Today’s problem — free all day, every step. Every day has one.
Ivan and Helen — half his money
Ivan gave half of his money to Helen. He then spent $18 and was left with $12. How much money did Ivan have at first?
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The pattern behind it: Working backwards
You know how it ended. Undo each step, last one first.
In this one. Undo the story backwards: the $18 he spent and the $12 he was left with go back together to rebuild the half he kept, and one half doubles to the whole.
How to spot it
The question gives the final amount after a sequence of changes and asks what the amount was 'at first' or 'to begin with'.
Common mistake
Children undo the steps in the same order they happened rather than in reverse, or forget that a percentage profit is added to the cost price, so the final price is 120% of it, not 100%.
Try one like it
Standard Mrs Lim's withdrawal — half to her son Mrs Lim withdrew some money from the bank. She gave half of it to her son for his tuition fees. She then spent $24 on groceries an…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.