Maths · Function Machines & Inverse
Function Machine
Work out which two gears turn these numbers into those numbers.
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Why this works
A function machine does the same thing to every number that enters it. You found the rule backwards - from the outputs - which is inverse thinking. And the order of the gears is part of the rule: ×3 then +1 turns 2 into 7, while +1 then ×3 turns the same 2 into 9. Same gears, different machine.
Helping a child through Function Machine
It runs in 2 steps
- 1. Deduce the gears. Drag gears into the machine so every ticket comes out right.
- 2. Run it. New number going in. Predict the output BEFORE you pull the lever.
Hints, least revealing first
- Look at 2 → 7 and 4 → 13. When the input goes up by 2, the output jumps by 6. What multiplies by 3?
- Try ×3 first: 2 becomes 6, but the ticket says 7. What tiny gear finishes the job?
- The order of the gears changes the answer. ×3 then +1 gives 7; +1 then ×3 gives 9.
When they finish it: “The machine hums!”
3 11+ skills this exercise practises
Each of these has its own page, with a worked example on it.
- Evaluate an algebraic expressionSubstitute one supplied value and calculate the expression.
- Use a term ruleUse an algebraic rule to calculate a named sequence term.
- Apply a number code ruleApply one arithmetic mapping to a letter or number code.
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