CCGPS MathematicsUnit-by-Unit Grade Level WebinarCoordinate Algebra & Accelerated Coordinate

Algebra/Analytic Geometry AUnit 5: Transformations in the Coordinate Plane

September 20, 2012

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CCGPS MathematicsUnit-by-Unit Grade Level WebinarCoordinate Algebra & Accelerated Coordinate

Algebra/Analytic Geometry AUnit 5: Transformations in the Coordinate Plane

September 20, 2012

James Pratt – jpratt@doe.k12.ga.usBrooke Kline – bkline@doe.k12.ga.usSecondary 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.usSecondary 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.

Source: Swann, M : Gaining diagnostic teaching skills: helping students learn from mistakes and misconceptions, Shell Centre publications

“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”.

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 PracticeEducation Week’s Blog > EdTech Researcher – Justin ReichDan Meyer Blog – Dan MeyerMTT2K 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 TeachersTeacher 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 5What 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 5View across grade bands

• K-8th Recognize and identify geometric figuresDraw polygons on the coordinate planeExperiment with transformations in and out of the coordinate plane

• 10th-12th CongruenceSimilarityFunction Transformations

Examples & Explanations

http://www.shodor.org/interactivate/activities/Transmographer/

Examples & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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 & ExplanationsPerform 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

AssessmentHow 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/Curriculum-Instruction-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?

Resources• Common Core 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/

•BooksVan 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/

• BlogsDan Meyer – http://blog.mrmeyer.com/Timon Piccini – http://mrpiccmath.weebly.com/3-acts.htmlDan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/

Resources• Dana Center’s CCSS Toolbox - PARCC Prototyping Project

http://www.ccsstoolbox.com/

ResourcesLearnzillion.com

• 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.aspxto join the 9-12 Mathematics email listserve.

Brooke KlineProgram Specialist (6‐12)

bkline@doe.k12.ga.us

James PrattProgram Specialist (6-12)

jpratt@doe.k12.ga.us

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