Here are four ways that I have used Desmos so far this year...and I've included a fifth I will use when I get to Trig. I am sure this list will grow and grow. I used it almost every day last week. The sliders are so easy...they just appear when you type in a letter other than x. So user friendly!
1. Facts about quadratics...even more than just what "a" does to a quadratic...what happens when the discriminant is greater than 0, equal to 0, or less than 0 can be reiterated using Desmos when other methods are not "clicking" for students. It's a great visual. I was tutoring a student yesterday, and he understood the relationship between x-intercepts and the discriminant when traditional methods were not working for him. I will be teaching this next week in class and look forward to it.
2. Piecewise functions. My students struggle drawing piecewise functions. Many do not truly understand domain restrictions. They end up drawing the whole graph without domain restrictions and their graph fails the vertical line test. Enter Desmos. I used this during class, and particularly during extra help over and over again. I found this video when I was googling about piecewise functions. It's excellent and is from mathcoachblog by @bobloch. He also has a variety of Desmos videos that I strongly recommend: http://mathcoachblog.com/desmos-classroom-file-cabinet/. I also used this one in class on inequalities, and I used it over and over again in extra help: Investigating Polynomial Inequalities using Desmos. I will also use Desmos next week when talking about inverse functions and restricting domains of functions so that the inverse will be a function.
4. Fun activities, such as Central Park. Students need to move dividers to fit a proper number of cars in the lot...but then this changes as they have to calculate the spaces and finally use variables to get the answer. I was really surprised that so many of my Pre-Calculus students struggled with the variables! This is a perfect thing to do on a half day or the day before a holiday.
5. Trig, Trig, Trig! Unwrapping of the unit circle. I found this here: https://twitter.com/jkindred13/status/464825125612032000.
Honestly, I could go on and on. There is great stuff on Calculus, Conics...and really neat things on sequences...I saw this one on sequences again on mathcoachblog--it's awesummmm haha!
Here is a similar picture of what you can do with sequence and series:
This is more info from Desmos:
And so is this:
And two more amazing links I will continue to explore: https://sites.google.com/a/bbns.org/desmosdemos/ and Desmos youtube channel.