Session will be begin at 8:00 am CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 1: Similarity, Congruence, and Proofs May 7, 2013 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 Analytic Geometry Unit 1: Similarity, Congruence, and Proofs May 7, 2013 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. James & Brooke

Expectations and clearing up confusion Intent and focus of Unit 1 webinar. Framework tasks. GPB sessions on Georgiastandards.org. Standards for Mathematical Practice. Resources. http://ccgpsmathematics9-10.wikispaces.com/ James

What is a Wiki? James http://ccgpsmathematics9-10.wikispaces.com/

CCGPS Mathematics Sequence for Implementation Brooke

CCGPS Mathematics Resources for Implementation Brooke

Welcome! The big idea of Unit 1 Understanding congruence/similarity in terms of transformations. Why do SSS, ASA, & SAS work? Why does AA work? Standards for Mathematical Practice Resources Brooke

Feedback http://ccgpsmathematics9-10.wikispaces.com/ James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Secondary Mathematics Specialists Brooke

Parent Communication Explanation to parents of the need for change in mathematics What children will be learning in high school mathematics Parents partnering with teachers Grade level examples Parents helping children learn outside of school Additional resources Brooke http://www.cgcs.org/Page/244

Parent Communication An overview of what children will be learning in high school mathematics Topics of discussion for parent-teacher communication regarding student academic progress Tips for parents that will help their children plan for college and career Brooke http://www.achievethecore.org/leadership-tools-common-core/parent-resources/

Parent Communication An overview of what children will be learning in high school mathematics Topics of discussion for parent-teacher communication regarding student academic progress Tips for parents that will help their children plan for college and career Brooke http://www.achievethecore.org/leadership-tools-common-core/parent-resources/

Wiki/Email Questions MCC9-12.G.CO.6 What’s the difference between 8th grade MCC8.G.2 and what we do in Analytic Geometry? MCC9-12.G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. James

Wiki/Email Questions MCC9-12.G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. Can you provide more information about this standard: Do we need the students to be able to prove the medians of a triangle meet at a point? Do the students need to know centroid, incenter, circumcenter, and orthocenter? Do the students need to know how to apply each proof listed in this standard to “skill based” problems? James

   Brooke

Cost: $50 for GCTM members and $60 for GCTM non-members    Cost: $50 for GCTM members and $60 for GCTM non-members Travel expenses will be reimbursed for all participants who complete the academy and are Georgia certified K-12 educators under contract with a Georgia school Registration will opened on April 1, 2013 Registration closing dates: Academy 1 – May 15, 2013 Academy 2 – May 22, 2013 Academy 3 – May 29, 2013 Academy 4 – June 5, 2013 Payments must be received prior to the closing date of registration Brooke

Call 1-855-ASK-GCTM (ext 4) for questions about the academy    Visit www.gctm.org for more details concerning these quality professional development opportunities Call 1-855-ASK-GCTM (ext 4) for questions about the academy Peggy Pool – GCTM Vice President for Regional Services and Director of Academies, Academies2013@gctm.org Brooke

Activate your Brain 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 Brooke Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

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

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

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

Activate your Brain 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: ABCD is a parallelogram Brooke ∠DAX ≅ ∠BCX and ∠ADX ≅ ∠CBX since they are opposite interior angles. 𝐴𝐷 ≅ 𝐵𝐶 since opposite sides of a parallelogram are congruent. Adapted from Illustrative Mathematics G.CO Are the Triangles Congruent?

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

What’s the big idea? Understand congruence in terms of rigid motions. Understand similarity in terms of similarity transformations. Prove theorems involving similarity. Prove geometric theorems. Make geometric constructions. Brooke

Standards for Mathematical Practice What’s the big idea? Standards for Mathematical Practice Brooke

What’s the big idea? SMP 3 – Construct viable arguments and critique the reasoning of others Student Sample Work Feedback/Critique and Revision Brooke Expeditionary Learning http://elschools.org/student-work/butterfly-drafts

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

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

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

Examples & Explanations 𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ABC ≅ △DEF James 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 reflection of the plane which does not move D or E and which maps C’’ to F. James Adapted from Illustrative Mathematics G.CO.8 Why does SSS Work?

Examples & Explanations 𝐴𝐵 ≅ 𝐷𝐸 , 𝐴𝐶 ≅ 𝐷𝐹 , 𝐵𝐶 ≅ 𝐸𝐹 . Show △ABC ≅ △DEF James 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. James 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. James 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. James Adapted from Illustrative Mathematics G.CO.5, G.CO.12 Reflected Triangles

Proofs in CCGPS Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two‐column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. James http://www.mathematicsvisionproject.org/secondary-two-mathematics.html

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 𝐴𝑋 𝐵𝑋 = 𝐷𝑋 𝐶𝑋 A B X C D James Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

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 𝐴𝑋 𝐵𝑋 = 𝐷𝑋 𝐶𝑋 Are the two triangles similar, if so describe the sequence of transformations. James Adapted from Illustrative Mathematics G.SRT.2 Are They Similar?

Examples & Explanations The lengths AX, XB, CX, and DX satisfy the equation 𝐴𝑋 𝐵𝑋 = 𝐷𝑋 𝐶𝑋 Rotate △ABX 180 degrees about point X, so ∠AXB coincides with ∠DXC. Then dilate △ABX by a factor of 𝐷𝑋 𝐴𝑋 . This moves A to D, since 𝐴𝑋( 𝐷𝑋 𝐴𝑋 )=𝐷𝑋 , and likewise moves B to C. Therefore △AXB is similar to △DXC James 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. James

Resources http://secc.sedl.org/common_core_videos/index.php James

Resources http://www.shodor.org/interactivate/ James

Resources Brooke http://www.illustrativemathematics.org/

Resources Common Core Resources Assessment 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.php Illustrative 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 Brooke

Resources Professional Learning Resources Blogs 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 Expeditionary Learning: Center for Student Work - http://elschools.org/student-work Blogs Dan Meyer – http://blog.mrmeyer.com/ Timon Piccini – http://mrpiccmath.weebly.com/3-acts.html Dan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/ Brooke

James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us 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. Follow on Twitter! Follow @GaDOEMath Brooke Kline Program Specialist (6‐12) bkline@doe.k12.ga.us James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us James & Brooke These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.