CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 4: Extending the Number System September 3, 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 Analytic Geometry Unit 4: Extending the Number System September 3, 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 4 Incorporating Standards for Mathematical Practice Resources Welcome!

Wiki/ Questions

Imaginary numbers I see that we teach imaginary numbers prior to teaching students about quadratic equations, factoring, etc. Should this be reversed? Wiki/ Questions

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

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 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 4 – Model with mathematics SMP 5 – Use appropriate tools strategically

Resources

Coherence and Focus K-9 th  Algebraic expressions  Properties of operations  Rational and irrational numbers  Radicals and integer exponents with numerical expressions 11 th -12 th  Polynomial identities and equations  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 Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2

Examples & Explanations Adapted from Illustrative Mathematics N-RN Extending the Definitions of Exponents, Variation 2

Examples & Explanations 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 Adapted from Sophia.org Adding and Subtracting Polynomials in the Real World

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Examples & Explanations Adapted from Illustrative Mathematics N-CN, A-SSE Computations With Complex Numbers

Assessment – Released Items We have posted a set of released […] 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.' […] Resources.aspxhttp:// Resources.aspx ~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability (excerpt from an sent to K-12 Assessment Directors from Dr. Fincher)

Assessment – Released Items

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

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.