Being able to solve equations or do difficult geometry problems are very important skills to help students have success in future classes. But if we want students to really understand why we study mathematics, they need to see and understand how it is really used. This goes back to our school motto- we learn not for school, but for life. The Pythagorean theorem has been important to construction for thousands of years, but students don’t grasp the challenges of it until they see it in a real project.
Every year we have a field day at Powhatan, full of traditional track and field events. This includes a distance race, and we finish the day with this signature event consisting of relays around a 200 yard oval track.
What people may not realize is that the geometry class spends a few days painting that oval track on our sports fields. To do this, we set two 50 yard straightaways, and two semi circles each 50 yards long. So we have a rectangle with semi circles at either end. But the rectangle is so large, that to get a small error in measurement can really alter the lengths. The students use right triangles made by the Pythagorean Theorem to set the right angles, the formula for the circumference of a circle to find the radius, and try to measure as carefully as they can to lay out the track. Like in real life, they will have errors, and have to make corrections, they will need to double check and redo parts. They discover how things like small domes in the ground will make their track several feet off. The mathematics gives them the tools to succeed, but the experience of projects like this makes the mathematics come alive for the students. They also learn that when they work in the real world, things are not always neat and clean. They require knowing skills, understanding , perseverance and a willingness to ask questions to make the project work.
When they run that race a few weeks from now, they track in real math- learning not for school, but for life.