# Engaging students: Central and inscribed angles

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission comes from my former student Theresa (Tress) Kringen. Her topic, from Geometry: central and inscribed angles.

What interesting word problems using this topic can students do now?

After defining the terms central angle and inscribed angle, students can use a central angles to draw a pie graph or pie chart. They can depict the data using a visual. Based in the percentage of any part of a whole, they will crate a fraction of the whole circle by dividing 360 degrees by that percentage to give the piece of the pie in which they needed to find.

Say a student is given the data below and asked to graph the data into a pie chart:

Students’ favorite colors:

Blue                10

Yellow             3

Red                 7

Orange            3

Green              10

Purple             6

Pink                 9

Other              2

Students would be required to give percentages based on the 50 students with the percentages listed as: Blue 20%, Yellow 6%, Red 14%, Orange 6%, Green 20%, Purple 12%, Pink 18%, other 4%. This would correspond to the percentage of the 360 degree central angle.

To tie in inscribe angles, I would have to students explain why a pie chart would not work with inscribed angles.

How does this topic appear in high culture?

In order to engage students I could help them understand inscribed angles by relating it to the camera angle in their video games. Describing an inscribed angle as a camera angle on their video game would help them understand it better. As they move throughout the game, their camera angle changes. Based on the camera’s location, you are able to see a certain portion of the screen. If there isn’t much of an angle, the range of view is small or zoomed in. This could be explained as the radius of the circle. The smaller the radius, the less view there is. Thus, the opposite is true. If the radius is large, the camera has a larger view of the object. If the camera has a larger angle of view, more is visible in the camera. I would then relate this to the arc length that the angle creates. I would explain that if the angle of the camera is small, the area of the arc length, or view of the camera would also be small. If the angle of the camera is larger, the arc length or view of the camera is much larger.

How can technology be used to effectively engage students with this topic?

Once students are given the application problem listed above, I could then engage them further by asking them to use word or excel to graph the information given into a document. They would be required to make a chart of the data with the listed percentages of each parameter along with the degree of the angle that the parameter requires to make the pie graph. I would require this since the technology would calculate this on its own without the student having to put in the effort. To make it fun, I would give the students a few extra minutes to make their pie graph their own by customizing it to reflect their personality and style.

To further engage them, I could also ask that each student create a questionnaire that asked each student what their favorite choice of any given set of choices were. They would be required to have at least 7 responses as to make a 7 piece pie chart, but they would be able to choose the topic, and find the information for their parameters on their own. Once they did this, they would be required to make an additional pie chart with their results to present to the class.

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