CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Coordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry A
Unit 5: Transformations in the Coordinate Plane
September 20, 2012
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CCGPS Mathematics
Unit-by-Unit Grade Level Webinar
Coordinate Algebra & Accelerated Coordinate
Algebra/Analytic Geometry A
Unit 5: Transformations in the Coordinate Plane
September 20, 2012
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary Mathematics Specialists
These materials are for nonprofit educational purposes
only. Any other use may constitute copyright infringement.
Expectations and clearing up confusion
• This webinar focuses on CCGPS content specific to Unit 5, Coordinate
Algebra and Accelerated Coordinate Algebra/Analytic Geometry A.
• For information about CCGPS across a single grade span, please
access the list of recorded GPB sessions on Georgiastandards.org.
• For information on the Standards for Mathematical Practice, please
access the list of recorded Blackboard sessions from Fall 2011 on
GeorgiaStandards.org.
• CCGPS is taught and assessed from 2012-2013 and beyond.
• A list of resources will be provided at the end of this webinar and these
documents are posted in the 9-10 wiki.
http://ccgpsmathematics9-10.wikispaces.com/
Expectations and clearing up confusion
• The intent of this webinar is to bring awareness to:
 the types of tasks that are contained within the unit.
 your conceptual understanding of the mathematics in this
unit.
 approaches to the tasks which provide deeper learning
situations for your students.
We will not be working through each task during this
webinar.
Welcome!
• Thank you for taking the time to join us in this discussion of
Unit 5.
• At the end of today’s session you should have at least 3
takeaways:
 the big idea of Unit 5
 something to think about…some food for thought
 how might I support student problem solving?
 what is my conceptual understanding of the material in this unit?
 a list of resources and support available for CCGPS mathematics
Welcome!
• Please provide feedback at the end of today’s session.
Feedback helps us become better teachers and learners.
Feedback helps as we develop the remaining unit-by-unit webinars.
Please visit http://ccgpsmathematics9-10.wikispaces.com/
to share your feedback..
• After reviewing the remaining units, please contact us with
content area focus/format suggestions for future webinars.
James Pratt – jpratt@doe.k12.ga.us
Brooke Kline – bkline@doe.k12.ga.us
Secondary Mathematics Specialists
Welcome!
• For today’s session have you:
 read the mathematics CCGPS?
 read the unit and worked through the tasks in the unit?
 downloaded and saved the documents from this session?
• Ask questions and share resources/ideas for the common
good.
• Bookmark and become active in the 9-10 wiki. If you are still
wondering what a wiki is, we will discuss this near the end of
the session.
Misconception?
What do we do with mistakes and
misconceptions?
• Avoid them whenever possible?
"If I warn learners about the misconceptions as I teach,
they are less likely to happen.
Prevention is better than cure.”
• Use them as learning opportunities?
"I actively encourage learners to make mistakes and to
learn from them.”
Diagnostic teaching.
“Traditionally, the teacher with the textbook explains
and demonstrates, while the students imitate; if the
student makes mistakes the teacher explains again.
This procedure is not effective in preventing ...
misconceptions or in removing [them].
Diagnostic teaching ..... depends on the student taking
much more responsibility for their own understanding ,
being willing and able to articulate their own lines of
thought and to discuss them in the classroom”.
Source: Swann, M : Gaining diagnostic teaching skills: helping students learn
from mistakes and misconceptions, Shell Centre publications
Activate your Brain
Seven circles of the same size are placed in the pattern
shown below:
Find as many rigid motions of the plane as you can
which take this figure onto itself.
Adapted from Illustrative Mathematics: G-CO.3
Misconceptions
It is important to realize that inevitably
students will develop misconceptions…
Askew and Wiliam 1995; Leinwand, 2010; NCTM, 1995; Shulman, 1996
Misconceptions
Therefore it is important to have strategies for
identifying, remedying, as well as for avoiding
misconceptions.
Leinwand, 2010; Swan 2001; NBPTS, 1998; NCTM, 1995; Shulman, 1986;
Importance of Dealing with
Misconceptions
1) Teaching is more effective when misconceptions are
identified, challenged, and ameliorated.
2) Pupils face internal cognitive distress when some
external idea, process, or rule conflicts with their existing
mental schema.
3) Research evidence suggests that the resolutions of
these cognitive conflicts through discussion leads to
effective learning.
Some principles to consider
• Encourage learners to explore misconceptions through
discussion.
• Focus discussion on known difficulties and challenging
questions.
• Encourage a variety of viewpoints and interpretations to
emerge.
• Ask questions that create a tension or ‘cognitive conflict'
that needs to be resolved.
• Provide meaningful feedback.
• Provide opportunities for developing new ideas and
concepts, and for consolidation.
Activate your Brain
Seven circles of the same size are placed in the pattern
shown below:
Find as many rigid motions of the plane as you can
which take this figure onto itself.
Adapted from Illustrative Mathematics: G-CO.3
Activate your Brain
Seven circles of the same size are placed in the pattern
shown below:
Find as many rigid motions of the plane as you can
which take this figure onto itself.
Adapted from Illustrative Mathematics: G-CO.3
What’s the big idea?
• Overview
• Key Standards
• Enduring Understandings
• Essential Questions
• Strategies for Teaching & Learning
What’s the big idea?
