Understanding Function Machines for 11 Plus Maths
21 October 2026
What is a function machine
A function machine is a simple way to show how a number changes as it passes through one or more steps. Each step does something to the number, such as adding, subtracting, multiplying or dividing.
Why function machines matter in 11 plus maths
Function machines appear often in 11+ GL and CEM style exams. They help children practise following instructions, applying operations in the correct order, and spotting patterns.
Key insight: Function machines build early algebra skills
Learning to work with function machines helps children get ready for algebra. They learn to follow a sequence of operations and understand how to reverse them using inverse operations.
Worked example
Let's say the function machine has two steps. First, multiply by 4. Then, add 3.
Input number: 5
Step 1: 5 × 4 = 20
Step 2: 20 + 3 = 23
The correct answer is 23.
Tips for tackling function machine questions
Remind your child to work through each step in order, writing down each answer before moving to the next. If the question gives the output and asks for the input, work backwards using the opposite (inverse) operation at each stage.
Common mistakes to avoid
Children can sometimes mix up the order of operations or forget to apply each step separately. Encourage your child to check their work and use rough notes for each stage.
