Understanding function machines for 11+ maths
21 October 2026
What is a function machine
A function machine is a simple way to show how a number changes when you follow a set of steps. Each step is a mathematical operation, such as adding, subtracting, multiplying or dividing.
Children see these in 11+ exams as diagrams, short stories or tables. Understanding how to work through the machine is key for reasoning questions.
Why function machines matter for 11+
Function machines are a core topic in 11+ maths, especially for GL and CEM style tests. They help children practise following instructions, spotting patterns and using logical thinking. These skills are tested in many 11+ reasoning questions.
How to work through a function machine
Start with the input number. Follow each operation in the order given.
Check your working at each step. If you make a mistake early on, it affects the final answer.
If you are given the output and need to find the input, work backwards using the opposite operation at each step.
Worked example
Step 1: Start with an input number, for example 5.
Step 2: The machine adds 3. 5 + 3 = 8
Step 3: The machine then multiplies by 4. 8 × 4 = 32
The correct answer is 32.
Using inverse operations to work backwards
If you know the output and need to find the input, reverse each step in the opposite order. For example, if the output is 32:
First, divide by 4: 32 ÷ 4 = 8
Then, subtract 3: 8 - 3 = 5
So the original input was 5.
Key insight: Understanding the order of operations and how to use inverse operations is essential for success with function machines. Encourage your child to check each step carefully and practise working both forwards and backwards.
Summary and reassurance
Function machines are a useful tool for building reasoning skills in 11+ maths. With regular practice, children can become confident in following steps and reversing them when needed.
Supporting your child with function machines helps them tackle a wide range of 11+ questions with greater confidence.
