10.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION FEB 2015 NORMAL IS A STATE OF MIND BEST FORGOTTEN, BUT A USEFUL DATA STRUCTURE

10.2 TODAY’S AGENDA  Sharing our classroom artifacts: Connecting to the Mathematics Teaching Practices  Access and Equity: Continuing our conversations  Break  Grade 11, Lesson 9: Using a Curve to Model a Data Distribution  Reflection on the Lesson  Closing remarks & For Next Time

10.3 LEARNING INTENTIONS AND SUCCESS CRITERIA We are learning to…  Collect evidence of the 8 Mathematics Teaching Practices in classroom artifacts  Consider multiple facets of access and equity as it pertains to mathematics teaching and learning  Understand the characteristics of a normal distribution

10.4 LEARNING INTENTIONS AND SUCCESS CRITERIA We will be successful when we can:  Connect our classroom artifacts to evidence of one or more of the eight Mathematics Teaching Practices  Connect times when we have experienced inequity to our students’ experiences in learning mathematics  Distinguish normal distributions from non-normal distributions using characteristics of the data set

10.5 ACTIVITY 1 SHARING OUR ARTIFACTS CONNECTING TO THE P2A MATHEMATICS TEACHING PRACTICES

10.6 ACTIVITY 1 CONNECTING ARTIFACTS AND MATH TEACHING PRACTICES  In your pairs, discuss what aspects of the Mathematics Teaching Practices are evident in your classroom artifacts  As a storyteller, present the context and how the artifacts illustrate 1-2 of the MTPs.  As a listener, what do you notice and wonder about the artifacts and their relationships to the MTPs? 1. Establish mathematics goals to focus learning 2. Implement tasks that promote reasoning and problem solving 3. Use and connect mathematical representations 4. Facilitate meaningful mathematical discourse 5. Pose purposeful questions 6. Build procedural fluency from conceptual understanding 7. Support productive struggle in learning mathematics 8. Elicit and use evidence of student thinking

10.7 ACTIVITY 1 CONNECTING ARTIFACTS AND MATH TEACHING PRACTICES Collaborate with another nearby pair that discussed some of the same Mathematics Teaching Practices. What did you learn about the MTPs you discussed across the different sets of artifacts?

10.8 ACTIVITY 2 DISCUSSING ISSUES OF ACCESS AND EQUITY PRINCIPLES TO ACTIONS

10.9 ACTIVITY 1 DISCUSSING ISSUES OF ACCESS AND EQUITY Organization of Principles to Actions  Effective Teaching and Learning (8 Mathematics Teaching Practices)  Essential Elements  Access and Equity  Curriculum  Tools and Technology  Assessment  Professionalism

10.10 ACTIVITY 2 DISCUSSING ISSUES OF ACCESS AND EQUITY In your own notebook, write briefly about a time in which you experienced inequity.

10.11 ACTIVITY 2 DISCUSSING ISSUES OF ACCESS AND EQUITY Discuss the belief given to your group. Specifically:  What aspects of this belief resonate with you?  What aspects of this belief do not?  Are there special cases, circumstances, or instances in which this belief may or may not apply?

10.12 ACTIVITY 2 DISCUSSING ISSUES OF ACCESS AND EQUITY Do you believe that academic Standards (like CCSSM) are important? Why or why not?

Break

10.14 ACTIVITY 3 USING A CURVE TO MODEL A DATA DISTRIBUTION ENGAGE NY GRADE 11, LESSON 9

10.15 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING Center, shape, and spread (Grade 6) Variability and MAD (Grade 6) Standard Deviation and residuals (Grade 9) Normal distribution and curve modeling (Grade 11) Assumptions of statistical tests (Statistics/ AP Statistics)

10.16 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING Mean ±1 MAD Mean ±1 SD

10.17 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING

10.18 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  Turn and talk: what is a relative frequency histogram?

10.19 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  Study the data on heights of procompsognathid dinosaurs in Lesson 9.  What structure or patterns do you see in the table?  What structure or patterns do you see in the histogram?  Discuss your group’s answers to Exercises 1 through 4.

10.20 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  Discuss Exercises 5 through 8.

10.21 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  Read Example 2 (Gas Mileage and the Normal Distribution) and complete Exercise 9.

10.22 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  What is a normal distribution?  As teachers, we should be aware that normal distributions are not just any bell-shaped curves. Rather, they are described by a very specific function family.  The standard normal distribution is described by the function

10.23 ACTIVITY 3 NORMAL DISTRIBUTION AND CURVE MODELING  A normal distribution with mean μ and standard deviation σ is described by the function Image source:

10.24 ACTIVITY 4 REFLECTING ON THE LESSON

10.25 ACTIVITY 4 REFLECTING ON THE LESSON  What aspects of the 8 Mathematics Teaching Practices did you see (or not see) as we taught the lesson?  In what ways did this lesson attend to issues of Access and Equity?

10.26 FOR NEXT TIME  Complete the problem set for Grade 11, Lesson 9  Respond to the following prompt: Identify a demographic aspect of your student population that is an important consideration when thinking about access and equity. Identify a few ways that can we make our mathematics teaching more relevant and accessible to this population.  Bring in artifacts for analysis and discussion.