1. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 1: Transformations, Congruence, and Similarity May 8, 2012 Session will be begin at 4:30 pm While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

2. CCGPS Mathematics Unit-by-Unit Grade Level Webinar 8 th Grade Unit 1: Transformations, Congruence, and Similarity May 8, 2012 James Pratt – jpratt@doe.k12.ga.usjpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usbkline@doe.k12.ga.us Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

3. Welcome! Thank you for taking the time to join us in this discussion of Unit 1. At the end of today’s session you should have at least 3 takeaways:  the big idea of Unit 1  something to think about…some food for thought  how might I approach this unit next fall?  what is my conceptual understanding of the material in this unit?  a list of resources and support available for CCGPS mathematics

4. Welcome! For today’s session:  read the standards  read the unit  downloaded and saved the documents from this session Ask questions and share resources/ideas for the common good.

5. Welcome! Please provide feedback at the end of today’s session.  Feedback helps us become better teachers, and it helps you to reflect upon your learning.  Feedback helps us as we develop the remaining unit-by-unit webinars.  Please visit http://ccgpsmathematics6-8.wikispaces.com/ to provide us with your feedback, ask questions, and share your ideas and resources.http://ccgpsmathematics6-8.wikispaces.com/ After reviewing the remaining units, please contact us with content area focus/format suggestions for future webinars. James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usjpratt@doe.k12.ga.usbkline@doe.k12.ga.us Secondary Mathematics Specialists

6. Clearing up confusion This webinar focuses on CCGPS content specific to one grade level and one unit within that grade. For information about CCGPS across a single grade span, please access the list of recorded GPB sessions on Georgiastandards.org. For information about the Standards for Mathematical Practice, please access the list of recorded Blackboard sessions from Fall 2011 on GeorgiaStandards.org. CCGPS is taught and assessed from 2012-2013 and beyond. PARCC assessments begin in 2014-2015. A list of resources will be provided at the end of this webinar.

7. Activate your Brain Are the following two figures congruent? Use transformations to justify your answer.

8. Activate your Brain Are the following two figures congruent? Use transformations to justify your answer. 1.Rotate

9. Activate your Brain Are the following two figures congruent? Use transformations to justify your answer. 1.Rotate 2.Translate

10. Activate your Brain Are the following two figures congruent? Use transformations to justify your answer. 1.Rotate 2.Translate 3.Figures are congruent because the second figure can be obtained from the first by a sequence of a rotation and a translation!

11. SEDL Common Core Support Video: MCC8.G.2 Sequence of Transformations to Demonstrate Congruence http://secc.sedl.org/common_core_videos/index.php?action=vi ew&id=781

12. What’s the big idea? Enduring Understandings Essential Questions Key Standards Overview

13. What’s the big idea? Unit 1: Transformations, Congruence and Similarity Geometry Understand congruence and similarity using physical models, transparencies, or geometry software. New Content Transformation – came from 7 th grade Similarity – came from 7 th grade Congruence – not addressed in this manner

14. What’s the big idea? Developing deep understanding of transformations of geometric figures. Using informal arguments to establish geometric facts.

15. Navigating a Unit Table of Contents  Overview  Standards  Enduring Understandings  Essential Questions  Selected Terms and Symbols  Classroom Routines  Strategies for Teaching and Learning  Evidence of Learning  Tasks

16. Navigating a Unit What’s New? Concepts and Skills to Maintain Strategies for Teaching and Learning Evidence of Learning

17. Navigating a Unit What’s New? Task Table  Task Type  Grouping Strategy  Task Description

18. Navigating a Unit What’s New? Classroom Routines  SMP’s (analyzing, estimating, reasoning, describing patterns, defending, discussing, peer feedback, contentious discourse, answering, etc.)  Collaborative skills (How collaborative are your collaborative activities?)  Productive Struggle  Classroom technology, materials…how to use materials in a productive manner.  Journaling/Notebook  Development of own understanding  The regular use of routines is important to the development of students’ number sense, flexibility, fluency, collaborative skills and communication.

