# Engaging students: Graphing a hyperbola

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 comes from my former student Biviana Esparza. Her topic, from Precalculus: graphing a hyperbola.

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

Prior to learning about conics and hyperbolas in precalculus, students should be able to identify different shapes and figures and learn to identify cross sections of prisms, pyramids, cylinders, cones, and spheres, from geometry class. In algebra 2, students learn to write quadratic equations and learn vocabulary such as vertex, foci, directrix, axis of symmetry, and direction of opening, all which are used when dealing with hyperbolas as well.

How has this topic appeared in pop culture?

The sport of baseball originates back before the Civil War and has come to be known as America’s pastime. On average, 110 balls are used in a major league baseball game, because the balls are usually tossed out if they’ve touched the dirt. Baseballs have a rubber or cork center, wrapped in yearn, and covered with leather sown together tightly by 108 stitches of red string. The stitches are in a hyperbola shape if looked at from a certain angle and depending on how the pitcher has held the stitches, different pitches are thrown.

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

Desmos is a great, interactive website that has many activities that can be used in the classroom. One of the activities it has is called Polygraph: Conics. The Desmos activity is similar to the board game Guess Who? in which students are in pairs and will ask yes or no questions to guess the graph of a hyperbola or ellipse of their choosing. This activity encourages students to make good questions and use precise vocabulary and academic language when describing conics, specifically over ellipses and hyperbolas, so that they can win the game.