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.us
Secondary Mathematics Specialists
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These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

• 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

• Located on the 9-12 math section of 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

Direct Link to Page

Direct Link to Page

Direct Link to Page

Direct Link to Page

Direct Link to Page

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

Direct Link to Page

• 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

• Flipbook Access: Detailed Information
About Each Standard
• Unit Descriptions: Overview
• Webinar Information
• Assessment Resources and Instructional
Support Resources
• Internet Resources
• Curriculum Map

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

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

From CA EOCT Study Guide Pg 166

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

• 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.

• More user-friendly
• Provide teachers with task summaries
• Give teachers tools necessary to quickly analyze tasks
• Provide tasks from different sources

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

• 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

• Perform geometric transformations
• Map the new figure onto the original figure

• Geometer’s Sketchpad activity
- OR -
Alternative activity
(transformations performed using other tools)

• Compare a new polygon’s vertices to the vertices of a preimage, using algebraic notation to describe the transformation(s)

• Create six images and compare Figures 2-6 to
Figure 1, writing rules for the transformation(s)

• Representing transformations algebraically
• Congruence and similarity in terms of transformations
• Parallel & perp. lines with transformations

Unit 5 Challenges
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 http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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 http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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) http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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 http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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) http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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 http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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) http://www.geogebratube.org/material/show/id/18488/

Unit 5 Challenges
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?
http://www.alecjacobson.com/weblog/?p=1659

Unit 5 Challenges
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).
http://www.alecjacobson.com/weblog/?p=1659

Unit 5 Challenges
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).
http://www.alecjacobson.com/weblog/?p=1659

Resources
• GaDOE Resources
 Fall 2011 CCGPS Standards for Mathematical Practices Webinars 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
 2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx
 Georgia Mathematics Teacher Forums http://ccgpsmathematics9-10.wikispaces.com/
 CCGPS Mathematics Frameworks and Comprehensive Course Overviews 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

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.

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

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

Georgia Virtual School Content

Georgia Virtual School Content

Georgia Virtual School Content

Georgia Virtual School Content http://cms.gavirtualschool.org/Shared/Math/Algebra_1_CCGPS/06_Transforma tions/index.html

Resources
• Professional Learning Resources
 Inside Mathematicshttp://www.insidemathematics.org/
 Annenberg Learner http://www.learner.org/index.html
 Edutopia – http://www.edutopia.org
 Teaching Channel http://www.teachingchannel.org
 Ontario Ministry of Education http://bit.ly/cGZlce
 Achieve http://www.achieve.org/
 Expeditionary Learning: Center for Student Work http://elschools.org/student-work
• Blogs
 Dan Meyer – http://blog.mrmeyer.com/
 Robert Kaplinsky http://robertkaplinsky.com/
• Books
 Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

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

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.
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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.