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P4–P5–P6 Units and parts

Today’s problem — free all day, every step. Every day has one.

Four volunteers collected recyclable cans for a school drive.

Four volunteers collected recyclable cans for a school drive. Aiden collected 15 fewer cans than Mei. Farah collected 4 times as many cans as Mei. Devi collected 20 fewer cans than Farah. Altogether the four volunteers collected 265 cans. How many cans did Devi collect?

One step of the worked solution to Four volunteers collected recyclable cans for a school drive., drawn in pencil.
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The pattern behind it: Units and parts

Cut one amount into equal shares. One number tells you what a share is worth.

In this one. Write everyone in Mei-units, then add back the fixed shortages 15 and 20 so the total becomes exactly 10 equal units.

In allone share

How to spot it

A single amount is split by a ratio, a fraction or a percentage. One extra number gives you the leftover, the difference, or the value of one share.

Common mistake

Children match the given number to the wrong number of shares, using the whole bar when the number covers only the leftover or the difference between two people's shares.

Try one like it

Standard Class trip savings — four classmates Four classmates saved money for a class trip. Liam saved $15 less than Sara. Priya saved twice as much as Sara. Tom saved $9 less …
All 11 with this pattern →

The 33 problem patterns

All 33 patterns, one to a page — the 19 behind Primary 5 and 6 word problems, and the skills the younger years are built on. The bar model, how to spot it in the question, and the mistake children make. A booklet you can print. Free.

A PDF, and a note when new solutions go up.