1. 14.1 WELCOME TO COMMON CORE HIGH SCHOOL MATHEMATICS LEADERSHIP SCHOOL YEAR 2015-2016 SESSION 14 20 APRIL 2016 CLOSING THE CYCLE

2. 14.2 TODAY’S AGENDA  Eureka Math G10 M5 L20 and L21: Cyclic Quadrilaterals  Big ideas discussion  Break  Leadership Panels  Closing remarks and reflections  Final assessments  Celebratory reception at 42 Ale House

3. 14.3 SAVE THE DATE  Milwaukee Area Math Council Meeting Saturday 14 May 2016, 9am-noon, UWM Enderis Hall 1 st floor  We would like for as many of you as possible to participate in panels on teacher development, curriculum, and professional development.  Are you in?

4. 14.4 ACTIVITY 1 CYCLIC QUADRILATERALS EUREKA MATH TM GRADE 10 MODULE 5 LESSONS 20 AND 21 As you engage, consider: what aspects of the four Big Ideas do you notice in the lesson? Record tangible examples to share at the lesson’s conclusion.

5. 14.5 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Triangles  Draw three points on a piece of paper.  Can you draw a circle that passes through all three of your points? Explain why or why not.

6. 14.6 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Quadrilaterals  Now draw four points on a piece of paper.  Can you draw a circle that passes through all four of your points? Explain why or why not.

7. 14.7 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Quadrilaterals  Definition Quadrilateral ABCD is cyclic if it can be inscribed in a circle; i.e. if there is a circle passing through all four points A, B, C, and D.  What relation must hold between the angles at A and C, if quadrilateral ABCD is cyclic?

8. 14.8 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Quadrilaterals  We have seen, that if quadrilateral ABCD is cyclic, then opposite vertex angles must be supplementary (add up to 180 O ).  Is the converse true?

9. 14.9 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Quadrilaterals  Suppose that opposite angles in quadrilateral ABCD are supplementary. We can certainly draw a circle through A, B and C.  Must D also lie on this same circle?  Hint. Apply the secant and inscribed angle theorems to angles B and D. You have to exclude two cases: that D is outside the circle, and that D is inside the circle.

10. 14.10 ACTIVITY 1 CYCLIC QUADRILATERALS Cyclic Quadrilateral Theorem  Quadrilateral ABCD is cyclic if and only if opposite angles are supplementary.

11. 14.11 ACTIVITY 1 CYCLIC QUADRILATERALS Area of a triangle  Explain why the area of triangle ABC is given by ½ bc sin(A).  Express this formula in words, without explicitly referring to the symbols in the diagram.

12. 14.12 ACTIVITY 1 CYCLIC QUADRILATERALS Area of a cyclic quadrilateral  Explain why the area of cyclic quadrilateral ABCD is given by ½ (AC)(BD) sin(w), where w is the (acute) angle between the diagonals.  Hint: add up the areas of four triangles.  Express this formula in words, without explicitly referring to the symbols in the diagram.

13. 14.13 ACTIVITY 1 CYCLIC QUADRILATERALS Ptolemy’s Theorem  For a cyclic quadrilateral ABCD, (AC)(BD) = (AB)(CD) + (BC)(AD)  Express this formula in words.  Draw a cyclic quadrilateral on a piece of paper, and verify that Ptolemy’s Theorem appears to be true.

14. 14.14 ACTIVITY 1 CYCLIC QUADRILATERALS An Application of Ptolemy’s Theorem  Draw a rectangle ABCD inscribed in a circle.  What does Ptolemy’s Theorem say about this situation?

15. 14.15 ACTIVITY 1 CYCLIC QUADRILATERALS  There are several pages devoted to Ptolemy's Theorem on the Cut The Knot website.Ptolemy's TheoremCut The Knot  Ptolemy’s theorem can be used to prove the addition laws for the sine and cosine functions.addition laws for the sine and cosine functions Since Ptolemy’s theorem can also be used to prove the Pythagorean theorem, this means that all of trigonometry is summarized or encoded in this one theorem!

16. 14.16 ACTIVITY 2 “BIG IDEAS” DISCUSSION FROM NCTM ESSENTIAL UNDERSTANDINGS FOR GEOMETRY GRADES 9-12

17. 14.17 ACTIVITY 2 “BIG IDEAS” DISCUSSION  Reflect on your own about how the focus on the Big Ideas allowed you to make connections between this lesson and other Geometry concepts.  Add some notes to the Big Ideas packet from last time regarding tonight’s lesson.

