Function Machines and Ratio Problems: Calm Guidance for 11+ Maths
19 October 2026
Understanding function machines
A function machine is a simple way to show how numbers are changed using a rule. You put a number in, the machine follows the rule, and out comes a new number. Function machines help children practise working with operations like addition, subtraction, multiplication, and division in a clear, step-by-step way.
Connecting function machines to ratio
Ratio problems often require more than one step. Function machines can help break down these steps. For example, if a question asks to double a quantity and then divide by three, a function machine can show each stage clearly. This visual approach can make ratio and proportion questions less daunting.
Practical example
Suppose a recipe uses a ratio of 2:3 for flour and sugar. If you want to scale the recipe, you can use a function machine: first multiply the original amount by the scaling factor, then use the ratio to find the new quantities. This helps children see the link between the rule (the function) and the ratio.
Key insight: Function machines help children understand the sequence of actions in ratio problems. By breaking down each step, they support clear thinking and reduce errors when solving multi-step questions.
Supporting your child at home
Encourage your child to draw their own function machines when practising ratio questions. Ask them to explain each stage out loud. This builds confidence and helps them check their work as they go.
Building towards exam questions
GL and CEM 11+ exams often include questions that mix ratio with step-by-step calculations. Practising with function machines at home prepares children for these multi-step problems, making the process feel more manageable.
