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…
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.
Michael’s sequels are additional questions about a context within a lesson.
And it is also worth thinking about when the next lesson ought to be a sequel
to the current one.
Consider the case of
Polygraph: Lines.
Students play an engaging game that requires them to notice and discuss
features of graphed lines for which they may not yet have words. As teacher,
you introduce some of those words as the game moves along. But even if you
don’t play Polygraph again, the game itself has created a rich space for
asking additional questions, and for moving students further along in their
mathematical journeys.
That’s where
Polygraph: Lines, Part 2
comes in. In this sequel to the original Polygraph, students encounter
increasing, decreasing, steepness, and
intercepts in the context of thinking about situations that could arise
in playing Polygraph.
Students sketch, write, and see each others’ responses in the service of
better understanding the algebra of lines. All of it made possible by the
original context of Polygraph. That’s what makes
Polygraph: Lines, Part 2
this week’s Friday Fave.
