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# Playin' Against All Odds - Day 2 of 5

Lesson 4 of 12

## Objective: SWBAT weigh possible outcomes associated with probability games that they create. SWBAT analyze decisions and strategies using probability concepts.

*45 minutes*

#### Entry Card Game

*10 min*

***Need: 2 Decks of Cards***

Once the students have entered the classroom, I begin the period by holding one deck of cards and asking the students “Who wants to play my game?”

I give the students three options to win:

1) Draw a Heart

2) Draw a Jack

3) Draw the 5 of Clubs

After I explain my game, I start around the room selecting eager participants. Prior to letting them select a card, however, I force the student to designate which method they are going to try to win by. For example, if a student says that they want to try to win by drawing a Jack, and instead they draw the 5 of Clubs, then they lose! They must win by the method of their choosing. (If they are mathematically-wise then they will choose option #1!) I repeat this for 8-10 students because the game goes rather quickly. It is fun to see which students play “with their gut” rather than play the mathematical odds. P(Heart) = ¼. P(Jack) = 1/13. P(5Clubs) = 1/52. At the end we total up the winners and losers along with their selected method of winning. Although the sample size is quite small, it is a great way to revisit the introductory probability principals from yesterday’s lesson as well as talk about experimental VS theoretical probability! It is also fun to discuss human nature and the intrinsic desire to go against the odds and win the unthinkable. Just why is it so tempting?!

Next I tell the students that I am going to make things a little more interesting, and to take out their notes. I explain a new version of my game, and write it on the board next to my previous version.

In this new game, there are two decks of cards.

This time, I give the students 4 options to win:

1) Draw and Queen of Hearts AND then an Ace of Spades (from the same deck)

2) Draw an Ace of Spades (from the first deck) AND an Ace of Hearts (from the second deck)

3) Draw both an 8 AND a King from one deck, or one from each deck.

4) Draw a 7 OR a RED card from one deck, or one from each deck.

After writing the rules and allowing the students to copy them down, I give them a minute to sink in. This time, the probabilities are less obvious to the students!

Because things can come across a little overwhelming, I start small with my questioning…

**Do you think you will have a better or worse chance of winning this game compared to the last game? (MP1)*

**If there are more “different ways” to win, why is the probability less this time? (MP2)*

**Talk with your table about which option you think will be best. Why? (MP3)*

**What is different about this game compared to the last game? *

**In what situations is one event impacting another? In what situations are the events separate?*

* *

As the discussion continues to develop, the students will lead the conversation right down the road of multiple probabilities! This is likely something that they will need to know as they begin thinking about developing their game, so I welcome them to their first workshop of the project!

#### Resources

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#### Exit Homework

*1 min*

To wrap up the day of work, I circulate the students’ homework assignment - Probability Worksheet #2 Homework. Because I know (and want) the students energy to be primarily focus on the creation of their game, I do not make the homework assignment due until the end of class on DAY #4 of the activity (this lesson is DAY #2). A series of optional review/extension workshops will be provided to assist the students who need additional support on the worksheet. Let the games begin… literally!

An answer key and common student misconceptions are posted in the following lesson.

#### Resources

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- UNIT 2: Exponential and Logarithmic Functions
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- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
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- LESSON 1: Introduction to Probability
- LESSON 2: Deal or No Deal!?
- LESSON 3: Playin' Against All Odds - Day 1 of 5
- LESSON 4: Playin' Against All Odds - Day 2 of 5
- LESSON 5: Playin' Against All Odds - Day 3 of 5
- LESSON 6: Playin' Against All Odds - Day 4 of 5
- LESSON 7: Playin' Against All Odds: Game Time! - Day 5 of 5
- LESSON 8: It's PROBABLY time to clean up any loose ends...
- LESSON 9: The Language and Logic of Probability
- LESSON 10: Writing for Understanding
- LESSON 11: Probability Unit Review
- LESSON 12: Probability Quiz