Math Forum - Project of the Month

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German Version

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February 1999 Project of the Month

A Counting Exercise

Take a 1x1 square. Count how many squares there are total (duh). Now take a 2x2 square. Count the total number of squares (including the larger one that is formed by the outside of the whole thing). Take a 3x3 square and find the total. How many squares would there be in a 10x10 square? How about an NxN square?

Now do the same thing with triangles - take a look at the pictures below. How many total triangles in a triangle that's 10 units on a side? How about N units?

Make sure you explain your answer thoroughly. The students who submit winning entries to the Project of the Month are rarely the only ones who had the right answer, but they are always the ones who submitted the clearest and most complete explanation.

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