The Pizza Problem
Part I: Entry
For this problem, I brought in a Costco pizza and put it on the table at front. We started class with a number talk, and once students started to get curious about the pizza, I asked them what they wanted to know. The dimensions of the pizza and the pizza box are available in the captions of the images below, but if you do this problem in class, I would strongly recommend just bringing in a pizza.
We did this problem in the context of our "From Patterning to Algebra" unit. The grade 8 Curriculum and Connections expectation is to develop formulas for the circumference of a circle, area of a circle, volume for right prisms, and surface area of a cylinder.
Part II: Attack
Students worked together in groups of 3 to solve this problem. They had a total of maybe three hours to work on this problem in class over the course of a week. The problem the students decided to work on was, "What are the area and circumference of the pizza?", and the extension was, "If we had 27 mini-pizzas (one for every student in the class), with the same total volume as this regular-sized pizza, what would the dimensions of each mini-pizza be?"
Part III: Check, Reflect, Review
On Friday, we looked through student solutions together, and we found a rough estimate for the circumference, surface area and volume. The purpose of this activity was not to necessary find exact solutions for those dimensions, but rather to develop general formulas.
Attempt 1: Developing the Formula for the Area of a Circular Pizza [3:26]
Attempt 2: Turning a Circular Pizza into a Rectangle [0:47]