Reasoning · Grade 3-1 Applying Fractions
Problem
Two thirds went, so the 200 won left is one third — 600 won before.
Spending two-thirds leaves one-third, so the leftover is one of three equal parts - triple it to rebuild the whole.
3.NF.A.1Work BackwardsSpending two thirds leaves one third behind, so tripling the leftover rebuilds what there was before the purchase.
The money was cut into three equal shares, two were spent and one stayed, so the leftover is one of three identical parts.
Multiplying by three undoes the sharing into three, so tripling walks the calculation backwards to the amount before spending.
The step before also spent two thirds: 600 × 3 = 1800.
Same idea again: two-thirds gone means one-third stays, so the 600 is one part of three.
3.NF.A.1Work BackwardsThe first step spent a half: 1800 × 2 = 3600.
Half spent leaves half, so the leftover 1800 is one of two equal halves - double it for the whole.
3.NF.A.1Work BackwardsUndoing all three, she began with 3600 won.
Chaining the three reverse steps lands us back at the original pile of money.
3.OA.D.8Work BackwardsStart from the 200 won at the end and undo each spend - 'two-thirds gone means one-third left' - so it only needs Grade 3 fraction sense!