CCGPS Mathematics Unit-by-Unit Grade Level Webinar Coordinate Algebra & Accelerated Coordinate Algebra/Analytic Geometry A Unit 6: Connecting Algebra and Geometry Through Coordinates October 11, 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 Coordinate Algebra & Accelerated Coordinate Algebra/Analytic Geometry A Unit 6: Connecting Algebra and Geometry Through Coordinates October 11, 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 6 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 6 The importance of mathematical communication  How can I help my students become more effective mathematical communicators?  What does research say about communication? Resources Welcome!

Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

My Favorite No

Wiki/ Questions & Announcements Are Coordinate Algebra students expected to simplify radicals? Estimate - Yes!Rewrite (Simplify) - No!

Wiki/ Questions & 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

Find the equation of the line that passes through (5, 4) and is parallel to the line that contains (1, 1) and (-3, 9).

Mathematical Communication The development of students’ mathematical communication shifts in precision and sophistication throughout the primary, junior and intermediate grades, yet the underlying characteristics remain applicable across all grades. CBS Mathematics

Mathematical Communication Mathematical communication is an essential process for learning mathematics because through communication, students reflect upon, clarify and expand their ideas and understanding of mathematical relationships and mathematical arguments. Ontario Ministry of Education

Mathematical Communication Developing effective mathematical communication Categories of mathematical communication Organizing students to think, talk, and write Updating the three-part problem-solving lesson  Gallery Walk  Math Congress  Bansho (Board Writing)

Mathematical Communication “Because mathematics is so often conveyed in symbols, oral and written, communication about mathematical ideas is not always recognized as an important part of mathematics education. Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so.” Cobb, Wood, & Yackel

Mathematical Communication “The role of the teacher during whole-class discussion is to develop and to build on the personal and collective sense- making of students rather than to simply sanction particular approaches as being correct or demonstrate procedures for solving predictable tasks.” Stein, Engle, Smith, & Hughes

Mathematical Communication When teacher talk dominates whole-class discussion, students tend to rely on teachers to be the expert, rather than learning that they can work out their own solutions and learn from other students. CBS Mathematics

What’s the big idea? Deepen understanding of linear graphs and equations. Deepen understanding of the Pythagorean Theorem. Develop an understanding of distance between two points. Develop an understanding of partitioning a directed line segment. Standards for Mathematical Practice.

 Passive/receptive

 Minimal student explanations, comparisons

Research - Communication Research tells us that student interaction – through classroom discussion and other forms of interactive participation – is foundational to deep understanding and related student achievement. But implementing discussion in the mathematics classroom has been found to be challenging. Dr. Catherine D. Bruce

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

Mathematical Communication Tips on Getting Started 1.Organizing the classroom learning environment 2.Preparing yourself mathematically 3.Coordinating student discussion and analysis of solutions

Coherence and Focus K-8 th  Finding perimeters of geometric figures  Graphing on the coordinate plane  Determining horizontal and vertical distances on the coordinate plane  Pythagorean Theorem 10 th -12 th  Transformations on the coordinate plane  Coordinate proofs with geometric figures  Coordinate proofs with quadratics and conics

Task Structure Misconceptions Understandings Pre- Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post- Assessment

Task Structure Misconceptions Understandings Pre- Assessment Feedback Discussion Explanations Collaborative Task Improvement Deeper Understanding Post- Assessment All three are communication

Examples & Explanations Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?

Examples & Explanations Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle?

Examples & Explanations Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle? Find the slopes of the sides.

Examples & Explanations Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle? Find the slopes of the sides.

Examples & Explanations Given the points P(5, 4), Q(3, -6), R(0, -10), S(2, 0), is the resulting figure a rectangle? Find the slopes of the sides. Two sets of parallel sides. No perpendicular sides.

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Find the coordinate of point T, that is 2/5 of the distance from A(-2, -3) to B(8, 7).

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6).

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths.

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths.

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths.

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths.

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths. Perimeter is

Examples & Explanations Determine the perimeter of a triangle with vertices A(1, 2), B(2, 5) and C(5, 6). Determine the following lengths. Perimeter is

Find the equation of the line that passes through (5, 4) and is parallel to the line that contains (1, 1) and (-3, 9).

Students do not necessarily talk about mathematics naturally; teachers need to help them learn how to do so. The role of the teacher during whole-class discussion is to develop and the build on the personal and collective sense-making of students. …learning that they can work out their own solutions and learn from other students.

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 9-12 Mathematics listserve. 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.