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
Subtract 10 from a number
Round to the nearest 10
Multiply by 5
Divide by 3 and give the remainder
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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