Lesson plan

Identify the distinguishing characteristics of a linear function by analyzing the graphs of perimeter and area patterns

teaches Common Core State Standards CCSS.Math.Content.8.F.A.3 http://corestandards.org/Math/Content/8/F/A/3
teaches Common Core State Standards CCSS.Math.Practice.MP1 http://corestandards.org/Math/Practice/MP1
teaches Common Core State Standards CCSS.Math.Practice.MP2 http://corestandards.org/Math/Practice/MP2
teaches Common Core State Standards CCSS.Math.Practice.MP4 http://corestandards.org/Math/Practice/MP4
teaches Common Core State Standards CCSS.Math.Practice.MP8 http://corestandards.org/Math/Practice/MP8

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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