Thursday, April 5, 2018
Teach 180: Riemann Sums (Day 133)
In Calculus yesterday, we began to investigate the idea of approximating area under a curve by using rectangles. Although I can draw a diagram of this situation and students can look at static pictures showing width of the rectangles decreasing and the number of rectangles increasing, I could tell that they still couldn't fully understand the dynamic process of decreasing the width of the rectangles and increasing the number of rectangles.
Thank you to Desmos for coming to the rescue! This page is wonderful, because you can change the function, the number of rectangles and how the rectangles are formed (left endpoint, midpoint, or right endpoint). The next time I teach this topic, I plan on showing my students this video twice and asking them what they think is going on in terms of the area and the rectangles. I purposefully recorded it without audio. Feel free to use the video and put your own audio over top or play it in class and have students comment on it as it plays.