Function machines

The Maths Habit

This machine makes a shape bigger. Then it colours it in. What comes out? What went in?

Make it biggerColour it inInOut??

A big coloured square. A small white star.

4× 28+ 1
Input
The number that goes in.
4× 28+ 19
Output
The number that comes out.
+ 3undoes− 3
× 2undoes÷ 2
Inverse
The step that undoes another step.

Find the output.

5× 210+ 313
1Do the first step.
5× 2=10
2Do the second step.
10+ 3=13

Start at the input. Do the steps in order.

Which step comes first?

2+ 4× 3
× 3+ 4
+ 4: start at the input

Find the output.

3× 412+ 517
1Do the first step.
3× 4=12
2Do the second step.
12+ 5=17

Find the output.

7× 214+ 620
1Do the first step.
7× 2=14
2Do the second step.
14+ 6=20

Find the output.

3× 412+ 517
1Do the first step.
3× 4=12
2Do the second step.
12+ 5=17

Find the output.

6× 530− 327
1Do the first step.
6× 5=30
2Do the second step.
30− 3=27
Remember1Do the first step.2Do the second step.

Find the output.

3× 412+ 517
1Do the first step.
3× 4=12
2Do the second step.
12+ 5=17

Find the output.

2+ 57× 321
1Do the first step.
2+ 5=7
2Do the second step.
7× 3=21
Remember1Do the first step.2Do the second step.

Find the output.

3× 412+ 517
1Do the first step.
3× 4=12
2Do the second step.
12+ 5=17

Find the output.

8× 1080− 773
1Do the first step.
8× 10=80
2Do the second step.
80− 7=73
Remember1Do the first step.2Do the second step.

Find the output.

9× 327+ 128
1Do the first step.
9× 3=27
2Do the second step.
27+ 1=28

Find the output.

4+ 610× 550
1Do the first step.
4+ 6=10
2Do the second step.
10× 5=50

Find the output.

7× 535− 827
1Do the first step.
7× 5=35
2Do the second step.
35− 8=27
Remember1Do the first step.2Do the second step.

  1. What undoes + 6?

    − 6

  2. What undoes − 2?

    + 2

  3. What undoes × 4?

    ÷ 4

  4. What undoes ÷ 5?

    × 5

Find the input.

5× 210+ 313
undo
1Undo the last step.
13− 3=10
2Undo the first step.
10÷ 2=5

Start at the output. Undo the last step first.

Find the input.

7× 321+ 223
undo
1Undo the last step.
23− 2=21
2Undo the first step.
21÷ 3=7

Find the input.

6× 424+ 125
undo
1Undo the last step.
25− 1=24
2Undo the first step.
24÷ 4=6

Find the input.

7× 321+ 223
undo
1Undo the last step.
23− 2=21
2Undo the first step.
21÷ 3=7

Find the input.

7× 535− 233
undo
1Undo the last step.
33+ 2=35
2Undo the first step.
35÷ 5=7
Remember1Undo the last step.2Undo the first step.+ and − undo each other× and ÷ undo each other

Find the input.

7× 321+ 223
undo
1Undo the last step.
23− 2=21
2Undo the first step.
21÷ 3=7

Find the input.

5+ 49× 218
undo
1Undo the last step.
18÷ 2=9
2Undo the first step.
9− 4=5
Remember1Undo the last step.2Undo the first step.+ and − undo each other× and ÷ undo each other

Find the input.

7× 321+ 223
undo
1Undo the last step.
23− 2=21
2Undo the first step.
21÷ 3=7

Find the input.

9× 1090− 585
undo
1Undo the last step.
85+ 5=90
2Undo the first step.
90÷ 10=9
Remember1Undo the last step.2Undo the first step.+ and − undo each other× and ÷ undo each other

Find the input.

4× 28+ 715
undo
1Undo the last step.
15− 7=8
2Undo the first step.
8÷ 2=4

Find the input.

9× 436− 333
undo
1Undo the last step.
33+ 3=36
2Undo the first step.
36÷ 4=9

Find the input.

7+ 18× 540
undo
1Undo the last step.
40÷ 5=8
2Undo the first step.
8− 1=7
Remember1Undo the last step.2Undo the first step.+ and − undo each other× and ÷ undo each other

Function machines worksheet, page 1

Function machines worksheet, page 2

Answer sheet

Is the first undo right? Thumbs up: yes. Thumbs down: no.

  1. × 2 then + 5, output 17   first undo − 5

    Yes

  2. × 3 then − 4, output 20   first undo − 4

    No: + 4

  3. + 3 then × 5, output 25   first undo − 3

    No: ÷ 5

  4. × 5 then + 1, output 41   first undo ÷ 5

    No: − 1

  5. − 3 then × 4, output 28   first undo ÷ 4

    Yes

  1. A machine does × 5 and then one more step. An input of 3 gives an output of 19. What is the missing step?

    + 4

  2. Make your own two step machine. An input of 2 must give an output of 11.

    × 4 then + 3 (one way)

  3. Machine A does + 2 then × 3. Machine B does × 3 then + 2. Put 4 into each one. Do you get the same output?

    No: 18 and 14

  1. 8 → × 3 → + 4 → ? Find the output. Step 1 is given: 8 × 3 = 24.

    28

  2. ? → × 5 → + 2 → 42 Find the input.

    8

  3. I think of a number. I multiply it by 4. Then I take away 1. I get 27. What is my number? Show your steps.

    7
Exit tickets to print