Properties of Operations
3rd Grade


Alabama Course of Study Standards:
5

Develop and apply properties of operations as strategies to multiply and divide. 
Arkansas Academic Standards:
3.OA.B.5

Apply properties of operations as strategies to multiply and divide
For example: 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).
Note: Students are not required to use formal terms for these properties. 
Arizona  K12 Academic Standards:
3.OA.B.5

Apply properties of operations as strategies to multiply and divide. Properties include commutative and associative properties of multiplication and the distributive property. (Students do not need to use the formal terms for these properties.) 
Common Core State Standards:
Math.3.OA.5 or 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.) 
Georgia Standards of Excellence (GSE):
3.PAR.3.4

Use the meaning of the equal sign to determine whether expressions involving addition, subtraction, and multiplication are equivalent. 
Massachusetts Curriculum Frameworks:
3.OA.B.5

Apply properties of operations to multiply.^{14}
For example: When multiplying numbers order does not matter. If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known (Commutative property of multiplication); The product 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); When multiplying two numbers either number can be decomposed and multiplied; one can find 8 x 7 by knowing that 7 = 5 + 2 and that 8 × 5 = 40 and 8 × 2 = 16, resulting in 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56 (Distributive property); When a number is multiplied by 1 the result is the same number (Identity property of 1 for multiplication). 
New York State Next Generation Learning Standards:
3.OA.5

Apply properties of operations as strategies to multiply and divide. Note: Students need not use formal terms for these properties. e.g., 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) Note:A variety of representations can be used when applying the properties of operations, which may or may not include parentheses. The area model (NY3.MD.7c) is a multiplication/division strategy that applies the distributive property (NY3.OA.5) 
Ohio's Learning Standards:
3.OA.5

Apply properties of operations as strategies to multiply and divide. For example, 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). Students need not use formal terms for these properties. 
Tennessee Academic Standards:
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 solved by (3 × 5) × 2 or 3 × (5 × 2) (Associative property of multiplication). One way to find 8 × 7 is by using 8 × (5 + 2) = (8 × 5) + (8 × 2). By knowing that 8 × 5 = 40 and 8 × 2 = 16, then 8 × 7 = 40 + 16 = 56 (Distributive property of multiplication over addition). 
Wisconsin Academic Standards:
3.OA.B.4

Apply properties of operations as strategies to multiply and divide. Student use of the formal terms for these properties is not necessary. 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.) 
Alabama Course of Study Standards:
6

Use the relationship between multiplication and division to represent division as an equation with an unknown
factor. 
Arkansas Academic Standards:
3.OA.B.6

Understand division as an unknownfactor problem
For example: Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
Arizona  K12 Academic Standards:
3.OA.B.6

Understand division as an unknownfactor problem (e.g., find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8). 
Common Core State Standards:
Math.3.OA.6 or 3.OA.B.6

Understand division as an unknownfactor problem. For example, find
32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
Mississippi College and CareerReadiness Standards:
3.OA.6

Understand division as an unknownfactor problem, where a remainder does not exist. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
North Carolina  Standard Course of Study:
3.OA.6

Solve an unknownfactor problem, by using division strategies and/or changing it to a multiplication problem. 
New York State Next Generation Learning Standards:
3.OA.6

Understand division as an unknownfactor problem. e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
Tennessee Academic Standards:
3.OA.B.6

Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
Wisconsin Academic Standards:
3.OA.B.5

Understand division as an unknownfactor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 
Pennsylvania Core Standards:
CC.2.2.3.A.2

Understand properties of multiplication and the relationship between multiplication and division. 
Pennsylvania Core Standards:
M03.BO.2.1.1

Apply the commutative property of multiplication (not identification or definition of the property). 
Pennsylvania Core Standards:
M03.BO.2.1.2

Apply the associative property of multiplication (not identification or definition of the property). 
Pennsylvania Core Standards:
M03.BO.2.2.1

Interpret and/or model division as a multiplication equation with an unknown factor. 
Florida  Benchmarks for Excellent Student Thinking:
MA.3.AR.1.1

Apply the distributive property to multiply a onedigit number and twodigit number. Apply properties of multiplication to find a product of onedigit whole numbers. 
Florida  Benchmarks for Excellent Student Thinking:
MA.3.AR.2.3

Determine the unknown whole number in a multiplication or division equation, relating three whole numbers, with the unknown in any position. 
