Cogito
Grade 7 Math · Chapter 5 · Lesson 1
Why a Negative Times a Negative Is Positive
A pattern that has to keep going.
10 problems · about 19 minutes · 7.NS.A.2
What this lesson teaches
The child explains why the product of two negative numbers is positive.
- A positive times a negative is negative.
- A negative times a negative is positive.
- The reason is that the pattern must keep going.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Signed Fractions and Decimals: −3.5 + 1.25 = ?
Answer -2.25
Why −2.25.
Review — The Additive Inverse: −5 − (−8) = ?
Answer 3
Why 3.
Warm Up
Straightforward practice. Get the method working first.
4 problems(−9) × (−3) = ?
Answer 27
Why 27.
Why is a negative times a negative positive?
Answer Any other answer would break the pattern.
Why Consistency with the pattern forces it.
(−3) × (−5) = ?
Answer 15
Why Both negative.
(−8) × 2 = ?
Answer -16
Why One negative.
Build It Up
The same ideas with more to keep track of.
2 problems(−36) ÷ (−4) = ?
Answer 9
Why Division follows the same signs.
20 ÷ (−5) = ?
Answer -4
Why One negative.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Product: (−4) × (−6) = ?
Answer 24
Why 24.
The Other Product: (−7) × 3 = ?
Answer -21
Why −21.