# Engaging students: Finding x- and y-intercepts

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 Deetria Bowser. Her topic, from Algebra: finding $x-$ and $y-$intercepts. Unlike most student submissions, Maranda’s idea answers three different questions at once.

E1. How can technology (YouTube, Khan Academy [khanacademy.org], Vi Hart, Geometers Sketchpad, graphing calculators, etc.) be used to effectively engage students with this topic? Note: It’s not enough to say “such-and-such is a great website”; you need to explain in some detail why it’s a great website.

One example of an engaging form of technology that involves finding x- and y-intercepts of lines is mangahigh.com. Under the algebra section, there is a tab for finding x and y intercepts which once clicked provides an option to start a game (“Algebra.”). In this game, the student is expected to look at lines and quickly decipher what is known about the x and y intercepts of the line in question. Before the game begins, the student is able to choose the difficulty of the game as well as the number of questions. After the game is completed students are able to review their answers. Implementing this website into the classroom will help students gain quickness in identifying x and y intercepts. Additionally, this game is also a quick and fun way to evaluate students understanding of x and y intercepts, without forcing them to take a quiz.

D1. What interesting things can you say about the people who contributed to the discovery and/or the development of this topic? (You might want to consult Math Through The Ages.)

The topic of x and y intercepts falls under a much broader topic called analytical geometry.The article “Analytic geometry” defines analytical geometry as “[a] mathematical subject in which algebraic symbolism and methods are used to represent and solve problems in geometry” (D’Souza). One of the people who discovered this topic was René Descartes. René Descartes was actually a french modern philosopher who also made discoveries in the realms of science as well as mathematics. Descartes “dismissed apparent knowledge derived from authority,” meaning that he made his discoveries based on what he thought rather than taking ideas from scientists, philosophers and mathematicians (Watson). He discovered analytical mathematics (along with Fermat) in the 1630s (D’Souza). He also “he stressed the need to consider general algebraic curves—graphs of polynomial equations in x and y of all degrees” (D’Souza). Mentioning Descartes in class, and explaining his accomplishments in Mathematics as well as modern philosophy and science, will encourage students to realize that they can succeed in more than one subject . Also, Descartes can be used as an influence in the building of ideas in the classroom, since he did not just accept ideas already created.

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

The topic of x and y intercepts appeared on a “pop culture blog” called the comeback.com. In an article posted in November 2016, a former UCLA and current Cleveland Indians baseball player named Trevor Bauer helped one of his fans with her math homework (Blazer). This article describes a girl asking Bauer for help determining the slope of a line and the y – intercepts via Twitter. Her specific question involves the equation 2y=x (Blazer). He then explains that “for every 1 unit on the x axis go 2 units on the y axis. y intercept is where it crosses the y axis. Make y 0 and figure x” (Blazer). Since Bauer is a professional baseball player, he already has a great influence over people. Showing students this article about Bauer will show students that even people who play baseball for a living still have the knowledge of Algebra.

References
“Algebra.” Mangahigh.com – Algebra,
http://www.mangahigh.com/en-us/math_games/algebra/straight_line_graphs/find_the_x_and_y_intercepts_of_lines. Accessed 15 Sept. 2017.

Blazer, Sam, et al. “Trevor Bauer helped a fan do their math homework on Twitter.” The
Comeback, 13 Nov. 2016,