A function machine takes a number in, does something to it, and sends a new number out. This one has a two-step rule: first multiply, then add. To find the output, put the input through both steps in order. For In 8 with the rule × 2 + 1: first 8 × 2 = 16, then 16 + 1 = 17, so Out is 17. Always do the steps in the order the machine shows them, and remember to do BOTH — the multiply and the add.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- input
- the number that goes into the machine
- output
- the number that comes out
- rule
- what the machine does to the input
Worked examples
Rule × 2 + 1, In 8
- 1.8 × 2 = 16.
- 2.16 + 1 = 17.
= 17
Rule × 3 + 2, In 4
- 1.4 × 3 = 12.
- 2.12 + 2 = 14.
= 14
Rule × 2 + 5, In 6
- 1.6 × 2 = 12.
- 2.12 + 5 = 17.
= 17
For parents
Method: Draw the rule as two boxes in a row.
What to say: Ask 'what does the first box do?' then 'now what does the second box do?'
Common mistakes:
- Doing only the × and forgetting the + (In 8 → 16).
- Adding first then multiplying, which changes the answer.