By Nick Corley
When I first starting using desmos.com in the classroom, I liked it because it was colorful and I could quickly graph any equation I wanted to. I also liked that it was free. Desmos got me away from picking points and using line drawing tools which can be tedious. As time went on, and I starting using Desmos more regularly, I started to understand how powerful of a tool it really was.
You have several options in Desmos to edit the actual coordinate plane. You can label each axis, which is great for word problems and real-life applications. You can turn the grid marks on and off. You can also turn each axis on and off. Turning off the y-axis and the grid marks makes a nice number line. In addition, you can modify the range of values for each axis, and change between degrees and radians. You can also share the graphs you create, which allows you to share the web URL, print the image, export the graph, or embed the graph. I have used this to create assessments for my students. You or your students can also use it to create presentations.
As an Algebra I teacher, most of my year is spent exploring linear and quadratic functions and their graphs. If I input an equation into one of the expression lines of Desmos, I have several options about what can be done with the equation: change the color, change the line style, and even create a table of values for the equation. This is all done on the same screen, which allows me to connect representations of function, their graphs and their solutions. Not only will Desmos do this for virtually all types of equations, it will also do this for inequalities with the correct half-plane shaded.
Another tool I love is the ability to make notes in the expression lines. If you want to share a graph with students you can write an explanation to go with it. Desmos also allows you to insert a table of values, which can help you identify patterns visually. You can also perform a regression of that data, which can help find the best model for those values, such as a line of best fit.
My students enjoy uploading and using images on Desmos. Once the image has been uploaded to Desmos you can edit its location and its size. As a teacher, I can upload an image of a football and have it travel the path of a parabola. I have directed my students to upload an image and recreate the image using all the different types of functions they have learned, which is a great end of the year project.
My favorite Desmos tools are sliders. Not the tasty little sandwiches, sliders are variables or constants (other than x or y) that you can change the value of or animate. When you type a variable other than x or y into an expression line, the Desmos calculator asks if you want to add a slider. When you say yes, you can choose a range of values, a step size, and a speed at which you want it to change. As the values for this slider change, the graph of the function containing this variable changes in real time along with it. This feature allows you to explore many graphs in a short period of time, which is a more efficient way of learning new functions.
Sliders can help students quickly understand why something like “b” in slope-intercept form (y = mx + b) is the y-intercept and affects the height of the line. Sliders can also be used in the football example previously mention to make the football fly through the air. (Seen below.)
For math teachers at higher levels, Desmos can also graph implicit functions, find derivatives and integrals, graph parametric equations, and graph using polar coordinates. Teachers at the middle school level can use Desmos to teach about the coordinate plane and its parts, or to practice plotting ordered pairs.
The Desmos graphing calculator is online at desmos.com, and it is also a free app that can be found on most devices. In addition to the free graphing calculator, Desmos has a new geometry tool that can be found at desmos.com/geometry and an activity site that can be found at teacher.desmos.com.
These tools have made me a more effective and efficient teacher, and I know they can do the same for you. To find out more about all of the Desmos tools go to learn.desmos.com.
Nick Corley is an eighth-grade mathematics teacher at Northfield Middle School in Atlantic County. He can be reached at email@example.com. You can follow him on Twitter at @MrCorleyMath and read his blog at mrcorleymath.wordpress.com.