## Applications of Linear Functions: Circumference vs. Diameter

As the size of a circle changes, so does the size of the diameter and that of the circumference. In fact, there is a linear relationship between these two measures. This relationship can be modeled with a linear function. In this module students will study this linear function and examine its properties, including the fact that the slope of this function is π itself.

This is a hands-on module in which students will measure the diameters and circumferences of a number of different containers. This data gathering will lead to graphing the data. From that students develop a linear model using the Desmos graphing tool. Students will see that the relationship between circumference and diameter has to do with π. In fact, the slope of the linear function is π itself.

For the hands-on part of the lesson, make sure you have all the materials: Different size cylindrical containers (bottles, cups, etc.), string, marker, and a ruler (preferably a caliper). Collect all the student data and use the embedded Desmos graphing tool to graph the data and explore the linear function.

The module concludes with an overview video about the number π.

#### Math Concepts

- Functions
- Geometry
- Circles

#### Learning Objectives

- Create a linear function model for circumference vs. diameter
- Graph the function and interpret slope, y-intercept, domain, and range

#### Prerequisite Skills

- Understands the basics of linear functions

Common Core Standards | CCSS.MATH.CONTENT.8.F.A.3, CCSS.MATH.CONTENT.8.F.B.5 |
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Lesson Duration | 20 mins |

Grade Range | 8th - 10th Grade |