On the left, a blue figure with an area of 41 square units, arranged in centered columns 1, 3, 5, 7, 9, 7, 5, 3, 1. On the right, the same figure, imbedded in a 9x9 square, with the same 41 squares in blue, plus 40 green squares (10 in each corner, arranged as stairs 4, 3, 2, 1)

The blue figure removed and the green squares rearranged into columns with heights of 2, 4, 6, 8, 8, 6, 4, 2

I wondered what would happen if we “finished” the square by filling in the corners.

Looking at just the green area, I rearranged the pieces to look similar to the original figure. The figure felt similar, but like an “even” version.

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#MTBoS

Two shapes. On the left, an area of 41 squares. One way to describe them is in 9 vertical columns, with 1 square, 3 squares, 5 squares, 7 squares, 9 squares, then 7, 5, 3, and 1. The figure on the right can be described as a similar figure, rotated 45 degrees, except the columns would be arranged 1, 3, 5, 7, 9, 11, 9, 7, 5, 3, 1.

Last May’s Community of Math Instructors (CAMI) monthly teachers’ circle meeting started with some attention for some fairly simply-structured figures.

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#MTBoS #ITeachMath

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