Function Machines and Formulae: Year 6

Year 6 maths worksheets on function machines and substituting into formulae: 36 questions in three levels (All, Most, Some) with answers. Free PDF.

7-page A4 PDF from the Tiger Shark Education question bank. All: Work out what comes out of a function machine. Most: Work backwards to find the input or a missing step. Some: Substitute a value into an equation. Each level is two pages of six questions, each with a squared working area, and the last page has every answer, with short working for multi-step questions. Each level is also available as its own 3-page PDF. Example questions from the Some level: 2x + y = 8. Use the equation to find y when x = 3 / 3x + y = 14. Use the equation to find y when x = 3.

What are function machines and formulae? A function machine takes an input, applies one or more operations and gives an output. Working backwards with the inverse operations finds the input. Formulae express relationships in algebra, such as perimeter = 2 × (length + width). These ideas form the Year 6 algebra objectives.

Common mistakes and tips: Children often apply the operations in the wrong order or forget to reverse the order when working backwards. Insist that they write each step. With formulae, a common slip is not using brackets correctly or substituting the wrong value. Practising with simple, real formulae (cost = £3 × number of tickets) builds confidence.

Questions on this topic appear year after year in the KS2 maths SATs. Because each sheet starts with the core skill and builds to test-style problems, it works both for teaching the topic and for spotting gaps during revision.

Teaching ideas: use the All level to check prerequisite knowledge at the start of a lesson, then move children onto Most or Some when they are ready. Squared working space encourages neat written methods. The answer page includes short working for multi-step questions, so pupils can self-mark and see where they went wrong.

Spotting misconceptions: the mistakes children make on this topic are usually consistent, so look for patterns across their answers rather than marking each question in isolation. A short follow-up on the specific misconception, using concrete resources or diagrams, is often more effective than setting more of the same questions.

Use All for children working towards the expected standard, Most for secure Year 5 skills and Some for SATs-standard practice: three entry points to the same lesson. Suits whole-class differentiation, intervention groups, homework and SATs revision, and upper KS2 generally.

Part of a set of 42 Year 6 maths topics.