WEBVTT

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[Music]

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Kathy Huggins: My
name is Kathy Huggins,

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and I teach seventh-grade math
at the Papillion Junior High,

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part of the Papillion-La
Vista School District.

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Huggins: Yesterday,

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we talked about how you
can have a rectangle

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with a one set perimeter
in different areas, right,

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and vice versa--a
rectangle with one area

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with different perimeters,
so we are going to build

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on that task today

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with something called
the Fencing Task.

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Huggins: I chose the task

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because we have been studying
area and perimeter lately,

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and I wanted them to be
able to apply those skills.

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Another major goal is just
for them to have experience

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with problem solving,

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struggling with the
problem a little bit,

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and exploring a variety of
different ways to approach it.

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Huggins (to class): The 24
feet of fence makes up all

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but one side of the pen

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because one side
of the pen is...

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Student: The school.

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Huggins (to class):
The school, okay,

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and it's a normal flat wall of
the school, but you don't have

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to put fence up against that
wall because rabbits can't get

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over the school, so they're
fenced in on that one side

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by the building and they need
fencing elsewhere however you

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decide to do that.

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Huggins: The goal for the
lesson was twofold: One,

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a general process
goal of an opportunity

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to do some problem
solving, which we seem

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to never have enough of; the
other was the content goal

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of looking at area and
perimeter and the relationship

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between the two, where one
of those, in this case,

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the perimeter or the
amount of fence, is fixed.

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Student 1: Ten,
Ten, and then four.

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Ten, ten...

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Student 2: Five, five, and 14.

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You know I had the right idea.

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Huggins: The importance
of a task of this type is

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that it gives context
to some of the things

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that we have been learning
about--area and perimeter.

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Geometry in and of itself
is rich contextually,

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but they really need a
situation to be able to latch

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on to, and I think that this
particular situation was

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something that the
students understood

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and were able to relate to.

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Student 3: I'm going to
write 24 on all of these.

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We never did 11.

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What did you get for 11?

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Student 4: 71.5.

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Student 3: What was 2?

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Student 4: Oh, it was 6.5.

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Student 3: Wait,
because 11 plus 11 is 22.

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Student 5: Unless
you did 6.5 plus 6.5.

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Student 4: That's what I did.
6.5 plus 6.5.

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Student 5: He does 6.5 plus 6.5, 
and then he adds the 11.

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Huggins: Within an individual
problem, what I will do

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when we process the problem
is I will have students

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who have done it
different ways share those

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different methods.

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To share their strategies,
I definitely want

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to take the time to explore
what the different kids are

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coming up with and then
plan what order I want them

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to present them in.

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What we will often
do when we're sharing

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out strategies is I will
try to get a student

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to demonstrate what seems to
be the most common response.

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This time, the 8x8 pen was
definitely the one I saw

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in almost every group

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within the first three
minutes of the task.

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And so we started
with that one

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when we shared out as well.

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And then what you want to
do is go in the directions

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that different students had
proceeded in and make sure

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that you get all

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of the possible
responses and strategies.

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They always come
up with something

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that I had not expected.

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In this task today
the triangle,

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trying the triangle
solution, having the same area

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as the rectangle--that was
one possible direction

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that I had not predicted
but was very excited to see

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that the kids came
up with on their own.

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The next step is
to try to build

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on that generalizing idea.

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That is, they were
able to come

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up with several
different strategies

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of solving this problem
and maximizing that area

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for the pen of a
given fence link.

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But now we want
to try to get them

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to generalize how
they could do

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that for any number
of feet of fencing.

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What I also want them to
be able to do is realize

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that while the fence
length is fixed,

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the perimeter itself is
not because the amount

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of feet along the side
of the school building

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that they are using
does vary depending

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on the shape they use.

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I think problem-solving
skills are super important

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for students to develop
because the kinds of problems

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that they are going to
face haven't even been

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invented yet.

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If they can develop the skills
that they need to be able

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to approach, tackle,
persevere, and look back

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and check and verify their
solutions to their problems,

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then no matter what
gets invented

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in the future they'll have a
better chance of succeeding.

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[Music]