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CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October 25, 2012 Session will be begin at 8:00 am While you are waiting, please do the following: Configure your microphone and speakers by going to: Tools – Audio – Audio setup wizard Document downloads: When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

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Page 1: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Accelerated Coordinate Algebra/Analytic Geometry AUnit 7: Similarity, Congruence, and Proofs

October 25, 2012

Session will be begin at 8:00 amWhile you are waiting, please do the following:

Configure your microphone and speakers by going to:Tools – Audio – Audio setup wizard

Document downloads:When you are prompted to download a document, please choose or create the folder to which the document should be saved, so that you may retrieve it later.

Page 2: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Accelerated Coordinate Algebra/Analytic Geometry AUnit 7: Similarity, Congruence, and Proofs

October 25, 2012

James Pratt – [email protected] Kline – [email protected] Mathematics Specialists

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

Page 3: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Expectations and clearing up confusion

• Intent and focus of Unit 7 webinar.• Framework tasks.• GPB sessions on Georgiastandards.org.• Standards for Mathematical Practice. • Resources. • http://ccgpsmathematics9-10.wikispaces.com/• CCGPS is taught and assessed from 2012-2013 and beyond.

Page 4: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• The big idea of Unit 7• Understanding congruence/similarity in terms of transformations.

Why do SSS, ASA, & SAS work? Why does AA work?

• Resources

Welcome!

Page 5: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Feedbackhttp://ccgpsmathematics9-10.wikispaces.com/

James Pratt – [email protected] Brooke Kline – [email protected] Mathematics Specialists

Page 6: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Mathematical Communication•Developing effective mathematical communication•Categories of mathematical communication•Organizing students to think, talk, and write•Updating the three-part problem-solving lesson•Tips for getting started

Page 7: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Research - Communication•The value of student interaction•Challenges the teachers face in engaging students•The teacher’s role•Five strategies for encouraging high-quality student interaction

1. The use of rich math tasks2. Justification of solutions3. Students questioning one

another4. Use of wait time5. Use of guidelines for Math Talk

Page 8: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

My Favorite No

https://www.teachingchannel.org/videos/class-warm-up-routine

Page 9: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• Unit 6 FrameworksCONCEPTS/SKILLS TO MAINTAIN It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas. • simplifying radicals • calculating slopes of lines • graphing lines • writing equations for lines

Wiki/Email Questions

Page 10: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• Teacher Edition – page 20

Unit 6: New York Learning Task

Page 11: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• Teacher Edition – page 43

Unit 6: Geometric Properties Task

Page 12: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• MCC9‐12.F.BF.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. (Focus on vertical translations of graphs of linear and exponential functions. Relate the vertical translation of a linear function to its y‐intercept.)

Wiki/Email Questions – Unit 3

Page 13: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

AnnouncementsSystem Test Coordinators, Please note that we have posted today a revised EOCT Coordinate Algebra Study Guide.  You can find the guide at the GaDOE webpage below:http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/EOCT-Guides.aspx

The purpose of this revised posting was to edit the information that appeared on pages 147 – 148 regarding strategies to fitting a line to data.  The GaDOE Curriculum Division has determined that strategies for fitting a line to data may include estimation (“eye-balling”) and/or the use of technology. The previous version of the Study Guide specified that median-median was a required method for this purpose.  However, that is not the case.  As a result, the pages referenced above, and those that contained related problems, have been edited to clarify this point.

Please share this with the appropriate content experts in your local systems as you determine is appropriate.  The GaDOE Curriculum Division’s math specialists will be sharing this information with their contacts in local systems as well.Thank you!

Tony EitelDirector, Assessment AdministrationAssessment & AccountabilityOffice of Curriculum, Instruction, and Assessment

Page 14: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

In each of the following diagrams, two triangles are shaded. Based on the information given about each diagram, decide whether there is enough information to prove that the two triangles are congruent.

Activate your Brain

In circle O, AB is congruent to CD

ABCD is a parallelogram

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

Page 15: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

The two triangles are congruent by SAS:

Activate your Brain

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

ABCD is a parallelogram

Page 16: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

The two triangles are congruent by SAS:We have AX ≅ CX and DX ≅ BX since the diagonals of a parallelogram bisect each other, and ∠AXD ≅ ∠CBX since they are vertical angles.

