Work backwards
- Free
- Grades 5–6
- 4 sections · 4 questions
Work backwards
Four questions, one idea: when the answer is given and the question is missing.
- Answer key on its own page
- Reopen this exact paper
- Letter & A4 ready

The answer key prints on a separate page.
What's on this test
Every other paper on this site assembles the skills of a unit. This one assembles a single idea across four subjects, in the order that idea gets harder. Section 1 states a GCF and an LCM — two facts about two numbers, and neither one names them. Section 2 states an area and a perimeter, which is the same move wearing a shape. Section 3 hands over a DIFFERENCE, and there is nothing to factorize at all until a² − b² = (a + b)(a − b) is remembered — the list has to be created before it can be cut down. Section 4 removes the arithmetic altogether and leaves only clues: nine thousand four-digit numbers, and four relations that between them admit exactly one.
How the paper is put together
One question per section, which is not a typo. A Challenge question's answer is a route the child writes out rather than a number they produce, so three of them fill a page with room to work — and a paper that asked for ten would be asking for stamina instead of thinking. The answer key prints the reasoning for each, because a child who reached the answer by luck and one who reasoned to it deserve different feedback.