Input–output machines and sequence rules
A number goes into a machine and another comes out. Find what the machine does, then find the rule of a number sequence.
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Guide
This studio follows function machines (Years 3–6) and sequence rules (Year 6). A machine does the same thing to every number that goes in, for example "add 7".
The input is on the left and the output on the right. When we know the output and want the input, we run the machine backwards: instead of adding 7, we subtract 7.
In a two-step machine the order matters: first step one, then step two. To go backwards, start with the last step.
A sequence can be made from the number before (term-to-term, e.g. "double it") or from the position (position-to-term, e.g. "3 × position + 2"). The second kind lets you find the 20th term without writing all the others.
Ask "how do you know?" A rule must work for every row, not just one.