7.NS.A.1b 7th Grade The Number System

Adding Integers

Understand addition of rational numbers; a number and its opposite sum to zero, and sums can be shown on a number line.

How to explain it

Students add integers with the same and different signs using absolute value reasoning (SUMS) and the number-line jump model, recognize that opposites sum to zero, and apply properties of operations as strategies for multi-addend sums in real-world contexts.

The anchor students hold onto: SUMS: Same signs add · Unlike signs subtract · Magnitude keeps the sign · Sum of opposites is 0.

Where this leads next, students will subtract integers by rewriting each difference as adding the opposite — the same number-line and sign reasoning you used here carries straight over to that skill.

Worked examples

Example 1 Same Signs

−4 + (−9)

Step 1Same signs (both −)

Step 2Add: 4 + 9 = 13

Step 3Keep the sign: −

Step 4A: −13

Answer−13

Example 2 Unlike Signs

−12 + 5

Step 1Unlike signs

Step 2Subtract: 12 − 5 = 7

Step 3|−12| > |5| → negative

Step 4A: −7

Answer−7

Common mistakes

What students write Added |values| on unlike signs: −9 + 5 → 9 + 5 = 14, so −14

The fix Unlike signs subtract: 9−5=4; |−9|>|5| gives −4

Try this Jamal says −9 + 5 = −14. Find his mistake, then show the correct sum using the SUMS rules.

What students write Correct subtraction, wrong sign: 11 − 4 = 7, so answer is 7

The fix |−11| > |4|, so the answer must be negative: −11 + 4 = −7

Try this Keisha says −11 + 4 = 7. Her subtraction 11 − 4 = 7 is correct, but her answer is wrong. Explain why, and give the correct sum.

Teacher tip

Head off the two predictable errors before they happen. First: Unlike signs subtract: 9−5=4; |−9|>|5| gives −4 Second: |−11| > |4|, so the answer must be negative: −11 + 4 = −7