9.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 1 17 SEPT 2014 TAKING CHANCES (IN CONTENT AND PEDAGOGY)

9.2 TODAY’S AGENDA  Welcome and overview of the year  Our Beliefs about Mathematics Teaching and Learning  High-Leverage Mathematics Teaching Practices reading & activity  Break  Probability content: engage ny Grade 7, Lessons 1 and 2  Housekeeping: Syllabus & Expectations  Closing remarks & For Next Time

9.3 ACTIVITY 1 WELCOME AND OVERVIEW OF THE YEAR A Quick Refresher for Our Colleagues  Where do you teach?  What is your teaching load this year?  How are you thinking about integrating statistics and probability?

9.4 ACTIVITY 1 WELCOME AND OVERVIEW OF THE YEAR Our focus for this year  Extend our study of statistics and probability with an emphasis on the probability thread (Grades 7 and 11 in engage ny )  Become familiar with the high-leverage Mathematics Teaching Practices (MTP) in NCTM’s Principles to Actions (P2A)  Use the MTP to analyze our own practice  Begin thinking about leadership and mentoring

9.5 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Articulate our beliefs about mathematics teaching  Identify and describe high-leverage mathematics teaching practices  Relate the notion of chance to the mathematical construct of probability

9.6 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Create a visual representation of our beliefs about mathematics teaching  Name the 8 Mathematics Teaching Practices in Principles to Actions and describe how our teaching relates to them  Interpret probabilities and calculate them based on theoretical situations and data

9.7 ACTIVITY 2 ARTICULATING OUR BELIEFS AS MATHEMATICS TEACHERS

9.8 ACTIVITY 2 BELIEFS ABOUT MATHEMATICS TEACHING Why this activity, and why now?  Our beliefs about teaching shape how we approach both learning mathematics and teaching mathematics  Sometimes we act in ways aligned with our beliefs, and other times we act in ways that are not  As we think about our pedagogy and teach this year, reflecting on our beliefs regularly will be important

9.9 ACTIVITY 2 BELIEFS ABOUT MATHEMATICS TEACHING Consider and describe “what is at the heart of your mathematics teaching that students need to experience regularly”.  Begin by writing beliefs statements on sticky notes. For example:  Mistakes and confusion are an essential part of the process of learning mathematics.  I believe that it is important for students to have some opportunities to work together and some opportunities to work alone.  Organize your ideas into a concept map format on poster paper. Locate the ideas that most closely related to the “heart of your mathematics teaching” nearest the center of the map.  Our beliefs about teaching shape how we approach both learning mathematics and teaching mathematics  Sometimes we act in ways aligned with our beliefs, and other times we act in ways that are not  As we think about our pedagogy and teach this year, reflecting on our beliefs regularly will be important

9.10 ACTIVITY 2 BELIEFS ABOUT MATHEMATICS TEACHING  Next, consider the numbered list of 78 statements on the sheets provided.  Add any of these belief statements that you see fit on a differently-colored sticky note. Please mark the number in the lower right-hand corner.

9.11 ACTIVITY 3 PRINCIPLES TO ACTIONS

9.12 ACTIVITY 3 PRINCIPLES TO ACTIONS “Principles to Actions describes the conditions, structures, and policies that must exist for all students to learn. It addresses the essential elements of teaching and learning, access and equity, curriculum, tools and technology, assessment, and professionalism. Finally, it suggests specific actions that teachers and stakeholders need to take to realize our shared goal of ensuring mathematical success for all.” Principles to Actions, Preface, p. vii

9.13 ACTIVITY 3 PRINCIPLES TO ACTIONS  Read pages 7-12 in Principles to Actions.

9.14 ACTIVITY 3 PRINCIPLES TO ACTIONS  How do we make sense of this?

9.15 ACTIVITY 3 PRINCIPLES TO ACTIONS Individually, write on the graphic organizer how you believe each of these parts are connected to each other.

9.16 ACTIVITY 3 PRINCIPLES TO ACTIONS Share your connections with your group. Then create a physical model of your connections.

9.17 ACTIVITY 3 PRINCIPLES 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?

Break

9.19 ACTIVITY 4 CHANCE EXPERIMENTS & ESTIMATING PROBABILITIES BY COLLECTING DATAENGAGE NY /COMMON CORE GRADE 7, LESSONS 1–2

9.20 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.

9.21 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.

9.22 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.

9.23 ACTIVITY 4 CALCULATING AND INTERPRETING PROBABILITIES Learning Intentions for Lessons 1 and 2: We are learning to …  Use informal language to describe the probability of an event using a probability scale from 0 to 1.  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.

9.24 ACTIVITY 4 CALCULATING AND INTERPRETING PROBABILITIES Success Criteria for Lessons 1 and 2: We will be successful when we can …  Describe the probability of several events using a probability scale that assigns the number 0 to an event that is “impossible” to 1 that is an event that is “certain.”  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.

9.25 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.

9.26 ACTIVITY 4 CALCULATING AND INTERPRETING PROBABILITIES

9.27 ACTIVITY 4 CALCULATING AND INTERPRETING PROBABILITIES

9.28 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.

9.29 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 Lessons 1 and 2.

9.30 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.

9.31 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.

9.32 ACTIVITY 5 SYLLABUS & EXPECTATIONS

9.33 ACTIVITY 5 ASSIGNMENTS & EXPECTATIONS  We will be engaging in regular, small-scale assignments that involve:  Planning for the use of the Mathematics Teaching Practices in your classrooms  Bringing back and discussing those artifacts in our sessions  Our general structure to sessions will feature:  Time for sharing, analyzing, and discussing artifacts  The study and discussion of one or more of the Mathematics Teaching Practices  Work on the content of probability

9.34 ACTIVITY 5 ASSIGNMENTS & EXPECTATIONS

9.35 ACTIVITY 5 ASSIGNMENTS & EXPECTATIONS

9.36 FOR NEXT TIME  Read Principles to Actions, pages 7-23  Complete the Problem Sets for Grade 7, Lessons 1 and 2  Put a set of beliefs sticky notes on your desk; record new beliefs as they occur to you as you teach  Write a brief reflection on the following: In considering the introduction to Principles to Actions and your beliefs about teaching mathematics, what aspects of your teaching practice are you most compelled to examine closely over the course of this year?