Desmosify Your Worksheet

[cross-posted to the Desblog]

Sometimes I see a worksheet online and I say to myself, “That should stay a worksheet. Paper is the right home for that math. Any possible benefit from moving that math to a computer is more than outweighed by the hassle of dragging out the laptop cart.”

Other times I see a worksheet and it seems clear to me that a different medium would add – you name it – breadth, depth, interest, collaboration, etc.

That’s the case with Joshua Bowman’s implicit differentiation worksheet, which he shared on Twitter. It’s great in worksheet form. But the Desmos Activity Builder can add a lot here while subtracting very little. Activity Builder is the right home for this math.

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Here is the activity I built in Activity Builder:

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And here are some differences, from small to large:

Simplify Assignment Collection

Bowman is asking his students to do their work in Desmos anyway and then copy and paste their calculator link into a Google Doc for feedback.

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Activity Builder simplifies that collection process. Students do their work in the Desmos activity. Desmos sends you all of their graphs, quickly clickable.

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Ask More Questions

When students see worksheets with seventeen questions running (a) through (q), they lose their mind. Let’s lighten their cognitive load and keep question (q) out of their visual space while they’re considering question (a).

This isn’t necessarily an improvement, especially if my new questions just ask students to repeat the same dreary work several hundred times. So:

Ask More Interesting Questions

I added six more questions to Bowman’s worksheet, and they share particular features.

First, they ask students to work at several different levels, from informal to formal. For example, I wanted to ask questions about:

  • a blank graph – “What do you think the shape of the graph will be?”
  • the graph – “Add up all the intercepts. What is that sum?”
  • the graph and some tangent lines – “Multiply their slopes. What is the product?”

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These questions move productively from informal understandings to formal understandings, but they don’t live well together on the same piece of paper. You can’t ask students, “What do you think the shape of the graph will be?” when the graph is farther down the page.

Another example:

Bowman’s worksheet asks students to find the equation of the tangent lines to the intercepts of the graph. Some students may use sliders, other students may differentiate implicitly.

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I can quickly figure out which group is which by asking them to multiply their slopes together and enter the product in a new question. Which students differentiated and which students experimented?

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Long before I ask students to calculate that product, I ask them to simply estimate its sign. Envision the tangent lines in your head. Without knowing their exact slopes, what will their product be? That’s an informal understanding that assists later, formal understandings.

So again:

  • Simplify assignment collection.
  • Ask more questions.
  • Ask more interesting questions.

Best of all, this Desmosification took minutes. Start somewhere. The tools are all free forever. Thanks, Joshua, for sharing your worksheet and letting us take a crack at it.

Featured Comments

Brandon Dorman:

I also like how the overlay view of your student answers could help lead to new questions, like seeing trends for student mis/understanding.

Jamie Mitchell:

This is great…but I need more. I want a way to be able to provide feedback to my students as they work through these activities.

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

18 Comments

  1. Reply
    This is great…but I need more. I want a way to be able to provide feedback to my students as they work through these activities.

    I especially need a way to provide feedback if I am using a Desmos Activity as an evaluation or assessment.

    Any suggestions out there?

  2. Reply

    @Jamie Mitchell I was thinking of using the overlay function to show back to students sort of like how “My Favorite No” models. Ie, show them the overlaid graphs and ask them to describe misunderstandings they see.

  3. Reply

    @Jamie Mitchell Could you combine this with a Moodle lesson and branch based on a student’s response to the question? That way you could anticipate common errors or misconceptions and then use specific branches to address those errors or misconceptions which would provide immediate, individual feedback to each student as they’re working through the problems…

  4. Reply

    This is my favorite thing to do with activity builder; take good activities/explorations and make them more meaningful and powerful for the students. Keep up the great work.

  5. Reply

    I don’t know who added the “Just add sliders” link that I just now noticed, but please send my profound thanks. I’ve wanted to know how to use sliders for a while. I use Desmos all the time, but just as a graphing calculator. This will get me started to greater ambition.

  6. Reply

    Jamie Mitchell:

    This is great…but I need more. I want a way to be able to provide feedback to my students as they work through these activities.

    This is a really fair point. We’re very interested in helping teachers to give feedback within activities. We aren’t certain about the best way to make that happen. If you ever wanted to send along an example or two of how you’d like to give feedback in an activity, that’d help our process a lot. dan@desmos.com.

