CCGPS Mathematics Unit-by-Unit Grade Level Webinar Analytic Geometry Unit 5: Quadratic Function September 17, 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.
Transcript
CCGPS MathematicsUnit-by-Unit Grade Level Webinar
Analytic GeometryUnit 5: Quadratic Function
September 17, 2013
Session will be begin at 8:00 amWhile 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.
• 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
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.' […]
~ Dr. Melissa Fincher, Associate Superintendent for Assessment and Accountability(excerpt from an email sent to K-12 Assessment Directors from Dr. Fincher)
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/
