Desmos: Your Smart Graphing Calculator

“Do I have to buy a graphing calculator?”

This was the first question asked by a student in a grade 10 math class during my final practicum. A very honest question. I know when I start reading any course syllabus, the first question on my mind is, do I have to buy a textbook?

And so came the introduction of Desmos —a free online graphing calculator.  But far from the fact that it’s free and doesn’t need any fancy equipment to use in class (students can access it from any personal device), Desmos has a lot more to offer. Think of the smartphone you’re using now, and then think of what you were using before that. That’s Desmos. It’s a smart graphing calculator, and graphing is just one of its features.

What I found to be most helpful before using it; however, was observing an experienced teacher put it into action. This is definitely something I would recommend when it comes to integrating new technology in the classroom. Reading about it or watching tutorials online on how to use it is extremely helpful, but watching someone put it into action or even having the opportunity to engage with it offers you a full view of that desired outcome.

The big picture; what does Desmos offer you:

  1. Online graphing calculator —no account needed; if you have internet access, simply go to desmos.com and start graphing from any personal device. If you want to save your work; however, you need to be signed in under your account (free). You can also download it as an App on your device.
  2. Pre-made Classroom Activities that you can use as-is or adapt/edit to fit your own classroom needs —simply sign up for a free account to access them.
  3. Custom activities via Desmos Activity Builder —design and create your own digital math activity online to integrate into your lesson.

Classroom activities or custom activities are simply a series of interactive slides that students can work their way through either at their own pace, while still engaged with their peers (see below), or using teacher pacing (whole class working on the same slide).

Here is a screenshot of a classroom activity offered by Desmos that I tried with my students during practicum.digital-activites Some features you can add into your digital activities include; text, notes, hidden folders (from students), student input, multiple-choice questions, images, videos, and graphs. Students can also interact with their graphs, sketch their thoughts, type their response, or have their work carried forward from a previous slide to continue solving.

What does it offer your classroom:

  • Allows you to focus on the math in an engaging way
  • Allows students to see how their graph changes in real-time depending on their input
  • Supports social interaction in and out of the classroom
    • Students are able to see peer responses and provide them with instant feedback or critique their work
    • Teachers can build a strong PLN with other educators using Desmos to share/discuss ideas and/or collect feedback
  • Safe learning environment: you can choose to anonymize student names when sharing responses and have them take on famous mathematician’s names instead
  •  Teacher/student pacing: have the whole class working on the same slide together while facilitating a discussion or allow them to work at their own pace while still getting that feedback and support from their peers -students can also continue to work on the activity from home
  • Pause the class: grab your students’ attention at once by pausing their work to showcase a solution or start a discussion that can help them carry forward
  • Formative assessment: check-in on responses while your students are working to provide them with instant feedback or use it to guide your next move.

Here are some screenshots of what the teacher can see as students are working. These responses can also be shared with the class as a focus on discussions. Activity link.

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Breaking it down; how to use it:

Note: One of the best things I like about Desmos is that it’s not just designed with students in mind, but teachers as well. The instructions and support offered for this tool are unlike any I have seen; albeit I’m still starting off my career in teaching, but I’m sure experienced teachers who have used it would argue the same.

Team Desmos offers video tutorials on its graphing calculator features and classroom activities. A full PD package is also ready for download if you’re looking to share the learning with others. You can access them here or you can also check out their user guide loaded with visuals.

Classroom Example:

Here is an example of a lesson I adapted from my intermediate mathematics course at uOttawa that integrated Desmos into Pear Deck into hands-on.

Task: What is the maximum number of pieces you could get using 20 straight cuts?

pizza-problem

First, we experimented with this:

Then, after noting the quadratic relation, we used Desmos to find our solution:screen-shot-2017-01-29-at-3-24-16-pm

In this lesson, I integrated Desmos online graphing calculator into my original plan and provided a link on Pear Deck for students to easily access it. Overall, I think they enjoyed the activity in itself and going through that productive struggle in trying to figure out the solution really paved the way for Desmos as a math tool to help us solve problems. I think what students like most about using Desmos is that it’s easy to use; you don’t spend the majority of the time explaining how to use it, but in actually using it.

With time management in consideration, I think next time I try this lesson, I will use Desmos Activity Builder for the graphing portion. Linking it to Pear Deck for students to access on their own doesn’t allow you to see their work once finished to be able to assess/offer feedback.

I still have a lot of learning and experimenting to do in integrating Desmos into the classroom, but it’s definitely a tool I would recommend to try and introduce to your students.  

3-Act Math: Super-Sized Coffee

This was the first lesson I did to start off my practicum. It’s entirely based on a 3-Act Task by Dan Meyer. Originally, I had my lesson set-up inline with the task to target the question: How many gallons of coffee would it take to fill up the super-sized cup? 

Walking through the plan with my mentor, however, she noticed that the students might be quick to solve this one—given that they had some similar practice before—and suggested that we start with the extension question instead: How many regular-sized cups of coffee would it take to fill up the super-sized cup? This would also offer them a new challenge during the conversion process.

dimensions

What I appreciate the most about great mentors is that feedback is always offered with choice. Even though my plan was fully written-out and I was now playing around with my slides on Pear Deck 20-minutes before I walk into my lesson, the decision to change the plan was still mine to make. Of course knowing that your mentor will be there to back you up when you need the support makes risk-taking much easier.

Moving on, I presented the entire task via Pear Deck here (full credit to my AT, for showing me how to properly set-up a 3-Act Math Task on Pear Deck and choice of wording).

ACT 1: Gourmet Gift Baskets Video (making/filling-up the super-sized cup) followed by: wonder

So, “why are they wasting coffee?” To try and set a new world record! But before finding out if they were successful or not, we focused on, “how many average cups could fill the large cup?” We estimated numbers that are too high, too low, made a best guess, and then it was time to solve.

ACT 2: What information do we need to help us solve?

I presented the image of the super-sized cup along with its dimensions on the screen, and acting on another pro-tip, I simply placed my Starbucks coffee cup on a high table—front and center—and left it up to the students to get their own measurements. Most measured in centimetres, but one group went with inches instead. They worked on this task in VRG on VNPS.solving

All groups applied the right formula to find the volume of the super-sized cup and average cup but ended-up with different numbers. With support from my AT, here’s what we discussed:

small-cup-dimensions

1. The top diameter of the Starbucks coffee cup is 8cm and the base diameter is 6cm. We had to take this into consideration to get a more accurate sense of how much coffee can actually fit inside the small cup. One of the students suggested that we take their average and so we did.

2. Most students aimed to convert the volume of the large cup into centimetres, but did a length conversion instead. My AT highlighted the difference and then we talked a little about the method of operation they used to solve (subtraction vs. division). It was then time to wrap-up the lesson. error-conversion

The following day I asked two of the students to use the portable keyboard available in the classroom to explain and model the steps for converting volume before sending them back to their boards to finish solving.

Here are some of the answers we got:answer_coffee20161108_115943

ACT 3: Video result (available in Pear Deck link): were they able to set a new world record/how many gallons of coffee is that?

We didn’t actually get around to watching the video result mainly because it took me sometime to get a good handle on time management during practicum, but we worked on a consolidation handout to allow for individual reflection/practice on conversion—which is the area I found they struggled with the most.

Overall, I really enjoyed this task and one that I would definitely try again. I felt it was really rich in its content and offered students a nice visual to develop their conceptual understanding of volume and conversion. Time management and better preparation to be able to offer strategic support during productive struggle will be my areas of improvement for next time.