KS2 SATs 2018 — Mathematics Papers 2 & 3: Reasoning

The idea

Some problems tell you the end of a story and ask for the beginning: a number was changed several times, and you only know the final result. Working forwards is hard because the start is missing, so work backwards instead.

Start from the final answer and undo each step, last step first. Undoing means using the inverse operation: undo adding by subtracting, undo subtracting by adding, undo multiplying by dividing, and undo dividing by multiplying.

Write the undoing steps in a clear chain, one step per line, so you do not miss one or undo the same step twice. When you reach the start, test your answer by running the original story forwards — it should finish exactly on the result the question gave you.

Worked example

A number is multiplied by 3, then 14 is added. The result is 50. What was the starting number?

1. Work backwards from 50. Undo adding 14 by subtracting: 50 − 14 = 36.
2. Undo multiplying by 3 by dividing: 36 ÷ 3 = 12.
3. Check forwards: 12 × 3 = 36, and 36 + 14 = 50, which matches.

Answer: 12

Watch out

• Undoing the steps in the same order they happened instead of in reverse.
• Using the same operation instead of its inverse when undoing.