Free New Desmos Activity: Transformation Golf

[cross-posted to the Desmos blog]

We’re excited to release our latest activity into the world: Transformation Golf.

Transformation Golf is the result of a year’s worth of a) interviews with teachers and mathematicians, b) research into existing transformation work, c) ongoing collaboration between Desmos’s teaching, product, and engineering teams, d) classroom demos with students.

It’s pretty simple. There is a purple golf ball (a/k/a the pre-image) and the gray golf hole (a/k/a the image). Use transformations to get the golf ball in the hole. Avoid the obstacles.

Here’s why we’re excited to offer it to you and your students.

Teachers told us they need it. We interviewed a group of eighth grade teachers last year about their biggest challenges with their curriculum. Every single teacher mentioned independently the difficulty of teaching transformations — what they are, how some of them are equivalent, how they relate to congruency. Lots of digital transformation tools exist. None of them quite worked for this group.

It builds from informal language to formal transformation notation. As often as we ask students to define translation vectors and lines of reflection, we ask them just to describe those transformations using informal, personal language. For example, before we ask students to complete this challenge using our transformation tools, we ask them to describe how they’d complete the challenge using words and sketches.

The entire plane moves. When students reach high school, they learn that transformations don’t just act on a single object in the plane, they act on the entire plane. We set students up for later success by demonstrating, for example, that a translation vector can be anywhere in a plane and it transforms the entire plane.

Students receive delayed feedback on their transformations. Lots of applets exist that allow students to see immediately the effect of a transformation as they modify it. But that kind of immediate feedback often overwhelms a student and inhibits her ability to create a mental concept of the transformation. Here students create a transformation, conjecture about its effect, and then press a button to verify those conjectures. Elsewhere in the activity we remove the play button entirely so students are only able to verify their conjectures through argument and consensus.

Students manipulate the transformations directly. Even in some very strong transformation applets, we noticed that students had to program their transformations using notation that wasn’t particularly intuitive or transparent. In this activity, students directly manipulate the transformation, setting translation vectors, reflection lines, and rotation angles using intuitive control points.

It’s an incredibly effective conversation starter. We have used this activity internally with a bunch of very experienced university math graduates as well as externally with a bunch of very inexperienced eighth grade math students. In both groups, we observed an unusual amount of conversation and participation. On every screen, we could point to our dashboard and ask questions like, “Do you think this is possible in fewer transformations? With just rotations? If not, why not?”

Those questions and conversations fell naturally out of the activity for us. Now we’re excited to offer the same opportunity to you and your students. Try it out!

I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.


  1. Love the activity and would really like to see how you did this in Desmos. Why are you being stingy with the editing rights! Sharing is caring…

  2. I like how Desmos is taking so many things into consideration when developing an interactive activity: teachers’ interviews, research into current tools, etc. That way, they can figure out what the teachers and students really need and will use once it’s out in the world. Teaching transformations in a classroom could be dry because it involves not-so-intuitive notations that many are unfamiliar with. This activity will definitely make this unit more engaging and enjoyable.
    My favorite part about this applet is that it has delayed feedback. It is important that the teacher provide students with opportunities to evaluate and critique their own or one another’s conjectures, which is often ignored in applets without delayed feedback. I am definitely going to utilize this when I get to teach transformations and I’m sure my students will enjoy it.

  3. My favorite part about this activity is that it addresses a misconception that I didn’t know I had until about a year ago: I did’t realize that transformations affect the entire plane, just just an object on the plane. The way that this new activity makes this visually palpable is a great step forward. Thanks.