(upbeat music)
- Hi, my name is Josh Udy.
I'm the Curriculum Manager
for Elementary Mathematics
for Houston Independent School District.
In this video, I will be
I'll begin by reading the first problem.
First, I'm going to
represent what the garden is.
I can do this using a rectangle
or a strip diagram model.
Here I see the garden and I know
that there are 24 plants growing in it,
so I'll label that here,
maybe indicate that
there's 24 plants in all.
I know in the problem that five-sixths
of the plants are vegetables.
This means that I need to
partition my whole garden
in two-sixths because
the denominator indicates
how many parts of equal size
the whole is partitioned into.
So I can divide my strip
diagram into sixths.
I know that five  -sixths of
the garden is vegetables.
I might even wanna color this.
Just because vegetables
are green I chose green.
This shows that five-sixths
of the garden are vegetables,
but it doesn't answer the question.
The question asks how
many vegetable plants
are growing in the garden?
This means that students need
to understand the whole garden
has 24 and it was broken into six parts,
so how many plants must there
be in each of those parts?
I know the whole is 24 and I've
I broken it into six parts.
This means that I can take 24
divided by six which is four.
So I'm going to represent four black dots,
I hope you can see this,
in each part of my garden.
Here I've represented all 24 plants,
I've shown that the garden
is broken into sixths
and I've also shaded in
five of those sixths.
The question said, how many
vegetables are in the garden?
So I need to count
four, eight, 12, 16, 20.
I know that five-sixths of 24
plants is 20 plants in all.
Here you'll want to
point out to the students
that the five indicates how many times
they count the four plants over and over,
so they count five groups of four.
Let me represent this
using a number sentence.
The question said
five-sixths of the plants
in the garden are vegetables.
Students can represent
this same five-sixths of 24
which they can learn
means five-sixth times 24.
Here referring to my picture,
I know that a sixth is four
but I have five of them
and so my answer is 20
vegetable plants in the garden.
Now I'm going to represent
and solve our second problem.
Let me read it.
I'm going to represent this   problem using
an open number line.
I'll start by just drawing a line.
I know that Tom has five feet of string,
so I can mark off zero and five
and I can go ahead and mark off one feet,
two feet, three feet, four feet of string,
and then five feet.
This represents that he
has five feet of string.
The question says that
he uses three-fourths
of his string for a project.
Allow your students time
to struggle with this.
I'm asking them to represent
three-fourths of five
on a number line and
there is no way right now
to clearly represent fourths
because it's broken into five equal parts.
As your students explore this idea,
they will probably offer an idea
or a solution along the lines
of maybe we should break
each number into fourths.
So encourage them to do this.
If I make three tick marks in between
each interval count of
one, I can see fourths.
I still have five feet of string
and now I have it
partitioned into fourths.
So the question might be that you ask
how many total interval marks
do we have on our number line?
Students can see that there
are 20 interval counts
on the number line.
We need to show
three-fourths of the string
that Tom had because that's
what he used for his project.
If the students understand that
there are 20 interval counts
on the number line, they
then need to be prompted
or guided to figure out what
one-fourth would look like.
Essentially I'm saying, here's
my whole piece of string,
it's five feet long,
what's a fourth of that?
When broken into 20 I can think,
well, what's a fourth of 20 tick marks?
A fourth of 20 is five tick marks,
let's see, one, two, three, four, five.
I'm gonna draw a big line right down here.
This shows that we have
five interval tick marks.
Let me keep doing that again and again.
One, two, three, four, five.
This shows five more interval tick marks,
one, two, three, four, five
and then finally one,
two, three, four, five.
Here the students should see
that I partitioned the whole length,
the whole five feet of
string into four equal parts.
I did this by first separating
each of the intervals
from zero to one or one to two.
Each of the intervals
between each whole number
into four equal parts
and then when looking at all 20 together,
I divided it into four parts by saying
there's five small interval tick marks
in between each of the sections.
So the question asks,
he used three-fourths of
the string for a project,
so how much string did he use?
Let me pull out another color.
This distance from zero
to one and one-fourth
represents one-fourth of the five.
This represents two-fourths of the five.
This represents three-fourths of the five.
This means that Tom used one,
two, three feet of ribbon
and three and one-fourth,
three and two-fourths,
three and three-fourths feet of ribbon.
Can you see that?
This means that Tom used three
and three-fourths feet of
string for his project.
(upbeat music)
