Welcome to Common Core High School Mathematics Leadership

1. Welcome to Common Core High School Mathematics Leadership 2014-2015 School Year Session 2 • 1 Oct 2014 I’m a model, you know what I mean?(for a probability situation)

2. Today’s Agenda • Continuation of High-Leverage Mathematics Teaching Practices activity • Debrief on MTP 1 and 2: Goals and Tasks • Modeling teaching: sign-up and study of an engageny lesson • Break • Probability content: engageny Grade 7, Lessons 2, 8, and 9 • Closing remarks & For Next Time

3. Learning Intentions and Success Criteria We are learning to… • Understand mathematics teaching practices 1 and 2 (goals and tasks) • Articulate the key constructs in Principles to Actions and their relationships to each other • Describe theoretical and estimated probabilities numerically and using models

4. Learning Intentions and Success Criteria We will be successful when we can: • Describe the relationships between Mathematics Teaching Practices 1 and 2 and the challenges in implementing them • Articulate relationships between teaching, student learning, and the constructs in Principles to Actions at a general level • Calculate theoretical and estimated probabilities and relate them to models of probability situations

5. Activity 1 Principles to actions: Organizing Key constructs

6. Activity 1Principles To actions Individually, write on the graphic organizer how you believe each of these parts are connected to each other.

7. Activity 1Principles To actions Share your connections with your group. Then create a physical model of your connections.

8. Activity 1Principles To actions • Discuss with your group: • What aspects of your own practice do you see in the Mathematics Teaching Practices? • What aspects of the Mathematics Teaching Practices do you see as opportunities for growth and development? • In what ways does your school and district context afford you to enact some of the MTPs well? • In what ways does your school and district context constrain your ability to enact some of the MTPs well?

9. Activity 2 Debriefing Mathematics Teaching Practices 1 and 2

10. Activity 2Mathematics teaching Practices 1 and 2 With your small group, discuss the following: • What are the important considerations in teaching related to establishing mathematical goals? • What sources do you have to help think about appropriate and rigorous mathematical goals? • What is the overarching message of P2A about choosing mathematical tasks to use with students? • What challenges do these two teaching practices pose?

11. Activity 2Mathematics teaching Practices 1 and 2 What aspects of Mathematics Teaching Practices 1 and 2 did you see in the work we did on probability last session?

12. Activity 3 Modeling Lessons from engageNY

13. Activity 3 Modeling lessons from engageny • You will be taking over the presentation of content lessons for 7 of our upcoming sessions • We will feature a survey of probability and statistics content from later in Grade 7, Grade 8, and Grade 11 • Review the lessons available as indicated on the next slide, and sign up for a lesson you would like to present in groups of no more than 3

14. Activity 3 Modeling lessons from engageny Fall 2014 Spring 2015 Grade 11, Lessons 10-11Normal distributions Grade 11, Lessons 14-15Sample variability in the sample proportion Grade 11, Lesson 17-18Sample variability in the sample mean • Grade 7, Lesson 12Using probability to make decisions • Grade 7, Lesson 18Estimating a population mean • Grade 7, Lessons 22 & 23Using sample data to decide if two populations are different • Grade 8, Lesson 12Nonlinear models in a data context

15. Break

16. Activity 4 Modeling & calculating theoretical & Estimated probability EngageNY/Common Core Grade 7, Lessons 2, 8, and 9

17. Activity 4 Calculating and Interpreting Probabilities Targeted CCSSM: • Grade 7 Statistics and Probability • 7.SP.C.5 • Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. • 7.SP.C.6 • Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.

18. Activity 4 Calculating and Interpreting Probabilities Targeted Standard 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.

19. Activity 4 Calculating and Interpreting Probabilities For these two lessons, a focus will be developed on the following Mathematics Teaching Practice: Implement tasks that promote reasoning and problem solving. • Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

20. Activity 4 Calculating and Interpreting Probabilities Learning Intentions for Lessons 2, 8, and 9: We are learning to … • Calculate and interpret a probability as a proportion generated when a chance experiment is repeated many times. • Estimate probabilities based on data that explain the outcomes of an event. • Use probabilities to predict approximate relative frequencies. • Use theoretical and estimated probabilities to model mathematical situations.

21. Activity 4 Calculating and Interpreting Probabilities Success Criteria for Lessons 2, 8, and 9: We will be successful when we can … • Design and interpret the results from chance experiments that are summarized by proportions and interpreted as probabilities. • Interpret the likelihood of outcomes of an event based on estimated probabilities. • Distinguish between and calculate theoretical and estimated probabilities based on a model of a probability situation.

22. Activity 4 Calculating and Interpreting Probabilities The introduction to probability is based on an understanding of the likelihood of an “event” happening. Use the Spinner Game and the likelihood of an event occurring as a way to analyze outcomes discussed in the exercises. The following spinners are used in the exercises to discuss the likelihood of selected colors to occur. Use these spinners to answer the questions in the exercises.

23. Activity 4 Calculating and Interpreting Probabilities

24. Activity 4 Calculating and Interpreting Probabilities

25. Activity 4 Calculating and Interpreting Probabilities Move through the exercises to complete the probability scale outlined in the lessons and outlined on the whiteboard. After discussion of the exercises, individually complete the Exit Ticket for Lesson 1. As a whole group, discuss responses to the exit ticket.

26. Activity 4 Calculating and Interpreting Probabilities Discuss the Carnival Game in Lesson 2. Complete the exercises outlined in Lesson 2. As a whole group, discuss responses. After the exercises have been completed and discussed, move to the Exit Ticket for Lesson 2. Discuss responses and the connection to the learning intentions and success criteria for Lesson 2.

27. Activity 4 Calculating and Interpreting Probabilities Discuss the Targeted Standard for Mathematical Practice MP.2. 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.

28. Activity 4 Calculating and Interpreting Probabilities Discuss the following Mathematics Teaching Practice. Implement tasks that promote reasoning and problem solving. • Effective teaching of mathematics engages students in solving and discussing tasks that promote mathematical reasoning and problem solving and allow multiple entry points and varied solution strategies.

29. For Next Time • Read Principles to Actions, pages 24-34 • Complete the Problem Sets for Grade 7, Lessons 2, 8, and 9 • Write a brief reflection on the following:The Discourse Mathematics Teaching Practice introduces Five Practices for Orchestrating Productive Discussions. Where do you see aspects of these Five Practices in your own teaching, and where might you be interested in developing your teaching further related to these practices? • Bring a task that you have used recently in your classroom that promotes reasoning and problem-solving (MTP 2) and a lesson plan or statement of your goal that accompanied the task (MTP 1). Please bring 5 copies for discussion.