Cogito
Grade 7 Math · Chapter 5 · Lesson 3
Why Two Negatives Make a Positive
Not a rule to memorise — a pattern that has to continue.
10 problems · about 19 minutes · 7.NS.A.2
What this lesson teaches
The child explains why (−1)(−1) = 1 by continuing a multiplication pattern.
- Continuing a multiplication pattern forces (−1)(−1) = 1.
- An even number of negative factors gives a positive product.
- An odd number of them gives a negative product.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Rational Numbers in Problems: −4 + 5 × (−3) = ?
Answer -19
Why −19.
Review — Why a Negative Times a Negative Is Positive: (−9) × (−3) = ?
Answer 27
Why 27.
Review — Signed Fractions and Decimals: −3.5 + 1.25 = ?
Answer -2.25
Why −2.25.
Warm Up
Straightforward practice. Get the method working first.
3 problems(−6) × (−4) = ?
Answer 24
Why 24.
(−3) × (−6) = ?
Answer 18
Why Two negatives.
(−7) × 3 = ?
Answer -21
Why One negative.
Build It Up
The same ideas with more to keep track of.
2 problems(−2) × (−2) × (−2) = ?
Answer -8
Why Three negatives.
(−1) × (−1) × (−1) × (−1) = ?
Answer 1
Why An even count of negatives.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Product: What is (−4) × (−5)?
Answer 20
Why 20.
The Mixed Signs: What is (−4) × 5?
Answer -20
Why −20.