1. CCGPS Mathematics Coordinate Algebra Update Webinar Unit 5: Transformations in the Coordinate Plane October 15, 2013 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 Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

2. What are update webinars? Update on the work of the 2013 Resource Revision Team  Overall revisions  Unit 5 revisions Addressing areas which teachers have found to be more challenging Resources

3. 2013 CA Resource Revision Team

4. Coordinate Algebra/Acc CA Comprehensive Course Overview Located on the 9-12 math section of www.georgiastandards.org www.georgiastandards.org Designed to provide clarification of CCGPS Mathematics Standards Organized to link together many sources of information pertinent to CCGPS Coordinate Algebra/Accelerated Coordinate Algebra

5. Begin at www.georgiastandards.org Direct Link to Page

6. Select the CCGPS ELA/Math Tab Direct Link to Page

7. Select the Mathematics option under Browse CCGPS Direct Link to Page

8. Select the 9-12 option in the Mathematics section Direct Link to Page

9. Expand the Coordinate Algebra Course Direct Link to Page

10. Select the Comprehensive Course Overview Expande Coordinate Algebra Direct Link to Page

12. Table of Contents Outlines the Major areas of Focus for the Course Fully Interactive when viewed via internet Hover over a section and select to access the section quickly

13. Sections of Interest Flipbook Access: Detailed Information About Each Standard Unit Descriptions: Overview Webinar Information Assessment Resources and Instructional Support Resources Internet Resources Curriculum Map

14. Formative Assessment Lessons (FALs)

15. CCGPS Math Wiki Space

16. Coordinate Algebra EOCT Released Items Released Items Housed in the Assessment Division of GADOE http://www.gadoe.org/Curriculum-Instruction-and- Assessment/Assessment/Documents/Coordinate%20Algebra%20R eleased%20Items%20Booklet.pdf Released Items Commentary Housed in the Assessment Division of GADOE http://www.gadoe.org/Curriculum-Instruction-and- Assessment/Assessment/Documents/Coordinate%20Algebra%20Rel eased%20Items%20Commentary.pdf There are 20 released items and commentary about each item available for Coordinate Algebra

17. EOCT Released Item Commentary

18. EOCT Released Item #15

19. Data on Released Item #15

20. Relate back to EOCT Study Guide http://www.gadoe.org/Curri culum-Instruction-and- Assessment/Assessment/D ocuments/EOCT%20Coord inate%20Algebra%20Study %20Guide%20Revised%2 0August%202013.pdf From CA EOCT Study Guide Pg 162

21. Additional EOCT Study Guide Example From CA EOCT Study Guide Pg 166

22. Unit 5 Frameworks The following tasks in Unit 5 are related to this released item: Exploring Reflections and Rotations Mirrored Mappings Coordinating Translations Transformations in the Coordinate Plane

23. Purpose of Tasks Problem-Based Learning Provide several entry points to the standards. Teachers should review all tasks in a given unit to determine which tasks would be appropriate for their students. Tasks can be adapted to fit the needs of your classroom.

24. Goals of Unit Revisions More user-friendly Provide teachers with task summaries Give teachers tools necessary to quickly analyze tasks Provide tasks from different sources

25. Updates to Unit Frameworks TASK TABLE Outlines the tasks by type, content and standard. Provides suggested times Hyperlinks to PDFs and Word Docs

26. Updates to Unit Frameworks

27. Unit 5 The tasks primarily address: – Transformations: translations, reflections, rotations, dilations – Observe / describe effects of transformations (and compositions of transformations) on figures in the coordinate plane – Understand congruence and similarity in terms of transformations

29. Guided Notes Rotations

30. Practice Reflections

31. Intro to Reflections, Translations, & Rotations (Learning Task) Perform geometric transformations Map the new figure onto the original figure

32. Exploring Reflections & Rotations (Learning Task) Geometer’s Sketchpad activity - OR - Alternative activity (transformations performed using other tools)

33. Compare a new polygon’s vertices to the vertices of a preimage, using algebraic notation to describe the transformation(s) Coordinating Translations (Homework Task)

34. Transformations in the Coordinate Plane (Learning Task) Create six images and compare Figures 2-6 to Figure 1, writing rules for the transformation(s)

35. Representing & Combining Transformations (FAL)

38. Culminating Task Representing transformations algebraically Congruence and similarity in terms of transformations Parallel & perp. lines with transformations

39. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? A.180 o counter clockwise B.45 o counter clockwise C.60 o counter clockwise Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

40. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? A.180 o counter clockwise Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

41. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? A.180 o counter clockwise A ’ (2, -2) B ’ (-1, 1) C ’ (-1, -1) Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

42. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? B.45 o counter clockwise Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

43. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? B.45 o counter clockwise A ’ (-.12, 3.12) B ’ (4.12, 3.12) C ’ (2.71, 4.54) Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

44. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? C.60 o counter clockwise Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

45. Triangle ABC with points A(2, 4), B(5, 1), and C(5, 3) is rotated about point D(2, 1) the following degrees. What are the coordinates of the images of the vertices? C.60 o counter clockwise A ’ (-.6, 2.5) B ’ (3.5, 3.6) C ’ (1.77, 4.6) Unit 5 Challenges http://www.geogebratube.org/material/show/id/18488/

46. On “Alec’s Web Log” an alternative method in rotating a point about a point other than the origin is given. In the blog, the method that is used in our Unit 5 frameworks (translate the center of rotation to the origin, rotate, translate the center of rotation back) is given along with the following method: Rotate both the point and the center of rotation about the origin, translate the center of rotation back to it’s original location. Does this method work? Unit 5 Challenges http://www.alecjacobson.com/weblog/?p=1659

47. On “Alec’s Web Log” an alternative method in rotating a point about a point other than the origin is given. In the blog, the method that is used in our Unit 5 frameworks (translate the center of rotation to the origin, rotate, translate the center of rotation back) is given along with the following method: Rotate both the point and the center of rotation about the origin, translate the center of rotation back to it’s original location. Does this method work? To determine if the alternative method is valid, let’s use both methods to rotate the point A(4, 6) 90 o clockwise about the point B(3, 1). Unit 5 Challenges http://www.alecjacobson.com/weblog/?p=1659

48. To determine if the alternative method is valid, let’s use both methods to rotate the point A(4, 6) 90 o clockwise about the point B(3, 1). Unit 5 Challenges http://www.alecjacobson.com/weblog/?p=1659

49. GaDOE Resources  Fall 2011 CCGPS Standards for Mathematical Practices Webinars - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series - https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx  Georgia Mathematics Teacher Forums - http://ccgpsmathematics9-10.wikispaces.com/http://ccgpsmathematics9-10.wikispaces.com/  CCGPS Mathematics Frameworks and Comprehensive Course Overviews - https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx  Mathematics Formative Assessment Lesson Videos - https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative- Assessment-Lessons-Videos.aspx https://www.georgiastandards.org/Common-Core/Pages/Mathematics-Formative- Assessment-Lessons-Videos.aspx Resources

50. 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.

51. CCGPS Resources  Georgia Virtual Learning - http://www.gavirtuallearning.org/Resources.aspxhttp://www.gavirtuallearning.org/Resources.aspx  SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtchttp://bit.ly/RwWTdchttp://bit.ly/yyhvtc  Illustrative Mathematics - http://www.illustrativemathematics.org/http://www.illustrativemathematics.org/  Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.htmlhttp://www.mathematicsvisionproject.org/index.html  Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/http://www.ccsstoolbox.com/  Tools for the Common Core Standards - http://commoncoretools.me/http://commoncoretools.me/  LearnZillion - http://learnzillion.com/http://learnzillion.com/ Assessment Resources  MAP - http://www.map.mathshell.org.uk/materials/index.phphttp://www.map.mathshell.org.uk/materials/index.php  Illustrative Mathematics - http://illustrativemathematics.org/http://illustrativemathematics.org/  CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/http://www.ccsstoolbox.org/  Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/http://www.smarterbalanced.org/smarter-balanced-assessments/  PARCC - http://www.parcconline.org/http://www.parcconline.org/  Online Assessment System - http://bit.ly/OoyaK5http://bit.ly/OoyaK5 Resources

52. Georgia Virtual School Content Click here to access shared content Go to www.gavirtuallearning.org/Resources.aspx No password required!www.gavirtuallearning.org/Resources.aspx

53. Georgia Virtual School Content

56. http://cms.gavirtualschool.org/Shared/Math/Algebra_1_CCGPS/06_Transforma tions/index.html

57. 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  Ontario Ministry of Education - http://bit.ly/cGZlcehttp://bit.ly/cGZlce  Achieve - http://www.achieve.org/http://www.achieve.org/  Expeditionary Learning: Center for Student Work - http://elschools.org/student-workhttp://elschools.org/student-work Blogs  Dan Meyer – http://blog.mrmeyer.com/http://blog.mrmeyer.com/  Robert Kaplinsky - http://robertkaplinsky.com/http://robertkaplinsky.com/ Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

58. Feedback http://www.surveymonkey.com/s/WZKG5G2 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.usjpratt@doe.k12.ga.usbkline@doe.k12.ga.us

59. Thank You! Please visit http://ccgpsmathematics9-10.wikispaces.com/ to share your feedback, ask questions, and share your ideas and resources! Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx to join the 9-12 Mathematics email listserve. Follow on Twitter! Follow @GaDOEMathhttp://ccgpsmathematics9-10.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.