My pre-calculus instructor last quarter enjoyed teaching about functions by playing what he called his game. He spoke of inputs, rules and outputs, saying, "I'll give you two and you give me the third."
We would spend a lot of time with sequences, for instance he might present "2, 4, 8, 16, 32" for outputs and we could guess he was talking about the powers of 2 (exponents) and etc. Of course his game was more difficult than this example -- like the Fibonacci series or other things that people with their master in math like but this isn't that bad.
Here then is a derivative on the "game". I will give three outputs (a sequence) and then somebody can guess a number and I'll answer saying, "True" if the next number follows my rule or "False" if it does not.
Here's the first set of 3:
(1, 4, 6)
Now your part is to make a guess about what number or numbers might come next. Together we will build up a set of numbers that follow the rule. The purpose of the guessing is to discover the rule that I'm using. Sounds easy, doesn't it?
We would spend a lot of time with sequences, for instance he might present "2, 4, 8, 16, 32" for outputs and we could guess he was talking about the powers of 2 (exponents) and etc. Of course his game was more difficult than this example -- like the Fibonacci series or other things that people with their master in math like but this isn't that bad.
Here then is a derivative on the "game". I will give three outputs (a sequence) and then somebody can guess a number and I'll answer saying, "True" if the next number follows my rule or "False" if it does not.
Here's the first set of 3:
(1, 4, 6)
Now your part is to make a guess about what number or numbers might come next. Together we will build up a set of numbers that follow the rule. The purpose of the guessing is to discover the rule that I'm using. Sounds easy, doesn't it?
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