Maryland Math 7.NOS.A.1.c
The Standard
- 7.NOS.A.1
- Add and subtract rational numbers using multiple strategies and representations.
Rewrite subtraction as addition using the additive inverse (p − q = p + (−q)). Use strategies such as number lines and applying absolute value of the difference to determine the distance between two rational numbers and solve problems in context.
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 rewrite subtraction as addition of the opposite, even when the number being subtracted is negative. They use a number line or the absolute value of a difference to find how far apart two rational numbers are.
What Mastery Looks Like
- Given -2.5 and 3, a student writes 3 - (-2.5) = 3 + 2.5 and finds a distance of 5.5. They can explain why the change from 3 to -2.5 is negative, but the distance is positive.
Common Misconceptions
- Students may calculate 3 - (-2) as 1 instead of 5. Some give a negative distance or subtract the numbers' absolute values instead of finding the absolute value of their difference.
How to Assess It
- Exit ticket: A thermometer reading drops from 2.5°C to -3°C. Rewrite the signed change as addition of an opposite, then show the distance between readings on a number line.
Lesson moves
Ways to Teach It
Place -2.5 and 3 on a taped floor number line, walk the gap, and write 3 - (-2.5) as 3 + 2.5.
Have students explain in writing why a change from 2°C to -3°C is negative but the distance between readings is positive.
Deal pairs of signed decimal cards; partners rewrite each subtraction as addition of the opposite, then check distances on a number line.
Compare bank balances of -$12.50 and $8; write the subtraction as addition of the opposite and find the gap.
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Related Standards
- 7.NOS.A.2.b
Interpret quotients of rational numbers in context and represent division of signed numbers in different forms, such as −(p/q) = (−p)/q = p/(−q) when the diviso...
- 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...
- 1.NOS.C.8
Use the inverse relationship between addition and subtraction to subtract.
- 7.NOS.A.1
Add and subtract rational numbers using multiple strategies and representations.
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