Explore and develop methods to solve each of the situations. Discuss in groups how the methods and/or strategies were developed, how and why the methods developed may be different, why and when different methods are used.
Situation 1:
If two dice are tossed, how many ways can you toss a sum of 7 or a sum of 11?
Situation 2:
A pair of dice is thrown. How many ways can the dice thrown show doubles or a sum over 7?
Situation 3:
Participants at a two-day conference could register for only one of the days or both. There were 231 participants on Friday, and 252 participants on Saturday. The total number of people who registered for the conference was 350. How many participated in the conference on both days?
Situation 4:
A diner serves a bargain breakfast which includes eggs (over-easy, poached, or scrambled); pancakes or toast; and juice (orange, tomato, or grapefruit). A breakfast must include one selection from each category. What are the different possible breakfasts? How many possible breakfasts are there?
Situation 5:
Pete Seria decided to offer a special on his famous pizza pies. He limited the special to cheese pizzas with or without pepperoni and with a choice of thin crust, thick crust, or stuffed. How many different versions of pizza are possible?
Situation 6:
How many ways are there of answering a test having 5 true-false questions?
Situation 7:
The mathematics section of some version of the PSAT (Preliminary Scholastic Aptitude Test) have had 30 multiple-choice questions with 5 options each, and 20 multiple-choice questions with 4 options each. How many ways are there to answer this section?