11+ Maths: Understanding Function Machines (GL & CEM style)
19 October 2026
What are function machines
Function machines are a way of showing how numbers can be changed by a series of operations, like adding, subtracting, multiplying, or dividing. In 11+ maths, your child may see these as diagrams or step-by-step instructions, especially in GL and CEM style questions.
How function machines appear in GL and CEM
GL questions often present function machines as a clear sequence of steps, sometimes in a flowchart. CEM style might use word problems or less structured formats, where your child must spot and follow the operations hidden in the question.
Helping your child approach function machine problems
Encourage your child to write down each step as they go, rather than trying to remember every operation in their head. For example, if the question says 'multiply by 2, then add 5', jot down the result after each part before moving to the next. This helps to avoid mistakes, especially when more than two steps are involved.
Working backwards and inverse operations
Some questions may give the output and ask for the input. In these cases, your child will need to use inverse operations in reverse order. Practising both forwards and backwards helps build confidence for both GL and CEM styles.
Key insight: Function machines build the foundation for algebra, as children learn to apply rules to numbers and, later, to unknowns. Mastering these helps with reasoning and problem-solving across the 11+ curriculum.
Tips for calm practice at home
Use simple examples first, then gradually add more steps or mix up the order of operations. Discuss with your child how each operation changes the number, and encourage them to check their answer by working through the steps again.
