# Day 15: Area and the Pythagorean Theorem

So we are now on second semester! The final exams were pretty good. Second semester actually has no proofs, but I don’t mention that to the kids.

As it is second semester, I lose a few kids that were only taking the first semester to replace 1st semester’s grade and I gain some new students who are replacing second semester’s grade. Because of this, I wanted a good group activity to get the new students acclimated. I saw Sarah’s post on the game “31-derful” and decided to try this out. I loved it and was amazed at how the kids were actually all engaged in solving it with their group for the entire time. It took most groups around 30 minutes to complete and the last group finished in 45 after listening to some strategies that were shared. About 20 minutes in, I had one student from each group come into a huddle with me and we shot off some ideas for getting the rows and columns to work. This definitely gave some groups a push. A few were still doing guess-and-check, but this gave them an idea of how they could work a little more efficiently. I loved that at the end, we had all different sets of 31 and we had groups that used wildly different strategies. Here are some pictures:

Next, we got into our first unit of the new semester – Area. This starts with the formulas for the area of a rectangle, triangle, parallelogram, trapezoid, and rhombus/kite. We talk about where these formulas come from and do a lot of examples. We then get into the Pythagorean Theorem and its converse and some special right triangles. I showed the best video about how knowledge of the Pythagorean Theorem and isosceles triangles makes you sound really smart, even if you have no idea what you’re talking about: Wizard of Oz. I then gave the class the last hour to do the Wheel of Theodorus. I have never done it before, but I saw a coworker’s results when she did it and I just couldn’t pass up the chance. I told them to finish for homework. I’m excited to see how they turn out.

L’annee est au mi-chemin!