Des-blog

While the Fave frequently refers to the Desmos Activity Building Code while going about the daily work, the Fave has been thinking a lot recently about offering students interesting ways to be right.

Last week, the Fave featured Challenge Creator, which is chock full of interesting ways to be correct. But there are plenty of other structures in place in a wide range of activities for giving students this opportunity.

For example, we frequently ask students to decide which of two (or more) responses is correct, as in this example from Land the Plane.

A typical class will have students using the y-intercept, students using the slope, and students using both to reason about this task. These students will use formal and informal language, which then provides a launching point for interesting conversation in a classroom even if everyone is right. Some typical responses might include:

• Roman because 8 makes more sense as the starting point
  
• Roman is right, because the equation should have a negative slope and a positive y intercept.
  
• Roman. You’re going down 2 , so the slope is -2
  
• Roman is correct, because his coefficient is negative and so is the slope of the line on the graph.
  

Four correct answers in an interesting mix of ideas and words; all at a teacher’s fingertips in the dashboard.

We frequently present examples and non-examples in order to introduce a new mathematical idea to students. In Marcellus the Giant, we show scale giants and non-scale giants and then ask students to make some conjectures about what makes a giant a scale giant.

The collection of observations in a typical classroom will include angles, side lengths, some generalized ideas about doubling or tripling of lengths. There will be informal language about what the giant “looks like”. None of these will be a full and complete definition of the idea of similarity, but each of them contains a kernel of truth on which the activity and subsequent instruction can build.

A third example of offering interesting ways to be right is a favorite of the Fave: Which One Doesn’t Belong?

Because each of the four options has at least one reason to be the one that doesn’t belong, and also because students are creative people with clever ideas, you’ll get lots of interesting right answers to a well-designed Which One Doesn’t Belong? set such as the one in Inequalities on the Number Line.

Tapping into the minds of students is fascinating work, and it’s what makes offering students interesting ways to be right this week’s Friday Fave.

The Friday Fave—like the rest of the Desmos team—is excited about supporting math classrooms as social and creative spaces. One of our favorite tools for doing so is Challenge Creator; in which students build challenges, which go into a class gallery for their classmates to solve.

When we built Challenge Creator, we expected that students would be motivated to work on tasks their peers had designed. We also expected that they would be fired up to think hard about designing challenging tasks for their classmates. What we didn’t expect—but which turns out to be true—is that we can count on students to make a wide range of mathematically important examples.

For example, in our classroom testing we found that the small sample below is typical of a dashboard in Land the Plane, where you need to write an equation that describes a flight path for the plane to send it down the middle of the runway.

Students make challenges with positive and negative slopes, with points that are on and off the axes, and they make challenges with horizontal and vertical runways.

Knowing that students consistently vary the task in these ways means we at Desmos can build a shorter activity. We don’t need to build every important variation into the activity because the kids will do that! And then they’ll eagerly work on these challenges because their classmates designed them.

Social, creative mathematics isn’t just more engaging; it can also be more challenging and rich. That’s why Challenge Creator—and two activities with Challenge Creator built in—are this week’s Friday Fave. Go give Land the Plane and Pomegraphit a spin, and let us know what challenges your students dream up for each other!

And don’t forget another tool for social and creative mathematical work: Polygraph. Here are two of the Fave’s fave Polygraphs (but don’t limit yourself to these; we’ve got dozens of them!):

Polygraph: Hexagons

Polygraph: Parabolas

The Friday Fave has been watching the Olympics, which on broadcast television in the United States means 1000 rounds of figure skating, plus cutaways to Lindsey Vonn, and to other Americans winning at other things.

One of those other things that Americans have won at, and so the Fave has been able to watch on network television, is the half-pipe. This led to the Fave and the Fave’s daugther (Lil Fave?) wondering how they make half pipes.

Here’s how:

That thing is called the Pipe Monster, for obvious reasons. Credit and thanks to Zaugg America for the image.

Once you know how the half pipe is made, you’re likely to get curious about related things. Like how do they make the pile of snow for the Pipe Monster to carve? How fast does the Pipe Monster drive down the pipe? How much snow are we talking about here?!?!?

This is the sort of question that Andrew Stadel has been working hard to help people get better at both asking and answering. If you’re not familiar with Estimation 180, get yourself over there right away to find estimation tasks for each of the 180 days of the school year, in sets of increasing difficulty and sophistication.

All of which brings us around to this week’s Friday Fave, which is an Estimation 180/Desmos mashup that Mr. Stadel has been working on. He used Activity Builder to build a richer environment for his estimation tasks, including dynamic visual representations and a robust teacher dashboard for collecting and sharing student responses. He’d like you to use what he built.

It’s really exciting to see teachers putting Des-tools to work in ways we could not have imagined on our own.

But don’t take the Fave’s word for it. Head on over to Estimation 180 and check it out now.