In this video segment from Cyberchase, Bianca wants to pick up a pizza to share with her two friends. Each of the three friends has topping preferences, so Bianca hopes to create a pizza that will satisfy all of their requests. In order to organize the preferences, Bianca draws a Venn Diagram and then arranges the pizza toppings according to the diagram.
Here are some Frame, Focus and Follow-up suggestions for using this video in a math lesson.
What is Frame, Focus and Follow-up?
Frame: Suppose you and your two friends want to create a data display representing your favorite movies. Each of you must choose your top five movies (it's possible that some of your favorites might be the same). How might you display this data?
Focus: In this video segment, watch to see how Bianca organizes the pizza topping preferences. How does she show a topping that two of the friends want? How does she show a topping that only one person wants?
Follow Up: What do the intersecting areas on a Venn Diagram show us? Why does the middle section of Bianca's pizza have no toppings? When does it make sense to use a Venn Diagram to represent data?
BIANCA: I bet I know your favorite thing to eat. I bet it’s pizza. It’s my favorite. I could eat it every night. Sometimes, when it’s left over, I eat it cold for breakfast. I’m getting together for pizza with my friends Darcy and Lupe. I told them I would take care of ordering it. I heard this place “John’s” makes a good pie. And since I take my pizza very seriously I don’t want to take any chances. I want to check it out before placing an order. I need to know what you would rate this pizza?
MAN: Out of this world.
BIANCA: Does it bother you that the olives are touching the pepperoni? Does it bother you that the spinach is touching the mushrooms?
BIANCA: It doesn’t? Well, the pizza looks really good. But I have to make sure our toppings don’t mix, especially anchovies, which Darcy and Lope love, which is, I don’t understand that. They are so disgusting, they are so like slimy and they have creepy hairs all over them and they are so like salty and they make you want to drink like 500 gallons of water.
RESTAURANT EMPLOYEE: Hi!
BIANCA: I want to order a really special pizza.
RESTAURANT EMPLOYEE: Okay.
BIANCA: One that gives different people exactly what they like. Darcy likes anchovies, peppers and onions. Lupe likes anchovies, pepperoni and pineapple, and I like mushrooms, onions and pepperoni, and above all, no anchovies.
RESTAURANT EMPLOYEE: Look, I’ve got a lot of tables I have to get to, you’re going to have to figure out how to put that together.
BIANCA: Okay, maybe a diagram would help. I’ll put what Darcy wants in a red circle, Lupe’s preferences in a blue circle, and my favorite in a green circle. This is what we want: Darcy and Lupe both like anchovies; Lupe and I like pepperoni; Darcy and I like onions. Only Darcy gets peppers, only Lupe gets pineapples and only I get mushrooms.
RESTAURANT EMPLOYEE: You’ve got to be kidding.
BIANCA: No. I’m not kidding. Okay, start at the beginning. Here’s Darcy’s circle, Lupe’s circle, and mine. So Darcy gets peppers, onions and anchovies. Lupe gets anchovies, pepperoni and pineapple. And I get pepperoni, mushrooms and onions. This middle section is empty because there’s no one ingredient that all three of us like to eat. Perfect! It’s got everything that everybody wants and each of us can avoid eating what we don’t like. That means there are pieces for me without the dreaded, nasty, foul, gross, yucky anchovies. Look, I made it myself, will you just pop it in the oven?
RESTAURANT EMPLOYEE: Sorry, we’re closed for the day.
RESTAURANT EMPLOYEE: Yes, closed.
BIANCA: Oh, no. Darcy and Lupe will never forgive me. I promised to bring them pizza.
RESTAURANT EMPLOYEE: Well, I think we have an extra one lying around, you can have that.
BIANCA: Well, I guess it’s better than going home empty handed. What kind do you have left?
RESTAURANT EMPLOYEE: It’s the house specialty – anchovy!
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