For my first post, I'm going to talk about ways to use Desmos as a teaching tool. As teachers, we always want our students to be able to develop knowledge and explore without our guidance, but it does not always work out as nicely as we want it to. Desmos can give students the opportunities to explore and make conjectures about algebra functions, geometry shapes, and trigonometry functions, to name a few. By manipulating the functions and observing what happens, students can draw conjectures from these observations and create knowledge that is more meaningful to them. In this blog post, I'm going to talk about a lesson I used in my Algebra I class, but it can be used in other classes and grades depending on the level of your students. It could also be adapted for other purposes by changing the functions being used and the questions asked.
An important note I want to mention before I discuss the lesson is that the students need to be familiar with Desmos and know how to use it independently of the teacher in order for this lesson to go smoothly. Otherwise, students will be constantly asking for help on how to input the functions, and you will never get them to work independently from you. By having a prior lesson use Desmos, students can learn the basics enough to use it for this lesson.
The purpose of the lesson I created was to explore the effects of transformations on functions and develop conjectures on the patterns they observed. I created a step-by-step worksheet to guide them through this process so they could work independently. However, to ensure they were on the right track, I also made them get my initials before they could move on to the last page and the homework. This way I could give them freedom to explore and learn but also check for understanding.
The worksheet had vocabulary for transformations, and we had already discussed the different types of parents functions in a previous lesson. The first question dealt with applying various shifts upwards to a quadratic function and the second problem involved applying various shifts downwards to a quadratic function. For example, graph y = (x^2), y = (x^2) +1, y = (x^2) +2, and y = (x^2) +3 and write below what happens as you add the numbers. Then I had a place for them to make a conjecture about what they would think would happen if they added n to the function. I did the same for shifts down, shifts left, and shifts right. I did not include stretches or compressions because I felt that it would be to confusing to add on top of the shifts. For each of the different questions, I included a graph so they could copy what was showing on their Desmos. As I said before, I then made them check with me before moving on. In this brief meeting, I would check over their answers and graphs and then ask probing questions if they had not seemed to understand the shifts. Such as, "well what did you notice about the graphs?" and "what would happen if I added 10? 20?", etc. I would also make sure they understood the difference between up and down shifts and left and right shifts and how to recognize them.
Finally, the back page was a short worksheet that had a place for them to write their general rules in terms of any function, and it also contained problems that combined shifts and required them to make conjectures about what would happen and then test their results by graphing in Desmos.
While many teachers use Desmos as just an extension of the hand-held graphing calculator, its flexibility can allow students to move beyond just mindlessly graphing functions and allow for meaningful learning experiences. If any of you have tried this lesson plan out, or have used Desmos in a meaningful way in your classroom, please shared your experiences in the comments!
