Monday, May 11, 2015

Pythagorean theorem in 2D then 3D

On Thursday instead of completing practice problems out of CPM course 3 we worked on Dan Meyer's taco cart lesson. It's a great lesson that covers rates and in addition to the theorem. I was impressed with how my students demonstrated their thinking:

Andre demonstrates his understanding of right triangles. As you can see he refuses to write the square root sign. My goal was to continually compliment yet demand more clarity and evidence from every student to show where they got numbers from and how labeling could help.

CPM introduced acute, obtuse, right, and non-triangles through the use of squares and their side lengths you can put on card stock. You then compare the small and medium squares areas to the large squares areas to determine what type of triangle it is. Here's a pic of students working on the activity:

Many rich discussions arose: why does adding the legs not equal the hypotenuse? When I got answers in seconds I asked if I'm going to see you in 5 minutes do I say I'll see you in 300 seconds? Also, some students after using their calculators said 4.58 minutes was 4 minutes 58 seconds.... Great conversations. They groaned at the slowness of video then were pleasantly surprised by the fast forward. Haha. 

That was on Thursday. Now on Monday we started with looking at the Pythagorean Theorem in 3 dimensions. My 1st period students seemed super sleepy so I decided to ask if anyone had a fish tank at home. I then proceeded to reveal that the current Autozone store in the neighborhood used to be a pet store (1 student knew that) and I had worked there as a high schooler (when I was a few years older than them). I told them how I would buy feeder goldfish from work and feed them to my Oscars. They were enthralled, and some grossed out.

I also modified this task, Fish Tale (get it?? told students it's a pun),  by yummy math by taping paper strips over the dimensions so students specifically asked for what they needed to solve. I also required students to draw the diagram with me step by step. I first asked them what shape it was called. I asked them why it wasn't a cube. How did they KNOW it was a rectangular prism like they said?

The key point to helping them draw it (some had difficulty)was making a rectangle (the front face) with another congruent rectangle spaced up and to the left from it. I had them color code the different pathways. I also demonstrated how erasing the lines and making them dashed showed it was behind your view. By not giving students the dimensions, they had to come up with asking for the length, height, and width, which helped them differentiate between them.

Kehl used the same method as I did. It takes more steps but was how we visualized it.

But Jerod's method caused my brain to explode with clarity once he showed me the more efficient way that I sheepishly hasn't worked out before but was delighted that worked. 

Galvin neatly organized his work to show how he got his solutions. Haha, he even labeled the problem title with (pun!). This was a great lesson too because I didn't use any of my precious copies on the copy machine.

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