Des-blog

What will you build today?

At Desmos, we hope you’ll build an awesome online lesson that will engage, challenge, and enlighten your students. So really, we hope you’ll build young minds.

Activity Builder is a tool for helping you do just that. Whether you build something simple like a check for understanding to use in the middle of your lesson (Everybody graph a parabola with the vertex at (1,1)!) or a multi-step activity with multiple interactive graphs and rich questions, Activity Builder allows you and your students to move beyond the constraints of the paper handout.

You can see your students’ graphs on your dashboard—either individually or collectively—while they’re working. You can see students’ answers to the questions you ask and keep track of their progress through the activity.

Click on through to see how it works and get building.

See Match My Line and Match My Parabola for examples that you can use in your own classroom. Hopefully they’ll inspire you to build your own and share your creation with the world.

As soon as we released Polygraph, teachers asked for two things:

(1) Quadrilaterals, and

(2) The ability to make their own.

Quadrilaterals

This was the easy part. Today we give you two (TWO!) versions of Polygraph: Quadrilaterals. There is the basic version and the advanced one. You and your students can play either one, or both. If your goal is to lay the groundwork for the standard hierarchy of quadrilaterals, Polygraph: Basic Quadrilaterals is a great place to start. If your goal is to challenge your students to notice and describe subtle but important differences among geometric figures, Polygraph: Advanced Quadrilaterals is right in your wheelhouse.

Enjoy.

Building your own Polygraph

Given that one of the Desmos guiding principles is Trust Teachers, we knew what was the right thing to do when teachers asked to build their own Polygraph versions.

And now we have done it, so you can have at it. Welcome to Custom Polygraph.

You pick a name for your version of Polygraph. You make 16 graphs using our familiar graphing calculator interface. You save it. You use it in class. Easy peasy.

Anything you can put in the usual Desmos graphing calculator interface you can put in a Polygraph example: graphs, images, points, etc. Want to make your own polygons? Graph line segments and turn off the axes (or leave them on: coordinate geometry, anyone?)

You can tweak your custom Polygraph before or after you use it in class—it’s totally editable.

You can send your friends the link and they’ll be able to use it, too. (Don’t worry—they can’t edit yours; they’ll have to make their own if they want to build on your ideas.)

Click here to get started.

Words are fun.

Words are powerful.

Vocabulary lists—for most of us—are not so much fun.

Whether it is French class (-ir verbs) or Geometry (types of triangles), most of us have memories of long lists of words out of context and feeling as though we have no hope of remembering them all, nor any purpose for doing so.

And we also know well the pleasure of having just the right word handy at just the right time—what the French call le mot juste.

We have designed Polygraph to foster the pleasure and the power of words without the drudgery of the lists.

Here is how it works.

Each student has a partner. One student is the picker, the other is the guesser.

The picker picks one thing from a set of things. Depending on the version the teacher chooses, these things might be graphs of lines, or of parabolas, or of rational functions. They might even be hexagons!

The guesser sees the same things on her screen that the picker sees on his, but scrambled to prevent location being a clue.

Here the picker has selected a graph and will soon see the guesser’s questions on the screen.

The guesser types a question. The picker can answer yes, no or I don’t know. A well written question helps the guesser to eliminate one or more options. Desmos provides the tools to keep track of questions and eliminated options.

In the next task, we ask students to analyze questions like those the class asked. We ask students, Given these two hexagons (or lines or parabolas or…), which of these questions would be the best one to ask? and The answer to this question wasn’t helpful—how can you improve the question?

Picking and guessing create the need for words—students want to describe the subtle differences they see in the mathematical objects in front of them. Sharing questions provides opportunities to spread words among students—students read how their classmates have described these differences. Whole class conversation led by the teacher helps to formalize and cement the vocabulary—the teacher can introduce the standard words that describe these same differences.

Beth Herbel-Eisenmann has studied the development of informal vocabulary in classrooms. She has described how formal mathematics vocabulary can meaningfully arise from less formal vocabulary that students use to describe mathematical objects (e.g. dented hexagons become concave; slanty-up lines have positive slope, etc.)

With Polygraph, Desmos provides tools for doing this. Words should result from a need to describe our world—this is where they gain their power. There is no better time than now to develop your students’ power of expression, so click through and set up a game of Polygraph tout de suite!

(Shout out to Brenna Magnuson, Jennifer Carlson, Mona Yusuf, Ruth Pieper and Brandon Schwab—all current or former elementary education students at Normandale Community College who helped to design the hexagons in this lesson.)