Engaging students: Finding points in the coordinate plane

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 Derek Skipworth. His topic, from Pre-Algebra: finding points in the coordinate plane.

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

When I think of the coordinate plane, one of the first things that come to mind is mapping.  When I think of my teenage years, I think of how I always wanted more money.  By using these two ideas together, an activity could easily be created to get the students involved in the lesson: a treasure map!

The first part of the activity would be providing the students with a larger grid.  Then provide them with a list of landmarks/items at different locations (i.e. skull cave at (3,2)) that would then be mapped onto the grid.  By starting out with one landmark, you could also build off previously identified landmarks, such as “move 3 units East and 4 units North to find the shipwreck.  The shipwreck is located at what coordinates?”   These steps could also be based off generic formulas with solutions for x and y.  After all landmarks were identified, there would be a guide below that would trace out a path to find the treasure, which is only discovered after the full path is completed.

treasuremapCourtesy of paleochick.blogspot.com

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B. Curriculum: How can this topic be used in your students’ future courses in mathematics or science?

One of the good things about the exercise above is that it integrates several different ideas into one. A big one that stands out to me is following procedures.  This is vital once you get into high school sciences.  By building the map step-by-step, which each one building off the previous step, you cannot find the treasure without replicating the map exactly if you miss/misinterpret a step along the way.

As far as the coordinate plane, finding locations on the plane is important when graphing functions.  Being able to find the intercepts and any asymptotes gives you starting points to work with.  From there you generally only need a few more points to create a line of the function based off plotted points.  This also has applications in science/math when creating bar graphs/line graphs and similar graphs.

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D.  How was this topic adopted by the mathematical community?

As discussed in my Geometry class this semester (Krueger), the Cartesian plane opened up a lot of doors in the world of Geometry.  Euclid had already established a great working knowledge of a vast amount of Geometric ideas and figures.  One thing he did not establish was length.  In his teachings, there were relative terms such as “smaller than” or “larger than”.  No values were ever assigned to his figures though.  By introducing the Cartesian plane (and in effect, being able to plot points on said plane), we were able to actually assign values to these figures and advance our mathematical knowledge.  The Cartesian plane acts as a bridge between Algebra and Geometry that did not exist before.  Because of this, we can know solve problems based in Geometry without ever even needing to draw the figure in the first place (example: Pythagorean Theorem).

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