CCGPS Mathematics Coordinate Algebra Update Webinar Unit 5: Transformations in the Coordinate Plane October 15, 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.

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

2013 CA Resource Revision Team

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

Begin at Direct Link to Page

Select the CCGPS ELA/Math Tab Direct Link to Page

Select the Mathematics option under Browse CCGPS Direct Link to Page

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

Expand the Coordinate Algebra Course Direct Link to Page

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

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

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

Formative Assessment Lessons (FALs)

CCGPS Math Wiki Space

Coordinate Algebra EOCT Released Items Released Items Housed in the Assessment Division of GADOE Assessment/Assessment/Documents/Coordinate%20Algebra%20R eleased%20Items%20Booklet.pdf Released Items Commentary Housed in the Assessment Division of GADOE Assessment/Assessment/Documents/Coordinate%20Algebra%20Rel eased%20Items%20Commentary.pdf There are 20 released items and commentary about each item available for Coordinate Algebra

EOCT Released Item Commentary

EOCT Released Item #15

Data on Released Item #15

Relate back to EOCT Study Guide culum-Instruction-and- Assessment/Assessment/D ocuments/EOCT%20Coord inate%20Algebra%20Study %20Guide%20Revised%2 0August% pdf From CA EOCT Study Guide Pg 162

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

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

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.

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

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

Updates to Unit Frameworks

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

Guided Notes Rotations

Practice Reflections

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

Exploring Reflections & Rotations (Learning Task) 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) Coordinating Translations (Homework Task)

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

Representing & Combining Transformations (FAL)

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

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

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

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

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

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

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

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

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

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

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

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 - Assessment-Lessons-Videos.aspx Assessment-Lessons-Videos.aspx Resources

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.

CCGPS 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 - Resources

Georgia Virtual School Content Click here to access shared content Go to No password required!

Georgia Virtual School Content

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Resources Professional Learning Resources  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

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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) These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.