Carnival Booth Lab: worksheet
Write about the activity only. Leave out names, class periods, emails, and other personal details.
Play Carnival Booth Lab with your partner. Before each run, write your prediction in the level's table. After each level, record what happened, then answer the questions for that level. Use numbers from the debrief.
(+)-S.MD.2: Calculate and interpret the expected value of a random variable. (+)-S.MD.6: Use probabilities to make fair decisions.
Level 1: Fair game
| Your prediction ($ per player) | Prize you set ($) | E from the rules ($ per player) | Passed? |
|---|---|---|---|
1. Record what happened: the profit per player in your shortest run and your longest run of the $8 booth. Give the number of players for each. (+)-S.MD.2
2. Your $8 booth is a fair game. What does fair mean here? In the long run, who comes out ahead: the booth or the players? (+)-S.MD.6
3. Why can a short run land far from E = $0.00, even though the game is fair? What happens as more players play? (+)-S.MD.2
Level 2: Profit target
| Your prediction ($ per player) | Chance to win you set (%) | E from the rules ($ per player) | Passed? |
|---|---|---|---|
4. Record your longest run of the 25% booth: how many players, the profit per player, and the cash box. How close was the cash box to E × players? (+)-S.MD.2
5. Look at the histogram of single plays. What can the booth earn on one play? Why does no single play ever earn exactly $0.50? (+)-S.MD.2
Level 3: Two prizes
| Your prediction ($ per player) | Big prize chance you set (%) | E from the rules ($ per player) | Passed? |
|---|---|---|---|
6. Record your longest run of the 5.6% booth: how many players, the profit per player, and the cash box. How close was it to E? (+)-S.MD.2
7. A booth that forgets the $4 small prize sets the big prize chance to 8%. What is that booth's real E? What would 10,000 players do to its cash box? (+)-S.MD.2
Level 4: Bad luck or bad booth?
| Your prediction (% of afternoons that lose) | Afternoons you ran in all | Afternoons that lost money | Your estimate (%) | Passed? |
|---|---|---|---|---|
8. Before you run: an afternoon collects 20 × $3 = $60 and pays $10 to each winner. How many winners out of 20 make the afternoon lose money? Show the math. (+)-S.MD.2
9. Record your data: how many afternoons you ran in all, how many lost money, and the estimate you submitted. (+)-S.MD.2
10. The treasurer saw one losing afternoon and wants to shut the booth down. Is that a fair decision? Use your data and the expected value. (+)-S.MD.6
When a booth or an estimate missed
11. Pick one booth or estimate that missed. Which level was it, and what went wrong? Use E = cost − chance × prize, or your Level 4 data. (+)-S.MD.2
Wrap-up: the long run
12. Can a few plays tell you whether a booth is designed right? Use evidence from at least two levels. (+)-S.MD.2, (+)-S.MD.6
| Claim | |
|---|---|
| Evidence | |
| Reasoning |