19. Navigating a Unit Classroom Routines What might all of this look like in the classroom?  http://ccgpsmathematics6-8.wikispaces.com/ http://ccgpsmathematics6-8.wikispaces.com/ Also check out:  Inside Mathematics : Mathematical Community of Learners - http://www.insidemathematics.org/index.php/video-tours-of-inside- mathematics/classroom-teachers/157-teachers-reflect-mathematics- teaching-practices http://www.insidemathematics.org/index.php/video-tours-of-inside- mathematics/classroom-teachers/157-teachers-reflect-mathematics- teaching-practices  Edutopia.org - Chris Optiz  http://www.edutopia.org/math-social-activity-cooperative-learning- video http://www.edutopia.org/math-social-activity-cooperative-learning- video  http://www.edutopia.org/math-social-activity-sel http://www.edutopia.org/math-social-activity-sel

20. Unit 1 Transition Standard Teach 2012-13 MCC7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.

21. Coherence and Focus – Unit 1 What are students coming with?

22. Coherence and Focus – Unit 1 What foundation is being built? Where does this understanding lead students?

23. Coherence and Focus – Unit 1 View across grade bands K-7 th  Work with angles, lines of symmetry, and graphing geometric figures in the coordinate plane.  Facts about supplementary, complementary, vertical, and adjacent angles. 9 th -12 th  Describe transformations as functions.  Connect congruence criteria to transformations.  Formal proofs of congruence, similarity, and parallel lines cut by a transversal.

24. Examples & Explanations Understand congruence and similarity using physical models, transparencies, or geometry software.

25. Examples & Explanations For each vertex of the triangle in the form (x, y), create its image at the coordinates (2x, 2y). What is the result? CB A

26. Examples & Explanations For each vertex of the triangle in the form (x, y), create its image at the coordinates (2x, 2y). What is the result? CB A A: (4, 6) B: (7, 4) C: (4, 4)

27. Examples & Explanations For each vertex of the triangle in the form (x, y), create its image at the coordinates (2x, 2y). What is the result? CB A A: (4, 6) A’: (8, 12) B: (7, 4) B’: (14, 8) C: (4, 4) C’: (8, 8) A’ B’C’

28. Examples & Explanations For each vertex of the triangle in the form (x, y), create a second image at the coordinates (½x, ½y). What is the result? A’ B’C’ A: (4, 6) A’: (8, 12) B: (7, 4) B’: (14, 8) C: (4, 4) C’: (8, 8) CB A A’ B’C’

29. Examples & Explanations For each vertex of the triangle in the form (x, y), create a second image at the coordinates (½x, ½y). What is the result? A’ B’C’ A: (4, 6) A’: (8, 12) A”: (2, 3) B: (7, 4) B’: (14, 8) B”: (3.5, 2) C: (4, 4) C’: (8, 8) C”: (2, 2) CB A A’ B’C’ A” B”C”

30. Examples & Explanations For each vertex of the triangle in the form (x, y), create a second image at the coordinates (½x, ½y). What is the result? A’ B’C’ A: (4, 6) A’: (8, 12) A”: (2, 3) B: (7, 4) B’: (14, 8) B”: (3.5, 2) C: (4, 4) C’: (8, 8) C”: (2, 2) CB A A’ B’C’ A” B”C”

31. Examples & Explanations Use informal arguments to establish facts about:  the angle sum and exterior angle of triangles.  the angles created when parallel lines are cut by a transversal.  the angle-angle criterion for similarity of triangles.

32. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

33. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

34. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

35. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

36. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

37. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 1 2 t s

38. Examples & Explanations If lines m, n and p are parallel and cut by transversals t and s, find the measures of angles 1 and 2. m n p 67° 23° 67° t s

39. Examples & Explanations Adapted from the Arizona department of Education Show that m ∠ 3 + m ∠ 4 + m ∠ 5 = 180˚ if and m are parallel lines and t1 & t2 are transversals. Find the m ∠ a, m ∠ b, and the m ∠ c if line n and segment yz are parallel. n

40. Examples & Explanations Understand congruence and similarity using physical models, transparencies, or geometry software.

41. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

42. SEDL Common Core Support Video: MCC8.G.2 Using a Physical Model to Demonstrate a Reflection http://secc.sedl.org/common_core_videos/index.php?action=vi ew&id=781

43. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

44. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

45. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

46. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

47. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

48. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

49. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence?

50. Examples & Explanations Describe a sequence of transformations that results in the transformation of the blue figure to the red figure. Is there more than one possible sequence? 1.Reflected the figure in the y-axis. 2.Rotated the figure 90° clockwise about the point (2, -5). 3.Translated the figure vertically +10 units, or ten was added to the y-coordinate of each point of the figure: (x, y) → (x, y + 10).

51. Assessment How could it look? Examples of how balanced assessments can be assembled. http://map.mathshell.org/materials/tests.php  The target audience for these example assessments are: 1.teachers who have already started to work on their student’s mathematical practice skills 2.designers of future CCSSM-aligned assessments

52. Assessment How could it look? http://map.mathshell.org/materials/tests.php

53. Resource List The following list is provided as a sample of available resources and is for informational purposes only. It is your responsibility to investigate them to determine their value and appropriateness for your district. GaDOE does not endorse or recommend the purchase of or use of any particular resource.

54. Resources Common Core Resources  SEDL videos - https://www.georgiastandards.org/Common-Core/Pages/Math.aspx or http://secc.sedl.org/common_core_videos/https://www.georgiastandards.org/Common-Core/Pages/Math.aspx http://secc.sedl.org/common_core_videos/  Illustrative Mathematics - http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/  Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/http://www.ccsstoolbox.com/  Arizona DOE - http://www.azed.gov/standards-practices/mathematics-standards/http://www.azed.gov/standards-practices/mathematics-standards/  Ohio DOE - http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelation ID=1704 http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicRelation ID=1704  Common Core Standards - http://www.corestandards.org/http://www.corestandards.org/  Tools for the Common Core Standards - http://commoncoretools.me/http://commoncoretools.me/  Phil Daro talks about the Common Core Mathematics Standards - http://serpmedia.org/daro- talks/index.htmlhttp://serpmedia.org/daro- talks/index.html Books  Van DeWalle, Elementary and Middle School Mathematics, Teaching Developmentally - College Level Text  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

55. Resources Professional Learning Resources  Inside Mathematics- http://www.insidemathematics.org/http://www.insidemathematics.org/  Annenberg Learner - http://www.learner.org/index.htmlhttp://www.learner.org/index.html  Edutopia – http://www.edutopia.orghttp://www.edutopia.org  Teaching Channel - http://www.teachingchannel.orghttp://www.teachingchannel.org Assessment Resources  MARS - http://www.nottingham.ac.uk/~ttzedweb/MARS/http://www.nottingham.ac.uk/~ttzedweb/MARS/  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  PARCC - http://www.parcconline.org/parcc-stateshttp://www.parcconline.org/parcc-states

56. As you start your day tomorrow… Who dares to teach must never cease to learn ~ John Cotton Dana http://www.youtube.com/watch?v=JEa0xpWi7C4

57. Thank You! Please visit http://ccgpsmathematics6-8.wikispaces.com/ to provide us with your feedback, ask questions, and share your ideas and resources! Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx to join the 6-8 Mathematics email listserve.http://ccgpsmathematics6-8.wikispaces.com/https://www.georgiastandards.org/Common-Core/Pages/Math.aspx Brooke Kline Program Specialist (6‐12) bkline@doe.k12.ga.us James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.