1. 4.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP 2014-2015 SCHOOL YEAR SESSION 4 29 OCT 2014 DECISIONS, DECISIONS

2. 4.2 TODAY’S AGENDA  Probability content: Engage NY Grade 7, Lesson 15  Reading and discussion: Principles to Actions  Break  Model lesson: Engage NY Grade 7, Lesson 12  Lesson Planning (Lesson Debrief for tonight’s teachers)  Closing remarks & For Next Time

3. 4.3 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Understand mathematics teaching practices 1-5  Articulate the range of sampling processes and procedures in a probability modeling situation  Plan, teach, and reflect on a probability and statistics-focused lesson that embodies the Mathematics Teaching Practices

4. 4.4 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Identify aspects of MTP 1-5 in the content learning we have done in CCHSML  Describe how to take a sample to calculate probability  Use probability to make decisions  Develop our practice by participating in a lesson as learners/teachers and as coaches in planning and reflection

5. 4.5 ACTIVITY 1 SAMPLE VARIABILITY ENGAGE NY /COMMON CORE GRADE 7, LESSON 15

6. 4.6 ACTIVITY 1 CONCEPTUALIZING AND CREATING SAMPLES Targeted CCSSM: Grade 7 Statistics and Probability Focus Standards 7.SP.A.1Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. 7.SP.A.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

7. 4.7 ACTIVITY 1 CONCEPTUALIZING AND CREATING SAMPLES Targeted Standards for Mathematical Practice: MP.2 Reason abstractly and quantitatively. Students reason quantitatively by posing statistical questions about variables and the relationship between variables. Students reason abstractly about chance experiments in analyzing possible outcomes and designing simulations to estimate probabilities. MP.3 Construct viable arguments and critique the reasoning of others. Students construct viable arguments by using sample data to explore conjectures about a population. Students critique the reasoning of other students as part of poster or similar presentations.

8. 4.8 ACTIVITY 1 CONCEPTUALIZING AND CREATING SAMPLES Learning Intentions for Lessons 13-15: We are learning  To see the progression of student understanding of sampling exemplified in these Engage NY lessons  To understand that a random selection from a population tends to produce samples that are representative of the population  To understand sample variability

9. 4.9 ACTIVITY 1 CONCEPTUALIZING AND CREATING SAMPLES Success Criteria for Lessons 13-15: We will be successful when we can  Explain how the understanding of sampling grows across these lessons, and how these lessons connect to earlier Grade 7 lessons we have studied.  Select a random sample from a population and explain the relationship between the sample mean and the population mean.  Explain what it means to say that a random sample reflects the population from which it is drawn.

10. 4.10 ACTIVITY 1 SAMPLE VARIABILITY Review:  What is the definition of a random sample?  Why do we need random samples?

11. 4.11 ACTIVITY 1 SAMPLE VARIABILITY  A random sample of size n is a sample such that all possible collections of size n have the same chance of being chosen.  Random sampling is the only way we can be confident that the properties of a sample accurately reflect the properties of the whole population.

12. 4.12 ACTIVITY 1 SAMPLE VARIABILITY Lesson 15: Random Sampling Each table group should choose one random sample of 10 numbers (representing ages of coins) from Bag 1, and one random sample of 10 numbers from Bag 2. Draw and label 2 dot plots on chart paper: one for your Bag 1 sample, and one for your Bag 2 sample.

13. 4.13 ACTIVITY 1 SAMPLE VARIABILITY Bag 1 Population (Data on ages of 150 coins from textbook)

14. 4.14 ACTIVITY 1 SAMPLE VARIABILITY Bag 2 Population (Data on ages of 150 coins from Kevin’s garage)

15. 4.15 ACTIVITY 1 SAMPLE VARIABILITY Bag 2 Population disaggregated (The 150 coins from Kevin’s garage came from 2 different jars)

16. 4.16 ACTIVITY 2 READING AND DISCUSSION PRINCIPLES TO ACTIONS

17. 4.17 ACTIVITY 2 READING AND DISCUSSION: PRINCIPLES TO ACTIONS  Read your group’s assigned teaching practice  Consider the following:  In what ways have our probability lessons together modeled this Mathematics Teaching Practice?  In what ways have our probability lessons together missed opportunities to model this Mathematics Teaching Practice?

18. 4.18 ACTIVITY 2 READING AND DISCUSSION: PRINCIPLES TO ACTIONS  Now, move to your new group that will feature representatives from multiple Mathematics Teaching Practices.  Discuss what you noticed and wondered about our model lessons with respect to the Mathematics Teaching Practices.

19. Break

20. 4.20 ADMINISTRIVIA  Questioning analyses will be shared and discussed next time  As we begin the peer teaching process, “planning time” will encompass three distinct types of activity:  Continued planning for groups who have not yet taught  Coaching by groups that have finished teaching to support continued planning  Debriefing conferences for groups that have just finished teaching (observed and supported by other peer groups)

21. 4.21 GROUPS AND ROLES Class MeetingTeaching (Debrief Partners)PlanningCoaching 4 (today)A (facilitators)B, C, DE, F, G 5B (facilitators)C, D, EA, F, G 6C (F, G)D, EA, B 7D (A)E, F, GB, C 10E (B, C)F, GD 11F (D, E)None 12G (everyone)None A: Michelle, Allison, Hallie, Brian B: Walter, Molly, Lisa C: Lori, Mark S. D: Phil, Claire E: Mark H, Jenny F: Krista, Lindsay, Melissa G: Heather, Brooke, Alan

22. 4.22 ACTIVITY 3 USING PROBABILITY TO MAKE DECISIONS ENGAGE NY GRADE 7, LESSON 12

23. 4.23 ACTIVITY 4 PLANNING, COACHING, AND DEBRIEFING

24. 4.24 ACTIVITY 4 LESSON PLANNING Spend the next 30 minutes with your group in your assigned role (planning, coaching, debriefing). Class MeetingTeaching (Debrief Partners)PlanningCoaching 4 (today)A (facilitators)B, C, DE, F, G 5B (facilitators)C, D, EA, F, G 6C (F, G)D, EA, B 7D (A)E, F, GB, C 10E (B, C)F, GD 11F (D, E)None 12G (everyone)None

25. 4.25 FOR NEXT TIME  Read Principles to Actions, pages 42-48  Complete the Problem Sets for Grade 7, Lessons 12 and 15  Write a brief reflection on the following: The balance between procedural and conceptual knowledge is always a struggle in mathematics. After reading Principles to Actions, reflect on how you balance supporting conceptual and procedural knowledge in your classroom. Give specific examples if you can.