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 Jason Trejo. His topic, from Algebra: finding the slope of a line.

A2) How could you as a teacher create an activity or project that involves your topic?

I have to start off by giving some credit to my 5^{th} grade math teacher for giving me the idea on how I could create an activity involving this topic. You see, back in my 5^{th} grade math class, we were to plot points given to us on a Cartesian plane and then connect the dots to create a picture (which turned out to be a caveman). Once we created the picture, we were to add more to it and the best drawing would win a prize. My idea is to split the class up into groups and give them an assortment of lines on separate pieces of transparent graphing sheets. They would then find the slopes and trace over the line in a predetermined color (e.g. all lines with m=2 will be blue, when m=1/3 then red, etc.). Next they stack each line with matching slopes above the other to create pictures like this:

Of course, what I have them create would be more intricate and colorful, but this is the idea for now. It is also possible to have the students fine the slope of lines at certain points to create a picture like I did back in 5^{th} grade and then have them color their drawing. They would end up with pictures such as:

C1) How has this topic appeared in pop culture (movies, TV, current music, videogames, etc.)?

Sure there aren’t many places where finding the slope of a line will be the topic that everyone goes on and one about on TV or on the hottest blog or all over Vine (whatever that is), but take a look around and you will be able to see a slope maybe on a building or from the top of Tom Hank’s head to the end of his shadow. Think about it, with enough effort, anyone could imagine a coordinate plane “behind” anything and try to find the slop from one point to another. The example I came up with goes along with this picture I edited:

**Picture not accurately to scale*

This is the infamous, first double backflip ever landed in a major competition. The athlete: Travis Pastrana; the competition: the 2006 X-Games.

I would first show the video (found here: https://www.youtube.com/watch?v=rLKERGvwBQ8), then show them the picture above to have them solve for each of the different slopes seen. In reality this is a parabola, but we can break up his motion to certain points in the trick (like when Travis is on the ground or when Travis is upside down for the first backflip). When the students go over parabolas at a later time, we could then come back to this picture.

B2) How does this topic extend what your students should have learned in previous courses?

It has been many years since I was first introduced to finding the slope of the line so I’m not sure exactly when I learned it, but I do know that I at least saw what a line was in 5^{th} grade based on the drawing project I stated earlier. At that point, all I knew was to plot points on a graph and “connect the dots”, so this builds on that by actually being able to give a formula for those lines that connected the dots. Other than that, finding slopes on a Cartesian plane can give more insight on what negative numbers are and how they relate to positive numbers. Finally, students should have already learned about speed and time, so by creating a representation how those two relate, a line can be drawn. The students would see the rate of change based on speed and time.

__References__:

Minimalistic Landscape: http://imgur.com/a/44DNn

Minimalistic Flowers: http://imgur.com/Kwk0tW0

Graphing Projects: http://www.hoppeninjamath.com/teacherblog/wp-content/uploads/2014/03/Photo-Feb-25-5-32-24-PM.jpg

Double Backflip Image: http://cdn.motocross.transworld.net/files/2010/03/tp_doubleback_final.jpg

Double Backflip Video: : https://www.youtube.com/watch?v=rLKERGvwBQ8