How many pieces?

More ways into this idea

• Make it a gameHow Many Fit?Count the pieces into the wholes — then spot which question you were asked
• Test yourselfA fresh mixed set, whenever you likeExplanations after every question. Nothing is recorded.

Common sticking points

• The big one is expecting division to make things smaller. 4 divided by one third is 12 — and that is not a trick. The 12 counts thirds, and twelve thirds is still exactly four wholes.
• Another is reading 1/3 as if it were 3, so 4 ÷ 1/3 becomes 4 ÷ 3. One third is smaller than one, not bigger than three.
• A third is mixing up the two questions, because 4 × 1/3 and 4 ÷ 1/3 use the same two numbers. One asks how much four one-thirds come to; the other asks how many one-thirds fit inside four wholes.

Try this together

Take something you can cut into equal parts — a sandwich, a sheet of paper, a bar of chocolate. Ask two questions and write both answers down. First: if I take one third four times, how much have I got? Then: how many thirds are in these four whole ones? The surprise is that the second answer is bigger than what you started with — and that nothing was ever added.

1–5 minutes, no materials to buy, nothing to hand in.

Ontario curriculum details

• B2.8Multiply and divide whole numbers by unit fractions, using drawings

Plain-language summaries. See the full curriculum for every expectation and the official source.