  7. Reply

    As I said on Twitter, I really appreciate posts like this that model the process of taking a “flat,” non-dynamic activity and livening it up by “Desmosifying” it. I appreciate Jamie Mitchell’s comment about feedback, but during the Deliberate Practice phase of a learning cycle, I am often just looking for an activity that will empower students to practice on their own meaningful way.

    The value I see in these Desmosified activities is leverage, especially in large classes like mine.

    So thank you for this post and keep them coming!

    – Elizabeth (@cheesemonkeysf)

  8. Reply
    Dan, would you be willing to generalize your model for this particular activity – i.e. Predict – Verify – Reflect – Extend? Of course this follows closely to the 3-act idea, but I’m curious about what you view as an ideal structure for a “good” Desmos activity?
  9. Reply

    @Ryan, great question. Each week, I review over 100 random activities from the community, intent on a) building our pool of searchable activities, and b) creating some initial hypotheses about “what works.”

    And the sequence you defined shows up again and again. (I like how Patty puts it to work also.)

    It isn’t the only productive sequence, of course. Dylan Kane describes another.

  10. Reply

    I love the activity builder but in this case I’m not so sure the original activity isn’t a better option. Here’s why:

    1.submitting via google docs allows for a highly detailed and ongoing feedback dialogue. AB does not.

    2. Saving graphs in the Desmos app allows for revisiting and building families of related ideas and functions that AB cannot in near the same ongoing basis: learning is a static loop.

    Sometimes these points don’t matter, but here, they do.

  11. Reply

    Agreed interesting questions are key. Product of the tangent line being positive or negative is nice. Leftmost point is a great question.

    Predict the shape of the graph is too intimidating of a start. The sum of the x & y coordinates of all of the intercepts is a low entry bar, for sure, but maybe a little too low. Alternatives:

    • “Blotch Out” a section around (2,0) and ask for the other x-intercept;

    • The x-intercepts are 3 units apart, how far apart are the points with a y-coordinate of -2? Analogous question with y-intercepts;

    • Did you notice that the x-intercepts are pretty similar to the y-intercepts? If possible, list a few other pairs of points that have this sort of symmetry.

    Do you think there are there any two points that have the same slope?

    Imagine where the tangent lines at the x-intercepts meet & where those at the y-intercept meet. Do you think all 4 tangents meet at the same point? If not, which intersection would be farther from the origin?

    You mention some using sliders to get the slope. It seems odd that an “implicit differentiation” worksheet could be completed without actually having the ability to differentiate implicitly. If it were possible, I would disable the sliders for this activity.

    Screen 6: What method did you use? Good grief. I used the method that is the title of the handout or I slid sliders until it looked about right.

  12. Reply

    I was thinking about this some more and went through & did an implicit activity builder for this task. You are right. The task builder part of it is quick and easy to use. I believe it will be a helpful tool for me at some point.

    But, it is not easy or quick to come up with questions for the implicit task that benefit from the activity builder format.

    What did your activity builder add to the task? I can ask the class before providing the handout what they think the graph looks like, though I prefer the question on the handout of what does the shape look like. The latter questions on the handout do not give away the answer to the prior questions. It takes little more than a glance at their DESMOS screens to see how students are approaching the problem. On the other hand, if they are working in activity builder, I simply see an image of the graph on most of the pages (not their tangent lines & equations & sliders). By the same token, the students do not have access to the calculator feature on most of the screens (they are looking at a fixed image) and may need to toggle back and forth. The handout is clean and simply stated whereas activity builder preview shows 9 screen shots.

    Activity builder does seem like a promising tool. But, … something about a hammer and seeing nails everywhere.

  13. Reply

    @I Hodge

    The more I think of it and with your points in mind, the more I’m coming around to the conclusion that this activity is actually not well suited to the Activity Builder at all.

    The back and forth, single screen at a time, nature of AB is a big drawback in the reflection process for students, and for me when attempting to connect their recorded ideas with their recorded graphs in the AB. And for that matter when I attempt to assess their thoughts. It’s constantly back and forth between 10 screens for 30 students. Not efficient and you start to lose the plot(pun intended) quickly when reviewing such things.

    Instead, this activity actually seems ideal for Desmos standalone, uncoupled from the Activity Builder.

    The Activity Builder has its place – more of a loose investigative tool than serious assessment piece in my opinion – but this activity isn’t the place.

    Desmos alone along with a Google Doc or even old school piece of paper is superior.

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