18. 14.18 ACTIVITY 2 “BIG IDEAS” DISCUSSION  Big Idea 1: Working with diagrams is central to geometric thinking.  Big Idea 2: Geometry is about working with variance and invariance, despite appearing to be about theorems.  Big Idea 3: Working with and on definitions is central to geometry.  Big Idea 4: A written proof is the endpoint of the process of proving.

19. 14.19 ACTIVITY 2 “BIG IDEAS” DISCUSSION Revisit your concept map from Class 9 and add to it (in a different color) or create a new map if you’d like to start from scratch. Make sure you label them (Winter and Spring) and put your name on them.

20. Break

21. 14.21 ACTIVITY 3 LEADERSHIP PANELS

22. 14.22  Format of Leadership Panel Discussions (15 minutes each)  Slide summarizing each project & outcomes  What was successful about your overarching theme?  What was challenging across the projects?  What aspect of a colleague’s project is interesting or useful to you going forward?  Groups and topics:  Hoffman, Hongsermeier, and Moss: Supporting teacher growth  Sagrillo, Garrity, and Neuworth: Developing student teachers and alt-cert teachers  Pedrick, Kroll, Wells, and Gerlach: Curriculum development  Rekowski, Rozga, and Schmeling: Changing teaching, learning, and assessment ACTIVITY 3 LEADERSHIP PANELS

23. 14.23 SUPPORTING TEACHER GROWTH MARK, MELISSA, AND ALLISON Mark Lead the rewriting of the high school Geometry curriculum.  Rigor vs Accessiblity  What topics to keep?  Transformations?  What will the assessments look like?  What will be expected of all students?  What will be expected of top students?  May 9 th inservice on Big Ideas, Transformational activities, look at staffing and future Melissa  Increase high level tasks in Algebra I  Created 3 unit plans and 1 mini-unit with 1 new task in each Allison  Understand logistics of the school  Plan lessons/write assessments  Promote mathematical discourse  Classroom management (behavior)  Became more comfortable with Geometry material  Collaborated on day-to-day lessons and summative assessments  Worked on discourse/reading strategies  Implemented expectations policy

24. 14.24 DEVELOPING BEGINNING TEACHERS JENNY, ANDREA, & MADELINE Andrea  Hosting a student teacher  Strong in lesson planning and conceptual activity  Challenges with precision, assessment, and learning targets  Social presence a significant challenge Jenny  hosted a Marquette student teacher in the Fall  worked on his formative assessment strategies,  later moved to his classroom management – ineffective management was getting in the way of teaching the 9th grade students. Madeline  Mentor to a new TFA teacher  Co-planned and demonstrated lessons  Strengths: planning and collaboration  Challenges: time, differing classes

25. 14.25 CURRICULUM DEVELOPMENT LORI, LINDSAY, WALTER, & CLAIRE Walter & Claire  Purpose: To combat the 40% failure rate in Algebra 1  How: Using the Math teaching standards to improve student success  Challenges: Administration not backing us on the proposal for a new class Lori & Lindsay  Create a textbook selection process for a Geometry adoption  Create rubrics for evaluating materials that will translate to other content area adoptions in the future

26. 14.26 CHANGING TEACHING, LEARNING, AND ASSESSMENT MICHELLE, MOLLY, & HALLIE Hallie  Very large misconceptions about what REAL Academy is  Alternative school = jail, punishment, not equal  Opportunity to share student’s experience  REAL Academy = choice, different way to do school, opportunity  Use of numbers and data to present the facts! Michelle  Current assessments are almost 100% procedural  Engage NY assessments are upper level questions, rigorous, and require perseverance with multiple steps/multiple parts problems Molly  Assessing is about more than a single right answer.  Work and process are just as important in determining student success as the answer.  Single Point Rubrics on assessments have allowed students to know exactly what is on the assessment, giving them a “checklist” of what is needed.  Assessment scores are more aligned to which objectives a student has met, rather than a percentage of correct scores.

27. 14.27 ACTIVITY 4 CLOSING REMARKS

28. 14.28 ACTIVITY 4 REFLECTING The last piece of It’s TIME that you read dealt with professional learning.  What aspects of professional learning did you take away from the CCHSML experience?  Where do you want to go next with your own professional learning?  In what ways might you help your colleagues learn and grow?

29. 14.29 ACTIVITY 4 REFLECTIONS  A reminder: our work was sponsored by the Title II(b) program that has been a part of the Elementary and Secondary Education Act (now ESSA).  If this program has supported your professional learning, a quick note to your Congressional representative helps to keep the funding streams open for teacher professional learning.

30. 14.30 ACTIVITY 5 FINAL ASSESSMENTS

31. 14.31 ACTIVITY 6 CELEBRATORY RECEPTION AT 42 ALE HOUSE 3807 S PACKARD AVE, ST FRANCIS