Work out which two gears turn these numbers into those numbers.
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.
Step 1. Deduce the gears. Drag gears into the machine so every ticket comes out right.
Step 2. Run it. New number going in. Predict the output BEFORE you pull the lever.
What to say if they get stuck
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.
How use a term rule differs from the skills beside it
The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: use an algebraic rule to calculate a named sequence term, and it stops where rule is supplied.
Apply one arithmetic mapping to a letter or number code. One invariant rule only.
Questions parents ask about use a term rule
Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.
Use an algebraic rule to calculate a named sequence term. It is one of 55 named maths skills in the 11+, in the algebra strand, and this page carries 1 interactive exercise that practises it.
The two steps are not interchangeable: multiplying after the second step gives a different value. The wrong answers on this skill are built out of that, not out of random numbers, so it is worth naming out loud before your child meets it under time pressure.
Point at the next move rather than explaining the whole rule. Do the multiplication first and the addition second - check the rule on one of the rows in the table before you use it.
The skill map draws the line here: Rule is supplied. A question past that line is testing a different named maths skill, which is worth knowing before you spend a week practising the wrong one.
The algebra strand holds 2 skills that are tested together, and the page next to use a term rule is evaluate an algebraic expression. Each has its own exercise and its own link, and none of them needs an account.
Use Function Machine, embedded on this page. It is the exercise the skill map attaches to use a term rule, it runs in the browser with no account to make, nothing is scored, and nothing a child does here is recorded or sent anywhere. It also has its own link, so you can send it to a child without sending them anywhere else first.
Knowing which maths topic to practise is most of the work
A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.
