The smoothies were a success, but they ran over into class-time and so I didn't have the whole period (as I thought I would) to teach. However, I was able to adapt fairly well and the lesson was great. First, I asked them what they knew about the Pythagorean Theorem. Kids started shouting out responses: a^2 + b^2 = c^2, right triangles, finding side lengths, and so on. This allowed me to have some idea of the student's prior knowledge and it made me feel comfortable spending less time lecturing and more time with practice problems. I then proceeded to lead the students through a mini-geometric proof of the Pythagorean Theorem:
If you find the area of the big square (a+b)^2 and then set that equal to the area of the 4 triangles (2ab) plus the area of the small square (c^2), you will get the Pythagorean Theorem! This isn't a formal proof, and you can certainly get more into this, but this was a cool way to show the kids how the theorem works and they thought it was interesting. Next, we did a few practice problems, one that was just a triangle and we found a missing side and one that was a word problem where they had to find the triangle and the missing length. After this introduction, I lead a small partner-up activity. This was my favorite part! It was fun and a little silly, it got the kids to partner up with someone random, and then they used their partner for the next activity. Here's how it works: I made a list of pairs...
Then, I cut the slips up, put them in a bowl, and had students draw a slip. Then, they had to go find their pair! It was wonderful watching the class clown pull out the "Angelina Jolie" slip, sighing, and saying, "Okay...where's Brad?" I thought this was a great activity, and sometimes, as a teacher, you have to do something to keep the class fun and amusing.
Once everyone found their partner, they got to work on a worksheet that had practice problems. They had to work with triangles, word problems, and then they had to create their own word problem for a partner to solve and then they had to check their work. Getting students to take their knowledge, understand it, and then use it was my goal here and I thought this worksheet helped to make it a success.
My feelings about today were reaffirmed later in my Methods class where we learned the importance of having students create and how this inspires high-ordered knowledge processes and critical thinking. Creating helps students develop mathematical literacy and allows them to have a sense of agency about their work.
My last day was a huge success and it made me feel really great about how far I have come since starting the School of Education Program in September. This whole year has led me down a fascinating journey and I have truly learned so much from observing teachers, students, and classrooms in action. Just this morning, I received an e-mail about placement for student teaching in the fall. I can't wait to start this new leg of my journey and I can't wait to find out where I will be!