ccgps mathematics coordinate algebra update webinar unit 5: transformations in the coordinate plane...
TRANSCRIPT
CCGPS MathematicsCoordinate Algebra Update WebinarUnit 5: Transformations in the Coordinate Plane
October 15, 2013
James Pratt – [email protected] Brooke Kline – [email protected] Mathematics Specialists
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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 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
Begin at www.georgiastandards.org
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
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 http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/Coordinate%20Algebra%20Released%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%20Released%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 Guidehttp://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Documents/EOCT%20Coordinate%20Algebra%20Study%20Guide%20Revised%20August%202013.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 NotesRotations
PracticeReflections
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(transformationsperformed usingother tools)
• Compare anew polygon’svertices to thevertices of apreimage,using algebraicnotation to describe the transformation(s)
Coordinating Translations(Homework Task)
Transformations in theCoordinate 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. 180o counter clockwiseB. 45o counter clockwiseC. 60o counter clockwise
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 180o counter clockwise
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 180o counter clockwiseA’(2, -2)B’(-1, 1)C’(-1, -1)
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 45o counter clockwise
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 45o counter clockwiseA’(-.12, 3.12)B’(4.12, 3.12)C’(2.71, 4.54)
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 60o counter clockwise
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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. 60o counter clockwiseA’(-.6, 2.5)B’(3.5, 3.6)C’(1.77, 4.6)
Unit 5 Challenges
http://www.geogebratube.org/material/show/id/18488/
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
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) 90o clockwise about the point B(3, 1).
Unit 5 Challenges
http://www.alecjacobson.com/weblog/?p=1659
To determine if the alternative method is valid, let’s use both methods to rotate the point A(4, 6) 90o clockwise about the point B(3, 1).
Unit 5 Challenges
http://www.alecjacobson.com/weblog/?p=1659
• 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
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 - 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
Resources
Georgia Virtual School Content
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Georgia Virtual School Content
http://cms.gavirtualschool.org/Shared/Math/Algebra_1_CCGPS/06_Transformations/index.html
Resources• Professional Learning Resources
Inside Mathematics- http://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
Feedbackhttp://www.surveymonkey.com/s/WZKG5G2
James Pratt – [email protected] Brooke Kline – [email protected]
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questions, and share your ideas and resources!Please visit https://www.georgiastandards.org/Common-Core/Pages/Math.aspx
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Brooke KlineProgram Specialist (6‐12)
James PrattProgram Specialist (6-12)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.