Numbers go into the machine on the left and come out changed on the right.
The machine does the same thing to every number. This rule is hidden.
Find a row where both numbers are shown. That row tells you the rule.
Write the rule in the machine's window and use it to fill all the gaps.
Example: the machine turns 3 into 5. So the rule is + 2.
If a number is missing on the right, calculate forwards. If one is missing on the left, calculate backwards.
Example
For parents
What does this exercise practice?
Working out a hidden rule from examples and applying it forwards and backwards. This is functional thinking in miniature, a first step toward terms and functions.
Common pitfalls
Children keep calculating forwards when the input is missing instead of working backwards. It helps to say both directions out loud on the complete row: in with + 2, out with − 2.
How to practice at home
Play machine. One of you thinks of a rule, the other calls out numbers and hears the result. Whoever guesses the rule gets to be the next machine.
Related: Rule houses, Spot the Mistake