<p> Diet Fractions</p><p>We are going to play a game called diet fractions. The rules are as follows:</p><p> Roll two dice.</p><p> Use the numbers to make a fraction less than or equal to one. (That is, put the smaller number in the numerator, the larger in the denominator. If you roll doubles, the fraction reduces to one.)</p><p> Player A wins the round if the fraction cannot be reduced; Player B wins the round if the fraction can be reduced.</p><p> A game consists of 50 rounds. </p><p>1. Determine who is player A and who is Player B. Make a guess – who do you think will win the game?</p><p>Player A ______Player B______(name) (name) (Cannot be reduced) (Can be reduced)</p><p>1. Choose one person to roll the dice and the other to record the results. You may want to change jobs after 25 rolls. </p><p>2. After you complete the game, come write your teams results on the board. Write down the fraction and put a checkmark in the winners box.</p><p>Fraction Player A Player B Fraction Player A Player B ( will not (reduces) (will not (reduces) reduce) reduce) 1. 26. 2. 27. 3. 28. 4. 29. 5. 30. 6. 31. 7. 32. 8. 33. 9. 34. 10. 35. 11. 36. 12. 37. 13. 38. 14. 39. 15. 40. 16. 41. 17. 42. 18. 43. 19. 44. 20. 45. 21. 46. 22. 47. 23. 48. 24. 49. 25. 50.</p><p>Diet Fractions An Introduction to Probability</p><p>Diet fractions is a dice game that can be used to introduce probability. The directions for play are on the student handout.</p><p> Introduce the concepts of events and probability. There are three major methods of assigning probabilities to events, and this game is designed to illustrate them.</p><p> Explain the game to the students (before handing out dice). Have students determine who is Player A and Player B and answer question 1.</p><p> After the students have completed the game, and written the results on the board, discuss the probability formula for relative frequency. Have each team determine the relative frequency for their 50 rounds. </p><p> Follow-up questions and discussion: </p><p>Did the player selected in question 1 actually win the game? In question 1, probability was assigned by intuition – not very scientific. This is one method that is commonly used.</p><p>Total the results on the board and find the relative frequency for the class. Do these results seem more accurate than the individual team results?</p><p> Is there a mathematical method that will assign probability? Hand out the sample space for rolling two dice, and discuss the concept of sample space and equally likely outcomes. Introduce the probability formula for determining probability when outcomes are equally likely.</p><p> Have students circle their winning rolls for diet fractions, and use the formula to determine their chance of winning the game.</p><p> Follow-up questions and discussion:</p><p>How did the results from the mathematical formula compare with the relative frequency results for their individual team?</p><p>How did the results from the formula compare with the relative frequency results for the entire class? Introduce the Law of Large Numbers.</p><p> Summary: The student has used intuition, relative frequency, and a mathematical formula to assign probability. The concepts of event, probability, sample space, equally likely outcomes, and the law of large numbers has been discussed and illustrated.</p><p>Presented by Donna Gorton, Math Instructor, Butler of Andover SAMPLE SPACE FOR ROLLING TWO DICE</p><p>Die #1 Die #2 Notes Die #1 Die #2 Notes</p>