## Monday, May 16, 2016

### Day 160: Volume, Trashketball, & Combo Histogram Box Plots

The estimation today was a glass of pennies. It has 3 angles and 1 of the photos shows 1 roll of pennies fitting diagonally at the bottom. I encouraged students to be riskier in their too lows and asked the class why students were putting 50 cents or 1 dollar as their too low. For the most part a majority of students underestimated.

Most students estimated how many rolls would fit in it. A few students talked about layering. During the video they were all guessing how many it would fit and lamenting how low they estimated.

Then I went over the lesson plans for the rest of the week. I then reviewed that they meet in different classrooms Monday, Tuesday, and Thursday of next week according to the schedule on my door. On Wednesday students will meet with the sub in H-1 and do an estimation followed with a lesson on the SBAC topic to make sure they understand the vocabulary of the task. Then Friday they will have a lesson.

To start class I gave students time to work together on solving the volume for a cylinder and a separate cone. In class discussions I asked students what we discovered with the sand demonstration last week. How are a cylinder and a cone related? At first some students said it was half as big. Then they remembered that the cylinder with the same base and height fit 3 cone fulls of sand. Therefore, students could pretend the cone was a cylinder and then divide their answer by 3 or multiply by 1/3.

Then we launched into Mr. Stadel's Trashketball lesson. EVERY single class a few people said, "Why is he wasting so much paper?" I ended up responding, "for the sake of quality math situations!" Students figured out it was how many trashketballs fit in the trash can. They asked for the diameter and the height of the cylinder. Regarding the sphere, students thought you'd have to find the circumference. Some students realized you could put it on a ruler and measure the diameter. Next year I'm going to have them actually reuse a crumpled ball and measure it themselves.

I like how the task gives students a page of formulas with pi and they have to discern which formula to use. I like how some students pointed out the sphere's volume was the only one with an exponent of 3, so it must be volume. I wonder how they could explain why the cylinder's volume doesn't have an exponent of 3.

They then basically divided the volume of the cylinder by the volume of the sphere. This theoretical answer is off by double digits and makes students think why. In some classes we didn't reveal the answer or have time for a student to present so we will launch class with that tomorrow.

 Warmup with cylinder and cone.
 Student volunteers dictated to me how they solved. I started with this question: "What advice would you give someone who did not know where to start with this problem?" Most students said you needed to know the volume was the area of the base * the height, and the area formula for a circle.
 This is the only student work sample I snapped a photo of. Will take more tomorrow.
In accelerated students finished putting together their combination box plot histogram of their 40 golf shots. I was impressed that without being prompted 1 group made a stem and leaf plot that helped them figure the max, minimum, and median easier.
 Steam and leaf plot
 A bin width of 20 worked pretty well for this group! The team member asked if the shape was skewed left. Yes! I could instantly see by this and the box plot that their team was pretty consistent overall! Their median was around 40 centimeters away from the hole.

I think this student is making sure he doesn't get points taken off for forgetting the units. SMP: attend to precision!