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Danielle Inserra: Today we are going to 
plan your lesson on subtraction problems.

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Sarah Novacek: Yes. 
Inserra: So, let's look at, first of all,

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the kids that are struggling.

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Novacek: She's great with adding them;
she can add the three-digit numbers,

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it's just the subtracting.

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Inserra: And where do
you see her break down?

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Because that seems typical
with kids that struggle;

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is that they are more successful
with addition compared to subtraction.

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Novacek: And the story problems--
do I add or do I subtract?

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That's another struggle for her.
Inserra: Okay, so the understanding

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of story problems, too.

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Novacek: And, I mean, she's successful 
with adding so I think she just

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wants to take the numbers
and add them every time.

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Inserra: Sure, sure. She is comfortable 
with and confident with it.

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Novacek: Yup.
Inserra: Well, I actually am wondering

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about using a diagram type
of way to represent with her.

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Novacek: Okay.
Inserra: Sometimes kids that struggle

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with that visual
representation of it,

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sometimes can be successful if
it's in like a tape diagram.

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Novacek: Okay.
Inserra: And in that way of

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representing it, it gives them
that visual understanding.

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And, you know, you had talked
about subtracting is difficult

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for her, so maybe seeing it
in this sense would help her,

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where you just want her to be
able to visualize...

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Novacek: Using that whole diagram.
Inserra: ...using this diagram.

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Novacek: Okay.

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Inserra: And then when she's ready, 
we can have this and incorporate

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that number line with it so she can see... 
Novacek: Show the relationship.

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Inserra: Yes.
Novacek: If you look at these, all

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of these answers are correct now,
Inserra: Yes.

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but her first time solving them she 
also, she didn't understand the story

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problem part of it so she was adding
the two numbers.

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Then when we moved on, then
she kind of looked at me,

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and she was like "No," and
she knew that wasn't right,

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so being able to understand
that, figure out...

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Inserra: So she didn't understand the
problem but she had enough sense to understand

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that what she was doing wasn't working.
Novacek: The answer was not right.

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Inserra: Yeah, so she was
able to monitor--that's great.

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Novacek: So she was the one who said,
"I need to do a number line."

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So she started and she successfully 
got, you know, she started

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at 37 and added up to a 100.

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But then when I asked
her what her answer was,

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"So how far away is 37 from
100?", her answer was, "100."

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And so kind of talking her
through that, so I am like,

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"You're telling me that if you
start at the mile marker 37

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and you drive to 100
it's 100 miles?" "Yeah."

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Not understanding the number
line, how this is the answer.

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Inserra: Let's think about these two, 
when we look at the lesson for Friday.

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When we're talking about solving
problems, our goal--let's think

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about what our end goal is for
them to be able to do and think

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about how these problems
meet that goal or how we might

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change them to meet our goal.
Novacek: Okay.

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Inserra: And maybe then we come up 
with a couple of different activities.

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I am guessing, I didn't ask but I'm 
assuming that we're not introducing

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any new vocabulary in this lesson?
Novacek: No.

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It's mainly just a review, 
so same vocabulary.

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Inserra: You're working on more 
subtraction problems and being able

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to visualize it.
Novacek: Yes.

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Inserra: Now, you know that 80 percent
of solving problems is being able

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to understand the problem first.

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And so, maybe with your ones that 
are struggling to understand the

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problem, maybe they could get with 
a buddy and read the problem and

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then have to re-tell the problem
to a friend.

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Novacek: Okay.
Inserra: Maybe they have to draw

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and figure out what that meaning of 
the problem is before we even begin.

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In the book it talks about how 
subtraction is more than, there are

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Inserra: And so they suggest students
to also give story problems that

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are not just that take away... 
Novacek: Yes.

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Inserra: ...but the comparison
model also and how many more

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from one number to another.
Novacek: Yes.

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Inserra: And so how do you think
you might incorporate that,

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into your whole group lesson?

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Novacek: I think whole
group, before I send them off

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to do their work, I want to be
able to get at least one example

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of each problem up on the
board or up on the chart paper.

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That they have that as a
visual because I do feel

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that that's one of the toughest parts 
of subtraction, is just

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the different types of story 
problems, knowing to subtract.

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Inserra: Sure.
Novacek: So if they are consistently given

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those types of problems, it will 
make them more successful.

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Inserra: Sure, and if they're
not able to come up with one,

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you'll have one ready to share with them?
Novacek: Yes, I'll model one and then

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see if they can use that model, my 
problem, to create another one.

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Inserra: The last part of the lesson 
is sharing and comparing strategies.

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Now throughout this unit, throughout 
the school year, you've used and

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taught lots of different strategies.
Novacek: Yes.

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Inserra: What are some that
you expect them to be using?

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Novacek: One that we have worked on is
starting at the smaller number and adding up.

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Inserra: So adding up with a number 
line and then possibly with...

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Novacek: Challenging them
with the equations.

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Inserra: Equations, okay.
What else do you see?

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Novacek: Breaking the
smaller number up into parts.

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Inserra: What we'll want to
think about is, when we ask kids

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to share their strategies,
what strategies we're going

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While students are sharing
strategies you are also engaging

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the rest of the students by
having them turning to talk.

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Novacek: Turn to talk: "What did
you just see?" "What did they

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just do first?" and "What did they do?" 
Inserra: And maybe why they did it that

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way and maybe if there is a strategy
that your peers just shared that

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you don't usually use, maybe you could 
think about using that next time.

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So encouraging them to pick up
a new strategy, internalize it,

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and then be able to
use it themselves.

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