1. 1.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SUMMER INSTITUTE 2014 SESSION 8 25 JUNE 2014 CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE

2. 1.2 TODAY’S AGENDA  Activity 1: Homework review and discussion  Activity 2: An Overview of the Overview!  Activity 3: Grade 11, Lesson 2: Calculating Probabilities of Events Using Two-Way Tables  Small group development of selected problems from this lesson  Reflecting on CCSSM standards Lesson 2  Break  Activity 4: Grade 11, Lesson 3: Calculating Conditional Probabilities and Evaluating Independence Using Two-Way Tables  Small group development of selected problems from this lesson  Reflecting on CCSSM standards aligned to grade 11, Lesson 3  Activity 5: Group presentations  Activity 6: Homework and closing remarks

3. 1.3 ACTIVITY 1 HOMEWORK REVIEW AND DISCUSSION Table discussion Discuss your write ups for the Day 7 homework tasks:  Compare your strategies with others at your table  Reflect on how you might revise your own solution and/or presentation

4. 1.4 Day 7 Homework:  Complete the problem set for Lesson 15.  Extending the mathematics: In Lesson 15, we saw how residuals can be used to estimate the degree to which a linear model fits a given data set. How could residuals be used to estimate the fit of a linear model? How might you use residuals to help you determine which type of model (linear, exponential, quadratic, …) is most appropriate for a given data set?  Reflecting on teaching: Does your current curriculum include as much statistics content in Grade 9 as the Engage ny materials? If not, how might you arrange to align your curriculum more closely to the CCSSM standards? ACTIVITY 1 HOMEWORK REVIEW AND DISCUSSION

5. 1.5 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to… Develop and use two-way frequency tables to calculate and interpret probabilities. Use a “hypothetical 1000” two-way table to interpret given probabilities. Connect probabilities to the context of an investigation.

6. 1.6 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can: calculate probabilities given a two-way table of data. construct a “hypothetical 1,000” two-way frequency table given probabilities. interpret probabilities in context.

7. 1.7 ACTIVITY 2 OVERVIEW OF THE OVERVIEW SO … WHAT’S IN GRADE 11? ENGAGE NY /COMMON CORE GRADE 6, LESSON 20

8. 1.8 ACTIVITY 2 OVERVIEW OF THE OVERVIEW Review the module title and the titles of the lessons from the Table of Contents of the grade 11 module (Algebra 2, Module 4) Review the Focus Standards addressed in this module Read at your table the standards for each cluster. Based on the clusters, describe what lessons you think would be involved within each cluster. What clusters, or standards within the clusters, are not clear to you at this time? Review and discuss the Foundational Standards and Terminology

9. 1.9 ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES In small groups, discuss Lesson 2, Example 1: Building a New High School Develop responses for exercises 1 to 8 Discuss as a whole group exercise 6 Discuss as a whole group exercises 7 and 8

10. 1.10 ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES In small groups, discuss Lesson 2, Example 2: Smoking and Asthma Read and discuss the launch of this example. Discuss how you think this data was collected. Develop as whole group the “hypothetical 1000” two- way table. No household member smokes At least one household member smokes Total Student indicates he or she has asthma Cell 1Cell 2Cell 3 Student indicates he or she does not have asthma Cell 4Cell 5Cell 6 TotalCell 7Cell 81000

11. 1.11 ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES Discuss the following exercises from Lesson 2, Example 2: Smoking and Asthma Exercise 12 Exercise 13 Exercise 14

12. 1.12 ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES Read and discuss the Lesson Summary for Lesson 2. What do you think was the focus of this lesson?

13. 1.13 Review and discuss what you think are the Focus Standards involved in this lesson. Use the Focus Standards outlined in the Overview to guide your selection. ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES Reflecting on the high school CCSSM standards aligned to Lesson 2

14. 1.14 Read Standards for Mathematical Practice.  Discuss what standards you think are developed in this lesson. Read the summary of the standards in the Overview. ACTIVITY 3 LESSON 2: CALCULATING PROBABILITIES OF EVENTS USING TWO-WAY TABLES Reflecting on CCSSM Standards for Mathematical Practice aligned to Lesson 2

15. Break

16. 1.16 ACTIVITY 4 LESSON 3: CALCULATING CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE USING TWO-WAY TABLES – PART 1 CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE ENGAGE NY /COMMON CORE GRADE 11, LESSON 2

17. 1.17 Read and discuss the launch for Example 1. Develop exercises 1 - 6 of Lesson 3 and discuss as a whole group. Develop exercises 7 – 9 of Lesson 3 and discuss as a whole group. Develop exercises 10 – 15 of Lesson 3 and discuss as a whole group. ACTIVITY 4 LESSON 3: CALCULATING CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE USING TWO-WAY TABLES – PART 1

18. 1.18 Summary questions for Lesson 3: What did the probabilities tell us about the students at Rufus King High School? Read the Lesson Summary. How are conditional probabilities calculated from a two-way frequency table? What do you think is the focus of the lessons that build on this lesson? ACTIVITY 4 LESSON 3: CALCULATING CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE USING TWO-WAY TABLES – PART 1

19. 1.19 Review and discuss what you think are the Focus Standards involved in this lesson. Use the Focus Standards outlined in the Overview to guide your selection. ACTIVITY 4 LESSON 3: CALCULATING CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE USING TWO-WAY TABLES – PART 1 Reflecting on the high school CCSSM standards aligned to Lesson 3

20. 1.20 Read Standards for Mathematical Practice.  Discuss what standards you think are developed in this lesson. Read the summary of the standards in the Overview. ACTIVITY 4 LESSON 3: CALCULATING CONDITIONAL PROBABILITIES AND EVALUATING INDEPENDENCE USING TWO-WAY TABLES – PART 1 Reflecting on CCSSM Standards for Mathematical Practice aligned to Lesson 3

21. 1.21 LEARNING INTENTIONS AND SUCCESS CRITERIA Review and discuss the learning intentions and success criteria We are learning to… Develop and use two-way frequency tables to calculate and interpret probabilities. Use a “hypothetical 1000” two-way table to interpret given probabilities. Connect probabilities to the context of an investigation.

22. 1.22 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can: calculate probabilities given a two-way table of data. construct a “hypothetical 10000” two-way frequency table interpret probabilities in context.

23. 1.23 Today’s group presentations: Grade 6, Lesson 5 Grade 6, Lesson 16 Grade 8, Lesson 6 ACTIVITY 5 GROUP PRESENTATION AND UPDATES

24. 1.24  See the Problem Set for Lesson 2. Complete Problem 2 (the Obedience School for Dogs)  Reflection on teaching: Based on your current progress with the resources, reflect on the following: Do you feel you are able to identify lessons for the students you will teach next fall? Explain how you think your students may react to this material. Do you feel prepared or comfortable in presenting selected lessons to your students? Explain. What topics or lessons are you the most uncomfortable with at this time? Explain why you selected these lessons. ACTIVITY 5 HOMEWORK AND CLOSING REMARKS