Desmos isn't just a calculator, it's a playground for exploring mathematical ideas. The activities below work across middle and high school, and each one can be built and auto-graded inside Glowsmith without writing any code.
1. Slope-intercept scavenger hunt
Show a line and have students identify its slope and y-intercept. Flip it around: give students an equation and have them match it to the correct graph from a set. This builds the mental link between an equation and its picture.
2. Function transformations lab
Let students drag a parent function like y = x^2 around the plane and observe how the equation changes. A guided worksheet where they record the effect of each transformation turns a demo into a discovery.
3. Quadratic vertex match-up
Give students parabolas and a list of vertex coordinates. They match each graph to its vertex, then to its equation in vertex form. Great for solidifying the connection between vertex form and the graph.
4. Systems of equations intersection hunt
Plot two lines and ask students to find the intersection point. Then swap in systems with no solution and infinite solutions, and ask students to explain how they can tell before solving.
5. Exponential growth exploration
Have students compare y = 2^x, y = 3^x, and y = 0.5^x on the same axes. Ask them to describe which grows faster and why, building intuition for exponential versus linear change.
6. Trigonometric wave drawing
Show a sine wave and let students adjust amplitude and frequency, watching the graph reshape live. Add a matching activity where they identify equations from graphs of waves.
7. Piecewise function design
Challenge students to design a piecewise function whose graph spells a shape or letter. It's a fun problem that forces them to think about domains and continuity.
8. Absolute value art
Transform the classic V shape of y = |x| by shifting, stretching, and flipping it. Students can compose several absolute value functions to build a simple picture, reinforcing transformations through creativity.
9. Distance formula verification
Place two points on a grid and have students calculate the distance between them using the formula, then verify by plotting a right triangle and checking the hypotenuse on screen.
10. Data plotting and best-fit lines
Give students a real-world data set, plot it, and let them experiment with lines of best fit. Ask them to justify their choice and use their line to make a prediction.
How to build these in Glowsmith
In Glowsmith, just ask for it. Prompts like "add a Desmos graph showing y = sin(x) and ask students to find the period" produce an embedded, interactive graphing widget with auto-grading built in. The system compares the student's graph state against the expected answer, so you get instant scoring without any manual checking.
Pick one activity from this list, build it in a couple of minutes, and assign it to your class this week.