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Analyzing Graphs

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Analyzing Graphs

4 different equations of functions each representing from a different function family. All functions represented in the same graph. Students play with calculators inputting values to see which correspond to the appropriate function in the graph.

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Approximate the Zero

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Approximate the Zero

Chunk a graph to use the relationships between distances on a graph to estimate the value of a zero of the graph.

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Building a quadratic function from f(x)=x²

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Building a quadratic function from f(x)=x²

Students sketch the parent function and then sketch different transformations of that function to compare them.

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Building Inverse and Composition Functions for temperature conversions

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Building Inverse and Composition Functions for temperature conversions

Interpreting functions conversion from Celsius to Fahrenheit and Kelvin to Celsius. Then create functions converting Kelvin to Celsius and it's inverse as well as explain what variables represent.
Note the wording might be easier for students to understand if "conversion" or "convert" were used. It might be useful to mention that the USA uses Fahrenheit, but most other countries use Celsius, and scientists use Kelvins.

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Changing Rate

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Changing Rate

Use sentences that describe different ways the rate of change is changing to zoom in on features of a function.

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Choosing an Appropriate Growth Model

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Choosing an Appropriate Growth Model

A table comparing the populations of three different cities every 10 years. Students figure out which family of functions best models each city.

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Comparing Graphs of Functions

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Comparing Graphs of Functions

Students use equations, graphs, and tables to compare linear, exponential, and quadratic functions. As students compare the functions they should use rate of change and end behavior to help differentiate the function families and their unique properties. Meant to be supported with some kind of graphing technology whether graphing calculators, Desmos, Geogebra, or some other similar tools.

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End Behaviour in Tables

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End Behaviour in Tables

Compare tables and graphs of polynomials to make connections between the intercepts and end behaviour between the two representations.

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End of Unit Assessment (Algebra II, Unit 1)

Algebra II
Unit 1: Families of Functions
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End of Unit Assessment (Algebra II, Unit 1)

After this unit, how prepared are your students for the end-of-course Regents examination?  The end of unit assessment is designed to surface how students understand the mathematics in the unit.  It includes spiralled multiple choice and constructed response questions, comparable to those on the end-of-course Regents examination.  A rich task, that allows for multiple entry points and authentic assessment of student learning, may be available for some units and can be included as part of the end of unit assessment.  All elements of the end of unit assessment are aligned to the NYS Mathematics Learning Standards and PARCC Model Frameworks prioritization. 

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Exploring Equivalency

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Exploring Equivalency

For each card students are given two representations and explain how they are the same function. Then they complete the other representations that are missing so that each card will end up with:
1. situation
2. formula
3. graph
4. table
5. function family 

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Function Features

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Function Features

A multiple-day resource that supports students in grappling with the way a graph's shape and key points distinguish function families.  

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Functions and Situations (Algebra II)

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Functions and Situations (Algebra II)

A Classroom Challenge (aka formative assessment lesson) is a classroom-ready lesson that supports formative assessment. The lesson’s approach first allows students to demonstrate their prior understandings and abilities in employing the mathematical practices, and then involves students in resolving their own difficulties and misconceptions through structured discussion.

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