Des-blog

The Friday Fave is thinking about sequels this week.

Michael Fenton spoke about sequels a while back, and you should hear what he has to say on the matter.

https://www.youtube.com/watch?v=IreYFX6d3bg

Michael’s sequels are additional questions about a context within a lesson. And it is also worth thinking about when the next lesson ought to be a sequel to the current one.

Consider the case of Polygraph: Lines. Students play an engaging game that requires them to notice and discuss features of graphed lines for which they may not yet have words. As teacher, you introduce some of those words as the game moves along. But even if you don’t play Polygraph again, the game itself has created a rich space for asking additional questions, and for moving students further along in their mathematical journeys.

That’s where Polygraph: Lines, Part 2 comes in. In this sequel to the original Polygraph, students encounter increasing, decreasing, steepness, and intercepts in the context of thinking about situations that could arise in playing Polygraph.

Students sketch, write, and see each others’ responses in the service of better understanding the algebra of lines. All of it made possible by the original context of Polygraph. That’s what makes Polygraph: Lines, Part 2 this week’s Friday Fave.

And here are two more activities with sequels:

Polygraph: Hexagons and Polygraph: Hexagons, Part 2

Function Carnival and Function Carnival, Part 2

We rarely ask students to do impossible things.

Or more to the point, we rarely ask students to design impossible tasks. After all, why would you?

The Friday Fave has an answer to that question actually. When you ask a student to design a task that’s impossible to solve, you engage in the student a particular kind of critical thinking. Success requires analyzing the structure of the task in a different way from solving a possible task.

Success requires considering what the solutions to the possible tasks all have in common, and then doing the opposite of that.

All of which brings us to this week’s Friday Fave: Linear Slalom.

In the standard version of Linear Slalom, we ask you to send a line through sets of slalom poles.

Once you’ve got the hang of it, we ask you to design an impossible slalom.

Think about this for a moment. What makes a linear slalom task impossible? Your mind may go to the vertical line test. But we actually let you write an equation for a vertical line, so you’ll need more insight than that.

Horizontal gates on the same horizontal line will work, as will vertical gates on the same vertical line. Is that all? What’s the general principle here, and why?

There’s a lot of math in just this one screen of this delightful activity, and there’s lots more math to be done as students head to the Challenge Creator to design possible slaloms for each other to solve.

But designing an impossible task is what makes Linear Slalom this week’s Friday Fave.

If parabolas are more your thing, try out Parabola Slalom.

And if you’re looking for more work with lines, here are two more lovely activities.

Card Sort: Linear or Nonlinear

Polygraph: Lines

Let’s say you’re building a Desmos activity that has some kind of animation in a graph. Maybe points going around the unit circle, or objects being launched in some kind of trajectory. Maybe you want a point to trace out a line.

Whatever it is, the Friday Fave recommends you use an Action Button to get things started.

You’ll need to turn on Computation Layer in Desmos Labs to do this, but after that it’s really quite simple (and don’t worry; there’s lots of support available).

First get your graph set up on your Activity Builder screen, using a slider to animate your thing. You can call that slider whatever you like, but T is nice because T stands for time (and while you can use lower-case t, it’s wise to reserve that for any parametric curves you might end up drawing).

Now put an Action Button on that screen, and give it a name.

Then head over the graph script and put that button to work.

The Fave used 6.28 in the parentheses so that the animation would last about 2 pi seconds. You can put anything you want there. Leave it blank for a default of 10 seconds.

Action Buttons. So simple; so useful. That makes them this week’s Friday Fave. And here are four activities that use Action Buttons to make a bunch of different things happen. Now that you have Computation Layer turned on, you can copy and edit them to see how those buttons work.

Click Battle

Laser Challenge

Build a Bigger Field

Racing Dots