Georgia 7.NR.1.9
The Standard
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
Georgia's K-12 Mathematics Standards · Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, percentages, fractions, and decimal numbers).
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students turn a situation into a multiplication or division expression with positive and negative fractions or decimals. They rearrange or regroup multiplication, distribute across sums, and use multiplication to check division.
What Mastery Looks Like
- A student selects an efficient property-based strategy and solves accurately with fractions or decimals. They keep signs and units correct and justify each rewrite using the situation.
Common Misconceptions
- Students may apply same-sign and different-sign rules incorrectly. They may distribute to only one term or assume division can be reordered like multiplication. Some ignore what a negative answer means in the situation.
How to Assess It
- Exit ticket: A diver descends 2.5 meters per minute for 12 minutes. Solve using (-2.5)(10 + 2), name the property, and interpret the sign.
Lesson moves
Ways to Teach It
Give pairs play money and debt slips to model five charges of $2.40, then rewrite the total using the distributive property.
Ask: Why can (-3.5)(8) become (-3.5)(10 - 2), but (-3.5) ÷ 8 cannot be reordered?
Play a matching game with scenario cards, original expressions, equivalent property-based expressions, and solutions with units.
Calculate each person's share when a $42.60 restaurant bill is split six ways, then check the quotient by multiplication.
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Printable 7.NR.1.9 Worksheet
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Related Standards
- 7.NR.1.8
Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them ...
- 7.NR.1.6
Make sense of multiplication of rational numbers using realistic applications.
- 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
- 7.PAR.2.1
Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
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