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 Cody Jacobs. His topic, from Algebra: parallel and perpendicular lines.

D1. What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Euclid is one of the most famous mathematicians of all time. His fame rests mostly on his 13 books commonly referred to as Euclid’s Elements. Euclid’s Elements are said to have a greater impact on the human mind that any other book except for the bible. Euclid contributed to the development of this topic based off the fact that his Elements have been used for centuries for teaching foundational geometry. The importance of Euclid’s books come from the minimal assumptions made, and the natural progression from simple results to more complex results. Euclid starts of listing 23 definitions and 5 postulates in which uses to prove theorems. His books contain over 400 theorems and proofs which layout the guidelines for how we use geometry today.

E1. How can technology be used to effectively engage students with this topic?

Desmos.com is a great website website that allows you to pick out activities your students can do. They have some activities regarding parallel and perpendicular lines where students shift the lines to make them parallel or perpendicular. I have used this website before regarding parabolas and students are fully engaged. Desmos has plenty of activities to choose from to find the right fit for your class, so do not be afraid to look around for a while. You can sign in as a teacher and make a code for your students to get into the activity. There are even some word problems so you can get a better understanding of what your students are thinking. I think Desmos is best used at the end of a topic, more as a general review over everything because the activities go through topics pretty fast.

B1. How can this topic be used in your students’ future courses in mathematics or science?

Students will continue to use parallel and perpendicular equations throughout their mathematical career. I am now in vector calculus and I am still using parallel and perpendicular lines in 3-dimensional planes. With that being said parallel and perpendicular lines are not going to disappear as you go further into math, in fact you have to start using different methods to find the parallel and perpendicular lines the farther you go. Soon it will no longer be as simple as duplicating the slope or finding the reciprocal. Parallel and perpendicular lines also play a key part in physics regarding vectors just as they do in vector calculus, when you try to find equilibrium forces.