7.NS.A.2a 7th Grade The Number System

Multiplying Integers

Understand multiplication of rational numbers by extending the properties of operations, including the rules for multiplying signed numbers.

How to explain it

Students multiply integers by multiplying absolute values and applying the sign rules (same signs positive, different signs negative), model a positive count of negative groups as repeated jumps on the number line, justify why a negative times a negative is positive using number patterns, and interpret integer products in real-world contexts.

The anchor students hold onto: MAPS: Multiply the absolute values · Ask if the signs match · Positive if same · Switch to negative if different.

Where this leads next, students will divide integers using the very same sign rules you applied to multiplication, then extend both operations to all rational numbers across the rest of the strand.

Worked examples

Example 1 Different Signs

(−3) × 4

Step 13 × 4 = 12

Step 2Signs differ → negative

Step 3Four jumps of −3 → −12

Step 4A: −12

Answer−12

Example 2 Same Signs

(−6) × (−4)

Step 16 × 4 = 24

Step 2Same signs → positive

Step 3A: 24

Answer24

Common mistakes

What students write Two negatives make a negative product: (−3) × (−7) = −21

The fix Same signs ALWAYS give a positive product: (−3) × (−7) = +21

Try this Theo says (−3) × (−7) = −21 because "two negatives stay negative." Find his mistake, then show the correct work using MAPS.

What students write The bigger factor sets the sign: (−4) × 7 = +28

The fix The ADDITION rule — products only ask if signs match: −28

Try this Lena says (−4) × 7 = 28 because "7 is bigger than 4, so the answer is positive." Explain her error, then give the correct product.

Teacher tip

Head off the two predictable errors before they happen. First: Same signs ALWAYS give a positive product: (−3) × (−7) = +21 Second: The ADDITION rule — products only ask if signs match: −28