11+ Maths: Understanding Function Machines (GL & CEM style)
21 October 2026
What are function machines
Function machines are a way of showing how a number changes as it passes through one or more mathematical operations. They are a common feature in 11+ GL and CEM style maths exams.
Why function machines matter
Understanding function machines helps children build confidence with number operations, spot patterns, and solve problems step by step. These skills are tested in many 11+ questions.
How function machines work
Each function machine has an input, one or more operations, and an output. Children are asked to find the output from a given input, or work backwards to find the input from the output.
Worked example
Start with the number 5.
First operation: multiply by 4.
Second operation: add 3.
Step 1: 5 × 4 = 20
Step 2: 20 + 3 = 23
The correct answer is 23.
Key insight: Practise working both forwards and backwards through function machines. Encourage your child to use inverse operations (like subtracting instead of adding) to check their answers and solve for missing inputs.
