graphing calculator picture desmos 9 equations patrick

I’ve always suspected students have trouble imagining what it means, for instance, to require a box have a square base and a fixed volume. Several classic problems deal with boxes whose surface area must be minimized, or whose volume must be maximized, under various constraints. Optimization takes up a chunk of time after derivatives have been introduced. Here is the amount of daylight each day at latitude 50°S:Īnd here’s what the amount of daylight would be like just a few degrees away from the equator, if Earth had the same axial tilt as Uranus (about 82 degrees): Here, for instance, is a graph depicting the amount of daylight on each of the year at latitude 35°N: This fall, however, I had students explore how the changing amount of daylight is affected by time of year, latitude, axial tilt, etc. I have in the past just mentioned this as an illustration of the derivative. Teaching calculus in the fall almost always leads to introducing derivatives near the equinox, around the time that days are getter shorter at their fastest rate. The ever-responsive and ever-creative Desmos team turned the blancmange curve into a mountain range, with a setting sun and moving train (you’ll definitely want to play with this one): After that, I made the blancmange curve, a classic example of a continuous but nowhere-differentiable function:

I first learned this while adding up sine functions à la Fourier sine series, which I wrote about here. That you could not only define variables but also define functions in a Desmos graph and use them elsewhere came as a revelation to me, as did the fact that you could create sums with a variable number of terms. Not all of these were used in class, as sometimes I just had to play around with some ideas.įirst, some play. For simplicity, I’ve removed a bunch of the “worksheet” structure to these, so that they have become more like demonstrations others can use as they wish. At the end of class, or afterwards if they had sections to finish, they would share their work with me so that I could review it.) I’ve shared some of these worksheets over time, but I thought it would be nice to have some of my favorites collected in a single place. On days we used worksheets, about half of the students would bring in laptops, and they would work in groups of 2–3. (A brief word about my teaching situation: at Smith, all students have a Google account for their email, and thus all have a school-related Google drive by which documents could be shared. Eventually I figured out that Desmos and Google docs could be used together to make more fully developed worksheets. I made “worksheets” that allowed students to interact with mathematical ideas in an incredibly direct way I also had fun creating them. Since then, the Desmos team has added a lot more features, without ever sacrificing user-friendliness (which, for those of us using Desmos to teach, is paramount).ĭuring the fall semester, I used Desmos extensively in my calculus classes at Smith College. The interactivity is kind of the whole point, so please do take a few moments to experiment with some of these.Īt the start of last summer, I announced that the Desmos graphing calculator had sold me on its usefulness “after just a few minutes of playing around”. Important note: You can click on any graph in this post to go to an interactive version.

Graphing calculator picture desmos 9 equations patrick