Des-blog

The Friday Fave is a big fan of tasks with more than one right answer. If the Fave asks Which One Doesn’t Belong? you’d better believe each of the options can be a right answer. If the Fave asks How do you know? well, it’s because the Fave really doesn’t know how you know, but really would like to, and there’s more than one right way of knowing.

So it is with the newest Desmos activity, Coin Capture. The challenge is write equations for lines that go through the coins, capturing them along the way.

In the introductory challenge, you can get them all with one line. But that’s just Desmos getting you started. As the screen numbers increase, so does the complexity of the challenge. Here are four solutions to the challenge on screen 3.

While we keep track of the number of lines you used, that’s not the only way to describe these. What kinds of thinking is behind each of the solutions above? Which is most interesting? Which one doesn’t belong? Posing the task is straightforward, but there are many right answers that vary in interesting ways. That’s the kind of thing that qualifies an activity for the Friday Fave.

Also there’s a challenge creator.

Now, while you’re thinking about coins and/or targets in the coordinate plane, here are three more delightful activities:

Penny Circle

Marbleslides: Lines

Mini Golf Marbleslides

The bell has rung, your classmates have settled into their seats, and the teacher stands at the front of the class next to a chalkboard and overhead projector, ready to deliver today’s lesson.

“All right, everyone,” she announces while gesturing towards the blank chalkboard, “please solve these equations using your handheld calculators– the ones with the broken displays.”

This assignment may sound outlandish, but students with visual impairments face similar challenges using technology in the math classroom every day. New technologies have the potential to empower students, but without care, they may instead present insurmountable barriers to access.

Our mission at Desmos is to help every student learn math and love learning math. Not some students. Every student. With that in mind, we introduced improvements to the calculator to ensure students who are blind or visually impaired have the same opportunities as their peers to discover the joy of learning math. Thanks to technologies like screen readers (which provide spoken or Braille feedback to mainstream computers, tablets, and phones), people who are blind or low vision have the opportunity to use the exact same programs as their peers. Naturally, it made sense to extend the utility of our existing calculator offerings to include screen reader support.

More recently, we extended this functionality to our activities, modifying them to meet the highest possible standard of accessibility our tools can offer. You can find all the screen-reader friendly activities here, or by visiting teacher.desmos.com and typing “screen reader” or “accessible” into the search bar.

So how did we make this happen? Many of the components of a Desmos activity have built in accessibility, meaning that you can interact with them via the keyboard and a screen reader. We added to this accessibility by adding narrations to graph screens to help students learn about a graph, interact with it, and receive feedback.

In this screen from Match My Line, when a student submits a correct equation, the screen reader tells them the number of lines that have been correctly graphed.

Students can also use the audio trace functionality from the graphing calculator to learn more about a graph within an activity.

Interested in learning more about Desmos accessibility? Get started at learn.desmos.com/accessibility, then dive deeper by watching our Introduction to the Desmos Graphing Calculator and Accessibility Tools webinar and heading to www.desmos.com/accessibility.

We’d love to hear your feedback! Let us know what you think at accessibility@desmos.com.

The Friday Fave would like to tel youl about a very handy calculator feature, and then invite you to do some math.

The feature first.

Imagine you’ve got a set of points, and you’ve named them A, B, C, and D. You probably want to make a quadrilateral from those four points, and it used to be difficult but now it is easy.

What sort of thing is a quadrilateral? Why, it’s a polygon. So you just tell the Desmos calculator that you want to make a polygon with those four points, and boom!

Alternatively, you may have specified the x-coordinates of your quadrilateral with a list, and the y-coordinates with another. Do not ask the Fave how the calculator can interpret two lists just as easily as it can interpret four points, but it can.

This second version of polygon is especially handy because you can operate on a list (you cannot yet operate on points except by dragging them around). So now let’s do a little math together, shall we?

What do you suppose our polygon will look like if we type polygon(X,Y-4)? Click through on the expression to find out.

What about polygon(2X,Y)?

And finally, what will polygon(Y,X) look like?

Bonus question: What transformation do you need to apply to make our polygon no longer be a kite, and how might we express that transformation algebraically?

Now that the Fave has you thinking about polygons, here are some delightful ways to extend your thinking…

Polygraph: Advanced Quadrilaterals

Polygraph: Basic Quadrilaterals

Polygraph: Hexagons

Polygraph: Hexagons, Part 2