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:
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
(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.
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.