NY Next Generation Math NY-3.OA.5

Math3rd GradeUnderstand properties of multiplication and the relationship between multiplication and division.

The Standard

Apply properties of operations as strategies to multiply and divide.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students use operation properties to make multiplication and division easier. They break apart or regroup factors and connect related calculations.
What Mastery Looks Like: The student solves 7 times 8 as 7 times 5 plus 7 times 3 and explains the distributive property. The student uses commutative and associative reasoning appropriately.
Common Misconceptions: Students may distribute to only one part or change the value while regrouping. They may assume division is commutative because multiplication is commutative.
How to Assess It: Ask students to solve 6 times 8 by breaking apart 8 and writing each step. Then ask whether 24 divided by 6 equals 6 divided by 24.

Lesson moves

Build a 7-by-8 array and split it into two smaller rectangles to show a distributive strategy.
Ask students which operation properties can turn 3 times 5 times 2 into an easier calculation.
Play Strategy Match by pairing products with equivalent decomposed expressions.
Rearrange equal rows of chairs to show why changing factor order keeps the total unchanged.

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