3.OA. 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.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.)

3.OA.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.

3.OA.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.

3.OA. 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.

Numbers and Operations in Base Ten

3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.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.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.

Numbers and Operations-Fractions

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

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

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Measurement and Data

3.MD.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.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 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.

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

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.

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.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.

Geometry

3.G.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.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 areas and describe the area of each part as ¼ of the area of the shape.

Operations and Algebraic Thinking3.OA. 3Use 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.5Apply 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.)3.OA.7Fluently 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.3.OA.8Solve 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.3.OA. 9Identify 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.Numbers and Operations in Base Ten3.NBT.1Use place value understanding to round whole numbers to the nearest 10 or 100.3.NBT.2Fluently 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.3Multiply 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.Numbers and Operations-Fractions3.NF.1Understand a fraction 1/bas the quantity formed by 1 part when a whole is partitioned intobequal parts; understand a fractiona/bas the quantity formed byaparts of size 1/b.3.NF.2Understand a fraction as a number on the number line; represent fractions on a number line diagram.3.NF.3Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.Measurement and Data3.MD.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.2Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). 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.3.MD.4Generate 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.5Recognize area as an attribute of plane figures and understand concepts of area measurement.nunit squares is said to have an area ofnsquare units.3.MD.8Solve 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.Geometry3.G.1Understand 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.2Partition 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 areas and describe the area of each part as ¼ of the area of the shape.