NYSED Grade 3 Draft Updated June 2019
New York State Next Generation Mathematics Learning Standards
Operations and Algebraic Thinking
NYS Next Generation Learning Standard
Understand properties of
multiplication and the
relationship between
multiplication and
division.
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.)
Note: Students need not use formal terms for these properties.
NY-3.OA.5 Apply properties of operations as strategies to multiply
and divide.
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: Students need not use formal terms for these properties.
Note: A variety of representations can be used when applying the
properties of operations, which may or may not include
parentheses.
3.OA.6 Understand division as an unknown-factor
problem. For example, find 32 ÷ 8 by finding the number
that makes 32 when multiplied by 8.
NY-3.OA.6 Understand division as an unknown-factor problem.
e.g., Find 32 ÷ 8 by finding the number that makes 32 when multiplied
by 8.
Multiply and divide
within 100.
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.
NY-3.OA.7a Fluently solve single-digit multiplication and related
divisions, using strategies such as the relationship between
multiplication and division or properties of operations.
e.g., Knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8.
NY-3.OA.7b Know from memory all products of two one-digit
numbers.
Note: Fluency involves a mixture of just knowing some answers,
knowing some answers from patterns, and knowing some answers
from the use of strategies.