Engaging students: Graphing with polar coordinates

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 Laura Lozano. Her topic, from Precalculus: graphing with polar coordinates.

 

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

An activity that I believe will go really well with graphing polar coordinates or any type of graphing lesson will be to convert the classroom floor into a graph. Also, I will have a selection of random objects like, a rubber ducky, boat, toy, etc. The size of the graph will depend on the size of classroom of course. If the classroom is really small then I would have to take this activity outdoors or maybe even the gym or anywhere with enough room for the graph and my students. The graph doesn’t have to be super big but I would use a graph no smaller than 8 feet by 8 feet area. I could create the graph lines with tape on the floor or draw them on big paper and tape the paper on the floor. I would start the activity with first talking about points on a Cartesian graph. An example could be to first have a students plot a couple points like (5, 4), (3, 6), or (-4, 2) on the board. Then transition them from Cartesian to polar coordinates by using the floor graph and have them discover how they relate by using the x and y coordinates to find the radius and the angle. Then later, after they get the hang of it, I would have the class split up into groups of two and let them choose an object, like a rubber ducky, boat, or toy, to set on the graph and have them write and tell me the point of their object.

 

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We see radars in the news almost all the time. One category that it is usually used in is weather. The weather center uses their radars to detect for any water particles, debris, and basically anything that is in the air that could be approaching. The way that they tell if a storm or any other weather change is coming is by the radar’s omitting radio waves. The radar omits waves that then come back to the radar if the waves clash with anything in the air. The radar can detect how far an object is by the time it takes for the wave to come back. It works just like an echo! Also, recently with the search of the Malaysian airplane, we saw it used more. The news will show a clip of aircraft radar or ship radar searching for something in the air or in the ocean. Radars look almost exactly like a polar graph does. On the left is a regular polar graph. On the right is a ship’s radar. Both graphs have angles with circles.

polar1

polar2

 

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How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic? Note: It’s not enough to say “such-and-such is a great website”; you need to explain in some detail why it’s a great website.

Graphing calculators can be used to discover polar coordinates and polar equations. I would first tell them to take out their calculators and just type in a random number from -10 to 10. I choose this interval because the graphing calculators have this window preset for graphing. I number that I randomly chose was the number 4. So I would go to the “Y=” button and type in 4. Then I would hit “GRAPH” and I should get a straight line horizontal line going through the y-axis at 4. I would then change the calculator mode and change from “FUNC” to “POL”. Then I would tell them to do the exact thing again with whatever number they chose. Once the hit “GRAPH” a circle should then come up. They then see how different polar graphs are from Cartesian graphs. Now, the graphs on a polar coordinate graph will all be circular instead of lines and curved lines like on the Cartesian graph.

 

Resources:

http://forecast.weather.gov/jetstream/doppler/how.htm

http://www.mi-net.ca/navigation.html

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