The note
How schools teach it now
Function machines are used from Year 3 onwards. To work backwards, children reverse the order and use the inverse of each step: + becomes −, × becomes ÷.
5-minute kitchen-table activity
Be a machine: your child says a number, you secretly double it and add 1, and say the answer. They guess your rule. Swap roles. Then ask: 'My machine gave 21. What went in?' (10.)
Worked example
A machine multiplies by 4, then subtracts 3. The output is 33. What was the input?
- Work backwards. Undo − 3 by adding 3: 33 + 3 = 36.
- Undo × 4 by dividing by 4: 36 ÷ 4 = 9.
- Check forwards: 9 × 4 − 3 = 33.
Answer: 9
Common mistakes to watch for
- Undoing the steps in the same order instead of reverse order.
- Using the same operation instead of the inverse.
- Not checking by running the answer forwards.
Encouragement
- Try saying
- “Can you run the machine backwards?”
- Rather than
- “Guess and hope for the best.”