Sept13_MathCAUnit3Update - Georgia Mathematics Educator
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CCGPS Mathematics Coordinate Algebra Update Webinar Unit 3: Linear and Exponential Functions September 13, 2013 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Secondary Mathematics Specialists Microphone and speakers can be configured by going to: Tools – Audio – Audio setup wizard These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement. What are update webinars? • Update on the work of the 2013 Resource Revision Team ο Overall revisions ο Unit 3 revisions • Addressing areas which teachers have found to be more challenging • Resources 2013 CA Resource Revision Team Coordinate Algebra/Acc CA Comprehensive Course Overview • Located on the 9-12 math section of www.georgiastandards.org • Designed to provide clarification of CCGPS Mathematics Standards • Organized to link together many sources of information pertinent to CCGPS Coordinate Algebra/Accelerated Coordinate Algebra Begin at www.georgiastandards.org Direct Link to Page Select the CCGPS ELA/Math Tab Direct Link to Page Select the Mathematics option under Browse CCGPS Direct Link to Page Select the 9-12 option in the Mathematics section Direct Link to Page Expand the Coordinate Algebra Course Direct Link to Page Select the Comprehensive Course Overview Expande Coordinate Algebra Direct Link to Page Direct Link to Page Table of Contents • Outlines the Major areas of Focus for the Course • Fully Interactive when viewed via internet • Hover over a section and select to access the section quickly Sections of Interest • Flipbook Access: Detailed Information About Each Standard • Unit Descriptions: Overview • Webinar Information • Assessment Resources and Instructional Support Resources • Internet Resources • Curriculum Map Formative Assessment Lessons (FALs) CCGPS Math Wiki Space Purpose of Tasks • Problem-Based-Learning--Check out Dan Meyer, Robert Kaplinksy’s websites • Provide several entry points to the standards. • Teachers should review all tasks in a given unit to determine which tasks would be appropriate for their students. Tasks can be adapted to fit the needs or your classroom. Most standards are covered by various tasks Goals of Unit Revisions • More user-friendly • Provide teachers with task summaries • Give teachers tools necessary to quickly analyze tasks • Provide tasks from different sources Updates to Unit Frameworks TASK TABLE • Outlines the tasks by type, content and standard. • Provides suggested times • Hyperlinks to PDFs and Word Docsv Updates to Unit Frameworks Unit 3 • Tasks primarily address: – Modeling situations with linear or exponential functions – Exploring function notation and transformations – Understanding sequences as functions Modeling Exponential Functions • • • • Having Kittens Multiplying Cells Community Service, Sequences and Functions Paper Folding (from Unit1) Having Kittens • Students explore if cats could realistically have 2000 descendants in a year and a half. Multiplying Cells • Short task • Students chart out cell populations over time. Community Service, Sequences and Functions • Student explore comparisons in making money in a linear and in an exponential model. Function Notation • Talk is Cheap • Building and Comparing Functions • Functioning Well High Functioning—Vertical Translations High Functioning—Even and Odd Functions MARS FAL • Designed by the shell center • Intended as student-driven, teacher-facilitated lessons that build conceptual understanding A look at MARS FAL: Comparing Investments Lesson Plan A look at MARS FAL: Comparing Investments Misconceptions A look at MARS FAL: Comparing Investments Activities A look at MARS FAL: Comparing Investments Student Work Unit 3 Challenges The coordinate plane shows two functions of π₯. π(π₯) is an increasing linear function. π(π₯) is an increasing exponential function. Based on the information, which statement is true for all real values of the domain x ≥ 0? A. B. C. D. π π₯ = π(π₯) for only one value in the domain π(π₯) = π(π₯) for many values in the domain π(π₯) > π(π₯) for all values in the domain π(π₯) < π(π₯) for all values in the domain Unit 3 Challenges MCC9β12.F.LE.