You and your partner will each roll a number cube 20 times. Before you begin, each of you will predict the sum of the 2 cubes that will come up most often. Who had the best prediction? Based on knowledge from the first game, make your predictions and play the game again.
This task was presented to first grade students who had been studying sums to 12. These students had little experience with problem solving and the topic of probability. This task will assess student competence in addition facts to 12. The task will also act as a pre-assessment on student knowledge of probability concepts. The task will also introduce students to recording data on charts and graphs and using graphs to draw conclusions. Students will work in partners, first making a prediction of the sum that will come up most often on the number cubes. Students will then toss the number cubes 20 times and record their sums in a chart. The students will then translate their chart to a graph and determine who is the "winner" of game number one. Students will hopefully use the information gathered throughout this experimental probability experiment to make a more informed prediction for game number two. Students are encouraged to make mathematically relevant comments and observations about the solution and process. 45 minutes This task can be tied to a unit on games, or fairs and carnivals. To help students understand the task, I modeled the game with a student volunteer in front of the class. The student and I each picked a sum we thought would be most probable. We rolled the number cubes 20 times and students in the class took turns figuring the sums. The sums were recorded on a piece of chart paper that took on the same format as the student worksheet. Then the sums were translated onto a graph and students analyzed the graph to determine a winner, as well as practice making relevant mathematical observations about the data. Students then chose partners and went off on their own to complete the activity. To assist students in better seeing the experimental probability with a more accurate sample size, students could combine their sums on a class graph that should better reflect the theoretical probability. Teachers may also want to take the opportunity to discuss which number cube combinations result in which sums and which sums have the most combinations.
- Number cubes (two per student)
- Worksheets provided (see pages 5-8)
Note: Students will need copies of pages two and three for game number two as well. The sum of seven theoretically has the most probable chance of occurring, although experimental probabilities will vary, especially due to sample size.
The Novice may or may not have correctly found the sums of the number cubes and may incorrectly fill out the chart. The Novice will transfer the sums to the graph and determine who won. On game number two the Novice will not use information gained from game number one to make a prediction. The student's "I noticed…" statements are rudimentary. Little or no language of probability is used to communicate.
The Apprentice may make some flaws when determining the sums of the number cubes, but will correctly fill out the chart. The Apprentice will transfer the sums to the graph and determine who won. On game number two, the student begins to show signs of basing a prediction on the mathematical experiment in game number one. The student's "I noticed…" statements begin to become analytical in nature. A little probability terminology may be used by the Apprentice.
The Practitioner accurately determines the sums on the number cubes and correctly fills out the chart and graph. On game number two, the student bases a prediction on the mathematical experiment in game number one. The student's "I noticed…" statement shows evidence of understanding the underlying concepts of probability. Some probability terminology will be used by the Practitioner.
The Expert accurately determines the sums on the number cubes and correctly fills out the chart and graph. On game number two, the student bases a prediction on the mathematical experiment in game number one. The student's "I noticed…" statement shows evidence of understanding the underlying concepts of probability and of statistics, as well as makes other mathematically relevant comments or observations. The Expert will use the language of probability and statistics to communicate ideas.
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