In another video,
we carefully looked at how to
deconstruct a three-dimensional figure
where the bases were polygons.
I want to take a moment to deconstruct a
cylinder.
Cylinders present extra problems for our
kids.  First of all, it's hard for them to
understand
how to deconstruct this because
while our polygonal prisms
and pyramids had sides that were either
triangles or parallelograms and
rectangles,
a cylinder doesn't.  So how are we going
to deconstruct this?
Well, when I look at a cylinder, we're
going to go back to what we said before.
What are the bases for a cylinder?
We can see that there are two bases.
Notice how they are also
congruent and parallel to each other
just like with our prisms.
So as students are deconstructing this,
we want them to look at
the two bases are circles.
So let's have them write that down.  Now
for a cylinder, we have
one base
and we have a second base remembering
that they're parallel
and congruent.  Now the next piece that
we've got to figure out
is this lateral surface and for a
cylinder
it's curved.
If you have the manipulatives to look at
the net.
it's helpful for students to be able
to unfold the figure and what we notice
is: it's a rectangle.  If you do not have
manipulatives that have nets that can be
pulled out of them
because these are kind of special, you
can always use an index card
that you've rolled up and you've
unrolled up and you use tape so that you
can show students
that the rectangle is the lateral
surface of the cylinder.
So that means
that on our drawing where we've
deconstructed it,
we have a rectangular shape.  Now what's
difficult for students is for them to
understand:
how do we label this?  Well
when I look at the shape of the cylinder
and we roll the net back up,
we can see that the rectangle is around
the outside of the circle.
And we might want to ask students how do
we measure the distance
around the outside of that circle?  We
measure the distance
around the outside of the circle
using circumference.
And remember to ask students how do we
calculate circumference?
That's two pi radius.
Now we have one more measure to make.  How
far is it
from one base to another base
in our rectangle?  That is
the height of this cylinder.  It connects
one base
to the other base and that is our height.
So this is how we can help students
deconstruct a cylinder.