Activate your Brain

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

ABCD is a parallelogram

Page 17: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

The two triangles are congruent by SAS:We have AX ≅ CX and DX ≅ BX since the diagonals of a parallelogram bisect each other, and ∠AXD ≅ ∠CBX since they are vertical angles.Alternatively, the two triangles are congruent by ASA:

Activate your Brain

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

ABCD is a parallelogram

Page 18: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

The two triangles are congruent by SAS:We have AX ≅ CX and DX ≅ BX since the diagonals of a parallelogram bisect each other, and ∠AXD ≅ ∠CBX since they are vertical angles.Alternatively, the two triangles are congruent by ASA:

Activate your Brain

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

ABCD is a parallelogram

∠DAX ≅ ∠BCX and ∠ADX ≅ ∠CBX since they are opposite interior angles. AD ≅ BC since opposite sides of a parallelogram are congruent.

Page 19: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Triangles are congruent. Triangle BOA is the result of reflecting triangle COD across the perpendicular bisector of AD

Activate your Brain

Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

In circle O, AB is congruent to CD

Page 20: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

What’s the big idea?•Deepen understanding of transformations.•Develop understanding of congruence and similar figures.•Develop understanding of geometric proof.• Standards for Mathematical Practice.

Page 21: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Coherence and Focus• K-8th

Identification of figures in different orientations Ratios and proportions Drawing of geometric figures with specific characteristicsTransformationsBasic congruence and similarity

• 10th-12th Transformations of functions Trigonometric Functions

Page 22: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 23: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Show that there is a translation of the plane which maps A to D

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 24: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Show that there is a translation of the plane which maps A to D

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 25: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & ExplanationsAB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 26: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & ExplanationsAB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Show that there is a rotation of the plane which does not move D and which maps B’ to E.

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 27: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Show that there is a rotation of the plane which does not move D and which maps B’ to E.

Examples & Explanations

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 28: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Examples & Explanations

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 29: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Show that there is a reflection of the plane which does not move D or E and which maps C’’ to F.

Examples & Explanations

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 30: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ABC ≅ △DEF

Examples & Explanations

Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Page 31: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.

Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Page 32: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.

Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Page 33: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

The triangle in the upper left is reflected over a line to the triangle in the lower right. Using a compass and straightedge, determine the line of reflection.

Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Page 34: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

In the picture below AD and BC intersect at X. AB and CD are drawn forming △AXB and △CXD.The lengths AX, XB, CX, and DX satisfy the equation

A

B

X

C

D

Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Page 35: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

In the picture below AD and BC intersect at X. AB and CD are drawn forming △AXB and △CXD.The lengths AX, XB, CX, and DX satisfy the equation

Are the two triangles similar, if so describe the sequence of transformations.

Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Page 36: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Examples & Explanations

The lengths AX, XB, CX, and DX satisfy the equation

Rotate △ABX 180 degrees about point X, so ∠AXB coincides with ∠DXC. Then dilate △ABXby a factor of . This moves A to D, since , and likewise moves B to C. Therefore △AXB is similar to △DXC

Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Page 37: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

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.

Page 38: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

• Common Core Resources SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc 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/Phil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFT

•Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.phpIllustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ PARCC - http://www.parcconline.org/ Online Assessment System - http://bit.ly/OoyaK5

Resources

Page 39: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

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

Capacity Building Series: Communication in the Mathematics Classroom - http://bit.ly/acoWR9 What Works? Research into Practice - http://bit.ly/SRYTuM

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

Page 40: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

ResourcesLearnzillion.com

• Review• Common Mistakes• Core Lesson• Guided Practice• Extension Activities• Quick Quiz

Page 41: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

ResourcesLearnzillion.com

~Thank you! Thank you! Thank you! This webinar was great, and the site has great resources that I can use tomorrow! I just shared it with everyone at my school! It is like going to a Common Core Conference and receiving all the materials for every session and having them in one place! I love it!

~I watch so many math videos for our common core lessons and I am speechless, how awesome all these small video clips are.

~Thanks for this.  I attended the webinar last week and really like this site.  I'm planning on having a PL session at school on Thursday.

https://attendee.gotowebinar.com/recording/2385067565478552832

Page 42: CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October

Thank You! Please visit http://ccgpsmathematics6-8.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 6-8 Mathematics email listserve.Follow on Twitter!

Follow @GaDOEMath

Brooke KlineProgram Specialist (6‐12)

[email protected]

James PrattProgram Specialist (6-12)

[email protected]

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