CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Analytic Geometry B/Advanced Algebra Unit 7: Rational and Radical Relationships September 19, 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 7: Rational and Radical Relationships September 19, 2013 James Pratt – Brooke Kline – Secondary Mathematics Specialists These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

The big idea of Unit 7 Incorporating SMPs into rational and radical expressions, equations, and functions Resources Welcome!

If we raise both sides of an equation to a power, we sometimes obtain an equation which has more solutions than the original one. Which of the following equations result in extraneous solutions when you raise both sides to the indicated power? Explain. Adapted from Illustrative Mathematics A-REI Radical Equations

What’s the big idea? Rewrite rational expressions Create equations that describe numbers or relationships Understand solving equations as a process of reasoning and explain the reasoning Represent and solve equations and inequalities graphically Interpret functions that arise in applications in terms of the context Analyze functions using different representations

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

Mathematical Understanding? understand-mathematics/

understand-mathematics/ Procedural skill and fluency Conceptual understanding The ability to apply mathematics Mathematical Understanding?

Coherence and Focus K-9 th  Rewrite expressions  Linear functions  Quadratic functions 11th-12th  Solve and graph functions  Model with functions.

Examples & Explanations Adapted from Illustrative Mathematics A-APR Combined Fuel Efficiency

Examples & Explanations Adapted from Illustrative Mathematics A-APR Combined Fuel Efficiency

Examples & Explanations Adapted from Illustrative Mathematics F-IF Average Cost

Examples & Explanations Adapted from Illustrative Mathematics F-IF Average Cost

Examples & Explanations Adapted from Illustrative Mathematics F-IF Average Cost

Examples & Explanations

Examples & Explanations

Examples & Explanations One can see 200 miles to the horizon if they are approximately at an altitude of 23,000 ft. or just over 4 1/3 miles. (slightly below cruising altitude for airlines)

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

Feedback James Pratt – Brooke Kline –

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.