Last One Standing Act 2 and Act 3

1. Last One StandingAct 2 and Act 3 A Kern High School District Anchor Task

2. Last One Standing

3. Last One Standing Act 2 Sit Down!

4. Last One Standing: Act 2 • Before we pass out the dice ... • All students – STAND UP! • Count off the number of students in class today for this experiment. • Sit down and record this number.This is our starting value.

5. Last One Standing: Act 2Prediction • Before we do the experiment, let’s make a prediction! • All students will stand at the start. • On the teacher’s signal, you will each roll your die once. • If you roll a 1, 2, 3, or 4, sit down!

6. Last One Standing: Act 2Prediction • The students still standing will roll again. • If you roll a 1, 2, 3, or 4, sit down! • This process will continue until ALL students are seated. • PREDICT: How many rounds (trials) will it take for the whole class to sit down?

7. Last One Standing: Act 2CLASS DISCUSSION • Record your own prediction quietly. • Share your prediction with your group. Explain your reasoning for your guess. • Share our predictions as a class. Record: • Our class’s lowest guess: • Our class’s highest guess:

8. Last One Standing Act 2 The Experiment

9. Last One Standing: Act 2The Experiment • Each student will need one die. • All students – STAND UP to begin! • On the teacher’s signal, you will each roll your die once. • If you roll a 1, 2, 3, or 4, sit down!

10. Last One Standing: Act 2The Experiment • Count the number of students still standing. • On the teacher’s signal, those standing will each roll their die once again. • If you roll a 1, 2, 3, or 4, sit down! • Continue this process until ALL are seated.

11. Last One Standing: Act 2The Experiment • Once everyone is seated, be sure to record the class’ experimental data for your summary: • The number of students standing foreach round (trial) • Before we write our summary, let’s perform the third and final experiment.

13. Last One Standing Act 3 Sit Down!

14. Last One Standing: Act 3Prediction • Before we do the experiment, let’s make a prediction! • All students will stand at the start. • On the teacher’s signal, you will each roll your die once. • If you roll a 6, sit down!

15. Last One Standing: Act 3Prediction • The students still standing will roll again. • If you roll a 6, sit down! • This process will continue until ALL students are seated. • PREDICT: How many rounds (trials) will it take for the whole class to sit down?

16. Last One Standing: Act 3CLASS DISCUSSION • Record your own prediction quietly. • Share your prediction with your group. Explain your reasoning for your guess. • Share our predictions as a class. Record: • Our class’s lowest guess: • Our class’s highest guess:

17. Last One Standing: Act 3CLASS DISCUSSION • Predict how many students will still be standing after four rolls of the dice. • Predict the names of the students that will still be standing after the four rolls. • Statistics:THE LAW OF LARGE NUMBERS

18. Last One Standing Act 3 The Experiment

19. Last One Standing: Act 3The Experiment • Each student will need one die. • All students – STAND UP to begin! • On the teacher’s signal, you will each roll your die once. • If you roll a 6, sit down!

20. Last One Standing: Act 3The Experiment • Count the number of students still standing. • On the teacher’s signal, those standing will each roll their die once again. • If you roll a 6, sit down! • Continue this process until ALL are seated.

21. Last One Standing: Act 3The Experiment • Once everyone is seated, be sure to record the class’ experimental data for your summary: • The number of students standing foreach round (trial)

23. Data Analysis Act 2: Act 3:

24. Last One StandingAct 2 and Act 3: Data Analysis • In your groups, summarize each of the two experiments using the RULE OF FOUR. Act 2: Act 3:

25. Rule of Four Multiple Representations of Mathematics 1. Numerical Representations:TABLES, PATTERNS 2. Visual Representations:GRAPHS, DIAGRAMS 3. Symbolic Representations:EQUATIONS, EXPRESSIONS 4. Verbal Representations:WORDS, DESCRIPTIONS

27. Data Analysis

28. Summary Act 1: Act 2: Act 3:

30. Summary Questions

31. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 1. Go back and look at your three predictions before each experiment. Were your guesses reasonable? How do they compare with the results of our experiments? Explain.

32. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 2. Summarize how the theoretical models compare with the experimental data collected in each experiment.

33. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 3. Examine the three graphs from the experiments. Explain how they are alike. Explain how they are different.

34. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 4. Examine the three theoretical function rules from the experiments. Explain how they are alike. Explain how they are different. Use precise mathematical vocabulary in your descriptions.

35. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 5. Look at the differences of the graphsand theoretical function rules of questions 3 and 4. List the function rules in the order of the decay factor (multiplier). Explain how the decay factor relates to each graph.

36. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 6. In each of the experiments, after a certain number of rolls of the dice, no students were left standing. However, the values from the theoretical function rules will never exactly reach the number ZERO. Is there a problem with our theoretical function rule? Explain your reasoning.

37. Last One Standing: Acts 1, 2, 3CLASS DISCUSSION and SUMMARY 7. Summarizeyour learnings from these experiments.

39. Last One Standing Extension

40. Last One Standing – Extension There are eighty students in third period PE class. Today, they are going to do a “Last One Standing” experiment with an eight-sided die. The students that roll a 2, 5, or 6 must sit down in each round. How many rounds will it take for the whole class to sit down?

41. Last One Standing – Extension