I went on a bike ride this morning. I have a new app for my phone that keeps track of my distance, route, and speed. It gives me average miles-per-hour, calories, and total time as well. Pretty amazing what these apps do – don’t need to do much thinking. However, it did get me thinking!

Obviously, the app is going off of speed and time, as well as GPS location, since it is mapping the actual route I take (very helpful for figuring out how to get back home). Miles/hr is impacted by my pedaling speed, hills, the gear I am in, and any stopping I do along the way (which trust me, happens – gotta catch my breath after some of the hills!) The size of my wheels and the distance covered in one rotation obviously is involved to some degree, but not something the app is calculating. My husband and I can be on the same bike ride, travel the same distance, go the same speed and number of miles, but his tires are much larger than mine. So my assumption is he is pedaling less than me due to the radius of his tires. Which means, in my perfectly logical way of thinking, I work out harder than my husband (lol)!

But this brings me to today’s mini-math lesson, which is exploring the distance traveled by a tire/wheel of a bike, car, truck, etc. Radius and rotation make a difference. I am using the fx-9750GII graphing calculator and an activity from one of the Casio Resource Books, Geometry , called *Traveling the Circle. *This is a geometry activity, that looks at the application of distance, circles, radius, degrees, radians, arc, arc lengths and more. Students explore how different radii/diamters and angle of rotation determine the distance covered by different tires. They also use the understanding of arc length to determine distance around a curved track (think a typical high school running track). They look at domes and circular shelving. In the process, they are collecting data, using formulas and applying ratios/proportions and looking at practical uses for needing to know the distance of arc lengths.

Attached is the PDF of the actual activity. It includes standards, some calculator tips that are specific to the fx-9870GII but obviously can be used/applied to any Casio graphing calculator since they follow the same steps. There are 4 different sections of the activity, each with questions, so it’s a nice look exploration of circles and arc length and how radius/diameter impacts the distance. There is also a video overview that goes through some of the basic operations/functions needed and used in the activity, such as creating tables, doing calculations, using formulas, etc.

- Traveling the Circle – Geometry
- Video Overview – Formulas and Table of Values and Rational Number Entry

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