The Four Triangle Problem

Last week my students worked hard to solve a Marilyn Burns (a highly respected Mathematical Educator)  lesson called The Four Triangle Problem.

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".

After the students have had a full block to make the shapes, I ask the groups to volunteer to bring up the shapes.   I glue them onto a blank piece of chart paper.   As I glue them I am classifying the shapes but do not share my sorting rule with the class until the end of the lesson.   Usually at that point one of the students has caught onto to what I am doing and volunteers to tell the class.   The above chart was the one the students constructed this year.