TroveTools

Function Machine

Calculation · Year 2–Year 6

A number goes in, the rule is applied, the answer comes out. Or run it backwards.

About the function machine

A machine with a rule on the front. Press Go and the left arm lifts the number into the hopper, the machine clunks, its cogs turn and it puffs smoke from the chimney, and the right arm lifts the answer out. The answer stays covered until you show it, so the class has the length of the run to work it out.

Inverse runs the same machine backwards. The answer goes in on the right, the plate turns + 30 into − 30, and the number you started with comes out on the left. It is the same two numbers both ways round, which is the whole idea of an inverse: taking away undoes adding and dividing undoes multiplying.

Guess the rule covers the plate instead. Feed a number in, see what comes out, feed another, and the pairs build up in a table beside the machine. One pair is not enough to be sure: 3 in and 6 out could be add 3 or times 2, and the second number is what tells you.

The rules are one step: add or take away up to 100, or multiply or divide by 2 to 12. Every machine gives a whole number. A take-away machine never goes below nought, and a division machine only takes numbers that divide exactly.

The machine makes a noise as it works. Turn the sound off with the Sound button and everything still happens on the board.

How to use it on your whiteboard

  1. 1Press Go, or tap the number on the left, and ask the class what will come out.
  2. 2Tap Show answer on the machine, or Answer on the toolbar, to uncover it.
  3. 3Press Inverse to run it backwards, and Go again.
  4. 4Press New for another machine with the same operation, or set the rule and the number yourself under Numbers.
  5. 5For Guess the rule, feed numbers in with Go and Next number, then ask the class for the rule before pressing Rule.

Questions

What is a function machine?
A way of drawing a rule. A number goes in, the machine does one thing to it, and a number comes out. It is how a lot of schemes introduce inverse operations and, later on, simple algebra: the rule is the start of what will one day be written as y = x + 30.
Can I set my own rule and number?
Yes. Open Numbers on the toolbar to choose the operation, the number in the rule and the number going in. New draws a fresh machine with the same operation if you would rather not choose.
Why does the second number matter on Guess the rule?
Because more than one rule fits a single pair. 4 in and 8 out is add 4 and it is also times 2. A second pair rules one of them out, and asking the class which number to try next is a good question in itself.
Does it work without sound?
Yes. The sound goes along with what the machine does on the board and never carries anything on its own. Turn it off with the Sound button, and if your computer is set to reduce motion the answer simply appears.
Do I need an account?
No. Trove Tools is free with no login, no subscription and no limits.