- Andrew Thein
The goal of this project was to create a sketch that explores finding the area underneath a parabola using integrals. More specifically, I wanted to look at what happens to the area under the parabola when the dimensions and bounds change. The main way this investigation is different from paper and pencil is that it enables me to show how all the values scale with each other as one element changes. Based on Standard Math Practice number 5, the Geogebra tools that I used include sliders that control the bounds of the integral, dimensions of the parabola, and number of rectangle "slices" on the second graph. It also uses measurements of the area, as well as the height and width of the parabolic equation. The two other Standard Math Practices I used when creating this sketch are Math Practice 4 and Math Practice 8. I used Standard Math Practice number 4, Model with Mathematics, by using the real world concept of hanging a curtain for the students to have something in their everyday life they can relate the math to. I used Standard Math Practice number 8, look for and express regularity in repeated reasoning, by showing how taking the areas of tiny rectangles underneath the parabola can get you a close estimate and by adding more and more rectangles, you can get closer and closer to the actual area, but never actually at the total area. The thing I enjoyed most about working on this project was setting up and seeing how everything scaled together. It is one thing to do a couple of sketches by hand to show how things change, but to see in real time how everything scales together is awesome. This was a concept I remember struggling with when I was learning integrals, especially the concept of adding rectangles underneath the shape to get a close estimate at the area. To me, this visualizes how the concept works and illustrates how integrals work to find the area underneath a shape.