Function Machine

We built a function machine and the kids figured out how it processed numbers.

This may look like an ordinary Triscuit box, but it's actually complex machine. Notice the input arrow labeled (x) and the output arrow labeled f(x). The kids put numbers into the machine, the numbers are processed and the answers are written on the backs of the small slips of paper. The kids then are challenged to figure out what the machine is doing.

The kids are free to put any number into the machine. When it comes out they make a table showing their inputs and outputs. Once the machine has processed several numbers, a graph is usually prepared to add a visual clue as to what the machine is doing.

Sometimes they need a little help organizing their data so they can better see what's happening to the numbers.

Decoding the function machine is an excellent exercise in logic skills and math. Each day the function machine is reprogrammed and therefore processes information differently.

Here are some ways the machine can process data;

Add 3 to a number
Input   Output
2             5
11          14
201        203

Subtract 10 from a number
Input     Output
1              -9
33            -23
109          99

Round to the nearest 10
Input      Output
12            10
9              10
24            20
48            50

Multiply by 5
Input      Output
4               20
20             100
-3              -15
-100         -500

Divide by 3 and give the remainder
Input     Output
10             1
8               2
6               0
100           1

This method of learning math by figuring out what is happening is critical for some children like my son. For him, there's no comparison to the function machine.


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