%20(5).png)
There are so many concepts in math where students can just "memorize the rules" and get by. Function transformations is definitely one of them, but it's SO much more interesting for students when you can show them WHY these rules work. It's even more engaging when they can discover the rules for themselves! And that's why I LOVE teaching function transformations!
Start with the Basics
Students need to be exposed to the different function families before you can start to transform them. In my Algebra 1 class we focus on the following families of functions: linear, exponential, quadratic, absolute value, cubic, square root and cube root.
To help students learn the differences between the function families we focus on the
characteristics of the parent functions using a graphic organizer. When I taught honors Algebra 1 I had students research and complete the graphic organizer themselves. Now I present the material to students using a scavenger-hunt-style walkaround activity.
To help students study the function families I have physical flashcards (and a corresponding Quizlet) and a quiz in hard copy and for use with Google Form. Each of these is available in my store.
My Favorite Discovery Lesson
My absolute favorite way to empower students to discover function transformation rules is to use sliders with Desmos. When you add sliders (as seen below), students can do their own exploration and watch what happens to the graph when different values change.
In Algebra 1 I have students focus on these four function transformations: y = f(x) + k, y = f(x + k), y = k*f(x) and y = f(k*x). To help guide their exploration I made a packet where students can record their observations and generalize the patterns to discover the function rules. This packet can be found in my store.
This activity is not only a great discovery activity, but is a fluency practice for creating graphs. I find that some of my students struggle to quickly graph on paper and this activity gives them the experience they need to strengthen that skill.
I made this packet before Desmos Activity Builder existed and while I definitely think it's still an effective material, I do also use the Activity Builder for further exploration. Below are some of my favorite activities. Many of them where made by "making a copy" and editing to meet my students' needs. This is one of my favorite ways to create Desmos Activities for my lessons! Check out how to do this in my Instagram Reel here!
Extending into a Project
If you're looking to extend this learning into a project, I've got you! When I taught honors this was one of my favorite projects of the year! Students were given the choice of creating a physical project, a digital project, an art-based project or taking a traditional exam to demonstrate their learning. In my store I have the directions, rubrics and exam (hard copy and Google Form) included.
If you have the time and if your students have the ability, creating Desmos Art is also a great culminating activity for function transformations! I found this Desmos Activity to help introduce the idea to your students; this set of in-depth directions to help students who want to dive deeper into the way functions can be used to create complex images; and this is the blog post from the official Desmos Art Contest from 2020.
Share your questions, comments and experiences in the comments below!
Share your favorite Desmos Activities!
What is your go-to tool for teaching function transformations?
What questions do you have using Desmos Activities?
Comments