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Unit 3 Challenges The coordinate plane shows two functions of π₯. π(π₯) is an increasing linear function. π(π₯) is an increasing exponential function. Based on the information, which statement is true for all real values of the domain x ≥ 0? A. B. C. D. π π₯ = π(π₯) for only one value in the domain π(π₯) = π(π₯) for many values in the domain π(π₯) > π(π₯) for all values in the domain π(π₯) < π(π₯) for all values in the domain Unit 3 Challenges The coordinate plane shows two functions of π₯. π(π₯) is an increasing linear function. π(π₯) is an increasing exponential function. Based on the information, which statement is true for all real values of the domain x ≥ 0? A. B. C. D. π π₯ = π(π₯) for only one value in the domain π(π₯) = π(π₯) for many values in the domain π(π₯) > π(π₯) for all values in the domain π(π₯) < π(π₯) for all values in the domain 21.71% 23.58% 40.16% 14.01% Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 1300(13 ) 18 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 1300(13 ) 18 939(13 ) 18 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 1300(13 ) 18 939(13 ) 18 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 13 = 1800(13 )2 18 18 13 = 1800(13 )3 18 18 1300 939 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Unit 3 Challenges Suppose you drop a basketball and the ratio of each rebound height to the previous rebound height is 1300:1800. Let β be the function that assigns to π the rebound height of the ball (in mm) on the πth bounce or rebound. Complete the chart below, rounding to the nearest mm. 1800(13 ) 18 13 = 1800(13 )2 18 18 13 = 1800(13 )3 18 18 1300 939 Adapted from Illustrative Mathematics F-LE Basketball Rebounds Assessment – Coordinate Algebra Released Items We have posted a set of released Coordinate Algebra EOCT items to the GaDOE website. In addition to the item booklet itself, you will find commentary and field test performance data. […] The items are posted on the EOCT webpage, under the link 'EOCT Resources.' A direct link to this webpage is provided below. Please scroll down the page and look under the heading 'Other Documents and Resources.' […] http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/EOCTResources.aspx ~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability (excerpt from an email sent to K-12 Assessment Directors from Dr. Fincher) Resources • GaDOE Resources ο Fall 2011 CCGPS Standards for Mathematical Practices Webinars https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx ο Spring 2012 CCGPS Mathematics Professional Learning Sessions on GPB https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx ο2012 – 2013 CCGPS Mathematics Unit-by-Unit Webinar Series https://www.georgiastandards.org/Common-Core/Pages/Math-PL-Sessions.aspx οGeorgia Mathematics Teacher Forums - http://ccgpsmathematics9-10.wikispaces.com/ οCCGPS Mathematics Frameworks and Comprehensive Course Overviews https://www.georgiastandards.org/Common-Core/Pages/Math-9-12.aspx οMathematics Formative Assessment Lesson Videos https://www.georgiastandards.org/Common-Core/Pages/Mathematics-FormativeAssessment-Lessons-Videos.aspx 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 Resources ο SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc ο Illustrative Mathematics - http://www.illustrativemathematics.org/ ο Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.html ο Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ ο Common Core Standards - http://www.corestandards.org/ ο Tools for the Common Core Standards - http://commoncoretools.me/ ο LearnZillion - http://learnzillion.com/ • Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.php ο Illustrative Mathematics - http://illustrativemathematics.org/ ο CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ ο Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/ ο PARCC - http://www.parcconline.org/ οOnline Assessment System - http://bit.ly/OoyaK5 ο Resources Resources • Professional Learning Resources ο Inside Mathematics- http://www.insidemathematics.org/ ο Annenberg Learner - http://www.learner.org/index.html ο Edutopia – http://www.edutopia.org ο Teaching Channel - http://www.teachingchannel.org ο Ontario Ministry of Education - http://bit.ly/cGZlce οAchieve - http://www.achieve.org/ • Blogs ο Dan Meyer – http://blog.mrmeyer.com/ ο Robert Kaplinsky - http://robertkaplinsky.com/ • Books ο Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8 Resources http://robertkaplinsky.com/ Resources http://robertkaplinsky.com/ Mathematical Understanding? http://robertkaplinsky.com/what-does-it-mean-tounderstand-mathematics/ Mathematical Understanding? • Procedural skill and fluency • Conceptual understanding • The ability to apply mathematics http://robertkaplinsky.com/what-does-it-mean-tounderstand-mathematics/ Feedback http://www.surveymonkey.com/s/WZKG5G2 James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@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 (6β12) bkline@doe.k12.ga.us James Pratt Program Specialist (6-12) jpratt@doe.k12.ga.us These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.
