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So there you just save up
on your paper just go

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like this you are wondering
those might be the

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same length, it may not be
the same length so just

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go like this so again how
much longer is it? Let's see

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about that much longer so it
takes much less time so you

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end up in this part ends up
just think about number

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of words being many times as
great then as well this one

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is about that long, this one's
about that long that one

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is about up to here then move
on so you see how much

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this one makes it cause then
you're not worrying about

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then you aren't actually doing
arithmetic you are really

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thinking in terms of magnitudes
because there also was

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some things like well you've
got point eight, negative

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point eight and what's the sum,
let's see a negative

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there are all kinds of things
coming in that make each

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step a pretty long discussion
and you don't want that

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Ok, well that was me then because
i misinterpreted how I

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was supposed to do this I thought
I was supposed to have

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them do arithmetic estimates that
are arithmetic but I

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didn't know I was supposed to
be doing arithmetic.

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Oh I see. So I thought that they
just weren't just doing

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magnitudes I thought they were
doing function values

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and adding them looking at the
function value looking

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at the y value beginning at
the x axis seeing its

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actual numeric value looking
at the other value. Right?

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So I was thinking the way that
I ask them to and so

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that's why I was supporting them.
You see all the steps

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you had to go through. Yea.
What we are trying to do is

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reduce the steps so that they
can really focus on the

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full variation and acts the
variation and the function

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values and the variation and
the sum if they can if we

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get them to think of those three
things and the closer

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we get them focusin on those
three things the easier it

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is going to be for them to construct two graphs