Unusually early springlike weather in large parts of the country has the
Friday Fave looking ahead to swimming pool season, and nothing goes with
swimming pools quite as well as algebra.
The Pool Border Problem
is a classic for a reason. There are many ways to count the tiles on the
border of a square pool. Different counting methods generate different
algebraic expressions, and we can check the equivalence of these expressions
by verifying that each will correctly count the number of tiles bordering an n
by n pool.
This new Desmos version adds iterative feedback. If you think the expression 3n+8 describes the number of tiles
bordering an n by n pool, we’ll let you see whether that
works for all values of n.
The expressions students write impact what happens on the screen, and the
activity turns a wide range of student input into meaningful feedback. The
expressions collect in the dashboard for the teacher to use for creating
classroom conversations.
Dive on in, the water’s fine, and
the pool’s border
is perfectly tiled!
The Des-Blog is home to the Friday Fave, which is a weekly post about some of
the favorite activities amongst the Desmos Teaching Faculty. This week we
asked the Desmos Fellows to share some of their favorite activities, and to
tell how these activities help students learn math.
Which One Doesn’t Belong?
First off, if you’ve never heard of the WODB puzzles, head
here for a brief introduction. Two of
our Fellows Fave submissions this week included a WODB task.
Shelley Carranza found her most
recent favorite after a visit to
Paul Jorgen’s class, where he
displayed the above
Desmos graph and
asked students to find a reason why each of the parabolas didn’t belong.
Students argued their positions using graphs and expressions, and built off of
each others’ thinking as they reviewed concepts and vocabulary from the
unit.
Allison Krasnow also shared
a
WODB activity
that she recently used with 4th grade students. Allison used the dashboard to
chose slides where the majority of the class had chosen 1 image and no one had
chosen 2 or 3 of the images. She then challenged students to come up with a
mathematical reason for why the other images didn’t belong. Allison also
supported students in developing academic language by having them discuss and
then rewrite their explanation using sentence frames.
A Day on the Town with the Bugs
Bob Lochel shared
this
delightful introduction to parametric functions where students explore whether
or not bugs traveling along intersecting paths will ever meet, and consider
why this is so.
A Leaky Cup
Anna Scholl’s students
collected data about the water level in a
A Leaky Cup
and used Desmos to build a model to predict when the cup would be empty.
Anna’s goal was to have students build a model using regression. Before
students reached that part of the lesson Anna found that they were applying
their knowledge of function transformations (a theme of the course) to try to
fit a model. Groups then compared models and strategies using the dashboard
before learning about regression.
If you’ve been following along with our work in the fellowship program you
know that Marbleslides has been a
recurring favorite, not to be left out of this Fellows’ Fave edition. We’ll leave you with this
recent lunchtime conversation between Paul Jorgens and a student of his who
had recently been introduced to Marbleslides:
“Mr. Jorgens. You have to tell me how to stop them!”
The structure should be familiar. We get you started with an estimation task,
then we get you to use algebra to increase precision and efficiency.
We ask students to imagine lines in their minds, and we ask them to write
equations for the lines they picture. But we don’t tell them how to do
it. Maybe slope-intercept form works best for you on screen 4, and standard
form makes sense on screen 8, or vice versa. Maybe one student attends to the
direction the airplane is pointing, and another notices the slope of the edges
of the runway.
This is all fine, all supported, and is fodder for classroom conversations
about equations of lines. Students practice, but not in a
do it this way because I said so kind of way; they practice in a
how can I get better at this fun task? kind of way. When students are
wrong, the runway lights signal the plane to turn around, and their plane
doesn’t land. Of course they get to try again.
