Today is rung 9 of 16 on this topic
Multiplying and dividing with fractions
Can do: Multiplies fractions, and divides a whole number by a unit fraction, understanding why the answer grows.
Why it matters
It overturns the deepest assumption in a child's maths: that multiplying makes bigger. Meeting that head-on prevents years of confusion.
What it looks like when it's wobbly
"Multiplying made it smaller — I must have done it wrong." And division by a fraction is pure guesswork.
⏱️ Two-minute check
"1/2 × 1/3? And how many quarters are in 3?"
Solid looks like: 1/6, and 12 — ideally explained rather than computed by a rule.
The full activity for this topic · 20 minutes
Half of a Third
- 1Fold a paper into thirds one way and halves the other. The overlap is one sixth, visibly.
- 2Say the language: "of" means multiply. Half of a third.
- 3For division, ask the question in words: how many quarter-pieces fit inside 3 whole ones?
- 4Draw it: three circles cut into quarters. Count them. Twelve.
- 5Now show that 3 ÷ 1/4 and 3 × 4 give the same answer, and ask why that makes sense.
If it's too hard
Unit fractions only, always with a drawing.
If it's too easy
Divide a fraction by a fraction, and explain in words rather than by the flip-and-multiply rule.
Say this
"How many quarters fit in three whole ones? Draw it — don't reach for a rule yet."