Pizza Party

Before the students begin this activity, discuss the relationships that are shown in the Venn diagram. This will help them to develop the logic and reasoning processes that they will need to use in this activity. The students need to identify the number of students in “and”, “or”, and “not” relationships. For example, ask the students to point out the people who want:
• mushroom and pineapple toppings
• onion and pineapple but not mushroom
• pineapple or mushroom but not both
• pineapple but nothing else.
Ensure that the students notice that Ms Martell is included in the “whole” of 24 people. Encourage them to express the fractions clearly in words (eight out of twenty-four), in numerals (8/24), and as simplified equivalent fractions (1/3).
Students who are having difficulty with question 1 could represent their equivalent fractions with materials, drawings, or number forms. For materials, they could use class members to act out the scenarios or use labels to represent each choice and manipulate these. For example, m = mushroom, p = pineapple, and o = onion. The 24 people could be labelled along a number line or along a strip graph.

Eight people have mushroom, and 8 + 8 + 8 = 24, so one section of 8 is one part out of the three parts that make 24. So 8/24 = 1/3.
Question 2 renames the whole in two further ways: as 72 because this is the total number of pieces needed for the 24 people and as 12 because this is the total number of pizzas. A ratio table may be a useful tool to show the students the connections between these:

Answers to Activity

1. a. 8 out of 24 (8/24, which is 1/3)
b. 12 out of 24 (12/24, which is 1/2)
c. 16 out of 24 (16/24, which is 2/3)
d. 4 out of 24 (4/24, which is 1/6)
e. 8 out of 24 (8/24, which is 1/3)
2. a. 12
b. i. 1/3 (24 out of 72 pieces)
ii. 4 (1/3 of 12)