Engaging students: Finding the equation of a circle

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 Kelsi Kolbe. Her topic, from Precalculus: finding the equation of a circle.

How can technology be used in order to engage the students on this topic?

A simple Desmos program can be used to see different circles and how the variables affect it. You can write a program on Desmos, where you have to manipulate a given circle to ‘collect all the stars.’ There are stars placed around where the circumference should be. Then the students you a variety of sliders to collect the stars. The sliders can change the radius, and move the circle left to right. I think this simple activity will introduce the parts of a circle equation, like the radius and the center, while the students have fun trying to beat their fellow classmates collect the most stars.

How could you as a teacher create an activity or project that involves your topic?

I think a circle themed “Clue” inspired activity could be fun. I would tell the students that there was a crime committed and the students had to use their math skills to figure out what the crime was, who did it, where they did it, and when they did it. The students would get an ‘investigation sheet’ to record their answers. Each group would start off with a question like, ‘Find the equation of a circle that has the center (2,3) and radius 7’. Each table would have an answer to the math questions that corresponds to a clue to answer one of the ‘who, what, where, where’ questions they are trying to figure out, and prompts the next question. Students would continue this process until one team thinks they have it and shouts “EUREKA!” then they say what they think happened and if they are right they win, if they aren’t we keep going until someone does.

How has this topic appeared in high culture (art, classical music, theatre, etc.)?

Circles are seen in a lot of different Islamic Art. Islamic art is known for its geometrical mosaic art. They had a deep fascination with Euclidean geometry. The circle specifically holds meaning in the Islamic culture. The circle represents unity under a monotheistic God. Their religion is so important it can be seen throughout every aspect of their culture. The repetitiveness also symbolizes god infinite nature. For example, his infinite wisdom and love. Along with circles, the 8-point star is also seen as a very powerful symbol. It represents God’s light spreading over the world. The symbols are very important in the Islamic culture and is shown beautifully in a lot of their art. It’s beautiful how they can pack one art piece with so much geometry and also their beliefs.

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