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Graph paper can be used to work through Problems C1-C9. If using the spreadsheet program to create the graphs, only use the data for the first six figures (or fill in the in-between entries in the table). Large jumps in inputs cause the spreadsheet graphs to distort and look less like parabolas. Since there are only a few data points for each, it might be just as easy to graph them by hand.
If you have trouble coming up with a rule for the triangular numbers, remember that the triangles you are building look a lot like the staircases built in a previous session. (In fact, the pattern is exactly the same.)
Groups: To wrap up this part, discuss how tables were filled in, particularly how missing inputs were found when given an output. Also compare rules. Some people will likely have come up with closed-form rules and others with rules like "add the previous output and the current input" (for triangular numbers). They might even have extended patterns like these:
<< back to Part C: Figurate Numbers
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