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.

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.

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.

Maybe have an open ended question where students can try powers other 2 to create something interesting.
Maybe challenge them to produce a particular graph given only its picture.
Or extend hyperbolic geometry to 3d? https://www.desmos.com/calculator/wed8h1huzs

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.

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.