Thursday, May 12, 2016

Day 157: Volume of Cone & Pyramid, Penny Golf, Wheel of Theodorus Examples

The estimation was the value of a roll of quarters. I liked how a student related it to a real life experience. She needed to get quarters for laundry so her mom gave her $20. The cashier gave her 2 rolls of quarters, so she reasoned that one roll must be $10. Other students said 10 groups of 4 quarters. I heard a few estimate $7.50 and only a couple over estimated. Students realize it must be a round number in whole dollars.
Students analyzed a small and large container of popcorn. The small was a cone, and the large was a cylinder. The small was $1.50 while the large was $3.50. Some students thought the large was double the size. Then we did a demonstration. Students saw and wrote down that the cone and cylinder had the same height. I asked how we could see if they had the same radius. They said you could put the bases together and see if they match up. They did.

Then I took estimates of how many cones of sand would fit in the cylinder. estimates ranges from 1.5, to 2, 2.5, 3, 3.5, and some even 4. Students were intently watching as I poured and saw it filled it 3 times. So, I said that if you know the volume of this cylinder, do we know the volume of this cone? Students said to divide by 3 or multiply by 1/3. Great.

Then they figured out the "fair price" of the large popcorn, as well as which one was the better deal. Students multiplied the small price by 3 to get $4.50 for a fair price for the large. This is also told them that the large was a better deal because it was a dollar cheaper than 3 smalls. Only a few students reasoned that if you divide 3.50 by 3, you get around $1.17, which is cheaper than the price of the small cone full.

Then they predicted with a prism and a pyramid. Some still thought the prism was twice as big as the prism, though some assumed the relationship would be the same as the cone and the cylinder.
Our sand and the materials I ordered for our department from Amazon.com.
In accelerated we went over the last problem from yesterday on inverse functions. Davin showed how we could solve for the x variable, and then switch the x and y variables at the end. This was a great method after reasoning with it yesterday.

Then we read about the 40 holes of golf task. I set up 8 golf holes with orange duct tape outside that were 200 centimeters away from the cement line. Each team member took turns and 1 threw 10 pennies 1 at a time. Then they worked together to measure their distance from the hole as they picked them up. Then they repeated so all group members went. Tomorrow they will organize their data using box and whisker, bar graph, histogram, or any of their choices. I'm going to push students to go for the ideal which is the combination box plot and histogram. Students will have to convince the rest of the class how consistent their team was and we will decide who the winner is based on how convincing their argument was.
Beautiful day to be outside collecting data.
Students enjoyed themselves.
I graded students Wheel fo Theodorus projects. The requirements were: first 5 triangle calculations, all sides labeled. Also, hypotenuse labeled with an I for irrational or an R for rational. Colorful or designed (1/2 a point). I also deducted 1/2 point if there were multiple triangles that were clearly not right triangles. I walked around the room when they started and emphasized the legs had to be perpendicular to form a right angle if you were using the Pythagorean theorem. Here's some of the work that stood out to me:
My niece would love this one, she's a huge Frozen fan. My brother's family dressed up as them for Halloween.

A patriotic student.
Cool colors.
This is a popular way to shade nowadays.
Taste the rainbow.
A peacock!
Pretty funny!
This one really spiraled around! Cute cat... cheshire?
Very creative... a "cornucopia."
Nice dress.
I like how this student decided to color code the triangles with rational hypotenuses.
A star wars fan!




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