Learn the 3-Step Method
1Follow the arrows forward.
Do the operations in order: 5 → ×2 → 10 → +3 → 13.
2Backwards: undo in reverse.
Output 13? Undo +3 first (−3 → 10), then undo ×2 (÷2 → 5).
3Each operation has an inverse.
+ ↔ − and × ↔ ÷. Undoing means using the inverse.
Worked Example
A machine does ×3 then −2. The output is 19. What was the input?
Watch Out! Common Mistakes
Reverse the order! Undo the LAST step first: +2, then ÷3 → 7.
Inverse! ×3 is undone by ÷3; +2 is undone by −2.
Ten seconds! Push your answer through forwards: 7 → ×3 → 21 → −2 → 19 ✓. If it doesn’t match, re-do the undo.
⬇ Cheat Sheet
- Forward: apply operations in order.
- Backward: inverse operations, reverse order.
- + ↔ − and × ↔ ÷.
- Always check by running forwards.
📖 Continue Your Journey
Quick summary
- Forward: apply each operation in order.
- Backward: use inverse operations in REVERSE order.
- Addition undoes subtraction; multiplication undoes division.
- Check every backwards answer by running it forwards.
Frequently asked questions
What is a function machine?
A diagram where a number enters, operations are applied in order (like ×2 then +3), and the result comes out. It's the friendly front-end of algebra.
How do you find the input from the output?
Undo the operations with their inverses in reverse order: for ×3 then −2 with output 19, add 2 (21) then divide by 3 (7).
Why must the order reverse when working backwards?
Like undressing in reverse of dressing — the last thing done must be the first thing undone, or the operations tangle.
Continue your child's learning journey
with the MindBlaze app.
Fun daily learning missions for children. Clear progress insights for parents — helping every child start secondary school ready to learn.
