|Grade span:||9 to 12|
Description:This is an example of a Math Game that focuses on developing students' understanding of data and probability while they determine if the game they are playing is fair. Students are encouraged to engage in rich mathematical discussions while testing their hypotheses.
- Communicate about mathematics (e.g., use mathematical language, compare their own thinking with other students' thinking, construct logical arguments to support their thinking)
- Use strategies to understand new math content
- Select and use the best method of representing and describing a set of data
- Use experimental methods to determine theoretical probability
- PDF - Teacher's Guide (PDF)
- PDF - Student Worksheet (PDF)
- Paper (graphing and other as needed)
- Calculators available
- A game marker (e.g., coin, counter)
- A number cube (die) with an even number of sides
- Print out accompanying PDFs and familiarize yourself with the scenarios students will be involved with. If necessary, make time to share the lesson with a day time mathematics instructor to converse about the standards and mathematics involved.
- Decide how you will organize students into pairs (allowing choice or assigning partners)
- Make sure all materials are available for all students
- Prepare a brief introduction of the game and the students' mission during the game. Students have probably had experiences playing dice games as well as games of chance. You may decide to ask students to share these experiences and to think about whether or not they felt the games were set-up fairly. Clarifying the task and peaking students interest in the lesson are the goals of this discussion.
What to Do:
- Give a brief introduction of the game and the expectations of the lesson.
- Ask students to familiarize themselves with the instructions and to get started as soon as their twosome is ready. Before playing, students are asked to predict which player they think will have the most wins. You can collect the predictions by putting tally marks on the board for Player 1 or Player 2. Be sure to ask students to talk about the reasoning behind their predictions.
- Circulate and stay involved while students play and answer the questions on the worksheet. While talking with students, try to generate student thinking without giving away answers or leading students down a particular line of thinking.
- For example, you can ask students, "How did you arrive at this answer?" or "What happened when you modified the game board?"
- Ask, "Are you surprised by the results? Why/why not? What is surprising to you?"
- Once students realize that Player 2 wins most of the time, ask, "Why would it be that Player 2 wins more often than Player 1?"
- To get students ready to answer the questions on the theoretical probability of the game, you can ask, "Based on what you know about probability, how often do you think Player 2 should win? All the time? Half the time? 5f of the time? How could you figure this out?"
- As students play the game, encourage them to bounce ideas around about who is winning and why. Student dialogue will enhance the richness of the game and the learning experiences associated with playing it.
- Be prepared for some students to move forward to the extensions and/or save the extensions for another day. You may decide that some students can take the extensions home to work on (and play with a family member) if they have a desire to do so.
- After students have played the game and answered the questions, lead a class discussion on fairness in games and what it means. This will allow students to affirm their learning by thinking through and comparing what they discovered (e.g. their thinking, their discoveries, their theories, their ideas) while they played.
For a small-group activity, students can sort buttons, cards, or numbers into two groups, trying to find the rule of the activity leader.
Evaluate (Outcomes to look for):
- All students are engaged and actively seeking answers
- Students are communicating effectively about mathematics (e.g., using mathematical language, comparing their own thinking with other student thinking, gaining clarification from each other)
- Students are using strategies effectively
- Students are effectively representing and describing data
- Students are using experimental methods and determining theoretical probability
- Students are exercising their imaginations and creativeness to modify/develop games.
Click this link to see additional learning goals, grade-level benchmarks, and standards covered in this lesson.