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Marbles — Priya and Zara swap shares
Priya and Zara had a total of 160 marbles. Priya gave of her marbles to Zara. Zara then gave of her marbles to Priya. In the end, each of them had the same number of marbles. How many marbles did each of them have at first?
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The pattern behind it: Constant total
Money moves between two people, so their total never changes.
In this one. Keep the total fixed at 160, use the equal ending to get 80 each, then undo the two gifts one at a time in reverse order.
How to spot it
One person gives, sells or loses an amount to the other, and nobody outside the two people gains or loses anything.
Common mistake
Children draw different totals before and after, or forget that moving an amount from one person to the other changes the gap between them by twice that amount.
Try one like it
Challenging Pebbles — Ali and Ben end up equal Ali and Ben had a total of 100 pebbles. Ali gave 2/7 of his pebbles to Ben. Ben then gave 1/6 of his pebbles to Ali. In the end, e…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.
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