Function machines for 11+ GL & CEM: a parent's guide to practice
19 October 2026
What are function machines
Function machines are a way of showing how a number changes as it passes through a series of operations. Each 'machine' performs a single step, such as adding 3 or multiplying by 2. In 11+ maths, children are often asked to work out what comes out of the machine, what went in, or even what the machine does.
Why function machines matter in the 11+
Function machine questions appear in both GL and CEM style 11+ exams. They test calculation skills, logical thinking, and the ability to follow a sequence of steps. Understanding these helps children build confidence for harder algebra later on.
Typical function machine questions
Your child might see a diagram with boxes and arrows, a sentence describing the steps, or a table showing input and output numbers. For example: 'A number goes into the machine. It is multiplied by 4, then 3 is subtracted. What is the output if the input is 5?' Sometimes, the question gives the output and asks for the input, or asks what operation each box performs.
Supporting your child at home
Encourage your child to write down each step, rather than working it out in their head. Practise both directions: input to output, and output back to input (the inverse). Use everyday numbers to make up your own function machine chains together, or refer to structured practice designed for the 11+.
Key insight: Step-by-step working helps avoid mistakes
Children often slip up by doing steps in the wrong order or skipping a part. Remind them to tackle each operation one at a time, writing down the result after every step. This builds accuracy and confidence.
