Maryland Math 7.NOS.A.2.a
The Standard
- 7.NOS.A.2
- Multiply and divide rational numbers using multiple strategies and representations.
Model multiplication of rational numbers using number lines, arrays, or area models to show how properties of operations (e.g., the distributive property) lead to rules for signed number multiplication, including (−1) × (−1) = 1.
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 show products of signed numbers on a number line, in an array, or with an area model. They use the distributive property to explain why multiplying two negative numbers gives a positive result.
What Mastery Looks Like
- A student can place (-2) × 2, (-2) × 1, (-2) × 0, and (-2) × (-1) on a number line and explain the pattern. They can use 0 = (-2) × (1 + (-1)) to prove that (-2) × (-1) = 2.
Common Misconceptions
- Some students say (-2) × (-3) = -6 because they see negative signs. Others add the factors and get -5. Some continue a number line pattern correctly but cannot explain why it works.
How to Assess It
- Give this exit ticket: Complete 0 = (-1) × (1 + (-1)) = -1 + [(-1) × (-1)]. What must (-1) × (-1) equal? Mark the result on a number line.
Lesson moves
Ways to Teach It
Tape a number line to desks and have students place cards for (-1) × 2, (-1) × 1, (-1) × 0, and (-1) × (-1).
Ask, “If (-1) × (1 + (-1)) = 0, what must (-1) × (-1) equal, and why?”
Play product match: pair factor cards like (-2) × (-3) with number-line points and equations that prove the products.
Reverse three $4 charges on a mock bank statement, then mark the $12 change on a number line as (-3) × (-4).
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Printable 7.NOS.A.2.a Worksheet
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Related Standards
- 7.NOS.A.2
Multiply and divide rational numbers using multiple strategies and representations.
- 4.NOS.B.5.d
Represent and explain the computation by connecting rectangular arrays, area models, and/or equations to the meaning of multiplication.
- 7.NOS.A.1.b
Model the addition of rational numbers as movement along a number line, where the direction and distance depend on the sign and magnitude of the addend. Show th...
- 7.NOS.A.2.c
Use properties of operations to multiply and divide rational numbers flexibly and efficiently.
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