# Pythagoras Problem Solving Redux

Year 9 and I are working through Pythagoras’ Theorem at the moment. After a little shuffling of units around, this is a little earlier than last year. An interesting consequence of this is that this is the first unit I’ve taught that I’ve blogged about previously.

Getting to go back and see what I did last year has made planning this year’s unit so much easier (which is why I really need to make more of an effort to blog this year). Today I took one of my previous lessons and improved it in the best way possible: by adding Desmos!

(One of my students stated that I’m a little too obsessed with Desmos. I can’t really deny that.)

The task was Problem Solving using Pythagoras. Students were given triangle problems for which they weren’t given all the information to answer the question. I had them go through a process of drawing a diagram, defining variables, choosing values for those variables as an example, and finally defining a general solution using a formula.

My students struggled with the last part a little last year. They seemed to be able to go through the mechanical steps of rearranging formulas, but couldn’t necessarily understand the connection between the formula and the problem, or the reason for finding the formula.

This year, we used Desmos to support finding the formula. For all of Desmos’s graphing awesomeness, it’s easy to forget it works really well as a calculator too. After students solved the problem using their own chosen values, I had them use Desmos to verify their formula agreed produced the same answer:

Firstly, this let students check their working. But also, it let students see the value of defining the formula: by changing the values of the independent variables, they could find their new solution, without going through the process of solving the entire problem all over again.

That image also shows the way I often use Desmos and the IWB together. If the graphing area is not being used, it can serve as empty space for me to draw all over.