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 Irene Ogeto. Her topic, from Geometry: defining the terms perpendicular and parallel.

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

In order to explore the terms perpendicular and parallel the students could create their own parallel and perpendicular lines using a compass and ruler. I would provide compasses and rulers for the class and we would do the activity together. I would walk the students through the step-by-step process. This activity would allow the students to not only see parallel and perpendicular lines but to actually create them. We could explore different methods of constructing parallel lines about a given point: Angle copy method, translated triangle method, rhombus method. Likewise, we could explore different methods of constructing perpendicular lines: perpendicular from a line through a point, perpendicular from a line to a point and perpendicular at the endpoint of a ray. If we have time we could also go in depth and prove why these constructions work. In addition, the students can use Geometers Sketchpad to do the constructions as well.

How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

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The topic of parallel and perpendicular lines has appeared in the “real” portion of the Cyberchase show on television. In this episode, Harry is meeting his cousin to get tickets to go to a game. Harry and his cousin are both on the same street but have trouble meeting up. Harry decides it would be best to meet his cousin where Amsterdam Ave intersects with 79^{th} street. This video could be shown at the beginning of a lesson as an engage when defining the terms parallel and perpendicular. Parallel and perpendicular lines are commonly found in roads and streets. Although this does not show that Amsterdam Ave and 79^{th} street necessarily intersect at a right angle, it shows the difference between parallel and intersecting lines.

http://pbskids.org/video/?guid=302989e5-9265-4110-ac81-0b1e89ac2c40

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

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Parallel and perpendicular lines are all around us, specifically in high culture. Parallel and perpendicular lines can be found in architecture. Many buildings have features that contain parallel and perpendicular lines. Most windows have parallel and perpendicular lines. Skyscrapers such as the New York Times Building, churches, schools, hospitals are all examples of some buildings that contain parallel and perpendicular lines. Parallel and perpendicular lines are also found in knitting, crocheting, and quilting patterns. Crochet scarfs can be made with parallel line patterns. Quilting is a technique which requires attention to detail and knowing the terms parallel and perpendicular can help speed up the quilting process. In addition, parallel and perpendicular lines can be found in art paintings. There are many paintings in the Dallas Museum of Art that contain parallel and perpendicular lines. An example is the painting *Ocean Park No.29* done by American painter Richard Diebenkorn (1922-1993).

References:

http://www.mathopenref.com/constperpendray.html

http://pbskids.org/video/?guid=302989e5-9265-4110-ac81-0b1e89ac2c40

http://www.threadsmagazine.com/item/4286/quilt-it-freehand/page/all

https://www.dma.org/collection/artwork/richard-diebenkorn/ocean-park-no-29