Function Machines Practice for 11+ Maths: GL & CEM Style Explained
21 October 2026
What are function machines
Function machines are a way of showing how numbers change when they pass through a series of mathematical steps. Each step is a simple operation, like adding, subtracting, multiplying or dividing. These questions appear often in the 11+ Maths exam, especially in GL and CEM style papers.
Why function machines matter for 11+
Understanding function machines helps children recognise patterns and build confidence with algebra. Practising these problems prepares them for both straightforward and multi-step reasoning questions.
Step-by-step example
Let's work through a function machine with two steps:
Input: 5 Step 1: Multiply by 4 Step 2: Add 3
First step: multiply by 4
Start with the input number, which is 5. Multiply 5 by 4.
5 × 4 = 20
Second step: add 3
Take the result from the first step, which is 20. Add 3 to this number.
20 + 3 = 23
The final answer
The output of the function machine is 23. This means if you put 5 into this machine, 23 comes out at the end.
Key insight: Practising function machines strengthens a child's algebraic thinking and problem-solving skills. It encourages them to break down problems into clear steps, which is vital for 11+ success.
