Function machines

The Maths Habit Handout to print

I think of a number,
double it and add 1.
Could my answer be 10?

Only from 4.5: whole numbers give odd answers

Input

The number that goes in.

Output

The number that comes out.

Inverse

The operation that undoes another.

Input× 3+ 2Output

Input	Output
4
7

Input+ 3× 2Output

Input	Output
1
4
10

Complete the table.

Input× 3+ 4Output

Input	after × 3	Output
2	6	10
5	15	19
9	27	31

Show why

Complete the table.

Input× 2+ 7Output

Input	after × 2	Output
3		13
6		19
10		27

Complete the table.

Input× 3+ 4Output

Input	after × 3	Output
2		10
5		19
9		31

Complete the table.

Input× 5− 2Output

Input	after × 5	Output
1		3
4		18
8		38

Complete the table.

Input× 3+ 4Output

Input	after × 3	Output
2		10
5		19
9		31

Complete the table.

Input+ 2× 4Output

Input	after + 2	Output
3		20
6		32
11		52

Complete the table.

Input× 3+ 4Output

Input	after × 3	Output
2		10
5		19
9		31

Complete the table.

Input÷ 2+ 5Output

Input	after ÷ 2	Output
4		7
10		10
18		14

Complete the table.

Input× 3+ 4Output

Input	after × 3	Output
2		10
5		19
9		31

Complete the table.

Input× 6− 8Output

Input	after × 6	Output
2		4
5		22
7		34
10		52

The output is 21. Find the input.

Input× 5+ 1Output

InputOutput

Answer sheet

1. One machine adds 3 then multiplies by 2. Another multiplies by 2 then adds 3. Which input gives the same output from both?

   None: they are always 3 apart

2. A machine has two steps. An input of 2 gives 7. An input of 5 gives 16. What are the two steps?

   × 3 then + 1

3. n → − 4 → × 3 → ? Write an expression for the output.

   3(n − 4) or 3n − 12

1. 5 → + 4 → × 3 → ?
   Find the output.

   27

2. ? → × 4 → − 7 → 25
   Find the input.

   8

3. n → + 5 → × 2 → ?
   Write an expression for the output.

   2(n + 5) or 2n + 10

Exit tickets to print