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
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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.