## Dice Games - How to WIN!

### Wesley UnderwoodSanta Rosa District Schools

#### Description

This activity is a fun way to teach Data Analysis and Numerical Occurrence. The student works with a partner to play a game. Each player gets twelve counters to be placed on the numbers on the game board. The players take turns rolling two dice. On each roll the sum of the two upturned numbers is determined. If the player has a counter on that number the student may remove the counter from the game board. Play continues until one of the players removes all twelve counters from the board.

#### Objectives

The student uses manipulatives to obtain experimental results, compares results to mathematical expectations, and discusses the validity of the experiment.

#### Materials

- Paper
- Pencil
- 24 Counter for each group
- Four Function Calculator
- Game Board
- Information Packet

#### Preparations

1. Print a Data Packet for each student.
2. Print a Game Board for each group.
3. Place 24 counters (preferably 12 each of a different color) and 2 six sided dice in a sandwich bag for easy distribution.

#### Procedures

Prerequisite Knowledge – The student needs to be able to:
1. Create a Line Plot.
2. Write the probability of an event.
3. Change a fraction to a decimal.
4. Change a decimal to a percent.
Note: This lesson is implemented directly following a unit on probability.

Day 1 - Part One: Experimental Data Collection and Analysis (Group Work)

1. Ask students if they have ever played a game with dice.

2. Encourage students to share about the different kinds of games they have played.

3. State: Did you know that you can increase your ability to win if you know the mathematics behind some games!

4. Distribute activity materials (Data Analysis and Numerical Occurrence packet) and (Packet containing two dice, 12 counters one color and 12 counters of a different color)

5. Instruct the students to leave all materials alone until instructed to use them.

6. Ask the students to look at the Data Analysis and Numerical Occurrence packet.

7. Read and Review the “Directions” on the front cover of the packet. Answer any questions.

8. Read and Review the “The Problem” on the front cover of the packet. Answer any questions.

9. Read and Review the “Part One: Data Analysis of the Experimental Data” questions on page 2. Answer any questions.

10. Read and Review the instructions for “Counter Placement Chart” instructions on page 3. Answer any questions.

11. Read and Review the instructions for “Sum of Two Dice Tally Sheet” on page four. Answer any questions.

12. Read and Review the instructions for “Sum Totals Distribution Line Plot” on page five. Answer any questions.

13. Instruct the students to remove and count “The Counters” from the packet. Tell the students that they should have twelve counters each.

14. Model the beginning of a game on the overhead or white board, making sure that the students understand how to set up a game, record counter placements, and sum tallies. Demonstrate to the students how to place the counters on the game board, complete the Counter Placement Chart (page 3 of packet) and the Sum of Two Dice Tally Sheet (page 4 of packet).

15. Instruct the students that they will only be playing one game on the first day.

16. Instruct the students to begin game one. Circulate around the room to assess the students understanding of the instructions. Correct mistakes and answer questions as necessary.

Day 2 – Part One: Experimental Data Collection and Analysis (Group Work)

17. Instruct the students to get into their groups.

18. Instruct the students that on Day 2 each group needs to complete games 2 – 5, the Sum Totals Distribution Line Plot, and the questions for Part One: Data Analysis of the Experimental Data on page 2 of the packet.

19. Ask a student from each group to retrieve the materials needed to continue the game.

20. Instruct the students to complete the lesson in class and at home as needed.

Day 3 Part Two: Experimental Probabilities Vs. Theoretical Probabilities (Individual Work).

21. Instruct the students to get out their Data Packet and pass out a four function calculator to each student.

22. Instruct the students to open their Packet to page 4.

23. Instruct the students to verify that the “Totals” on the bottom of the page 4 is completed.

24. Tell the students to transfer the “Totals” from page 4 to the Individual Experimental Data Table on Page 6.

25. Tell the students to find the total number of ALL Rolls.

26. Instruct the students to find their Individual Experimental Probability on page 6. Circulate around the room and answer questions as needed.

27. Using whole group instruction, gather the Experimental Probabilities from each group (see associated file for Game Total Tally Sheet) and write the information on the white board.

28. Instruct the students to complete the Class Experimental Probability section of page 6. Circulate around the room and answer questions as needed.

29. Instruct the students to complete the Area Model for Possible Sums from Tow Cubical Dice tables on page 7. Circulate around the room and answer questions as needed.

30. Instruct the students to complete the Questions for Part Two: Experimental Probabilities Vs. Theoretical Probabilities.
Note: This portion of the assignment may need to be completed for homework.

Day 4 Part Two: Experimental Probabilities Vs. Theoretical Probabilities (Individual Work).

31. Instruct the students to get out their packet and turn to page 8, Probability Comparison Chart.

32. Instruct the students to complete the Percentage of Probability Comparison Chart and answer the four questions at the bottom of page 8. Circulate around the room and answer questions as needed.

33. Instruct the students to return to their groups to discuss their findings.

Day 5 Conclusion: Grade, Review, and Discussion of Project.

34. Instruct the students to get out their Packet and a “RED PEN.”

35. Students review their data packet. Using transparencies from the Anticipate Answers (see associated file) the teacher leads the class through a group discussion on the most probable answers for the following:

1. Part One: Experimental Data Collection and Analysis
2. Part Two: Experimental Probabilities Vs. Theoretical Probabilities
3. Sum totals distribution line plot
4. Area model for possible sums from two cubical dice
5. Probability Comparison Chart and the final questions on page 4.

36. Collect and evaluate the packets for needed remediation.

Day 6 Evaluation:

Have the students write an essay to a fellow student that explains how to win the “Counter Placement Game” using the mathematical knowledge learned during Data Analysis and Numerical Occurrence activity. Successful understanding will be achieved if the student demonstrates knowledge that the numbers 4 – 10 are the best placement of counters and that a majority of the counters should be placed on the numbers 5 – 9. Students should use the findings from the activity to support their findings.

#### Assessments

Use the Counter Placement Chart, Sum of Two Dice Tally Sheet, and Sum Totals Distribution Line Plot Chart (see associated file) to formatively assess the students’ ability to use manipulatives to obtain experimental results and Identify patterns and make predictions. Provide corrective feedback as necessary.
Use the Experimental Probability Chart (see associated file) to formatively assess the students’ ability to calculate Experimental Probability.
Use the Area Model for Possible Sums from Two Cubical Dice Chart (see associated file) to formatively assess the students’ ability to mathematically calculate Theoretical Probability.
Use the Probability Comparison Chart and the Final Discussion Questions (see associated file) to formatively asses the students’ ability to compares experimental results to mathematical expectations, and discusses the validity of the experiment.

#### Attached Files

Game Board Document     FFile Extension: pdf

Game Data Packet     File Extension: pdf