# 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 Brittnee Lein. Her topic, from Geometry: perimeters of polygons.

How have different cultures throughout time used this topic in their society?

Finding the perimeter of a polygon has been a necessity since the implementation of architecture and engineering in society. Every advanced society has used this topic to their benefit. For example, if a person wanted to build a fence around their rectangular garden, but wanted to use the least amount of building materials possible, they could find the perimeter around the garden and then calculate how many planks of wood they would need to use before buying that wood. This is a much more effective method than buying the wood and then finding out how much one would need to use.

2. What interesting (i.e., uncontrived) word problems using this topic can your students do now?

A few interesting word problems I found online involve real world applications of decorating. Both of the problems I found are off of this website: http://www.bbc.co.uk/skillswise/worksheet/ma31peri-e3-w-perimeter-problems

Problem 1 is good for enforcing student understanding because it challenges them to think more abstractly than if the problem were merely stated as “what is the perimeter of the cake?”. This problem tests student understanding of both the meaning of a square and the meaning of perimeter.

Problem 5 is beneficial to students because it includes both a closed and an open question. The closed question allows students to practice what they have learned about finding the perimeter of a polygon and the open-ended question is worded in a way that challenges the student’s conceptual understanding. The student must not only compute the perimeter but also must explain his/her thinking. This problem also forces students to visualize the problem in their head.

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

An engaging activity that a teacher could create to reinforce the topic of finding the perimeter of a polygon is a game where students set out to stop a criminal from entering an a given area/robbing a bank. The students would have to find the perimeter of a building from a simple blueprint mapping the building’s structure (in this case it would just be the outline of the shape of the building with given dimensions). The student would be informed of how much area each officer can cover and they would then be expected to “secure the perimeter” by allotting a certain amount of police officers to the building and placing them along the perimeter (denoted by a given symbol). To ramp up the difficulty of the game, you could set a time limit for each building and have students compete against the clock to stop the robber and you could also increase the variety of officers in the game where each type has a specialty and can cover a different amount of area.

The idea for this activity is found on the website: https://www.teacherspayteachers.com/Product/Secure-the-Perimeter-Cover-the-Area-Hands-on-police-trainee-activity-2770696

References

“Secure the Perimeter! Cover the Area! Hands-on ‘Police Trainee’ Activity.” Teachers Pay Teachers, http://www.teacherspayteachers.com/Product/Secure-the-Perimeter-Cover-the-Area-Hands-on-police-trainee-activity-2770696.

Perimeter Problems.” BBC News, BBC, http://www.bbc.co.uk/skillswise/worksheet/ma31peri-e3-w-perimeter-problems.

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