# GeoGebra: Bringing Geometry to Life

Two major challenges faced by all math teachers are ensuring that students understand mathematical concepts and helping students see the significance of math in the world around them. When these two goals are achieved, students form a foundational framework in mathematics that enables them to pursue their aspirations to become productive, active members in society. There are several ways in which a teacher might try to engage students, but one of the most effective ways to achieve this end is through interactive problems that relate mathematics to the real world. Real world applications pique students’ interests because they demonstrate the practicality of a given mathematical concept. No student enjoys learning about a topic they feel carries no weight outside of the classroom, yet every student finds pride when they feel they have solved a problem with the potential to actually make a difference.

In the 21st century classroom, technology has opened the door to a new realm of possible ways to connect mathematics to the outside world. The key is finding technology that most effectively engages students’ critical thinking skills and interests so that they make sense of mathematical ideas and reason mathematically (Leinwand et al., 2014, p. 5). As highlighted by Dick and Hollebrands (2011), effective technology drives students to analyze a problem, implement a solving strategy, seek and use connections across various representations, and consider the reasonableness of technology-derived results. Many technological tools and applications meet these criteria, but this analysis will look at an example of a real world application problem that can be primarily solved using the dynamic geometry software GeoGebra.

Consider the following problem, in which students are asked to find the most economical location for a new stadium:

In the state of North Carolina, a specific region in the Piedmont area is known as the “Research Triangle” because its general geographic region is contained between three cities: Raleigh (approximate population: 380,173), Durham (approximate population: 479,624), and Chapel Hill (approximate population: 54,492). Suppose the state is planning on bringing in a professional baseball team and needs to build a new baseball stadium. An aerial map of the area is shown below with a second more simplified map of the area that can be used for the purpose of working on the problem. Imagine you are on the board that will decide on where the stadium will be located. The contractor has determined the cost of building new highways is \$125,000 per mile and the cost of resurfacing an existing highway is \$50,000 per mile. (Hollebrands & Lee, 2011)

The new stadium will be built at one of the four centers of the triangle: (a) centroid; (b) circumcenter; (c) incenter; (d) orthocenter. Given the information above and maps below, which location makes the most economic sense? Continue to the next page for the solving strategy.