PUP Math pizza, Clip 2 of 2: Whole and Half Pizzas with Four Toppings

This second clip in a set of two edited videos developed for the Private Universe Project in Mathematics, focuses on 12 fifth grade students during an extended session work individually and with their classmates to construct and justify solutions to two problems involving pizza choices. For the first problem, the students were asked to find all possible choices for "whole" pizzas when four toppings were available. The second problem extended the first by offering the additional option of pizza halves with different choices, still with four toppings available. The students construct various representations, including drawings and symbolic charts to find and justify their conclusions about the number of possible pizza choices. There are voice-over explanations that refer to the children's representations and strategies interspersed throughout the edited video episode, and interpretive narrative by researcher Carolyn Maher and several of the students who reflect about their earlier problem-solving activity several years later as high school students. First problem statement: Capri Pizza has asked you to help design a form to keep track of certain pizza choices. They offer a standard “plain” pizza with cheese and tomato sauce. A customer can then select from the following toppings: peppers, sausage, mushrooms and pepperoni. How many choices does a customer have? List all possible choices. Find a way to convince each other that you have accounted for all possibilities. Second problem statement: Capri Pizza has asked us to help design a form to keep track of certain pizza sales. Their standard “plain” pizza contains cheese. On this cheese pizza one, two, three, or four toppings can be added to either half of the plain pie or whole pie. How many choices do customers have if they can choose from four different toppings (peppers, mushrooms, sausage and pepperoni) that can be placed on either a whole cheese pizza or half of a cheese pizza? List all possibilities. Show your plan for determining these choices. Convince us that you have accounted for all possibilities and that there could be no more.Transcript is also available.Smithsonian Astrophysical Observatory. (1993). PUP Math pizza, Clip 2 of 2: Whole and Half Pizzas with Four Toppings [video].Resource vailable in QuickTime and Flash digital video formats