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## Linear Functions: Distance vs. Time

In this module students apply their knowledge of linear functions to the context of distance vs. time graphs. They look at data sets, graphs of coordinates, and algebraic representations of distance vs. time functions. Then students go on a field trip to a Nascar race to see how timing at the pit stop has an impact on distance vs. time data.

Students begin by analyzing linear function data by identifying the common difference. The goal is to see the relationship among the common difference and the slope of the linear function.

Students use the Desmos graphing calculator to explore graphs of data and equations. Both types of linear functions are explored:

• ax
• mx b

The goal here is to connect the slope of the distance vs. time graph to the speed of the car. Students then explore the graphs of cars with different speeds and initial distances.

Students then watch a video about Nascar pit crews and learn about the rapid-response pit crews who change the tires on the race cars and how the timing of this affects the distance vs. time graph of the cars. Students use the information in the video to analyze linear function models for different pit crew times.

Note: Be sure students are familiar with the concept of slope and the basic definition of a linear function.

Throughout the lesson various assessment items are included, which are then scored. A teacher's guide includes a detailed description of all components of this lesson.

This lesson addresses the Grade 8 Common Core Standards but it can also be used in grades 9 and 10 for review purposes.

This lesson can be assigned to individual students or teams of students. The lesson can be completed in about 20 to 25 minutes.

#### Math Concepts

• Functions
• Problem Solving
• Equations

#### Learning Objectives

• Model distance vs. time linear function data
• Write linear functions in slope intercept form
• Graph linear functions
• Solve problems involving speed

#### Prerequisite Skills

• Understanding of linear functions
• Familiarity with the slope formula
Common Core Standards CCSS.MATH.CONTENT.8.F.A.2, CCSS.MATH.CONTENT.8.F.A.3, CCSS.MATH.CONTENT.8.F.B.4 20 mins 8th - 10th Grade