ccgps mathematics unit-by-unit grade level webinar analytic geometry unit 4: extending the number...
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CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Analytic GeometryUnit 4: Extending the Number System
September 3, 2013
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CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Analytic GeometryUnit 4: Extending the Number System
September 3, 2013
James Pratt – [email protected] Kline – [email protected] 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!
• Multiply PolynomialsWhen do students multiply polynomials such as ?
Wiki/Email Questions
• Imaginary numbersI see that we teach imaginary numbers prior to teaching students about quadratic equations, factoring, etc. Should this be reversed?
Wiki/Email Questions
Complete the following tables.
Activate your Brain
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.
Activate your Brain
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 ()
Activate your Brain
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 ()
• The product of an irrational number and an irrational number is irrational.
SOMETIMES true ()
Activate your Brain
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 http://blog.mrmeyer.com/http://bit.ly/17QDmw9
http://www.schooltube.com/video/81f35b2779ef8d4727fd/http://www.youtube.com/watch?v=jRMVjHjYB6w
Coherence and Focus• K-9th
Algebraic expressions Properties of operations Rational and irrational numbers Radicals and integer exponents with numerical expressions
• 11th-12th 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
Use the population context to explain why it makes sense that we define to be and to be
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 we define to be and to be The equation for the populationis .
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 we define to be and to be The equation for the populationis .
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 & ExplanationsA 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 & ExplanationsA 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
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 where and are real numbers.
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 where and are real numbers.
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 where and are real numbers.
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 where and are real numbers.
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 where and are real numbers.
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 where and are real numbers.
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.' […]
http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Assessment/Pages/EOCT-Resources.aspx
~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability(excerpt from an email sent to K-12 Assessment Directors from Dr. Fincher)
Assessment – Released Items
Which statement is true about this expression?
A It is rational because it is the sum of two irrational numbers.
B It is irrational because it is the sum of two irrational numbers.
C It is rational because it is the sum of a rational number and an irrational number.
D It is irrational because it is the sum of a rational number and an irrational number.
Assessment – Released Items
Which statement is true about this expression?
A It is rational because it is the sum of two irrational numbers. 15.52%
B It is irrational because it is the sum of two irrational numbers. 28.14%
C It is rational because it is the sum of a rational number and an irrational number. 26.26%
D It is irrational because it is the sum of a rational number and an irrational number. 29.38%
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 - http://bit.ly/RwWTdc or http://bit.ly/yyhvtc Illustrative Mathematics - http://www.illustrativemathematics.org/ Mathematics Vision Project - http://www.mathematicsvisionproject.org/index.html Dana Center's CCSS Toolbox - http://www.ccsstoolbox.com/ Common Core Standards - http://www.corestandards.org/ Tools for the Common Core Standards - http://commoncoretools.me/ LearnZillion - http://learnzillion.com/
• Assessment Resources MAP - http://www.map.mathshell.org.uk/materials/index.php Illustrative Mathematics - http://illustrativemathematics.org/ CCSS Toolbox: PARCC Prototyping Project - http://www.ccsstoolbox.org/ Smarter Balanced - http://www.smarterbalanced.org/smarter-balanced-assessments/ PARCC - http://www.parcconline.org/ Online Assessment System - http://bit.ly/OoyaK5
Resources
Resources• Professional Learning Resources
Inside Mathematics- http://www.insidemathematics.org/ Annenberg Learner - http://www.learner.org/index.html Edutopia – http://www.edutopia.org Teaching Channel - http://www.teachingchannel.org Ontario Ministry of Education - http://bit.ly/cGZlce Achieve - http://www.achieve.org/
• Blogs Dan Meyer – http://blog.mrmeyer.com/ Robert Kaplinsky - http://robertkaplinsky.com/
• Books Van De Walle & Lovin, Teaching Student-Centered Mathematics, Grades 5-8
Feedbackhttp://www.surveymonkey.com/s/WZKG5G2
James Pratt – [email protected] Brooke Kline – [email protected]
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 us on Twitter
@GaDOEMath
Brooke KlineProgram Specialist (6‐12)
James PrattProgram Specialist (6-12)
These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.