Georgia 7.NR.1.4
The Standard
Show and explain subtraction of rational numbers as adding the additive inverse, p − q − p + (−q). Show that the distance between two rational numbers on the number line is the absolute value of their difference and apply this principle in contextual situations.
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 addition of the opposite and use number lines to explain why it works. They find distances between rational numbers and apply those distances to situations such as temperature or elevation.
What Mastery Looks Like
- A student can explain why 3 - (-5) equals 3 + 5 using opposites and a number line. Given two rational numbers, the student finds their nonnegative distance and interprets it in context.
Common Misconceptions
- Students may treat subtracting a negative as subtracting a positive. They may report a negative distance or add the absolute values of both numbers. Some reverse subtraction incorrectly when rewriting it as addition.
How to Assess It
- Ask: “A diver is at -6 meters and a fish is at 4 meters. How far apart are they? Rewrite the subtraction as addition and explain.”
Lesson moves
Ways to Teach It
Place rational number cards on a floor number line, then have students measure distances and rewrite each subtraction using the opposite.
Ask students to explain why subtracting -4 has the same effect as adding 4, using words, symbols, and a number line.
Play a matching game with cards showing subtraction expressions, equivalent addition expressions, and number-line diagrams.
Compare temperatures, elevations, or account balances by finding the absolute value of each pair’s difference.
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Related Standards
- 7.NR.1.3
Represent addition and subtraction with rational numbers on a horizontal or a vertical number line diagram to solve authentic problems.
- 6.NR.3.5
Explain the absolute value of a rational number as its distance from zero on the number line; interpret absolute value as distance for a positive or negative qu...
- 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
- 7.NR.1.2
Show and explain p + q as the number located a distance ∣q∣ from p, in the positive or negative direction, depending on whether q is positive or negative. Inter...
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