Function machines: forwards and backwards

The Maths Habit Handout to print

This machine changes every shape the same way. What comes out of the third one?
A big star came out. What went in?

A big square. A small star: going backwards, do the opposite.

Input
The number that goes in.
Output
The number that comes out.
Function machine
A machine that does the same thing to every number.
Opposite
The step that undoes it.

inout× 2+ 4inout÷ 2− 4going backwards
  1. Follow the arrows.Do each machine in turn.
  2. Going backwards, do the opposite.Start from what comes out. Undo the last machine first.

What comes out?

7+ 512 12

What comes out?

4× 312 12

What comes out? Follow the arrows. 9

2× 4+ 189

What comes out? Follow the arrows. 24

68+ 2× 324

What comes out? Follow the arrows. 9

2× 4+ 189

What comes out? Follow the arrows. 14

10− 3× 2714

What comes out? Follow the arrows. 9

2× 4+ 189

What comes out? Follow the arrows. 11

315× 5− 411

What comes out? Follow the arrows. 9

2× 4+ 189

What comes out? Follow the arrows. 10

9+ 6− 51510

What comes out? Follow the arrows. 9

2× 4+ 189

What comes out? Follow the arrows. 11

12÷ 3+ 7411

Function machines: forwards and backwards worksheet, page 1

What is the opposite?

+ 6 − 6

What is the opposite?

× 4 ÷ 4

Going backwards, which machine do you undo first?

413× 2+ 58 + 5, the last one

What went in? Going backwards, do the opposite. 5

17× 3+ 2going backwards51551517÷ 3− 2

What went in? Going backwards, do the opposite. 6

20+ 4× 220− 4÷ 2going backwards610610

What went in? Going backwards, do the opposite. 5

17× 3+ 2going backwards51551517÷ 3− 2

What went in? Going backwards, do the opposite. 5

19× 4− 119going backwards520520÷ 4+ 1

Function machines: forwards and backwards worksheet, page 2

Answer sheet

Thumbs up: right. Thumbs down: wrong.

  1. 5 → + 3 → × 2 → 16

    Right

  2. 4 → × 3 → − 2 → 14

    Wrong: 10 comes out

  3. 4 → × 2 → + 1 → 9

    Right

  4. 6 → + 4 → × 2 → 20

    Right

  5. 2 → × 5 → − 5 → 15

    Wrong: 5 comes out

  1. Find two different machines that turn 4 into 12.

    + 8 and × 3

  2. What went in? ? → × 2 → + 3 → × 2 → 26

    5

  3. A number goes through × 2 then − 4 and comes out as itself. What is the number?

    4

  1. What comes out? 6 → + 4 → × 2 → ?. Follow the arrows.

    20

  2. What went in? ? → × 3 → 21. Going backwards, do the opposite.

    7

  3. What went in?
    Going backwards, do the opposite.

    7
    11× 2− 311going backwards
Exit tickets to print