Des-blog

The Friday Fave is feeling nostalgic this holiday season, and is thinking back to the activity that started it all.

Desmos released Penny Circle a bit more than four years ago, in July 2013—our first activity. Penny Circle was well received by students, teachers, and curriculum aficionados alike. Embedding the Desmos graphing calculator into an online modeling activity that runs on any web browser, and supplementing it with tools for collecting and sharing data, and for teachers to see student work in real time gave teachers and students a new kind of mathematical power.

But the years did not treat the underlying technology kindly. Browsers evolved. Our ideas about how to use technology to support teachers’ work evolved.

All of which is why we’ve rebuilt Penny Circle using the Activity Builder platform. What originally took months to build took us a couple of weeks to rebuild from scratch inside of Activity Builder, a testament to the power of this platform.

So now is the time, fellow citizens of the math-learning internet! If you’ve not used Penny Circle before, it’s waiting for you here. If you used it a while back and it was showing its age technologically, try the updated form!

When your students are arguing over whether and why their data is linear, quadratic, or exponential you’ll be glad you did!

And while you’re thinking about modeling activities, here are a few more favorites the Fave recommends.

Charge!

Mocha Modeling: Starbucks Locations

Card Sort: Modeling

The Fave is feeling lucky, which is why Chance Experiments is this week’s Friday Fave.

Your students analyze a spinner, and they spin it virtually. But then they’ll design a spinner and test that out.

What does it mean for something to be “almost impossible” or “almost certain”? Does “almost impossible” differ from “unlikely”? How exactly? These are some of the big questions of probability and statistics–questions that Chance Encounters seeks to raise in your classroom.

And along the way, many other important questions will probably surface. How should I subdivide the spinner if I want to get exactly one red in 36 spins? Will a fair spinner always give 50% red? Will an unfair spinner ever give 50% red? Whether you are feeling lucky or not, these questions matter. Linger on them in your classroom.

And if spinners have you thinking about circles, here are three circle-based activities for you and your students.

Polygraph: Conics

Circle Patterns

Lawnmower Math

The Friday Fave has featured Pomegraphit before, but it’s just so much fun! Plus, it’s pomegranate season (no joke!)

One of the more important things that mathematicians do is pay attention to a single attribute at a time. How is 2 like 10? They’re both even. How is 2 different from 10? 2 is prime; 10 is composite. So is 2 like 10 or different from it? It depends on the attribute you care about.

In math when two things are the same, we say they are equivalent, and the way they are the same is an equivalence relation.

Fractions depend on equivalence. Similarity and congruence are kinds of equivalence. Abstract algebra depends on equivalence.

In Pomegraphit, we ask students to consider one attribute at a time of various fruits. First up is tastiness.

Then comes difficulty.

Next, students place their fruits on coordinate axes where one axis is tastiness and the other is difficulty. They argue (another important mathematical practice!) about the placement, and they decide which fruit is most controversial in their class.

So go work on mathematical abstraction and equivalence with your students. Then maybe you’ll be inspired to do the same thing with other familiar things in your lives—school lunches, perhaps. Or writing implements (How are gel pens like #2 pencils? How are they different?. Or….

And while you’re thinking about variables with your students, here are three more favorite activities for working with meaningful variables:

Lawnmower Math

Central Park

Pool Border Problem