In groups, the students had to find all the possible arrangements using four triangles, two of each colour, and tape together the four-triangle shapes they made. In each arrangement, each triangle must touch the side of at least one other triangle and follow the rule that the sides that touch must be the same length and match exactly.

In my many years of teaching, no one group has ever discovered all 14 non-congruent shapes... that is, until this year. One groups did discover all 14 shapes.

Many of you know I love math but this lesson is one of my favourites. It elicits mathematical language and introduces regular and irregular polygons. As well, students learn the term "congruent" when they see that shapes that can be flipped or rotated to fit exactly onto another shape are actually the same shape or in mathematical language, "congruent".

There are lots of ways to sort this shapes. Have students brainstorm ways the shapes they created are alike and ways they are different. The have your groups sort the shapes by one of the differences. IE some shapes are symmetrical, some aren't and the symmetrical shapes have different numbers of lines of symmetry. Perimeters vary too...Astounding things can happen when you compare these two sortings!

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