3rd Grade: Operations & Algebraic Thinking (3.OA)
Operations & Algebraic Thinking (3.OA)
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.
Multiplication with groups
Multiplication with groups
START
Multiplication with arrays
Multiplication with arrays
START3.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 using the inverse relationship of multiplication and division. For example, determine the unknown number that makes the equation true in each of the equations, 8 × ? = 48, 5 = □ ÷ 3, 6 × 6 = ?.
Determine unknown number in multiplication equation
Determine unknown number
in multiplication equation
Determine unknown number in division equation
Determine unknown number in division equation
START3.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.)
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.
Understand division as unknown factor problem
Understand division as unknown factor problem
START3.OA.C.7
Fluently multiply and divide within 100, using strategies such as the relationship between
multiplication and division or the properties of operations. (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8)
By the end of Grade 3, know from memory all products of two one-digit numbers.
Multiply within 100
Multiply within 100
START
Divide within 100
Divide within 100
START3.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.
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.
