ccgps mathematics unit-by-unit grade level webinar analytic geometry unit 5: quadratic function...

CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Analytic GeometryUnit 5: Quadratic Function

September 17, 2013

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CCGPS MathematicsUnit-by-Unit Grade Level Webinar

Analytic GeometryUnit 5: Quadratic Functions

September 17, 2013

James Pratt – jpratt@doe.k12.ga.usBrooke Kline – bkline@doe.k12.ga.usSecondary Mathematics Specialists

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.

• The big idea of Unit 5• Incorporating SMPs into quadratic functions• Resources

Welcome!

• Number of Standards in Unit 5My HS math teachers are collaboratively planning this week and are having some serious panic attacks with this unit (AG Unit 5). Their general consensus is that this unit is an entire course in and of itself considering that these students have little or no experience at all with quadratics.

Wiki/Email Questions

• Complex numbers and quadraticsComplex numbers are in Unit 4 and Quadratics are in Unit 5 of Analytic Geometry. Does this seem backwards?

Wiki/Email Questions

Which of the following could be the function of a real variable x whose graph is shown below? Explain.

Activate your Brain

Adapted from Illustrative Mathematics F-IF Which Function?

Activate your Brain

Adapted from Illustrative Mathematics F-IF Which Function?

What’s the big idea?• Interpret the structure of expressions.• Write expressions in equivalent forms to solve problems• Create equations that describe numbers or relationships• Solve equations and inequalities in one variable• Solve systems of equations• Interpret functions that arise in applications in terms of the context• Analyze functions using different representations• Build a function that models a relationship between two quantities• Build new functions from existing functions• Construct and compare linear, quadratic, and exponential models and solve problems

What’s the big idea?

Standards for Mathematical Practice

http://robertkaplinsky.com/

What’s the big idea?• SMP 1 – Make sense of

problems and persevere in solving them

• SMP 2 – Reason abstractly and quantitatively

Mathematical Understanding?

http://robertkaplinsky.com/what-does-it-mean-to-understand-mathematics

/

http://robertkaplinsky.com/what-does-it-mean-to-understand-mathematics

/

• Procedural skill and fluency

• Conceptual understanding

• The ability to apply mathematics

Mathematical Understanding?

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

The profit that a company makes selling an item (in thousands of dollars) depends on the price of the item (in dollars). If p is the price of the item, then three equivalent forms for the profit are:

Adapted from Illustrative Mathematics A-SSE Profit of a Company

Examples & Explanations

Which form is most useful in finding:a. The prices that give a profit of zero dollars?b. The profit when the price is zero?c. The price that gives the maximum profit?

Adapted from Illustrative Mathematics A-SSE Profit of a Company

Examples & Explanations

How many different ways can you think of to solve:

What are some of the different methods?

Adapted from Illustrative Mathematics A-REI Two Squares are Equal

Examples & Explanations

Suppose is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.

a. How high above the water is the springboard? Explain how your know.

Adapted from Illustrative Mathematics F-IF, A-REI Springboard Dive

Examples & Explanations

Suppose is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.

b. When does the diver hit the water?

Adapted from Illustrative Mathematics F-IF, A-REI Springboard Dive

Examples & Explanations

Suppose is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.

b. When does the diver hit the water?

seconds

Adapted from Illustrative Mathematics F-IF, A-REI Springboard Dive

Examples & Explanations

Suppose is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.

c. When does the diver reach the peak of the dive?

Adapted from Illustrative Mathematics F-IF, A-REI Springboard Dive

Examples & Explanations

Suppose is an expression giving the height of a diver above the water (in meters), t seconds after the diver leaves the springboard.

c. When does the diver reach the peak of the dive?The diver reaches the peak of the dive at the axis of symmetry.

second.

Adapted from Illustrative Mathematics F-IF, A-REI Springboard Dive

Examples & Explanations

Suppose Brett and Andre each throw a baseball into the air. The height of Brett’s baseball is given by:

Where h is in feet and t is in seconds. The height of Andre’s baseball is given by the graph:

Adapted from Illustrative Mathematics F-IF, Throwing Baseballs

How long is each baseball airborne?

Examples & Explanations

Brett :

and seconds

Adapted from Illustrative Mathematics F-IF, Throwing Baseballs

Examples & Explanations

Andre:

seconds

Adapted from Illustrative Mathematics F-IF, Throwing Baseballs

Activate your Brain

Adapted from Illustrative Mathematics F-IF Which Function?

Activate your Brain

Adapted from Illustrative Mathematics F-IF Which Function?

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

Assessment – Released Items

A. 48.25%

B. 19.18%

C. 22.06%

D. 10.03%

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

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 – 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 us on Twitter

@GaDOEMath

Brooke KlineProgram Specialist (6‐12)

bkline@doe.k12.ga.us

James PrattProgram Specialist (6-12)

jpratt@doe.k12.ga.us

These materials are for nonprofit educational purposes only. Any other use may constitute copyright infringement.