Des-blog

In Marcellus the Giant, students learn what it means for one image to be a “scale” replica of another. They learn how to use scale to solve for missing dimensions in a proportional relationship. They also learn how scale relationships are represented in a graph.

There are three reasons we wanted to bring this activity to your attention today.

First

Marcellus the Giant is the kind of activity that would have taken us months to build a year ago. Our new Computation Layer let Eli Luberoff and Dan Meyer build it in a couple of weeks. We’re learning how to make better activities faster!

Second

When we offer students explicit instruction, our building code recommends: “Keep expository screens short, focused, and connected to existing student thinking.”

It’s hard for print curricula to connect to existing student thinking. Those pages may have been printed miles away from the student’s thinking and years earlier. They’re static.

In our case, we ask students to pick their own scale factor.

Then we ask them to click and drag and try to create a scale giant on intuition alone. (“Ask for informal analysis before formal analysis.”)

Then we teach students about proportional relationships by referring to the difference between their scale factor and the giant they created.

You made Marcellus 3.4 times as tall as Dan but you dragged Marcellus’s mouth to be 6 times wider than Dan’s mouth. A proportional giant would have the same multiple for both.

Our hypothesis is that students will find this instruction more educational and interesting than the kind of instruction that starts explaining without any kind of reference to what the student has done or already knows.

That’s possible in a digital environment like our Activity Builder. I don’t know how we’d do this on paper.

Third

Marcellus the Giant allows us to connect math back to the world in a way that print curricula can’t.

Typically, math textbooks offers students some glimpse of the world – two trains traveling towards each other, for example – and then asks them to represent that world mathematically. The curriculum asks students to turn that mathematical representation into other mathematical representations – for instance a table into a graph, or a graph into an equation – but it rarely lets students turn that math back into the world.

If students change their equation, the world doesn’t then change to match. If the student changes the slope of the graph, the world doesn’t change with it. It’s really, really difficult for print curriculum to offer that kind of dynamic representation.

But we can. When students change the graph, we change their giant.

There is lots of evidence that connecting representations helps students understand the representations themselves. Everyone tries to connect the mathematical representations to each other. Desmos is trying to connect those representations back to the world.

The Friday Fave is delighted to bring you a trio of activities this week, inspired by Stefan Fritz, and edited with a good deal of love by Desmos.

In Inequalities on the Number Line, we start simply and informally. Move the point to show a number less than three. Any number less than three is good, although we encourage students to pick a number that their classmates won’t.

We’re building towards asking them about all numbers that are less than three, of course. But the formalities of the symbolic and graphical representations of this idea can wait because we want to build on what they know. One number, then three numbers, then all of the numbers your classmates picked.

We build on this representation in order to introduce the shaded number line, and even the open dot for strict inequalities.

Another quality making this set of activities a fave is that students do many kinds of things in each activity. They plot points. They engage in card sorts. They interpret number line representations as inequalities. They look for similarities and differences among a set of inequalities.

These activities represent some of our best thinking about the interactions between students’ informal mathematical ideas and the formal representations they need to learn, and about using electronic tools to engage students in meaningful mathematical activity.

But don’t take the Friday Fave’s word for it. Here are links to the whole set:

Inequalities on the Number Line

Compound Inequalities on the Number Line

Absolute Value Inequalities on the Number Line

There are two reasons why Point Collector is this week’s Friday Fave:

First, it combines practice with strategy.

Second, it’s the first lesson we’ve released with our “Computation Layer” technology.

Practice

Practice is an important part of a math education. Some practice is totally dreary, though. (You know what we’re talking about.) Our preferred form of practice has students repeating the same operations in the context of some larger strategy.

For example, in Point Collector, your students will practice writing lots of inequalities, but always in the context of the goal of capturing the highest score possible.

Give it a try.

Computation Layer

Point Collector is a more sophisticated activity than you’ve seen in the Friday Fave for a long while. Look at it! What you type in the input is plotted in the graph and the points you collect in the graph are reported in the note, along with the news that you have the highest score or that someone else in your class has an even high score, giving you fuel for continued practice.

Those connections and representations are enabled by a Computation Layer that lives on top of the activity. It looks like this:

Wild, right?!

The upside is that these internal tools will allow us to make more sophisticated activities and release them more quickly than ever before. Watch this space for more.