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[Music] Welcome to Problem
Solving in Pre-Algebra.

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I am Beth Klingher.

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I teach seventh- and
eighth-grade math here

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at Worthington Hooker School
in New Haven, Connecticut.

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The lesson was a pre-algebra lesson.

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It involved making a table of data

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and then transferring
that data into a graph.

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It was a word problem involving
a race between two children.

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The goal here was really to have
the kids take a real-life situation

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and be able to take that
information and put it

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into a numeric representation,
which was a graph.

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Many children could have
approached the lesson in many ways.

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It involved building on some of the
algebra skills we have been using

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for the past week or so, so that
actually gave them the preparation

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for then taking this data from their
table and building a graph of it.

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One of the things I was looking for was
to see if they could take a problem--

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a word problem-- and interpret what
the important facts were to begin with.

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After they built the graph, there is a
secondary step of looking at the graph

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and seeing, "How does this graph
actually relate to the word problem?

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What do the lines mean?"

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One line represented
one child in the race;

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another line represented
another child in the race.

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And actually looking at the
intersection point and understanding

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that that intersection point represented

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where one child overtook
the other in the race.

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I am a big proponent of open-ended
word problems, problem-solving skills.

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One of the things I really work
with my students on is learning how

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to attack an open-ended
problem and to be able

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to productively struggle
with that problem.

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It's not obvious at first what the
answer is, but they can use all

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of the number sense skills that
they have to attack that problem,

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and trying to encourage them to
get over their initial frustration

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in handling a problem and to persevere
and to work through the problem.

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I use visual representations
quite a lot.

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If somebody looks at a problem and
they are frustrated, they don't know

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where to begin, I always say,
"Draw a picture of what's going on.

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Get something down on paper
that gets you moving."

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And that's a great way to start working.

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It's also a great way
to solve many problems

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because a picture really
helps you orient things,

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whether it's something broken
up into parts or something--

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as an example, today's
lesson, we had a race.

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Well, you can actually show the race at
different points in time with a picture,

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and that really helps you
visualize what's going on.

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Many students who may have little blocks
against things, it would get them moving

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and understanding how a
problem could be solved.

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It's difficult to get students to move
from the concrete to the more abstract.

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I think one of the ways you
can help is a lot of practice

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because the more practice you have with
the concepts, the more you can start

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to understand how one concept
is connected to another

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or one problem is connected to another,
and you start understanding kind

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of a bigger-picture view of it.

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The other way I think is to show
problems in many different ways--

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visually, with manipulatives,
with numbers--

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and all of a sudden instead
of it just being an equation,

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you can see how the conceptual or
the concept can pull it together.

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For example, today's lesson, they had
a table, so they can look concretely

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at where the racers were
at each point in time.

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And that concrete table is then
brought into the visual graphic,

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which is a little less concrete.

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One of the additional challenges I gave
the students was to take the information

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that they had gleaned from the
problem, the table and the graph,

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and then move to the next step,
which is writing a linear equation.

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Now we haven't spent a lot of
time on equations this year,

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but a lot of them are ready for taking

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that next step, that
more conceptual step.

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The lesson today was really the first
time the students were taking some

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real-world examples and applying
some of their algebra skills

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to those real-world examples.

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We do it throughout the
year with word problems,

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but this is the first time we
really graphed a real-world problem.

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So my hope is that by
the end of the year,

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the students will have a
solid understanding about how

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to take a problem, a situation, and
not only to make a table and graph,

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but then to write an equation
based on that problem.

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To learn more about Problem
Solving in Pre-Algebra,

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please explore the additional resources
on the Doing What Works website.

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[Music]