For context, the book that I use for Algebra II starts in Chapter 2 with transformations of the absolute value function. Chapter 4 includes quadratics, Chapter 5 is cubics, and in chapter 6 it is square root and cube root functions. By the time students get to graphing of square and cube root functions they have done a lot of graphing by hand and talked about transformations several times.
1. Warmup: On the whiteboard I put a blank table of values for y=x^2 and y=x^3. Students talked with a partner about how to complete the table, and we wrote the values on the board. (Activating prior knowledge, partner talk, no technology, no paper)
2. Connecting concepts: I showed this Desmos pre-made sheet for parabolas in vertex form for a reminder of how a, h, and k transform a graph. Students watched and shared observations with partners, then we shared out as a class. The visual below stayed on the whiteboard for students to reference throughout the class (formative assessment, teacher uses technology, no paper)
3. Developing the concept: I asked students, what is the inverse of squaring? Cubing? What is the relationship between the points on a function and its inverse? We used our tables of values from the warmup to come up with a table of values for the square and cube root function. I wrote the standard form of each function below its table of values.
(anchor charts, no technology, no paper)
Steps 1-3 took about 10-15 minutes. We saved a lot of time by not requiring students to write anything down, and also by not having them do anything on the computer.
4. At this point in time students logged on to this Desmos Activity, and I modeled screen 1 for them.
One tip that helped students the most was to type in the standard form y=a*sqrt(x-h)+k (DON'T add sliders), and walk through my thought process. I asked myself the following questions:
- Did the y-values get multiplied by a number? If not, a is 1.
- Did the graph shift horizontally? If not, h is zero.
- Did the graph shift vertically? If not, k is zero.
So for screen 1 with a vertical shift of 2 we typed y=1*sqrt(x-0)+2. Students started asking questions about whether or not they could type the function in another way. I told them yes and emphasized that the focus was on the thinking process, which would help them complete the problems in our activity. (modeling, think-aloud, teacher and students using the technology)
5. Students were given a few minutes to complete screen 2, and move ahead to other screens if ready. We came back together one more time to go over screen 2, and I again modeled my thinking by asking myself the series of questions above. I called on students (popsicle-stick style) to answer my questions as I built the equation for our transformed function. (more think-aloud, formative assessment, equity)
6. Students work on the activity: I used the teacher dashboard to monitor student progress. The teacher dashboard allows easy collection of sooo much data. I am able to check in to see if all students have finished a particular screen, and if not I am quickly able to identify who isn't progressing in the activity and make adjustments accordingly. This type of info ensures active participation in a way that I can't make happen with a paper worksheet. Another great aspect of the teacher dashboard is that it becomes obvious very quickly if students are getting stuck on certain problems or if there are common misconceptions. Desmos is helping me to formatively assess student learning and make real time adjustments.
7. Summary/Closure of the activity: This one is tricky because often each class is different in terms of how far they get through an activity. I don't know if it is just me, but it seems like students can't generally finish all of the screens that I include in my Desmos activities. At first I thought this was a problem, but now I am taking a different view. Having extra screens provides a natural way to differentiate. If students are struggling on the beginning screens, I can adjust the assignment so they have a more reasonable goal. If students are excelling, I can send them to challenge screens. As long as I have a game plan for how I am going to bring the class back together and summarize the learning, I am fine with having too many screens. I am also allowing myself more flexibility in choosing a closing conversation, by letting it develop after I see where the students are at in their learning. Ideally one of the activity screens will work for a closing conversation so data can be collected. Students were successful with this activity, so a more challenging closing activity was appropriate. In one of the classes that I taught we looked at the screen below, both for the challenge, and for how it would help students with their homework assignment for the night. (Pair-work on computer, class discussion)
I'm very interested in continuing to explore how to use Desmos Activity Builder in instruction. I've seen how powerful it can be in helping to introduce and build connections between topics. One thing that I've learned this past semester is that planning for how to integrate a Desmos Activity into instruction is key to its success. The strategies in this blogpost are ones that I routinely incorporate when I use Desmos as a teaching tool, and they also aren't different from strategies used in my non-technology lessons (Activating prior knowledge, formative assessment, anchor charts, modeling, think-aloud, think-pair-share, calling on all students). There was a good amount of explicit instruction and modeling at the beginning to help students build the knowledge needed and to understand the directions. This was mostly done without the computer. Once the expectations and knowledge were in place students were prepared to practice using the Desmos Activity.
An area for growth: Teachers that I work with are sometimes concerned that there are no notes in place when we use a Desmos Activity to introduce material. I agree that there should be some sort of paper that students can reference throughout the chapter when they need to recall the learning. I want to stay away from requiring notes during the Desmos Activity because there can be processing issues for students due to too much input. This distracts from the learning. Maybe jotting down key ideas in a notebook or foldable at the end of class or the next day would work? Please share in the comments if you have ideas.
Next Steps: I want to continue to think about best practices for using Desmos in instruction. I'd like some sort of frame-work that I can use when I work with other teachers (I'm an instructional coach at the high school level). This would make for richer debrief conversations and help with sustaining professional learning. I'm also interested in using student work from the Desmos activities in summary conversations with students.
It would be great to hear from others that are using Desmos as part of instruction, so I hope that people keep blogging about their experiences. Audrey McLaren's Real-Time Story of the Desmos Activity builder has been a great starting point for learning about what other teachers are doing. You can read her post here.