# Engaging students: 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 Alyssa Dalling. Her topic, from Precalculus: the equation of a circle.

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

A fun way to engage students and also introduce the standard form of an equation of a circle is the following:

• Start by separating the class into groups of 2 or 3
• Pass each group a specific amount of flashcards. (Each group will have the same flashcards)
• Each flashcard has a picture of a graphed circle and the equation of that circle in standard form
• The students will work together to figure out how the pictures of the circle relate to the equation

This will help students understand how different aspects of a circle relate to its standard form equation. The following is an example of a flashcard that could be passed out.  C. How has this topic appeared in high culture (art, classical music, theatre, etc.)?

Circles have been used through history in many different works of art. One such type is called a tessellation. The word Tessellate means to cover a plane with a pattern in such a way as to leave no region uncovered. So, a tessellation is created when a shape or shapes are repeated over and over again. The pictures above show just a few examples of how circles are used in different types of art. A good way to engage students would be to show them a few examples of tessellations using circles. E. How can technology be used to effectively engage students with this topic?

Khan Academy has a really fun resource for using equations to graph circles. At the beginning of class, the teacher could allow students to play around with this program. It allows students to see an equation of a circle in standard form then they would graph the circle. It gives hints as well as the answer when students are ready. The good thing about this is that even if a student goes straight to the answer, they are still trying to identify the connection between the equation of the circle and the answer Khan Academy shows.

1. Joel says: