Des-blog

Des-Patterns may be the only Desmos activity designed with physical manipulatives (so far).

Whether you’re a modern-day quilter, a 17th-century French mathematician, or a five-year old at the Minnesota State Fair, the allure of a square—cut on the diagonal and colored—is irresistible.

In Des-Patterns, students manipulate electronic versions of these tiles and use the rules of algebra to do so.

First they translate.

They they reflect.

In the end, students have developed their spatial visualization skills, gotten an introduction to coordinate rules for simple transformations in the plane, and built their own designs for their classmates to add on to.

That’s a lot of mathy, creative goodness to derive from the humble square. Which is what makes Des-Patterns this week’s Friday Fave.

While you’re thinking about the plane, here are three more activities having to do with Cartesian coordinates…

Battle Boats

Mini-Golf Marbleslides

Polygraph: Points

Next week brings a holiday to the US—the home of the Fave—so the Friday Fave is taking next week off.

In the meantime, amuse yourself with a little gem that aims to bridge the gap between informal language and formal mathematical representations. At least, at most and the like are notoriously challenging for algebra students to interpret in symbols, even when they can act on these ideas as they appear in everyday life.

(Thanks to Matt Salomone for the fabulous tweet and image.)

The activity the Fave is speaking of is Absolute Value Inequalities on the Number Line. One of a suite of similarly structured activities, this one has students place points on the number line according to given constraints.

We ask students to predict what everyone’s points will look like in the aggregate. We show them what it really looks like, and ask them to verbalize a comparison between the two. We support students in translating these ideas into formal notation. Distance is the absolute value of the difference of the numbers makes more sense when you’ve already been thinking about the distance between numbers on a number line.

So go ahead and play around. The Fave will be back in two weeks’ time.

And while you’re thinking about lines, here are a few more activities on the theme.

Point Collector

Put the Point on the Line

Graphing Stories

The Friday Fave enjoyed a splendid Zero Derivative of Day Length Day this week, and hopes that you did too. In the Fave’s part of the world, the days are now getting shorter. Maybe in yours they’re getting longer. Either way, we all have Zero Derivative Day in common.

That got the Friday Fave thinking about daylight relationships more broadly, which leads the Fave to remind you of the activity Burning Daylight—this week’s Friday Fave.

If you are a math teacher with any affinity for applications or modeling at all (and that should be pretty close to everybody reading this right now), you probably see many beautiful things to notice in the following image, which compares Miami, Florida and Fairbanks, Alaska. Which is which?

In Burning Daylight, this task launches students into the real question, which is “Which city gets more total daylight?” Calculus is a useful tool for answering that question, but not an essential one.

Students model with trig functions; they develop their own ways of answering that big question, and then we ask a terrific question to get them thinking more deeply about the connections between the math and the reality.

Barrow, Alaska is the northernmost city in the United States. What does the graph of daylight hours look like for Barrow?

While you’re thinking about trig functions, here are a few other opportunities to play with sines, cosines, and all the rest:

Marbleslides: Periodics

Polygraph: Sinusoids

Trigonometric Graphing