Des-blog

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

The Friday Fave is thinking about the power of mathematical generality this week.

Mathematics is full of universal quantifiers: All, none, and every are common words in theorems and proofs. Every multiple of 12 is abundant (an abundant number is one whose factors sum to a value greater than the number itself). How many integer solutions for a, b, and c are there to a^n+b^n=c^n, for whole numbers n>2? None.

All, none, and every are important ending points of mathematical inquiry, but they are lousy invitations.

When the Fave is told to find ALL solutions, or to prove that there are NONE, it can feel like too much pressure. What if the Friday Fave inadvertently leaves one out at first? Much better to begin by considering a small number of solutions, or wondering whether any exist at all. Save generality for later.

And that, friends, is what Compound Inequalities on the Number Line is all about. Indicate a point on the number line that is greater than -3. That’s your first task.

Then do another, and another. And now what would it look like if you could see all of your classmates’ points? It might look something like this.

But that’s still not ALL points. Don’t worry. Students get there.

It’s just that generality is the stuff theorems are made, but examples are the stuff generality is made of. So we start there. Slowly formalizing students’ informal ideas—that’s the stuff the Friday Fave is made of.

And while you’re thinking about generality, maybe take a peek at these other activities that build the general from the specific.

What Comes Next?

Game, Set, Flat

Sector Area