## Wednesday, April 27, 2016

### Day 146: Fish Tale Pythagorean 3D (Notice, Wonder, Q's)

Today students noticed and wondered about the Fish Tale problem. I used it from Yummymath.com last year, but this time I didn't give the numbers or the wording to the problem, and asked them what they noticed, wondered, and any questions they had. The results were fantastic. It seems like more students were successful this way then last year. Interestingly, more students solved it the simpler way this year of seeing the 3 dimensional right triangle rather than the method that requires 1 more step using the Pythagorean Theorem.

Below I've embedded the Google Slides.  Slides 8, 9, and 10 were the slide duplicated from each period so that I could refer back to it. I wrote what students noticed, what they wondered, and their questions.

Sometimes when they ask questions, I'll immediately answer them by typing into parentheses () right after they ask it. I like how they noticed an unrealistic nuance of the problem: Betty is a fresh water gold fish and Stripe is a salt water clownfish (Nemo). I liked how students were interpreting the lines as the swimming paths and added some more details. After doing Taco cart, students asked if the fish swam at different speeds. I think I could add that element in next year as a sort of extension. I do want them more to focus on how to show their work so that a class mate that didn't understand it could by looking at their work.

An example of the 3 step process is below. I like how Jonathan drew another diagram in the bottom right to show how he saw the 3rd right triangle, whose leg was the diagonal of the floor of the rectangular base.
 Jonathan's detailed work.
 Afterwards we reviewed a word problem that had to be interpreted with a diagram, and then solved for the missing leg. The cliff was 75 feet tall, and a 96 foot rope was pulled tight. You had to figure out how far the rope was from the base of the cliff and where Mark was standing.

 This example by Bing in 4th period was great. He explained his work as he was writing it and got a nice applause.
 I scaffolded to students how to properly draw a rectangular prism with a dashed line to show the faces behind it that you couldn't see. I also asked them to color code the paths of each fish.
 Madison shared how she saw the 3 dimensional right triangle by peering in from the left hand face and seeing stripes purple path going from the bottom front left to the back top right. It's easy to see because she also

I didn't take a picture of accelerated but we used Desmos to confirm solving the system of equations and how the graphs reflected the points of intersections. Students worked better in their groups today than yesterday. They figured out that intercepts were where functions crossed the x or y axes and had a 0 as the x or y coordinate. Interceptions were where two functions crossed paths. They realized it wasn't just lines that could cross but a parabola and a linear function.