May8_800amAGBAAUnit1 - Georgia Mathematics Educator
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CCGPS Mathematics Unit-by-Unit Grade Level Webinar Accelerated Analytic Geometry B/Advanced Algebra Unit 1: Extending the Number System May 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 1: Extending the Number System May 8, 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. 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/ What is a Wiki? http://ccgpsmathematics9-10.wikispaces.com/ CCGPS Mathematics Sequence for Implementation CCGPS Mathematics Resources for Implementation Welcome! • The big idea of Unit 1 • Standards for Mathematical Practice • Resources Feedback http://ccgpsmathematics9-10.wikispaces.com/ James Pratt – jpratt@doe.k12.ga.us Brooke Kline – bkline@doe.k12.ga.us Secondary Mathematics Specialists 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 http://www.cgcs.org/Page/244 Parent Communication •An overview of what children will be learning in high school mathematics •Topics of discussion for parentteacher communication regarding student academic progress •Tips for parents that will help their children plan for college and career http://www.achievethecore.org/leadership-tools-commoncore/parent-resources/ Parent Communication •An overview of what children will be learning in high school mathematics •Topics of discussion for parentteacher communication regarding student academic progress •Tips for parents that will help their children plan for college and career http://www.achievethecore.org/leadership-tools-commoncore/parent-resources/ Wiki/Email Questions • Multiply Polynomials When do students multiply polynomials such as (π₯ + 1)(π₯ + 2)? Wiki/Email Questions • Imaginary numbers I see that we teach imaginary numbers prior to teaching students about quadratic equations, factoring, etc. Should this be reversed? Wiki/Email Questions • Conditional Probability and the Rules of Probability I don’t see the CP standards from Analytic Geometry in my copy of the Accelerated CCGPS Analytic Geometry B / Advanced Algebra standards, are we supposed to teach them? • 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 opened on April 1, 2013 • Registration closing dates: ο ο ο ο 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 • 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 Complete the following tables. Adapted from Illustrative Mathematics N.RN Operations with Rational and Irrational Numbers Based on the information from your chart, conjecture which of the statements is ALWAYS true, which is SOMETIMES true, and which is NEVER true. • The sum of a rational number and a rational number is rational. • The sum of a rational number and an irrational number is irrational. • The sum of an irrational number and an irrational number is irrational. • The product of a rational number and a rational number is rational. • The product of a rational number and an irrational number is irrational. • The product of an irrational number and an irrational number is irrational. Adapted from Illustrative Mathematics N.RN Operations with Rational and Irrational Numbers Based on the information from your chart, conjecture which of the statements is ALWAYS true, which is SOMETIMES true, and which is NEVER true. • The sum of a rational number and a rational number is rational. ALWAYS true. • The sum of a rational number and an irrational number is irrational. ALWAYS true. • The sum of an irrational number and an irrational number is irrational. SOMETIMES true ( 2 + (− 2) = 0) Adapted from Illustrative Mathematics N.RN Operations with Rational and Irrational Numbers Based on the information from your chart, conjecture which of the statements is ALWAYS true, which is SOMETIMES true, and which is NEVER true. • The product of a rational number and a rational number is rational. ALWAYS true • The product of a rational number and an irrational number is irrational. SOMETIMES true ( 2 × 0 = 0) • The product of an irrational number and an irrational number is irrational. SOMETIMES true ( 2 × 1 2 = 1) Adapted from Illustrative Mathematics N.RN Operations with Rational and Irrational Numbers What’s the big idea? •Extend the properties of exponents to rational exponents. •Use properties of rational and irrational numbers. •Perform arithmetic operations on polynomials. •Perform arithmetic operations with complex numbers. What’s the big idea? Standards for Mathematical Practice What’s the big idea? • SMP 3 – Construct viable arguments and critique the reasoning of others ο Student Sample Work ο Feedback/Critique and Revision Expeditionary Learning http://elschools.org/student-work/butterfly-drafts Coherence and Focus • K-9th ο Algebraic expressions ο Properties of operations ο Rational and irrational numbers ο Radicals and integer exponents with numerical expressions ο11th-12th ο Polynomial identities and equations ο Polynomial, square root, and cube root functions Examples & Explanations A biology student is studying bacterial growth, She was surprised to find that the population of the bacteria doubled every hour. Complete the following table: Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations