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- HSF-LE.A.1Distinguish between situations that can be modeled with linear functions and with exponential functions.
- HSF-LE.A.2Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
- HSF-LE.A.3Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
- HSF-LE.A.4For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

- HSF-LE.A.1aProve that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- HSF-LE.A.1bRecognize situations in which one quantity changes at a constant rate per unit interval relative to another.
- HSF-LE.A.1cRecognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

Bunnies and Exponential Growth

12th Grade Math

Â» Unit:

Exponential Functions

Big Idea:Students experience and describe exponential growth by looking at exponentially increasing bunny populations.

Explore the Rebound Height of A Ball

Algebra I

Â» Unit:

Exponential Functions

Big Idea:To compare an exponential decay function to an exponential growth function in the previous day's lesson from a table using the equation y=ab^x.

Counting the Change: Linear, quadratic, or exponential? (Day 2 of 2)

12th Grade Math

Â» Unit:

Exponential Functions and Equations

Big Idea:Students explore rates of change to identify function types and find patterns that help them to identify and define exponential functions.

Comparing and Contrasting Linear and Exponential Functions

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students compare linear and exponential functions, and, learn about actual and theoretical data.

Counting the Change: Linear, quadratic, or exponential? (Day 1 of 2)

12th Grade Math

Â» Unit:

Exponential Functions and Equations

Big Idea:Students explore rates of change to identify function types and find patterns that help them to identify and define exponential functions.

Sorting out the Change

12th Grade Math

Â» Unit:

Exponential Functions and Equations

Big Idea:Students identify the type of function (linear or exponential) which represents a situation & writes equations to model these situations.

Writing in Math Classroom, Part 3: Comparing and Contrasting Arithmetic and Geometric Sequences

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students work collaboratively to teach each other the similarities and differences between arithmetic and geometric sequences!

Creating and Interpreting Exponential Functions

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students work collaboratively to model different real world application of exponential functions!

Exponentials Functions Unit Test

12th Grade Math

Â» Unit:

Exponential Functions and Equations

Big Idea:Students will demonstrate their learning of Exponential Functions in this formal assessment.

Review Lesson on Exponential Functions

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students work in groups to review key concepts to solidify their understanding and use of exponential functions!

Emerging Pictures: Graphing Inequalities in Two Variables

Algebra I

Â» Unit:

Systems of Equations and Inequalities

Big Idea:Students plot points that satisfy and do not satisfy a linear inequality until they see a picture emerge in their graphs.

Comparing Investments: A Math Assessment Project Classroom Challenge

Algebra I

Â» Unit:

Everything is Relative: Linear Functions

Big Idea:Students compare simple and compound interest problems as a backdrop for distinguishing between linear and exponential functions across representations!

Two Methods, One Equation: Finding the Boundary Line

Algebra I

Â» Unit:

Systems of Equations and Inequalities

Big Idea:Hey, how did you find that line? Students examine two different ways to find the equations of boundary lines and work to understand why they are equivalent.

Linear and Exponential Functions Project

Algebra I

Â» Unit:

Functions

Big Idea:Show what you know. Students work on a poster project to show patterns of change in linear and exponential functions.

Increasing, Decreasing, or Constant?

Algebra I

Â» Unit:

Linear Functions

Big Idea:Students can identify the initial value when the input is 0, and determine the output and the slope of the line from a table, graph, and words.

HSF-LE.A.1a

Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

HSF-LE.A.1b

Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

HSF-LE.A.1c

Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.