•Develop a deep understanding of definitions of
basic geometric figures (angle, circle, perpendicular
line, parallel line, and line segment)
•Deepen understanding of transformations in the
plane.
What’s the big idea?
Standards for Mathematical Practice
Education Week’s Blog > EdTech Researcher – Justin Reich
Dan Meyer Blog – Dan Meyer
MTT2K Grand Prize Winning Video – What if Khan Academy
was Made in Japan?
•http://blogs.edweek.org/edweek/edtechresearcher/2012/08/what_if_
khan_academy_was_made_in_japan_mtt2k_grand_prize.html?utm_
source=twitterfeed&utm_medium=twitter
•http://www.youtube.com/watch?v=CHoXRvGTtAQ
Basic Understandings for Teachers
Teacher Misconception:
As long as students are getting the
correct answers, the students are
understanding the material.
Phil Daro on “Answer Getting” http://www.serpmedia.org/daro-talks/index.html
Questions that arose
• How is this different from 8th grade transformations?
Coherence and Focus – Unit 5
What are students coming with?
What foundation is being built?
Where does this understanding lead students?
•Concepts and Skills to Maintain
•Enduring Understandings
•Evidence of Learning
Coherence and Focus – Unit 5
View across grade bands
• K-8th
 Recognize and identify geometric figures
Draw polygons on the coordinate plane
Experiment with transformations in and out of the coordinate
plane
• 10th-12th
 Congruence
Similarity
Function Transformations
Examples & Explanations
http://www.shodor.org/interactivate/activities/Transmographer/
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆TRY with vertices T(-2, 3), R(3, 6), Y(1, -1).
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆TRY with vertices T(-2, 3), R(3, 6), Y(1, -1).
Perform the first transformation. Graph and state the
coordinates.
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆TRY with vertices T(-2, 3), R(3, 6), Y(1, -1).
Perform the first transformation. Graph and state the
coordinates.
T’(-3, -2), R’(-6, 3), Y’(1,1)
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆TRY with vertices T(-2, 3), R(3, 6), Y(1, -1).
Perform the first transformation. Graph and state the
coordinates.
T’(-3, -2), R’(-6, 3), Y’(1,1)
Perform the second transformation. Graph and state the
coordinates.
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆TRY with vertices T(-2, 3), R(3, 6), Y(1, -1).
Perform the first transformation. Graph and state the
coordinates.
T’(-3, -2), R’(-6, 3), Y’(1,1)
Perform the second transformation. Graph and state the
coordinates.
T”(-3, 2), R”(-6, -3), Y”(1, -1)
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆CAT with vertices
C(X1, Y1), A(X2, Y2), T(X3, Y3).
What are the vertices of the image?
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis on ∆CAT with vertices
C(X1, Y1), A(X2, Y2), T(X3, Y3).
What are the vertices of the image?
C’(-Y1, -X1), A’(-Y2, -X2), T’(-Y3, -X3)
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis.
Analyze the coordinates of the pre-image and the final
image. What is the transformation that is equivalent to the
two?
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Examples & Explanations
Perform the following sequence of transformation, Rotate
counterclockwise 90 degrees about the origin, reflect over
the x-axis.
Analyze the coordinates of the pre-image and the final
image. What is the transformation that is equivalent to the
two?
Reflection over y = -x
Adapted Teaching Channel Carousel Activity: Composition of Transformations
Assessment
How might it look?
• Mathematics Assessment Project http://map.mathshell.org/materials/tests.php
• Illustrative Mathematics - http://illustrativemathematics.org/
• Dana Center’s CCSS Toolbox: PARCC Prototype Project http://www.ccsstoolbox.org/
• PARCC - http://www.parcconline.org/
• Online Assessment System - http://www.gadoe.org/CurriculumInstruction-and-Assessment/Assessment/Pages/OAS.aspx
Assessment
Suggestions for getting started:
• Read the unit and work through the tasks with your colleagues.
The only way to gain deep understanding is to work through
each task.
• Make note of where, when, and what the big ideas are.
• Discuss the focus and coherence of the unit.
• Make note of where, when, and what the pitfalls might be.
• Look for additional tools/ideas you want to use.
• Determine any changes which might need to be made to make
this work for your students.
• Share, ask, and collaborate on the wiki.
http://ccgpsmathematics9-10.wikispaces.com/
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.
What is a Wiki?
• Common Core Resources
Resources
 SEDL videos - https://www.georgiastandards.org/Common-Core/Pages/Math.aspx or
http://secc.sedl.org/common_core_videos/
 Illustrative Mathematics - http://www.illustrativemathematics.org/
 Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/
Common Core Standards - http://www.corestandards.org/
 Tools for the Common Core Standards - http://commoncoretools.me/
•Books
Van DeWalle and Lovin, Teaching Student-Centered Mathematics, 6-8
•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
Resources
•Assessment Resources
MAP - http://www.map.mathshell.org.uk/materials/index.php
 CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/
 PARCC - http://www.parcconline.org/

• Blogs
Dan Meyer – http://blog.mrmeyer.com/
Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html
Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/
Resources
• Dana Center’s CCSS Toolbox - PARCC Prototyping Project
http://www.ccsstoolbox.com/
Resources
Learnzillion.com
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Review
Common Mistakes
Core Lesson
Guided Practice
Extension Activities
Quick Quiz
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.
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.