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Counting Outcomes: Ice Cream Sundaes and More

This lesson explores the principles of counting through fun examples, like ice cream sundaes. Students will learn how to determine the number of outcomes related to an event by applying the addition and multiplication principles of counting. The lesson begins with a warm-up on ice cream flavors and toppings, transitioning into practical examples involving creating burgers and pizzas. Essential questions drive the inquiry into how outcomes can be predicted, with a focus on simple permutations and combinations to derive different possibilities.

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Counting Outcomes: Ice Cream Sundaes and More

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  1. Warm-Up If ice cream sundaes come in 5 flavors (vanilla, strawberry, chocolate, butter pecan, fudge ripple) with 4 possible toppings (hot fudge, nuts, cherries, butterscotch), how many different sundaes can be made with one flavor of ice cream and one topping?

  2. Unit 5 Chances of Winning Concept 1 Outcomes of a Given Event Day 1

  3. Standards MA1D1 Students will determine the number of outcomes related to a given event. • Apply the addition and multiplication principles of counting • Calculate and use simple permutations and combinations

  4. Essential Question How do you determine the outcomes for a given event?

  5. Key Terms • Addition Principle of Counting • Multiplication Principle of Counting

  6. Fundamental Counting Principle-   It will allow us to count the number of ways a task can occur given a series of events.  Basically you multiply the number of possibilities each event of the task can occur.   It is like multiplying the dimensions of it.

  7. Warm-Up Discussion • How many flavors of ice cream were there? • How many choices of toppings were there? • How many different outcomes are possible?

  8. Practice • 1) Thomas goes to a Mc Donalds' restaurant and chooses to create his own burger. He has 2 different kinds of cheese, 3 different breads, and 3 different sauces he can choose from, but he can only choose one of each category. How many different ways can he create this burger? • 2) Diane is ordering pizza for her family. There are 4 different possible sizes of the pizza. Also, she has to choose one of 5 toppings to place on the pizza and one of 3 different types of cheese for the pizza. In addition, she must choose one of 3 different kinds of crust. How many different ways can she have her pizza?

  9. Addition Counting Principle • You decide that you are kind of hungry you can choose from a hamburger or chicken sandwich with the all the toppings or none, but you don’t have enough $ for a sandwich and ice cream. • How does that change the number of outcomes (choices) for this event?

  10. Addition Counting Principle

  11. Example of Addition Counting Principle

  12. Multiplication Counting Principle • You decide that you are kind of hungry you can choose from a hamburger or chicken sandwich with the all the toppings or none. You don’t have enough $ for a sandwich and ice cream, but your friend said he would spot you so you can get both? • How does that change the number of outcomes (choices) for this event?

  13. Multiplication Counting Principle • If a total event can be sub-divided into two or more independent sub-events, then the number of ways in which the total event can be accomplished is given by the product of the number of ways in which each sub-event can be accomplished.

  14. Example

  15. Summary and Closure Do Graphic Organizer #1 and Graphic Organizer #2 Do Math 1 Text book page 341 1-14

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