The student conducting the study wants to create a table with more entries; specifically, she wants to fill in the population at each half hour. However she forgot to make these measurements so she want s to estimate the values. Complete the following table: Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations What if the student wanted to estimate the population every 20 minutes instead of every 30 minutes. What multiplier would be necessary to be consistent with the population doubling every hour? Complete the following table: Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations Use the population context to explain why it makes sense that 1 2 1 3 3 we define 2 to be 2 and 2 to be 2 Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations Use the population context to explain why it makes sense that 1 3 1 2 3 we define 2 to be 2 and 2 to be 2 The equation for the population is π = 4(2)π‘ . π 1 2 = 1 4(2)2 = 4β 2 1 2 ∴ (2) = 2 Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations Use the population context to explain why it makes sense that 1 3 1 2 3 we define 2 to be 2 and 2 to be 2 The equation for the population is π = 4(2)π‘ . π 1 2 = 1 2 1 4(2)2 = ∴ (2) = 2 4β 2 π 1 3 = 1 4(2)3 = 1 3 ∴ (2) = 3 3 4β 2 2 Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2 Examples & Explanations A garden is created so that the garden bed is seven yards more than twice the width of the bed. A walkway is created around the garden that is 2 yards wide. Write an expression that represents the area of the walkway surrounding the garden. Adapted from Sophia.org Adding and Subtracting Polynomials in the Real World Examples & Explanations A garden is created so that the garden bed is seven yards more than twice the width of the bed. A walkway is created around the garden that is 2 yards wide. Write an expression that represents the area of the walkway surrounding the garden. Adapted from Sophia.org Adding and Subtracting Polynomials in the Real World Examples & Explanations A garden is created so that the garden bed is seven yards more than twice the width of the bed. A walkway is created around the garden that is 2 yards wide. Write an expression that represents the area of the walkway surrounding the garden. Area of large rectangle – Area of small rectangle π₯ + 4 2π₯ + 11 − π₯ 2π₯ + 7 = 2π₯ 2 + 11π₯ + 8π₯ + 44 − 2π₯ 2 + 7π₯ = 2π₯ 2 + 11π₯ + 8π₯ + 44 − 2π₯ 2 − 7π₯ = 2π₯ 2 − 2π₯ 2 + 11π₯ + 8π₯ − 7π₯ + 44 = 12π₯ + 44 Adapted from Sophia.org Adding and Subtracting Polynomials in the Real World Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 3 + 2π 2 − 5π 5 + 4π 17 − 13π − 5 + 3π 17 − 13π 2 −(5+ π )2 (52+7π ) 2 2 2 1 + π 13 − 4π 1 − π 1 + π + π2 + π3 Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 3 + 2π 2 − 5π = 3 2 − 5π + 2π 2 − 5π = 6 − 15π + 4π − 10π 2 = 6 − 15π + 4π + 10 = 16 − 11π Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 5 + 4π 17 − 13π − 5 + 3π 17 − 13π = 17 − 13π 5 + 4π − 5 + 3π = 17 − 13π π = 17π − 13π 2 = 13 + 17π Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 2 −(5+ π )2 (52+7π ) 2 2 2 (25 4 + 70π 4 49π 2 + 4 ) − (25 4 2 60π 48π + 4 4 15π + 12π 2 + 10π 4 + π2 4) −12 + 15π Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 1 + π 13 − 4π 1 − π = 1 + π 1 − π 13 − 4π = 1 − π 2 13 − 4π = 2 13 − 4π = 26 − 8π Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers Examples & Explanations Rewrite each of the following expressions involving complex numbers in the form π + ππ where π and π are real numbers. 1 + π + π2 + π3 = 1 + π + −1 + −π = 0 Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers 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. Resources Learnzillion.com • • • • • • Review Common Mistakes Core Lesson Guided Practice Extension Activities Quick Quiz http://www.learnzillion.com Resources http://www.illustrativemathematics.org/ Resources • Common Core Resources ο SEDL videos - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc ο Illustrative Mathematics - http://www.illustrativemathematics.org/ ο Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ οCommon Core Standards - http://www.corestandards.org/ οTools for the Common Core Standards - http://commoncoretools.me/ οPhil Daro talks about the Common Core Mathematics Standards - http://bit.ly/URwOFT • Assessment Resources ο MAP - http://www.map.mathshell.org.uk/materials/index.php οIllustrative Mathematics - http://illustrativemathematics.org/ ο CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ ο PARCC - http://www.parcconline.org/ οOnline Assessment System - http://bit.ly/OoyaK5 Resources • Professional Learning Resources ο Inside Mathematics- http://www.insidemathematics.org/ οAnnenberg Learner - http://www.learner.org/index.html οEdutopia – http://www.edutopia.org οTeaching Channel - http://www.teachingchannel.org ο Ontario Ministry of Education - http://bit.ly/cGZlce οExpeditionary Learning: Center for Student Work - http://elschools.org/student-work • Blogs οDan Meyer – http://blog.mrmeyer.com/ οTimon Piccini – http://mrpiccmath.weebly.com/3-acts.html οDan Anderson – http://blog.recursiveprocess.com/tag/wcydwt/ 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.
