You'll gain access to interventions, extensions, task implementation guides, and more for this lesson.

Big Ideas:
Functions can be linear or nonlinear.
Linear functions have a constant rate of change, a straight line graph, and an equation with a degree of 1 or 0.
Nonlinear functions do not have a constant rate of change. Their graphs are not a straight line and their equations have degrees greater than 1.
This task builds on students’ prior work with rate of change (7.RP.2) and understanding that a function describes the relationship between variables (8.F.1). It also builds on students’ prior work with equations with constant rate of change in the form y = mx + b (8.EE.6). This task is an introduction to how linear functions are distinct from nonlinear functions and provides the opportunity for students to explore area and perimeter patterns, represent them as tables, and analyze their graphs to discover the features of linear functions. This builds an understanding of what is not linear and creates a foundation for later work with nonlinear functions (logarithmic, exponential, rational, polynomial, etc.) (HS.F.LE.1, HS.F.TF.1)
Vocabulary: input, output, domain, range, linear function, nonlinear function, rate of change
Special Materials:
graph paper
rulers
colored pencils