11+ Maths: Understanding Function Machines (GL & CEM style)
21 October 2026
Function machines in 11+ reasoning
Function machines are a way of showing how a number changes when you apply one or more mathematical operations. In 11+ reasoning, children are often asked to work out missing numbers or reverse the process to find the starting value.
Key insight: Understanding each step in a function machine helps children build confidence with reasoning and algebra.
Step-by-step approach
Start by looking at each operation in the order it appears. Encourage your child to follow the arrows or steps one at a time, rather than trying to solve everything at once.
When the output is given and the input is missing, work backwards. Reverse each operation in the opposite order.
Worked example
Suppose a function machine multiplies a number by 3, then adds 4. The final answer is 19. What was the starting number?
First, reverse the last step: subtract 4 from 19.
19 - 4 = 15
Next, reverse the first step: divide 15 by 3.
15 ÷ 3 = 5
The correct answer is 5.
Supporting your child
Practise with different function machines, changing the order or type of operations. Use simple numbers at first, then increase the challenge.
Key insight: Talking through each step aloud can help your child spot mistakes and understand the logic behind each operation.
Encouragement for parents
Working through function machines together builds strong reasoning skills. Even a few minutes of practice can make a difference. Celebrate small successes and keep the atmosphere positive.
