Cogito
Grade 3 Math · Chapter 1 · Lesson 9
Multiplying by 0 and 1
Two special cases that trip people up.
10 problems · about 11 minutes · 3.OA.B.5, 3.OA.C.7
What this lesson teaches
The child multiplies and divides by 0 and 1 and explains why the answers are what they are.
- Multiplying by 1 leaves a number alone.
- Multiplying by 0 always gives 0.
- Reading it as "groups of" explains both.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Multiplying and Dividing by 3 and 4: 8 × 3 = ?
Answer 24
Why 8 × 3 = 24.
Review — Dividing by 2, 5, and 10: 40 ÷ 5 = ?
Answer 8
Why 8 × 5 = 40.
Warm Up
Straightforward practice. Get the method working first.
4 problems7 × 0 = ?
Answer 0
Why Seven lots of nothing is nothing.
Why does 6 × 1 = 6?
Answer It is one group of 6.
Why One group of six is six.
8 × 1 = ?
Answer 8
Why One group of 8.
8 × 0 = ?
Answer 0
Why Eight empty groups.
Build It Up
The same ideas with more to keep track of.
2 problems0 × 6 = ?
Answer 0
Why No groups at all.
9 ÷ 1 = ?
Answer 9
Why Shared between one person.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsEmpty Plates: 5 plates have no biscuits on them. How many biscuits are there?
Answer 0 biscuits
Why Five lots of nothing is nothing.
One Bag: One bag holds 9 marbles. How many marbles in all?
Answer 9 marbles
Why One group of 9 is 9.