Des-blog

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

Practice.

Everybody has thoughts on practice. Should it be assigned for homework or flipped and done during math class? How much is necessary? Is there such a thing as too much? Concentrated or interleaved?

So many questions, and the Friday Fave does not pretend to have the final word on matters of practice.

But the Fave DOES have resources.

Consider the line; a mathematical object useful for everything from drawing pictures to modeling our everyday world. Lines are worth getting to know in an intimate way. Practice—in some form and at some time—is going to be a part of building your mind’s relationship with lines.

This is where Match My Line comes in. We start simply—you’re only paying attention to the slope as you write an equation that sends a line through two points.

But soon you’re dealing with slopes and y-intercepts, and using whatever form of an equation for a line is useful to you—a form that may well change in response to the nature of each challenge.

You’re sketching. You’re settling disputes. You’re reflecting on the relationship between the form of a challenge and the form of the equation you’d like to use to solve it. All of this makes for meaningful practice with engaging technology. And it’s what makes Match My Line this week’s Friday Fave.

While you’re thinking about practice and matching, take a look at these other matching activities.

Match My Parabola

Match My Picture

Card Sort: Derivative Match