A1.F.2.1  Distinguish between linear and nonlinear (including exponential) functions arising from realworld and mathematical situations that are represented in tables, graphs, and equations. Understand that linear functions grow by equal intervals and that exponential functions grow by equal factors over equal intervals.
In a Nutshell
Students will distinguish and describe functions as linear or nonlinear functions. Using their knowledge acquired during this unit the students will determine whether linear equations are functions. Students will use tables, graphs, and equations to identify characteristics of nonlinear functions. Realworld situations are useful for students to understand the equal intervals that functions tend to grow. Graphing and creating tables for various equations can show how exponential functions grow as equal factors over equal intervals. Parent functions of other graphs will be introduced in order to determine the differences of linear and nonlinear.
Student Actions

Teacher Actions

 Students develop accurate and appropriate procedural fluency by creating tables, writing equations, and graphing functions to determine linear and nonlinear relationships.

Students develop a deep and flexible conceptual understanding by exploring linear and nonlinear functions to understand the relationship between the independent and dependent variables.

Students explore functions to determine whether they are linear or nonlinear and justify their reasoning mathematically to their teacher and peers.


Engage students with many different mathematical representations to connect the concepts of linear and nonlinear functions to their equations, graphs, tables, and charts.

Pose purposeful questions and examples to connect students to realworld situations by using examples of several different functions as they explore the similarities and differences of those functions.

Implement tasks that promote reasoning and problem solving by having students interpret the mathematical relationship between tables, graphs, and equations of linear or nonlinear functions.
 Encourage productive struggle as students work through realworld situations to determine whether a function is linear or nonlinear.

Key Understandings

Misconceptions


Students will recognize if a function is linear it can take the form of f(x)=mx+b.

Students will distinguish between linear or nonlinear functions by using tables, graphs, or equations.

Students will determine a parent function or its graph as linear or nonlinear.

Students understand that linear functions change by equal intervals while exponential functions increase by equal factors over equal intervals.


Students will mix up the input and the output and incorrectly identify a relationship as linear when it is nonlinear.

If a function is not in slopeintercept form, the students will not recognize it as a linear function.

When using tables to identify functions, students will not consider the rate of change and will look only to patterns.


OKMath Framework Introduction
Algebra 1 Introduction
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