CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Analytic Geometry B/Advanced Algebra Unit 3: Modeling Geometry August 8, 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 Accelerated Analytic Geometry B/Advanced Algebra Unit 3: Modeling Geometry August 8, 2013 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 3 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 3 Incorporating SMPs into geometric modeling Resources Welcome!

2013 AG Resource Revision Team

Feedback James Pratt – Brooke Kline – Secondary Mathematics Specialists

 Question: Why is MCC9-12.A.REI.7 addressed in both Unit 2 and Unit 3? Wiki/ Questions

Use the Pythagorean theorem to find an equation in x and y whose solutions are the points on the circle of radius 2 with center (1,1) and explain why it works. Adapted from Illustrative Mathematics G-GPE Explaining the Equation of a Circle

What’s the big idea? Translate between the geometric description and the equation for a conic section Use coordinates to prove simple geometric theorems algebraically Solve system of equations

What’s the big idea? Standards for Mathematical Practice

What’s the big idea? SMP 1 – Make sense of problems and persevere in solving them SMP 2 – Reason abstractly and quantitatively SMP 3 – Construct viable arguments and critique the reasoning of others SMP 6 – Attend to precision

What’s the big idea? SMP 1 – Make sense of problems and persevere in solving them SMP 2 – Reason abstractly and quantitatively SMP 3 – Construct viable arguments and critique the reasoning of others SMP 6 – Attend to precision

Coherence and Focus K-9 th  Write equivalent expressions  Solving equations for variables on interest  Pythagorean Theorem  Quadratic functions  Completing the square 11th-12th  Modeling with geometry  Equations of ellipses and hyperbolas

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid?

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid?

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid?

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid?

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid?

Examples & Explanations Adapted from %20Conics%20and%20Parabolas.pdf A flashlight mirror has the shape of a paraboloid of diameter 4 inches and depth 2 inches. Where should the bulb be placed so that the emitted light rays are parallel to the axis of the paraboloid? The bulb would need to be placed ½ inch from the rear of the flashlight mirror.

Examples & Explanations Adapted from Functioning with Parabolas Mathematics Vision Project

Examples & Explanations Adapted from Functioning with Parabolas Mathematics Vision Project

Examples & Explanations Adapted from Functioning with Parabolas Mathematics Vision Project

Examples & Explanations Adapted from Functioning with Parabolas Mathematics Vision Project

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Examples & Explanations You probably know that the smaller |a| in the standard form equation of a parabola, the wider the parabola. In other words y =.1x² is a wider parabola than y =.2x². How does this relate to the directrix and focus? As |a| decreases p increases, ie. the distance between the vertex and directrix and vertex and focus increases. Adapted from mathwarehouse.com Focus and Directrix of Parabola explained with pictures and diagrams

Use the Pythagorean theorem to find an equation in x and y whose solutions are the points on the circle of radius 2 with center (1,1) and explain why it works. Adapted from Illustrative Mathematics G-GPE Explaining the Equation of a Circle

For any point ( x, y ) on the circle. The horizontal length is | x – 1| and the vertical length is | y – 1|. The hypotenuse is 2. Adapted from Illustrative Mathematics G-GPE Explaining the Equation of a Circle

Assessment July 22, 2013 – State School Superintendent Dr. John Barge and Gov. Nathan Deal announced today that Georgia is withdrawing from the Partnership for Assessment of Readiness for College and Careers (PARCC) test development consortium. Instead, the Georgia Department of Education (GaDOE) will work with educators across the state to create standardized tests aligned to Georgia’s current academic standards in mathematics and English language arts for elementary, middle and high school students. Additionally, Georgia will seek opportunities to collaborate with other states. The press release in its entirety can be found at: Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123http:// Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

Assessment As GaDOE begins to build new assessments, please note that our Georgia assessments: will be aligned to the math and English language arts state standards; will be high-quality and rigorous; will be developed for students in grades 3 through 8 and high school; will be reviewed by Georgia teachers; will require less time to administer than the PARCC assessments; will be offered in both computer- and paper-based formats; and will include a variety of item types, such as performance-based and multiple- choice items. The press release in its entirety can be found at: Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123http:// Policy/communications/Pages/PressReleaseDetails.aspx?PressView=default&pid=123

Assessment We will continue to work with Georgia educators, as we have in the past, to reconfigure and/or redevelop our state assessments to reflect the instructional focus and expectations inherent in our rigorous state standards in language arts and math. This is not a suspension of the implementation of the CCGPS in language arts and math. ~ Dr. John Barge (excerpt from a letter to state Superintendents from Dr. Barge)

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.

CCGPS Resources  SEDL videos - or  Illustrative Mathematics -  Mathematics Vision Project -  Dana Center's CCSS Toolbox -  Common Core Standards -  Tools for the Common Core Standards -  LearnZillion - Assessment Resources  MAP -  Illustrative Mathematics -  CCSS Toolbox: PARCC Prototyping Project -  Smarter Balanced -  PARCC -  Online Assessment System - Resources

Professional Learning Resources  Inside Mathematics-  Annenberg Learner -  Edutopia –  Teaching Channel -  Ontario Ministry of Education -  Achieve - Blogs  Dan Meyer –  Robert Kaplinsky - Books  Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8

Resources

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. Follow us on 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.