Unit 8, Lesson 11
Probabilities in Games (Optional)
Geometry
11.1
Activity
Optional
20 mins
Rock, Paper, Scissors
Standards Alignment
Building On
Addressing
HSS-CP.A.2
Understand that two events
Instructional Routines
NoneMaterials
NoneActivity Narrative
In this activity, students use the context of a simple game to ask their own question involving independence of events Then they collect data to answer their question.
Students must model mathematically to determine what information they need to answer their question (MP4). They also construct a viable argument to answer their question (MP3).
Launch
Arrange students in groups of 2. Invite 2 students to demonstrate the game “Rock, Paper, Scissors.” Give students 10 minutes to play the games and record their results, then tell them to stop to analyze their data.
Students should be encouraged to think of their own hypotheses to study, but here are some examples of things for students who struggle to think of something.
- One of the options (for example, rock) tends to result in a win for me.
- The person who won last tends to win again more often.
- Playing the same option two games in a row tends to win more often on the second time.
Activity
NoneStudent Task Statement
There is a classic game called “Rock, Paper, Scissors.” Two people play by counting to 3 together, then making a hand gesture to resemble paper (hand flat, palm down), rock (fist), or scissors (two fingers extended).
- When paper and rock are shown, paper wins the round.
- When paper and scissors are shown, scissors wins the round.
- When rock and scissors are shown, rock wins the round.
- When both players show the same thing, the round is a tie.
Find a partner, and play the game with that partner 10 times in a row. Record the number of times you have played the game, the name of your opponent, what each person shows in each round, and who is the winner. After playing 10 games, find a new partner, play the game 10 times with this new partner, and record the results. Continue until your teacher tells you to stop.
Is the event “win the round” dependent on another event? Explain your reasoning.
Choose an event that you think might influence the probability of winning, then analyze the data using probability to determine whether the event you chose to study is independent of winning. Provide evidence to support your claim.
Student Response
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Building on Student Thinking
Activity Synthesis
The purpose of this discussion is for students to communicate how they used mathematics to justify their findings.
- “Which events did you choose to compare?” (I chose to compare the event of me displaying rock and winning.)
- “How did you determine whether or not the two events are independent?” (I computed
and compared that to . Because the probabilities were not close to the same, I think the events might be dependent.) - “What was challenging or interesting about this activity?” (I thought it was interesting because we collected our own data and actually used probability to answer questions.)
11.2
Activity
Optional
20 mins
Guess Which Card
Materials
Activity Narrative
In this activity, students apply conditional probability to make sense of a nonintuitive statistical problem. Students play a game of drawing a card from a bag and observing one side of the card. Students then must guess which card they drew based on what they see.
Lesson Synthesis
Here are some questions for discussion.
- “What did you find important, challenging, or otherwise notable about today’s lesson?” (It was really interesting to collect data to answer a question. I really felt like I was able to better understand the concept of probability.)
- “What mathematical work from this unit did you use in today’s activity?” (I used probability, conditional probability, the addition rule, and relative frequencies.)
- “How might the mathematical tools that you have learned in this unit help you outside of mathematics class?” (I think that when I see data that compares data using percentages in the news that I will really have to stop and think about the different factors that might account for any differences. I wonder why I never hear about independent and dependent events when I look at data in the news. I think it would be really interesting if people presenting the graphs or tables used by the news had to explain them using the concept of probability.)