NY Next Generation Math NY-7.NS.2.a
The Standard
Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use operation properties, especially the distributive property, to justify rules for multiplying signed numbers. They interpret signed products in real-world situations.
What Mastery Looks Like
- The student uses the distributive property to support that (-1)(-1) = 1. The student describes a negative product as repeated change in an appropriate context.
Common Misconceptions
- Students may memorize same-sign and different-sign rules without understanding them. They may confuse a negative factor with subtraction or create a context that does not match both signs.
How to Assess It
- Ask students to use 0 = (-3)(2 + -2) to justify the sign of (-3)(-2), then describe a matching context.
Lesson moves
Ways to Teach It
Build a table of signed products and use distributive-property patterns to extend through zero.
Ask students how the distributive property forces a negative times a negative to be positive.
Play context-product match with repeated gains, repeated losses, and reversed directions.
Represent repeated changes in debt, elevation, or temperature with signed multiplication expressions.
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Printable NY-7.NS.2.a Worksheet
A ready-to-print activity worksheet aligned to NY-7.NS.2.a, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- NY-7.NS.2.c
Apply properties of operations as strategies to multiply and divide rational numbers.
- NY-7.EE.1
Add, subtract, factor, and expand linear expressions with rational coefficients by applying the properties of operations.
- NY-7.NS.2
Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
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