Students have previously learned about functional relationships that are linear. In this unit, students will learn that there are functional relationships that are nonlinear. Like linear functions, some nonlinear functions behave in predictable ways and can be described with equations, words, graphs, and data tables. Students will begin to recognize features of nonlinear functions, such as curves and discontinuities. Students are likely to struggle with the concept that a nonlinear relationship can be a functional relationship.
Key Concepts:
 Not all functional relationships are linear.
 Some nonlinear functions do exhibit predictable behavior, and we can describe this behavior qualitatively.
 We can use equations, graphs, tables, and verbal descriptions to describe nonlinear functions.
Prior Knowledge Needed:
 Plot coordinate pairs.
 Understand that the rate of change in a linear function is a ratio of the change in vertical distance to the change in horizontal distance between any two distinct points.
 Perform basic operations with exponents.
 Create a data table from an equation by substituting in values for x to obtain corresponding y values.
Units on the Horizon:
 Solving linear equations (Grade 8, Unit 10)
 Solving a system of linear equations (Grade 8, Unit 11)
Lessons

Lesson objective: Understand that some functions are nonlinear. Students bring prior knowledge of comparing the rate of change for linear equations from 8.F.A.2. This prior knowledge is extended to comparing rates of change for nonlinear functions as st...

Lesson objective: Identify nonlinear functions based on tables and graphs. This lesson helps to build fluency with finding rates of change to determine linearity. Tables and graphs are used here because those are two of the representations with which st...

Lesson objective: Fluently identify whether equations are linear or nonlinear. This lesson helps to build fluency with graphing and identifying nonlinear functions. Graphs are used here, because they support visual identification of linear versus nonlin...

Lesson objective: Understand that even though the rate of change varies, we can make predictions about nonlinear functions. Students bring prior knowledge of making predictions for linear equations from 8.F.A.3. This prior knowledge is extended to nonli...

Lesson objective: Make predictions from patterns based on nonlinear tables and graphs. This lesson helps to build fluency with predicting input/outputs for nonlinear functions. Tables are used here because they provide a structure for analyzing rates of...

Lesson objective: Predict inputs or outputs of nonlinear functions using equations. This lesson helps to build procedural skill with calculating inputs and outputs for nonlinear functions. Tables are used here because using tables helps with organizatio...

Lesson objective: Solve problems involving nonlinear functions by using tables or graphs to find a rule or pattern. This lesson provides an opportunity for students to apply their knowledge and understanding of rates of change and unit rate to a realli...

Lesson objective: Understand that nonlinear functions can be represented using tables, graphs, and written descriptions. Students bring prior knowledge of different representations for linear functions from 8.F.A.3. This prior knowledge is extended to n...

Lesson objective: Find matching function representations consisting of equations, tables, and graphs. This lesson helps to build fluency with creating different representations of nonlinear functions. Equations, tables, and graphs are used here because ...

Lesson objective: Apply knowledge of representing functional relationships in the form of tables and graphs to solve a tiling pattern problem. This lesson provides an opportunity for students to apply their knowledge and understanding of linear and nonl...