# Engaging students: Perimeters of polygons

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 Tiffany Wilhoit. Her topic, from Geometry: perimeters of polygons.

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

Most activities around the topic of perimeter involve building a fence or a border. However, I feel as if that idea has been overused, and become boring to the students. One activity you could have your students do is to create a piece of art using polygons. There are many artists which create pieces of art using geometric shapes, such as Piet Mondrian. There are two different ways you could do this. The first could be to create a piece of work using polygons of various sizes and structures. The students could then calculate the perimeter of each polygon in their piece of art. There could be a minimum number of polygons the student must use, and you can put extra restrictions on how many different types of polygons the students must use as well. This would provide the students extra practice on determining perimeter of various polygons. Another way to do the project is to have the students create a piece of art using various polygons with the same perimeter. This would allow the students to see how shapes (and area) can change according to how the perimeter is arranged. The students would be able to grasp the idea of two (or more) polygons having the same perimeter, but being different sizes. Either one of these projects would allow the students to discover math while enjoying art.

How does this topic extend what your students should have learned in previous courses?

Students learn about perimeter starting in elementary school. The students learn to add up the four sides of a rectangle or square. Elementary students deal with very basic shapes, and discover the basic meaning of perimeter. As the students go through school the difficulty of the problems increases. The students learn about multiplying the length of one side by the number of sides to find the perimeter of a regular polygon. Soon, the students have to solve for missing sides. First they have to be aware that some sides are equal to other sides, and they just plug in the numbers. Then the students will use algebra to solve for the sides labeled as X or X plus some amount. The students continue to see perimeter throughout calculus. In calculus, the students will be asked to minimize or maximize the perimeter. The students see the topic or perimeter throughout their schooling, so it is necessary for them to have a good understanding of the topic.

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

There are several videos on Youtube with songs about perimeter to engage your students. One of the best ones I found was at http://www.youtube.com/watch?v=wynwRcc5q_U.

This video was a little silly, but it shared the idea of perimeter of polygons, and I think the students would enjoy it. The graphics are constantly changing which will help keep the attention of the students. This video shows some examples of polygons and their perimeter. However, the video only uses rectangles and triangles. One good point of the video is when it shows how to find the missing sides of different rectangles, however, by high school the students should already have a grasp on this. Nevertheless, it is still an engaging.

Another video I found to be very engaging can be found at http://www.youtube.com/watch?v=Xk-PyhjFWw4.

This video uses the beat of a song, but changes the words to discuss perimeter. I liked this video because it gave the examples of building a fence or walking around the block. These are examples the student would know already, and they would be able to remember if they needed help distinguishing between area and perimeter. The last half of the song discusses area. You could choose to play the entire video or just the portion on perimeter.

The last video can be found at http://www.youtube.com/watch?v=AAY1bsazcgM.

This video is an excellent review all about perimeter. The video goes into the topic pretty deeply, and would make a great review for the students. The video discusses the importance of units since perimeter is a measurement. It goes over a variety of topics, such as using multiplication to find perimeter of regular polygons, how to find missing sides of polygons, irregular polygons, and it even discusses why perimeter is one dimensional. This video is very informative, however, it is not the most engaging video, so it might be better off used as a review, or for the students having trouble.

Resources:

http://www.theartstory.org/artist-mondrian-piet.htm

http://www.teresacerda.com/teresacerdageometry.html