3.NF.A.2a

Understand a fraction as a number on the number line; represent fractions on a number line diagram.

#### 3.NF.A.3

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

#### 3.NF.A.3.a

Understand two fractions as equivalent if they have the same relative size compared to 1 whole.

#### 3.NF.A.3.b

Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent.

#### 3.NF.A.3.c

Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers.

#### 3.NF.A.3.d

Compare two fractions with the same numerator or the same denominator by reasoning about their size. Understand that comparisons are valid only when the two fractions refer to the same whole. Record results of comparisons with the symbols &gt;, =, or &lt;, and justify conclusions.

#### 3.NF.A.3a

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size

#### 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

#### 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.

#### 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.

#### 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 x = 48, 5 = ÷ 3, 6 x 6 = .

#### 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 = ?.

#### 3.OA.B.5

Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.) 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 of multiplication.)

#### 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.

#### 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 3, know from memory all products of two one?digit numbers.

#### 3.OA.D.10

When solving problems, assess the reasonableness of answers using mental computation and estimation strategies including rounding.

#### 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 (Order of Operations).

#### 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.