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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.

Investigating Linear and Nonlinear Tile Patterns

12th Grade Math

Â» Unit:

Linear and Nonlinear Functions

Big Idea:How many tiles will be in the 100th figure? Students develop their own shortcuts to find explicit rules for linear and nonlinear tile patterns.

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.

Comparing Exponential and Linear Functions Day 2

Algebra I

Â» Unit:

Exponential Functions

Big Idea:This lesson is designed to show that an exponential functions growth will eventually exceed the growth of a linear function.

Sequences, Spreadsheets, and Graphs

Algebra I

Â» Unit:

Linear and Exponential Functions

Big Idea:Writing formulas in a spreadsheet lays foundations for writing recursive rules for arithmetic and geometric sequences.

Games with Paper

8th Grade Math

Â» Unit:

Gimme the Base: More with Exponents

Big Idea:We can model the immense numbers created in the exponential process and find hands on activities that help all learners.

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!

Verbal Descriptions of Linear and Nonlinear Functions

12th Grade Math

Â» Unit:

Linear and Nonlinear Functions

Big Idea:When x changes, how does y change? Students make generalizations about this relationship and justify their generalizations.

Linear and Nonlinear Functions Summative Assessment

12th Grade Math

Â» Unit:

Linear and Nonlinear Functions

Big Idea:Use the time that students are working on the summative assessment to give them informal narrative feedback which they appreciate and which helps shape the culture of the classroom.

Constructing Linear and Exponential Functions

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students learn to create linear and exponential functions in different representations through the context of sorting out change.

Linear, Exponential, or Quadratic?

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Model different situations for Linear, Exponential, and Quadratic Functions using a collaborative activity from the Mathematical Design Collaborative (MDC).

Marketing Exponential Functions: A Group Performance Assessment Task

Algebra I

Â» Unit:

Exponential Functions

Big Idea:Students collaborate to identify, develop, and promote ways to use exponential functions to understand the world around us through mathematical modeling!

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.