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 again comes from my former student Brianna Horwedel. Her topic, from Geometry: classifying polygons.

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

A great activity for classifying polygons would be a card sort. Give students index cards with different ways to describe polygons on them. For example, the cards could say “has three sides”, “has five sides”, “has 4 equal sides”, “has four sides”, “triangle”, “quadrilateral”, “square”, “pentagon”. Also include cards with a pictorial representation of the polygons that you want them to identify. Have the students work in groups of three or four to match all of the cards. For example, “has three sides”, “triangle”, and the picture of a triangle would all be matched together. After about five to ten minutes of the students working in their groups, I would have a larger set of the index cards (probably on standard printer paper) that one person from each group would come up and place in the correct category/group.

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

There are tons of great polygon sorting games online. At the beginning of the unit I would have the students play Polygon Shape Game (http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/PolygonShapesShoot.htm). It is a great introductory game. It really helps the students understand what it means to be a polygon. The students have to pick out all of the shapes that are polygons on one round; on the next round, they have to pick out all of the shapes that aren’t polygons. Once students have a better understanding of what defines a polygon and different types of polygons, I would have them play Half a Min: Polygon (http://www.math-play.com/types-of-poligons.html). This game makes the students type in a type of polygon based on the hint given. This game is definitely harder than the first one; I would save it for maybe a review before a test.

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

Polygons occur frequently in abstract art, particularly the movement called De Stijl. It was inspired in part by the chaos of war. Dutch artists in 1917 wanted to contrast the messiness of war with art that consisted of balance, harmony, and the absence of individual expression. Piet Mondrian is one of the most famous artists to come from this particular movement. His work is created using grids, which creates various rectangles, and primary colors. Here is one of his paintings titles Broadway Boogie Woogie:

It would be really fun for the students to then create their own artwork in the De Stijl style using only polygons that we have previously discussed.

References:

http://visionandverse.blogspot.com/2014/08/the-art-of-piet-mondrian.html

http://www.abstract-art-framed.com/mondrian.html

http://www.math-play.com/types-of-poligons.html

http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/PolygonShapesShoot.htm