WEBVTT

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[Music]

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My name is Julia Franklin.

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I teach first grade at Tollgate
Elementary in Aurora, Colorado.

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In the lesson, I was teaching
them first about sharing equally

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and how to divide
things equally first,

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and then after that
we looked a little bit

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at dividing a whole into halves.

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(Franklin to Students): How
many cookies does each kid get

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if they share them equally?

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(Franklin): So it
has to be fair.

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There's three kids
and nine cookies.

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Deja, how many cookies
does each kid get?

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(Student): Three.
(Franklin): Three cookies.

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Deja, can you come show us
up here how you did that?

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Shake your hand if
you agreed with her.

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Use the arrow actually.

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Can you just drag them down?

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Ooh, she did them two at a time.

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Nice job. Did anybody
do it a different way?

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Ethan, can you come
show us what you did?

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What were you thinking?

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(Student): I am thinking
there's three people

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and there's nine cookies, 
so ...

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...they need, all of them need 
three because there's nine.

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(Franklin): Because there's nine?
So what do you know about

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3 plus 3 plus 3?
What does it equal?

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(Student): [Indiscernible]
(Franklin): It's ok. You're ok.

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(Franklin): So if there are
nine cookies and three kids,

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how many do they each
get so that it's equal?

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(Students):Three.
(Franklin): Three cookies.

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Shake your hand if you knew
3 plus 3 plus 3 equals 9.

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Lots of us know that, huh?

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Matthew, do you want to show us 
one different way to do it? Okay

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My goal for the part where
there was nine cookies

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and three kids was
that they would be able

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to divide the cookies equally

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after using their prior
knowledge of what is equal,

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now they can look at those
nine cookies and divide them.

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There is a lot of different
ways that kids divide equally,

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but they all got
to the same answer.

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(Franklin): I have a little
bit of a bonus question.

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This one's kind of hard.
I am going to have you

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turn and tell your neighbor
when you know the answer, okay?

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(Student): Oh.

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(Franklin): What if there
was one more cookie?

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What would we do
with that cookie?

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(Student): I would,
like, break three apart

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because if you add one more and
then add a little piece of him

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and then of him and then of him.

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(Student): Yeah, like, break 
it apart equally...

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(Students): [Indiscernible]

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(Student): If we had one
more cookie in there,

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we could break it three apart.

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(Franklin): So this
was an extra cookie.

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What are you going to
do with this cookie?

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Giovanni, come up here and show
what would do with the cookie.

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Here is the extra cookie.
What are you going to do, Giovanni?

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(Student): I would rip it
in three halves and give it

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to all those three kids.

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(Franklin): Rip it in three halves.

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So go ahead and do it --
show us how you would do it.

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Okay, so let's stick one
up there for each kid.

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(Franklin): Nice job, Giovanni.
Have a seat.

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Shake your hand if that's
what you were going to do.

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So does this look a
little more equal?

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(Students): Yeah.
(Franklin): A little more fair?

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One of the misconceptions
that I have noticed first

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graders have is referring
to thirds and fourths and

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fifths or whatever it is,
all of them are a half to them.

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I think that this is something
that is developmental,

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and they will learn it as
they go to higher grades.

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And it's something that we
just, in the primary grades,

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we need to build on that
language of fractions

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and just kind of help
them along the way.

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So when I hear kinds say,
they take a paper and tear

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into thirds and they call it halves,
I'll just maybe mention thirds,

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or mention parts, or something 
like that.

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In this small group, I
differentiated the lesson

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without the kids even knowing just
by having three different papers.

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And there was one paper where the 
kids were specifically

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working on their doubles.

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This paper was for kids
who still needed to practice

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with those doubles
and understand

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that if you know 3 plus 3 is 6,
then you can divide six cookies

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between two kids and
they each get three.

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Another paper was for someone
who already has a firm grasp

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on the doubles, and I
threw in that extra cookie

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to make it an odd
number to start working

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with the fraction part of it.

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There was another paper
where it had multiple kids.

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They were good at
dividing by two already,

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but this threw in
the extra kids.

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(Franklin): So you have
two kids and six cookies.

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They each get three?

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Two kids and 12 cookies,
they each get...?

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(Student): Six.

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(Franklin): What did you mostly
use to figure all these out?

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What strategy?
(Student):Doubles.

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(Franklin): Doubles. You used doubles 
a lot--three and three, six and six,

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five and five, four and four, two 
and two, seven and seven. Nice job.

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(Franklin): So how many did they each get?
(Student): Four.

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(Franklin): They each got four cookies?
(Student): Because these two are in half.

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(Franklin): But if you are
going to do four and four,

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then you have eight
cookies, so it's too many.

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How many cookies all together?

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You guys stopped because
you thought it was seven.

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Is it seven?
(Student): Look it.

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(Franklin): It's not.
Count them.

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(Student): Because it's 4 plus 4.

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(Franklin): Is it 4 plus 4?
Is this a whole cookie?

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(Student): Seven?
(Franklin): So it's seven cookies.

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How did you know it was seven?

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(Student): I put this one right here...
[Indiscernible]

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(Franklin): 3 plus 4 equals
7, so you actually have this

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as one cookie plus six more.
Okay, so you have seven cookies.

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So how many cookies do you have?
(Student): Seven and a half.

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(Franklin): Oh, there's seven all together...
(Student): Six and a half.

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(Franklin): But Giovanni, these
cookies are yours, right here.

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How many cookies do you have?
(Student): Three.

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(Franklin):Three?
(Student): Three and a half.

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(Franklin): There you go, so how
many cookies did each kid get?

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(Student): Three and a half.
(Franklin): Three and a half.

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How did you know, Christian?

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(Student): Because if you cover
up that one, it would be three.

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(Franklin): It would be three,
and then they have part of one.

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So they don't have three
and they don't have four,

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they have three and a half.
You remembered how to write it.

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[Music]