11+ Maths: Understanding Function Machines (GL & CEM style)
21 October 2026
What are function machines
Function machines are a common topic in 11+ Maths exams. They help children practise following a sequence of mathematical operations, step by step.
How function machines work
A function machine is a series of boxes or steps. Each box does one thing to a number. The number goes in, passes through each box, and comes out as a new number. Questions may ask for the output, the input, or the operation inside a box.
Worked example
Let's use a function machine with two steps: first multiply by 3, then add 5.
Start with the input 4.
First step: 4 × 3 = 12
Second step: 12 + 5 = 17
The correct answer is 17.
Key insight: Function machines can work forwards or backwards. If you know the output and need to find the input, work through the steps in reverse. Use the opposite operation for each box.
Tips for parents
Encourage your child to write down each step clearly. Practise both finding outputs and working backwards to find inputs. Use simple numbers at first, then try more challenging values as confidence grows.
