4 Triangles Exploration

This exploration comes from Marilyn Burns, and it goes very nicely with her book, The Greedy Triangle.  

In this exploration, small groups work together to see how many polygons they can make with four triangles. The trick is:  the construction of the polygons must follow a specific rule.

To get started, put your students in pairs or groups of three.  The students will need a large paper on which to place their findings. Students must use all four triangles to create their polygons.  The easiest way is to use post it notes and cut them diagonally to form congruent triangles.  You might want to give them two different colors of post it notes so that each polygon they form has two triangles of two different colors.  (The colors just help to make the lines between the triangles more distinguishable.)

As far as the rules, you might want to show them some that don't follow the rules and some that do and see if they can figure out the rules.   

 These two do not follow the rule.

This one follows the rule.

Here is the rule that their 4-triangles must follow:

Sides that touch must be the same length and match up exactly

As students make polygons that match this rule, have them tape onto their paper.  The goal is for them to find as many polygons as they can.  (There are 14).  

Be sure to build in time to have a discussion about what shapes were formed.  Consider taking the time to sort them and have the students decide what rule you used to sort them.  This end of exploration discussion is key to the students making sense of the exploration by talking about it, and it gives you more time to infuse more vocabulary into the lesson!

What do they think would happen if you gave them five triangles?  How would that change the number of polygons?

Possible ways to sort:  number of sides, types of angles, lines of symmetry, convex/concave, perimeter... Do your students know why you can't sort them by area?

Give this exploration a try and let me know what you think--better yet: What your students think!!