Sunday, January 8, 2012

Proving the Pythagorean Theorem

Even though, the math team didn't officially meet this week, but the 7th grade teacher, Molly, and I spent some time proving the Pythagorean Theorem.  She mentioned that she wanted her 7th graders to be able to come up with the Pythagorean Theorem on their own and asked if we could work on some ideas together.  I of course said yes!

She started off by asking me how I had taught it in the past, and I admitted that I had never really given my students the chance to explore the Pythagorean Theorem.  Looking at past lessons, I always told my students what the theorem was, and then we talked about it, but they had never discovered it on their own.  I did mention how one year, I had my students work in pairs on a mini-lab that explored the areas of squares and how they relate to the Pythagorean theorem.  Molly shared her idea that she wanted to use colored squares and have her students outline a right triangle and then compare the areas of the squares.  I shared that during my mini-lab, I had students create a 3x3, 4x4, and 5x5 square on graph paper and then (1) find the area of each square, (2) how are the squares of the sides related to the areas of the squares, (3) find the sum of the areas of the two smaller squares.  How does the sum compare to the area of the larger square, and finally (4) use grid paper to cut out three squares with sides 5, 12, and 13 units.  Form a right triangle with these squares.  Compare the sum of the areas of the two smaller squares with the area of the larger square.

As we talked, we got out some colored squares and graph paper, and began playing around with the Theorem.  We created different sized right triangles and manipulating the squares to see show how the area of the square of the legs would always equal the area of the square of the hypotenuse.  We started off approaching the Pythagorean Theorem as teachers, but very quickly found ourselves talking about the math behind the famous theorem.

After we had explored and talked for almost an hour, I suggested to Molly that we look at the Connected Math: Looking for Pythagoras ( book for some other possible ideas to teach her students, as well as the NLVM Pythagorean Puzzles (

(To be continued...)

What am I learning about collaboration?   
After working with Molly this week I learned that collaborative professional development doesn't have to be something formal... it can happen between two teachers to want to explore something together.  I also learned  that it helps to stop approaching things "as a teacher" sometimes, and to to just play around with the math and see what happens.  It was great getting the chance to work with Molly one on one this week and I am inspired to keep this action research going. 


  1. Hi Anna,
    I agree that professional development doesn't have to be something formal! It sounds like you had a terrific collegial experience. I got the sense from reading this section that you and Molly had a very balanced exchange - no one seemed to be "the director". I think it enhances not only this collaboration but also the desire to continue this type of sharing. I like that you not only explored the Pythagorean Theorem together but also accessed additional resources that could enhance your work with students. Super! Sharing resources can be incredibly valuable.

  2. Anna, acknowledging to Molly that you hadn’t given your students the chance to explore the Pythagorean Theorem is a huge step in creating a meaningful collaboration with Molly. Now you’re not the expert whom she came to for help. Now you’re colleagues figuring it out together! How wonderful for both of you!

    And yes, I love your awareness that collaboration doesn’t have to be a planned experience. By being open to exploring with Molly, you’re nurturing a superb foundation for continued collaboration.

    You wrote that it helps to stop approaching things “as a teacher.” What do you mean by that? Do you mean that you think you should know everything or that everything you learn has to have some student connection or else it’s not worthy of your time? I’m curious about what you actually mean by this statement…

    So happy that you’re inspired by your research! You know that just thrills me to read that!