Des-blog

The Friday Fave spent three of the last seven days in the company of large numbers of classroom teachers taking time to connect with each other, to deepen their mathematical knowledge, and to enrich their teaching practice.

Two of those days were with the third cohort of Desmos Fellows at Desmos HQ in San Francisco, and the third of them was with in Cleveland, Ohio at a pre-conference event for Twitter Math Camp.

These were days filled with people and work that embodied and enacted the phrase lifelong learning. Consider the following questions that are but a sample of those the Fave encountered at these events:

• How can we hack Activity Builder so that the calculator plots in the complex plane a complex number that a student types in the math input?
  
• How can we solve this problem using only middle school math, not anything you might expect to learn in high school?
• If you could have secondary teachers understand one thing about elementary school math learning, what would that be?
• What are some different ways of thinking about and representing proportionality?

These questions the Fave encountered in the last week—and more…so many more—are evidence of the dedication and care with which teachers approach their work. And that’s why the professionalism of teachers is this week’s Friday Fave.

A while back, we were very proud of our system for placing labels. “Works every time!” we trumpeted on our blog. We are still proud of this system, and it works every time if you’re using labels in the ways we had in mind back then.

But our users were determined to use labels in new and innovative ways for which that system didn’t work very well at all. Sometimes when you’re making a graph, you want to put a label in a particular place and not have it budge.

Now you can.

Once you have a label, you can click the wrench to adjust its location. You might want your label to the left, or the right, or above the point. You can do that, and you can change its size while you’re in there.

That’s what makes new, improved label placement this week’s Friday Fave.

Now here are a few activities that make use of labels…

Click Battle

Sugar Sugar

Predicting Movie Ticket Prices

Integer Game

This week’s Friday Fave is a feature in Desmos Geometry: Transformations.

In order to appreciate the transformations tools, you’ll need to think of a transformation as a function. A function has inputs and outputs, where the set of all possible inputs is the domain, and the set of all possible outputs is the range.

Functions come in families. If you’re thinking about algebra, you can talk about quadratic functions in general, but to find an output for a given input, you’ll need to specify which quadratic function you’re using—perhaps by specifying coefficients for your squared, linear, and constant terms.

That’s how transformations work in Desmos Geometry. Say you want to reflect a triangle. You’ll first need to specify the reflection, you’ll need to specify a line. Once you’ve defined the reflection, geometric objects are your domain. Select anything you’ve constructed, and apply the transformation to see its output.

Rotations work the same way. Specifying a rotation requires two things: a point around which to rotate, and a degree measure for the rotation. If you apply the transformation more than once, each output becomes the next input.

Once you’ve begun thinking about transformations as functions, you may find yourself using these simple objects to make complicated and beautiful things, such as those below (click through on each heading to get to a version you can play with). That’s what makes Desmos Geometry transformations this week’s Friday Fave.

Square tiling

Kaleidoscope

Triangle tessellation

Hexagons

While you’re thinking about transformations, here are some terrific activities using transformations in geometry and algebra.

Transformation Golf: Rigid Motions

Marbleslides: Periodics

Function Transformations: Practice with Symbols

Card Sort: Transformations