Paula's Pizza 1.1 2008/06/10 11:02:18.252 GMT-5 2008/06/17 13:36:35.072 GMT-5 IMP cosborne@keypress.com IMP cosborne@keypress.com Christine Osborne cosborne@keypress.com Key cosborne@keypress.com IMP Year 1 The Game of Pig

Intent In this activity, students make a list of all possible cases, giving them a clear picture for finding probabilities.

Mathematics Using systematic lists, students can find probabilities by counting possible outcomes and applying the basic definition of probability:

Progression Students are introduced to another tool for finding probabilities.

Approximate Time Brief introduction 20 minutes for activity (at home or in class) 15 minutes for discussion

Classroom Organization Individuals, followed by whole-class discussion

Doing the Activity As a class, read the introduction to Paula’s Pizza aloud. Clarify that all pizzas must have two different toppings; no pizza can be “double” pepperoni or “double” anything. Students will probably want to make a list of all possible two-topping combinations. Encourage them to be systematic, perhaps listing all the combinations with sausage, then those with onions (and not sausage), and so on. There are several ways to organize this list to ensure that no two-topping pizza is overlooked and that there are no duplicates.

Discussing and Debriefing the Activity Encourage students to compare their results. Did everyone find all the possible combinations, without duplication? With the list of 15 possibilities, students should realize that Paula’s probability of getting the pizza she ordered (Question 2) is 115 size 12{ { {"1"} over {"15"} } } {} and that her probability of getting something different is 1415 size 12{ { {"14"} over {"15"} } } {}. If students do not notice that these two probabilities add to 1, ask questions to help lead them to this observation. In Question 3, students just need to count that there are six combinations that include neither sausage nor pepperoni. They can then conclude that the probability of Paula getting a pizza she likes is 615 size 12{ { {6} over {"15"} } } {} and the probability of her getting a pizza she doesn’t like is 915 size 12{ { {9} over {"15"} } } {}.

Key Questions Can you list all the outcomes? What do you notice about the two probabilities in Question 2? Why is the sum of the probability of Paula not getting what she ordered and the probability of Paula getting what she ordered equal to 1?

Supplemental Activity A Pizza Formula (extension) challenges students to find a proof of the pattern and a closed formula.