Working Backward Word Problems

Rather than following a situation forward, children run it backward from the result to find the starting amount. For situations where an amount increased and for situations where it decreased, finding the size of the change and finding the starting amount are combined so that one consistent line of reasoning takes hold.

Reading a situation such as I was given 3 more and now have 12 as an addition, and answering 12 + 3 = 15, is common. The assumption that an increase means addition pushes every answer to the high side. The same assumption works in reverse for decreases, where subtracting anyway leaves the number too small.

The assumption held so far, that turning the situation straight into an expression gives the answer, breaks down here. A new way of reading is needed, tracing back from a number after an increase or a decrease to find the original amount, and this way of reading, used all the way through Order and Position Word Problems, keeps being used in Various Word Problems in grade 3, where several calculations are combined.