1. Secondary Mathematics Specialists
CCGPS Mathematics Coordinate Algebra Update Webinar Unit 6: Connecting Algebra and Geometry Through Coordinates November 8, 2013
James Pratt – Brooke Kline –
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 6 revisions
Addressing areas which teachers have found to be more challenging
Resources
James

3. 2013 CA Resource Revision Team
Brooke

4. Coordinate Algebra/Acc CA Comprehensive Course Overview
Located on the 9-12 math section of
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

11. This screen should appear when you select Comprehensive Course Overview
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
This fully interactive page will provide teachers with ease of access to the information that they need

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
These sections are designed to tie together many other areas of support offered by GADOE and other states implementing CCSS

14. Formative Assessment Lessons (FALs)
Follow the Task section, teachers will find detailed information in the FAL section with examples and links to videos of teachers using FALs

15. CCGPS Math Wiki Space

16. Coordinate Algebra EOCT Released Items
Released Items Housed in the Assessment Division of GADOE
Released Items Commentary Housed in the Assessment Division of GADOE
There are 20 released items and commentary about each item available for Coordinate Algebra

17. EOCT Released Item Commentary

18. EOCT Released Item #16

19. Solution to item #16 𝐺𝑃 𝑃𝐻 = 3 2 2𝐺𝑃=3𝑃𝐻 2 −1−𝑥, 5−𝑦 =3 𝑥−1, 𝑦+1
G (-1,5) P (x,y,) H (1,-1)
2𝐺𝑃=3𝑃𝐻
2 −1−𝑥, 5−𝑦 =3 𝑥−1, 𝑦+1
2 −1−𝑥 =3 𝑥−1
-2-2x = 3x – 3
5x = 1
X = 0.2
2 5−𝑦 =3 𝑦+1
10 – 2y = 3y + 3
5y = 7
Y = 1.4
𝑻𝒉𝒆 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆𝒔 𝒐𝒇 𝒑𝒐𝒊𝒏𝒕 𝑷 𝒂𝒓𝒆 (𝟎.𝟐, 𝟏.𝟒)

20. Data on Released Item #16

21. Sample Item From EOCT Study Guide
From CA EOCT Study Guide Pg 187

22. Solution to EOCT Study Guide Example
From CA EOCT Study Guide Pg 188

23. Unit 6 Frameworks
Show how this released item relates back to the Frameworks for Unit 4

24. Partitioning in Unit 6 “New York City”

25. Purpose of Tasks
Problem-Based-Learning--Check out Dan Meyer, Robert Kaplinksy’s websites
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 or your classroom.    Most standards are covered by various tasks

26. 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

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

28. Updates to Unit Frameworks

29. Unit 6 Partition a line segment
Determine slope and equations of parallel and perpendicular lines
Use slope and distance formula to prove simple geometric theorems in the coordinate plane

30. Equations of Parallel and Perpendicular Lines
Task
Basic Content Addressed
New York City
Slopes of Special Pairs of Lines
Euler’s Village
Partition a line segment into a given ratio
Determine slopes of parallel and perpendicular lines
Write equations of parallel and perpendicular lines given an equation of a line and a point not on that line

31. Geometric Properties on the Coordinate Plane
Task
Basic Content Addressed
Geometric Properties in the Plane
Equations of Parallel & Perpendicular Lines (FAL)
Square (Short Cycle Task)
Surveillance of the Village (Culminating Task)
Use slope and distance formula to prove simple geometric theorems algebraically
Find perimeter and area of polygons in a coordinate plane
Use equations of parallel and perpendicular lines to form geometric figures

32. Square (Short Cycle Task)
This short task focuses on using the distance formula and slope formula to determine if the points graphed will form the sides of a square.

33. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

34. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

35. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
At this point, I know that a rectangle has four right angles and opposite sides that are the same length.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

36. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
At this point, I know that a rectangle has four right angles and opposite sides that are the same length.
I need to show that adjacent sides are perpendicular, by using their slopes.
I need to show the lengths of opposite sides are equal.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

37. Unit 6 Challenges Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
I need to show that adjacent sides are perpendicular, by using their slopes.
Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3
Slope of 𝑄𝑅 = 6−(−3) −3−9 = −9 12 = −3 4
Slope of 𝑅𝑆 = −7−(−3) 6−9 = 4 3
Slope of 𝑆𝑃 = −7−2 6−(−6) = −9 12 = −3 4
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

38. Unit 6 Challenges Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
I need to show that adjacent sides are perpendicular, by using their slopes.
Slope of 𝑃𝑄 = 6−2 −3−(−6) = 4 3
Slope of 𝑄𝑅 = 6−(−3) −3−9 = −9 12 = −3 4
Slope of 𝑅𝑆 = −7−(−3) 6−9 = 4 3
Slope of 𝑆𝑃 = −7−2 6−(−6) = −9 12 = −3 4
The slopes of adjacent sides are opposite reciprocals of each other so the lines are perpendicular.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

39. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
I need to show the lengths of opposite sides are equal.
𝑃𝑄= (−6− −3 ) 2 + (2−6) 2 = (−3) 2 + (−4) 2 = 25 =5
𝑄𝑅= (9− −3 ) 2 + (−3−6) 2 = (12) 2 + (−9) 2 = 225 =15
𝑅𝑆= (9−6) 2 + (−3−(−7)) 2 = (3) 2 + (4) 2 = 25 =5
𝑆𝑃= (6− −6 ) 2 + (−7−2) 2 = (12) 2 + (−9) 2 = 225 =15
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

40. Unit 6 Challenges Opposite sides have the same length.
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
I need to show the lengths of opposite sides are equal.
𝑃𝑄= (−6− −3 ) 2 + (2−6) 2 = (−3) 2 + (−4) 2 = 25 =5
𝑄𝑅= (9− −3 ) 2 + (−3−6) 2 = (12) 2 + (−9) 2 = 225 =15
𝑅𝑆= (9−6) 2 + (−3−(−7)) 2 = (3) 2 + (4) 2 = 25 =5
𝑆𝑃= (6− −6 ) 2 + (−7−2) 2 = (12) 2 + (−9) 2 = 225 =15
Opposite sides have the same length.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

41. Unit 6 Challenges
Is the quadrilateral with vertices P(−6, 2), Q(−3, 6), R(9,−3), S(6,−7) a rectangle? Explain.
At this point, I know that a rectangle has four right angles and opposite sides that are the same length.
Adjacent sides are perpendicular and the lengths of opposite sides are equal, therefore the quadrilateral is a rectangle.
James
8.G, G-GPE, G-SRT, G-CO Is this a rectangle?

42. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

43. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

44. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

45. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

46. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

47. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

48. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

49. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

50. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

51. Unit 6 Challenges
Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).
Brooke

52. Resources GaDOE Resources
Fall 2011 CCGPS Standards for Mathematical Practices Webinars -
Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB -
2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series -
Georgia Mathematics Teacher Forums -
CCGPS Mathematics Frameworks and Comprehensive Course Overviews -
Mathematics Formative Assessment Lesson Videos -
Brooke

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.
Brooke

54. Resources CCGPS Resources Assessment Resources
Georgia Virtual Learning -
SEDL videos - or
Illustrative Mathematics -
Mathematics Vision Project -
Dana Center's CCSS Toolbox -
Tools for the Common Core Standards -
LearnZillion -
Assessment Resources
MAP -
Illustrative Mathematics -
CCSS Toolbox: PARCC Prototyping Project -
Smarter Balanced -
PARCC -
Online Assessment System -
Brooke

55. LearnZillion Revised
A more “user friendly” version of the Learnzillion lessons support learning new strategies, sharing with parents, helping absent students.
Brooke

56. LearnZillion Choose grade band: Choose domain: Choose topic/strand
Choose grade band:
Choose domain:
Choose topic/strand
and standard:
Brooke

57. LearnZillion
Brooke

58. LearnZillion “Quick Codes”
Brooke

59. Resources Professional Learning Resources Blogs Books
Inside Mathematics-
Annenberg Learner -
Edutopia –
Teaching Channel -
Ontario Ministry of Education -
Achieve -
Expeditionary Learning: Center for Student Work -
Blogs
Dan Meyer –
Robert Kaplinsky -
Books
Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Brooke

60. James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us
Feedback
James Pratt – Brooke Kline –
Brooke

61. James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us
Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 9-12 Mathematics listserve. Follow on Twitter!
Brooke Kline
Program Specialist (6‐12)
James Pratt Program Specialist (6-12)
James & Brooke
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.