Vertical Value: Part 2
By Cathy Yenca, posted February 15, 2016 –
1 of this post, I shared a task that helped students understand perimeter,
area, and their independence. Although in the past I used the task with seventh-
grade students, concepts such as perimeter and area are typically addressed
with third graders by today’s standards. However, I propose that a
well-designed task has “vertical value” when it spans multiple grade levels and
when it is used as a tool to cull student misconceptions.
recently transformed the aforementioned perimeter and area task into a digital
and more open-ended format using Desmos.
Desmos has several nifty tools that equip teachers to revamp lessons, placing
the roles of questioner and answerer on the students. In this instance, I used Desmos Polygraph, which
provides a mathematical take on a face-guessing board game that many of us
played in our younger years. Playing Polygraph is ideal in the classroom with
one device for every student. After students play a practice round of
face-guessing against the computer, they are provided with 16 digital “math cards,”
are randomly paired up, and are assigned roles in which they either ask or
Desmos Polygraph for the perimeter and area task took some planning on my
part. I wanted students to initially see 16 seemingly random rectangles. However,
there was nothing random about the dimensions for each rectangle I chose. The
first few rectangles were inspired by the paper-and-pencil version of this
making a plan, I created the Custom
Polygraph activity for my students. Having a successful Polygraph match
depends on the quality of student questioning and their use of academic
vocabulary. From the teacher dashboard, student questions can be viewed in real
time as well as after the game. It’s a treat to watch students succeed after a
failed match when better questions and vocabulary are used!
recently used this Polygraph with sixth-grade and seventh-grade students who
are taking an eighth-grade math course. Why? Because I know we’re heading
toward geometry units that address surface area and volume, so understanding
the concepts of perimeter and area are key. Could this task be used
successfully with multiple grade levels of students? In the comment section
below, I’d love to hear from teachers who use this Polygraph regarding the
grade-level of students, as well as a few of your favorite student questions. I’m
curious about the vocabulary that students use at different grade levels when
playing the same Polygraph, and hence, the “vertical value” of the activity.
are a few of my favorite questions from my own students when they played Polygraph:
Rectangles. Note the students didn’t mention perimeter or area explicitly at
all! We had just finished a unit studying proportional and nonproportional
linear functions, so it appears that timing may have shaped their questions. As
we approach geometry units this spring, I plan to let them play again. I wonder
how their questions might change?
Yenca, firstname.lastname@example.org, is a math
teacher in Texas. She tweets at @mathycathy and blogs about teaching
mathematics in a one-to-one iPad classroom at mathycathy.com/blog.
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