All About Triangles

I'm creating this blog to help tie together the blogs that my students are creating about their triangle investigations. I've been thinking a lot lately about how math in classrooms has very little to do with what mathematicians actually do (which is to create and investigate their own questions). I also know that my students always surprise and amaze me when I give them open ended projects. So, this is a bit of an experiment to see what they can come up with.

Here are the instructions I gave them:

Overview: In this project you will investigate relationships between the sides and angles of right triangles and communicate with your teacher and your classmates about your investigations and discoveries.

Questions: you will begin your investigation by looking at one or more of the following questions:

-We have discovered that there are patterns that appear in the lengths of right triangles with the angles 30-60-90 and with the angles 45-45-90. Are there any other angle combinations that show similar patterns?

-Pythagorean triples are right triangles that have integer side lengths. How many of these are there? Can you predict when they will occur?

-If you know the side lengths of a right triangle, can you predict what the angles will be?

-If you take a right triangle, and change one side length, how does that change the other side lengths? How does that change the angles of the triangle?

Students are also required to create and investigate at least one original question. Their first blog entry is due Tuesday, but a few have already posted, which has whet my appetite to see more of what they come up with.