A Part
of a Part

Multiplying a fraction by a fraction

Week 7 · Day 1 CG Quarter 1 · competency 8 45 minutes

Three quick ones

6 × 4	= 24
12 × 3	= 36
20 × 5	= 100

When you multiply, what happens to the number?

You said:

Multiplying makes it bigger

Teacher — do not correct this

Leave it on the board for the next forty minutes. It comes down at 0:33, crossed out by a learner's own hand.

12 × 12 = ?

Do not work it out. Predict.

Bigger than a half — or smaller?

Hands up. Count them.

Bigger

__

Smaller

__

Not sure

__

One of those groups is wrong. In twenty minutes you are going to prove it — not me.

One whole sheet. Fold it in half.

shaded one way = ½

first fraction

Now fold the other way. Shade again.

half again — but half of what?

first second both

Count the pieces.

1 piece of 4

12 × 12 = 14

A quarter. Smaller than a half.

Half of a third

2 columns × 3 rows = 6 pieces

12 × 13 = 16

Two questions, every single time

1. Is ⅙ smaller than ½?   Yes.
2. Is ⅙ smaller than ⅓?   Yes.

Smaller than both.

Together: ⅔ × ½

2 pieces of 6

23 × 12 = 26 = 13

Always give the simplest form.

Does the order matter?

⅔ × ½

½ × ⅔

Same picture, turned. Same answer: ⅓.

Your turn — fold, shade, count

Fold this	Then this	Pieces	Both marks	Product
½	½	4	1	¼
½	⅓	6	1	⅙
⅔	½	6	2	⅓
¾	½	8	3	⅜
⅔	¾	12	6	½

Ask every learner this — and only this

“Is your answer smaller than both the fractions you started with?”

Multiplying makes it bigger

↓

Multiplying by a number less than one makes it smaller.
A part of a part is smaller than both.

Tonight's question — do not answer it

Nobody folded a sheet into twenty pieces today. What if I asked you for ⅗ × ¾?

Exit ticket

¾ × ½

1. Before you work it out — will the answer be smaller than ¾? Smaller than ½?
2. Now find it.
3. In one sentence: why?

Quarter sheet of paper. Write your name at the top. Question 3 is the one that counts.