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.

CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Coordinate Algebra/Analytic Geometry A Unit 7: Similarity, Congruence, and Proofs October 25, 2012 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

Expectations and clearing up confusion Intent and focus of Unit 7 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. CCGPS is taught and assessed from and beyond.

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!

Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

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

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 tasks 2.Justification of solutions 3.Students questioning one another 4.Use of wait time 5.Use of guidelines for Math Talk

My Favorite No

Unit 6 Frameworks CONCEPTS/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/ Questions

Teacher Edition – page 20 Unit 6: New York Learning Task

Teacher Edition – page 43 Unit 6: Geometric Properties Task

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/ Questions – Unit 3

Announcements System 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: 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 Eitel Director, Assessment Administration Assessment & Accountability Office of Curriculum, Instruction, and Assessment

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. In circle O, AB is congruent to CD ABCD is a parallelogram Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

The two triangles are congruent by SAS: Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent? ABCD is a parallelogram

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. Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent? ABCD is a parallelogram

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: Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent? ABCD is a parallelogram

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: 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.

Triangles are congruent. Triangle BOA is the result of reflecting triangle COD across the perpendicular bisector of AD Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent? In circle O, AB is congruent to CD

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.

Coherence and Focus K-8 th  Identification of figures in different orientations  Ratios and proportions  Drawing of geometric figures with specific characteristics  Transformations  Basic congruence and similarity 10 th -12 th  Transformations of functions  Trigonometric Functions

Examples & Explanations AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ ABC ≅ △ DEF Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

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?

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?

Examples & Explanations AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ ABC ≅ △ DEF Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

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

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?

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ ABC ≅ △ DEF Examples & Explanations Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

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?

AB ≅ DE, AC ≅ DF, BC ≅ EF. Show △ ABC ≅ △ DEF Examples & Explanations Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

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

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

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

Examples & Explanations A B X C D Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

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

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

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.

Common Core Resources  SEDL videos - or  Illustrative Mathematics -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  Phil Daro talks about the Common Core Mathematics Standards - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  PARCC -  Online Assessment System - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Capacity Building Series: Communication in the Mathematics Classroom -  What Works? Research into Practice - Blogs  Dan Meyer –  Timon Piccini –  Dan Anderson –

Resources Learnzillion.com Review Common Mistakes Core Lesson Guided Practice Extension Activities Quick Quiz

Resources Learnzillion.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.

Thank You! Please visit to share your feedback, ask questions, and share your ideas and resources! Please visit to join the 6-8 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.