Georgia 7.NR.1.8
The Standard
Represent the multiplication and division of integers using a variety of strategies and interpret products and quotients of rational numbers by describing them based on the relevant situation.
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 model integer multiplication and division with number lines, counters, patterns, or equations. They explain what a rational product or quotient means in a given situation.
What Mastery Looks Like
- Students choose a useful model and calculate signed products and quotients accurately. They label units and explain whether a negative result represents loss, debt, direction, or another change.
Common Misconceptions
- Students may count negative signs without following the order of operations. They may think a negative answer is impossible in context or divide by a fraction's denominator only.
How to Assess It
- Exit ticket: Write and solve an expression for a debt changing by -$7.50 weekly for 4 weeks and a submarine changing -18 meters over 3 minutes. Explain each answer with units.
Lesson moves
Ways to Teach It
Use two-color counters to build four groups of -3, then use zero pairs and reversal to model (-4)(-3).
Ask pairs to write matching contexts for -24 ÷ 6 and -24 ÷ -6, then explain why the signs differ.
Play a card match where students pair rational expressions, answers, and context cards, then justify each sign before keeping the set.
Use a four-day bank fee of $3.25 per day, then calculate the account change and explain the negative product.
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Related Standards
- 3.PAR.3.2
Represent single digit multiplication and division facts using a variety of strategies. Explain the relationship between multiplication and division.
- 7.NR.1.6
Make sense of multiplication of rational numbers using realistic applications.
- 7.NR.1.9
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
- 6.NR.1.2
Multiply and divide any combination of whole numbers, fractions, and mixed numbers using a student-selected strategy. Interpret products and quotients of fracti...
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