NY Next Generation Math NY-7.NS.2.c

Math7th GradeApply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

The Standard

Apply properties of operations as strategies to multiply and divide rational numbers.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students use commutative, associative, distributive, identity, and inverse properties to multiply and divide rational numbers efficiently. They reorganize calculations without changing their value.
What Mastery Looks Like: The student rewrites (-4)(3/5)(-5/6) to pair convenient factors and obtains 2. The student explains which property supports each rearrangement.
Common Misconceptions: Students may use commutativity with division or regroup a quotient as though all operations were multiplication. They may cancel factors across addition or subtraction.
How to Assess It: Ask students to evaluate (-3/7)(14)(-1/6) efficiently and label the properties used to reorder, regroup, and simplify.

Lesson moves

Arrange rational-factor cards physically, then reorder and regroup them to create friendly products.
Ask students why changing division to multiplication by a reciprocal helps properties apply.
Play property strategy match with rational expressions and efficient rewritten forms.
Simplify a chain of signed rates or scale factors by grouping compatible rational factors.

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