# 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 Brianna Horwedel. Her topic, from Algebra: finding the slope of a line.

How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic?

Algebra vs. the Cockroaches is a great way to get students engaged in learning about slopes. The object of the game is to kill the cockroaches by figuring out what the equation of the line that they are walking on is. It progresses from simple lines such as y=5 to more complicated equations such as y=(-2/3)x+7. It allows the students to quickly recognize y-intercepts and slopes. Once finished, you can print out a “report” that tells you how many the student got correct and how many tries it took them to complete a level. This game could even be used as a formative assessment for the teacher.

http://hotmath.com/hotmath_help/games/kp/kp_hotmath_sound.swf

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

Last year, I was placed in an eighth grade classroom that was learning about slope. One of the things that really stuck out to me was that the teacher gave a ski illustration to get the students talking about slope. The illustration starts off with the teacher going skiing. She talks about how when she is going up the ski lift she is really excited and having a “positive” experience which correlates to the slope being positive. Once she gets off of the ski lift, she isn’t going up or down, but in a straight line. She talks about how she doesn’t really feel either excited or nervous because she is on flat ground. This corresponds to lines that have a slope of 0. She then proceeds to talk about how when she starts actually going down the ski slope, she hates it! This relates to the negative slope of a line. She also mentions how she went over the side of a cliff and fell straight down. She was so scared she couldn’t even think or “define” her thoughts. This is tied to slopes that are undefined. I thought that this illustration was a great way of explaining the concept of slope from a real world example. After sharing the illustration, the students could work on problems involving calculating the slope of ski hills.

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

Understanding how to find the slope of a line is crucial for mathematics courses beyond Algebra I and Algebra II. Particularly, knowing how to find the slope of a line is essential for finding tangent lines of curves. This comes in handy for Calculus when you have to use limits to determine the slope. If a student does not have a strong grasp of what slope means and what its relationship is with the graph and the equation in Algebra I, then they will have a difficult time understanding slopes of lines that are not straight.

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