11+ Maths: Understanding Function Machines (GL & CEM style)
21 October 2026
What are function machines
Function machines are a way to show how numbers change when you use different operations. They are often used in 11+ maths to test understanding of sequences of steps, such as adding, multiplying or subtracting.
Why function machines matter for 11+
In GL and CEM 11+ exams, children need to follow a series of operations and find either the output or the missing input. This skill helps with algebra and problem solving later on.
Worked example: two-step function machine
Suppose a function machine multiplies a number by 3, then adds 4.
Step 1: Start with the input 5
Step 2: 5 × 3 = 15
Step 3: 15 + 4 = 19
The correct answer is 19.
Common 11+ style questions
Children may be asked to find the output, work backwards to find the input, or spot the missing operation. Practising these different types helps build confidence for the exam.
Tips for parents
Encourage your child to draw the function machine as a diagram, breaking down each step. Use simple numbers at first, then try harder examples. Talk through each stage to check understanding.
Key insight: Function machines help children understand how numbers change through a sequence of operations, building essential skills for 11+ maths.
