03.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR SESSION 3 14 OCTOBER 2015 EVERYTHING OLD IS NEW AGAIN

03.2 TODAY’S AGENDA  Exploring the PRIME document  The Oldest Geometric Theorem (Eureka Math TM G10 M5 L1)  Break  “Big Ideas” discussion  Pre-observation tool  Modeling mentoring conversations  Homework and closing remarks

03.3 ACTIVITY 1 THE PRIME FRAMEWORK

03.4 ACTIVITY 1 THE PRIME FRAMEWORK  Analysis of Leadership  Discuss Scenario 3

03.5 ACTIVITY 1 THE PRIME FRAMEWORK Four aspects of the PRIME Framework  Teaching and Learning  Equity  Assessment  Curriculum

03.6 ACTIVITY 1 THE PRIME FRAMEWORK  Principles (4)  Indicators (3 per Principle)  Stages (3 per Indicator)  Stage 1: Leadership of Self  Stage 2: Leadership of Others  Stage 3: Leadership of Community See pages Questions to Discuss:  In what ways does the framework help you describe the leadership work that you currently do?  In what ways does the framework help you identify ways in which you could expand your leadership?  What challenges and questions does the framework raise for you?

03.7 ACTIVITY 1 THE PRIME FRAMEWORK  Leadership Pre-Observation Reflection Form  To help our observers understand your classroom, school, and district context  Connect your leadership proposal and the PRIME framework to the context in important ways  Provide tailored guidance and advice to help your leadership project be effective

03.8 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM EUREKA MATH TM GRADE 10 MODULE 5 LESSON 1

03.9 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Warm-up:  How could you carve a semi-circular trough out of a block of wood?

03.10 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Lesson goals  To understand Thales’ theorem and its converse

03.11 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Turn and talk:  What do we mean by the converse of a theorem?

03.12 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM  Mark points A and B on a white sheet of paper  Take a sheet of coloured paper, and push that paper up between points A and B on the white sheet  Mark on the white paper the location of the corner of the coloured paper, as in the figure to the right  Use a different colour than black to mark the point  Repeat this multiple times, pushing the coloured paper up at different angles.  What curve do the coloured points seem to trace?

03.13 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM  What curve do your marked points seem to trace?  Where might the centre of that semicircle be?  What would the radius of the semicircle be?  What would we need to show to prove that the marked points do indeed lie on a semicircle?

03.14 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Conjecture:  Given two points A and B, let P be the midpoint of the segment joining them. If C is any point such that ACB is right, then BP = AP = CP. In particular, C lies on the circle with center P and diameter AB.

03.15 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Hint:

03.16 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM How does this diagram help to prove our conjecture?

03.17 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Theorem (Converse of Thales’ Theorem) Given two points A and B, let P be the midpoint of the segment joining them. If C is any point such that ACB is right, then BP = AP = CP. In particular, C lies on the circle with center P and diameter AB.

03.18 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Theorem (Thales’ Theorem) If A, B and C are three points on a circle with diameter through A and B, then ACB is a right angle.

03.19 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM Lesson goals  To understand Thales’ theorem and its converse

03.20 ACTIVITY 2 THE OLDEST GEOMETRIC THEOREM  How could you carve a semi-circular trough out of a block of wood?  Use the ideas you have learned in this lesson to explain your answer.

03.21 ACTIVITY 3 “BIG IDEAS” DISCUSSION FROM NCTM ESSENTIAL UNDERSTANDINGS FOR GEOMETRY GRADES 9-12

03.22 ACTIVITY 3 “BIG IDEAS” DISCUSSION  Big Idea 4 was very prominent in this lesson.  Consider Essential Understanding 4c: Behind every proof is a proof idea.  During break, read pages about Essential Understanding 4c, and consider:  What was the proof idea in this lesson?

Break

03.24 ACTIVITY 3 “BIG IDEAS” DISCUSSION  Consider Essential Understanding 4c: Behind every proof is a proof idea.  What was the proof idea in our lesson tonight?  In what ways might we think about helping our students think about proof ideas as they approach the process of reasoning and proving?

03.25 ACTIVITY 4 MODELING MENTORING CONVERSATIONS

03.26 ACTIVITY 4 MODELING MENTORING CONVERSATIONS  Five phases of an instructional conference:  Launching  Reflecting  Reinforcing  Refining  Reflecting

03.27 ACTIVITY 4 MODELING MENTORING CONVERSATIONS Content Standards and Mathematics Goals Understand and apply theorems about circles. G-C.2 Identify and describe relationships among inscribed angles, radii, and chords. Big Ideas Big Idea #2: Geometry is about working with variance and invariance, despite appearing to be about theorems. 2a. Underlying any geometric theorem is an invariance… Big Idea #4: A written proof is the endpoint of the process of proving. 4c. Behind every proof is a proof idea. Standards for Mathematical Practice MP6 – Attend to precision. Definition of a circle, theorem vs. converse MP3 – Construct viable arguments and critique the reasoning of others. The process of proving is constructing an argument. Mathematics Teaching Practices MTP4: Facilitate meaningful discourse. I want to incorporate feedback from the last lesson to improve small group and whole group discussion.

03.28  Fill out the Leadership Plan and PRIME Framework with respect to your Leadership Project.  Provide feedback on the draft of the Leadership Project Pre-Observational Reflections form.  Once your Project Proposal is approved, schedule an observation visit with Henry or Butch to have the pre-observation conference. ACTIVITY 5 HOMEWORK AND CLOSING REMARKS