What Are Function Machines? A Simple Guide for Parents & Teachers

Feed a number in, turn the handle, and out pops a new number. That's the whole idea behind a function machine — one of the friendliest ways to introduce children to functions, rules, and the 'undo' thinking that algebra is built on. Here's what function machines are and how to use them.

How a function machine works

A function machine has three parts: an input, a rule, and an output. The rule is a single operation — something like × 3, + 5, − 2, or ÷ 4. You put a number in, the machine applies the rule, and the result comes out the other side.

With the rule × 3: put in 2, get 6; put in 5, get 15. The rule never changes, which is exactly what makes it a function — the same input always gives the same output.

Working backwards

The real power shows up when you run the machine in reverse. If the rule is × 3 and the output is 21, what went in? You undo the rule — divide by 3 — to get 7. If the rule is + 5 and the output is 12, you subtract 5 to find 7.

That 'undo' move is the heart of inverse operations: division undoes multiplication, subtraction undoes addition. Practising it in a function machine is the same skill children later use to solve equations.

Ways to use function machines

• Forward practice: give the rule and inputs, find the outputs.
• Backward practice: give the rule and outputs, find the inputs.
• Mix both in one machine so children decide whether to apply or undo the rule.
• For a challenge, hide the rule and give input–output pairs so they work out the rule itself.

Make your own function machine worksheets

Our function machine generator builds machines with clear rules and an IN → OUT table, including some rows that run backwards. Choose addition & subtraction or multiplication & division, play online with instant ✓ feedback and a celebration when every machine is solved, or download a printable PDF with the answer key. It's free, prints sharply in black and white, and needs no signup.