Maryland Math 7.NOS.A.2.c
The Standard
- 7.NOS.A.2
- Multiply and divide rational numbers using multiple strategies and representations.
Use properties of operations to multiply and divide rational numbers flexibly and efficiently.
Maryland College and Career Ready Standards for Mathematics (2025) · USE STRUCTURE AND REPRESENTATIONS TO REASON WITH RATIONAL NUMBERS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students multiply and divide positive and negative fractions, decimals, and integers. They use operation properties to find easier steps, and turn division by a nonzero number into multiplication by its reciprocal.
What Mastery Looks Like
- A student spots factors they can cancel before multiplying and keeps track of the result's sign. They can explain why changing the order of factors or breaking apart a product gives the same answer.
Common Misconceptions
- Students may flip the dividend instead of the divisor, or forget to change division to multiplication. They may cancel terms across addition or lose a negative sign.
How to Assess It
- Ask students to compute (-3/4) × (8/9) ÷ (-2/3). Have them show the reciprocal step, cancel factors, and explain why the answer is positive.
Lesson moves
Ways to Teach It
Use cards to build (-3/4) × (8/9) ÷ (-2/3), then replace ÷ (-2/3) with × (-3/2) and cancel factors.
Ask, 'Why can you cancel 3 and 9 in (-3/4) × (8/9), but not in (-3/4) + (8/9)?'
Play a matching game with cards showing -3(1/2 + 1/6), -3/2 - 1/2, and -2; partners explain each match.
A freezer cools 3/4°C each minute; calculate its temperature change after 2 2/3 minutes by canceling factors before multiplying.
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Printable 7.NOS.A.2.c Worksheet
A ready-to-print activity worksheet aligned to 7.NOS.A.2.c, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- 7.NOS.A.2
Multiply and divide rational numbers using multiple strategies and representations.
- 5.NOS.B.7.d
Use properties of operations and/or the inverse relationship between multiplication and division to multiply and divide.
- 5.NOS.B.5.c
Use properties of operations and/or the inverse relationship between multiplication and division to divide.
- 7.NOS.A.3.a
Apply properties of operations to efficiently compute with rational numbers and convert between forms when appropriate to support problem solving.
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