# Engaging students: Finding the slope of a line

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 Deanna Cravens. Her topic, from Algebra: finding the slope of a line.

C3. How has this topic appeared in high culture (art/sports)?

While one might not think of ski jumping as an art but more of a sport, there is definitely an artistic way about doing the jumping. The winter Olympics is one of the most popular sporting events, besides the summer Olympics that the world watches. This is a perfect engage for the beginning of class, not only is it extremely humorous but it is extremely engaging. It will instantly get a class interested in the topic of the day. I would first ask the students what the hill the skiers going down is called. Of course the answer that I would be looking for is the “ski slope.” This draws on prior knowledge to help students make a meaningful connection to the mathematical term of slope. Then I would ask students to interpret the meaning of slope in the context of the skiers. This allows for an easy transition into the topic for finding the slope of a line.

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

Look at this scene from Transformers, it shows a perfect example of a linear line on the edge of the pyramid that the Decepticon is destroying. This video easily catches the attention of students because it is from the very popular Transformer movie. I would play the short twenty second clip and then have some student discussion at the beginning of class. This could be done as an introduction to the topic where students could be asked “how can we find the steepness of that edge of the pyrmaid?” Then the students can discuss with a partner and then group discussion can ensue. It could also be done as a quick review, where students are asked to recall how to find the slope of a line and what it determines. The students would be asked to draw on their knowledge of slope and produce a formula that would calculate it.

How can this topic be used in your students’ future courses in mathematics or science?
Finding the slope of a line is an essential part of mathematics. It is used in statistics, algebra, calculus, and so much more. One could say it is an integral part of calculus (pun intended). Not only is it used in mathematics classes, but it is also very relevant to science. One specific example is chemistry. There are specific reaction rates of solutions. These rates are expressed in terms of change in concentration divided by the change in time. This is exactly the formula that is used in math classes to find the slope. However, it is usually expressed in terms of change in y divided by change in x. Slope is also used in physics when working with velocity and acceleration of objects. While one could think of slope in the standard way of ‘rise over run,’ in these advanced classes whether math or science, it usually better thought of as ∆y/∆x.

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