But this is fourth-grade module three lesson 14 and in this lesson we begin to solve division word problems with
remainders
Now the key thing about this lesson is when when we're talking about division
There's two different ways that students can think about division and oftentimes in old textbooks. They treat these two methods as
Synonymous as the same as if it doesn't matter
but in this lesson, and I'm going to really make a big point on this that there's two ways to think about division partitive and
Measurement, and we're going to talk about that on the next slide
And so as a teacher I want you guys to
really point out
The two different kinds of division and when you're writing your own homework
assignments or your quizzes or your tests make sure you include examples of both kinds of division
So let's take a moment to talk about those two different kinds of division so suppose we have
Let's see the problem. Oh
15 divided by 4 two ways that we could think about that problem
We could think of it as part of and we could think of it as measurement
So partitive me an example of partitive would be let's see 15
soccer balls sorted into four baskets
How many are in each basket so the idea of the word part of it means?
we know we're taking these 15, and we're sorting them into four parts into four buckets an
example of measurement would be
We have the same 15 soccer balls
But now we're going to be placing them in
Groups of four so now we know the size of each group we're wondering how many groups we need so 15 soccer balls
with four balls placed into each basket
How many baskets do we need so two different examples?
This lesson in particular
the
concept development
Kind of bounces back and forth between both kinds of division, but it's interesting in that the homework
almost
exclusively is
Measurement, and that's a little on the messed up side parents and teachers. We want to make sure we're doing both kinds of division
Especially since we talked about both kinds of division in the concept development
But in the homework all the homework problems are measurement so let's get
Talking about some specifics here
So for example 13 divided by 4. We can model this as part of and we
can model this as
Measurement and an example or how we would do that measurement
How we would do that well?
Let's see 13 divided by 4 with the partitive
Means we're going to take 13, and we're going to cut it into 4 parts so the idea would be we're gonna take
1
two three four parts and
We're going to take those 13, and we're going to sort them evenly into those four parts 1 2 3 4
5 6 7 8 9 10 11 and 12 and
Then we next one over would be 13 right so that means we have one
remainder so the answer would be
12 13 divided by 4
13 divided by 4 is 3
with 1 remainder
Because there's 3 in each of the four groups now
We could look at this and do it as as measurement, which is we're gonna say let's put
4 in each group, so we'd say
13 divided by 4 1 2 3 4
that constitutes a group
Now let's do
5 5
Well, that's a little thicker pen 5
6 5 6
7 8 that constitutes a group
We're going to keep going that's 8 so 9 10 11 12
that constitutes a group
Do we have enough to make another group? No, so there's our remainder and so again? We can see that our
Answer 13 divided by 4 is
3
Remainder 1 now what's the difference?
Over here right here what we just did 3 divided by 4
4 is the size of each group
3 is the number of groups
Over here 3
tells you the well 4 tells you how many groups you need and
The 3 tells you how how many are in each group both cases?
we have one left over and in both cases you get 3
Remainder 1 but boy depending on how we're thinking of these problems students
May have a hard time talking to the teacher
They may have a hard time talking to each other
Possibly because one kid is speaking from a part of this point of view
While the other kid is trying to talk from a measurement point of view and we want both students to understand
They're both likely right. We don't need to make one kid feel wrong and the other kid feel right or vice versa
So let's do this so Linda makes booklets using two sheets of paper
She has seventeen sheets of paper
How many of these booklets can she make will she have extra paper or how many sheets okay?
So the idea would be we are going to do 17 divided by two now
this says Linda makes booklets using two sheets of paper, okay, so
here's
One sheet one sheet
That ache that makes a booklet one sheet one sheet that makes a booklet one sheet one sheet that makes a booklet
again another booklet
Another booklet
Another booklets seeing how many booklets have we done well let's count how many pieces of paper
we've used 1 2 3 4 5 6 7 8 9 10 11 12
So I could go
13 14
15 16 I don't have enough to make an entire
booklet here's 17 and
So there's our answer so our answer is how many booklets can she make?
1 2 3 4 5 6 7 8 so her answer is
8
remainder 1 so she can make 8 booklets and
She'll have one page
leftover
one sheet
Leftover all right, so this is an example of
Measurement because we know how many are in each group and that it's a matter of counting how many groups we need
Another example, and I believe this one is also measurement technique
So this says Miss Rochelle wants to put her nine students into groups of six
How many groups of six can she make so the idea is she's gonna do 29 divided by six?
But in this case the groups have six in each of them
So that's gonna be one two three four five six. That's one group
Seven eight nine ten eleven twelve. That's another group thirteen fourteen fifteen sixteen seventeen eighteen
That's another group nineteen twenty twenty-one twenty-two twenty-three twenty-four
That's another group
Twenty-five twenty-six twenty-seven twenty-eight twenty-nine that's not quite a whole group so what have we done? Well we've got one group
two
Three four groups so her answer is 4 with a remainder of 5
So if she puts the remainings so how many groups can she make she can make four groups of?
Six kids and
Then the remaining is one group of
Five that are left over
And again another example and a third example where it's a measurement
version of division, so we've got Melissa and she has
43 toy soldiers and
She lines them up in rows of five to fight imaginary zombies how many of these rows can she make?
After making as many rows of five she puts the remaining soldiers in the last row how many soldiers are in that last row?
so basically we're gonna do rows of five and
we're gonna make 43 up all the way up to 43 so 1 2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 into 2 - 3 - 4 25
30
35
40 41 42 43
So how many rows did she make she made one two three four five?
six
seven eight
So she did 43 divided by five. She got eight rows
Plus she has a remainder of three through yet three little guys left over down there
All right
So as we wrap things up I'm gonna just belabor the point a little bit because teachers. I really want us to be
Thoughtful about the division that when you do a division problem
You've got two kinds partitive and measurement make sure
That when you are providing your students practice you're giving them plenty of
experience with both
Kinds of division and quite frankly this lesson didn't include a whole lot of both kinds. It was mostly
Measurement and that wraps up he being pretty negative, and I don't mean that
model for lesson three no fourth grade module three lesson 14