Today’s problem — free all day, every step. Every day has one.
Water tank — from three-quarters full to half
A tank was full. After removing 15 litres, it was full. What is the capacity of the tank?
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65 worked examples are free without a code, two from every pattern. No account, either way.
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 both fillings in the same fraction — 1/2 is 2/4 — and the 15 litres stops being a mystery: it is the gap between 3/4 and 2/4, one quarter of the whole tank.
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 …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.