Georgia 7.NR.1.5
The Standard
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
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 rewrite subtraction as adding the opposite. They reorder and regroup addends, make zero pairs, and split rational numbers into useful parts to calculate efficiently.
What Mastery Looks Like
- Students accurately calculate with positive and negative integers, fractions, and decimals. They can show why a chosen reorder, regrouping, zero pair, or number split keeps the expression equivalent.
Common Misconceptions
- Students may treat subtraction as commutative and swap terms without changing signs. They may also change the wrong sign when rewriting subtraction or assume any two negative signs make a positive.
How to Assess It
- Exit ticket: Evaluate -3.5 - 2.25 + 5.75, rewrite the subtraction as addition, show a useful regrouping, and label the property used.
Lesson moves
Ways to Teach It
Give groups signed fraction cards; students arrange them into zero pairs and compatible sums, then record the matching equation.
Ask students to explain why 6.8 - 2.3 + 3.2 can be rewritten as 6.8 + 3.2 + (-2.3).
Play Property Match with expression cards, equivalent regrouped forms, property names, and answer cards; students collect complete sets.
Use a mock bank ledger; students group deposits and withdrawals in convenient ways to find and explain the ending balance.
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Related Standards
- 1.NR.2.7
Apply properties of operations as strategies to solve addition and subtraction problem situations within 20.
- 7.NR.1.9
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
- 2.NR.2
Apply multiple part-whole strategies, properties of operations and place value understanding to solve real-life, mathematical problems involving addition and su...
- 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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