Program Information

Series: NASA Connect
Program: The Right Ratio of Rest: Proportional Reasoning
Segment Number: 3 (Watch entire program)
Duration: 00:09:17
Year Produced: 2005
Description:

In the third segment of the Right Ratio of Rest: Proportional Reasoning, Jennifer Pulley explains three types of rational numbers: Fractions, Decimals and Percents. Jennifer also describes ratios and proportions. In the third segment students at Cole Middle School conduct an activity in which they record and graph sleep data in different ways. The third segment ends with an inquiry based question posed by Derek Wang comparing time on Earth to time on Neptune.

NASA CONNECT™ is a series of Emmy®-award-winning, math-focused programs. Each program supports the national math, science, and technology standards and has three components that include (1) a 30-minute television broadcast; (2) a companion educator's guide; and (3) an online activity that further explores topics presented in the broadcast. These programs establish a connection between the math, science, and technology concepts taught in the classroom to those same concepts used everyday by NASA researchers.

For more information visit: http://connect.larc.nasa.gov/

Transcript

Thanks, Dr. Czeisler,
for that information.

We look forward to it.

Okay, students,
let's learn a little bit more
about rational numbers
so you can determine
your ratio of rest.

Numbers can be written
in different forms
depending on how
they're being used.

We're going to look at three
forms of rational numbers:

One way to write
a rational number
is as a fraction.

A fraction has a numerator
and a denominator.

For a rational number, both of
these must be whole numbers,
and the denominator
must not be zero.

The denominator is the number
of equal parts
you divide the whole into.

The numerator stands
for the number of pieces
you are considering
out of the whole.

For example, Norbert is going
to eat a pizza.

The pizza is cut
into 10 equal pieces.

He eats 7 pieces out of the 10,
so we can say he eats 7/10
of the pizza.

Even a whole number
can be written as a fraction
when you put it
over the number one.

Now, any fraction with the same
numerator and denominator
is equal to 1.

And if you think about it
for a minute, it makes sense.

If Norbert had 10 slices
in the whole pizza,
that is the denominator.

And if he ate 10 of them,
that is the numerator.

The resulting fraction
would be 10/10,
or 10 divided by 10,
and that equals 1 whole pizza.

Another way of describing
how much pizza Norbert can eat
is by using a decimal.

To express a fraction
as a decimal,
we divide the numerator
by the denominator.

In Norbert's case,
we divide 7 by 10, like this.

We call this "seven tenths."

Now we can say that Norbert has
eaten 0.7, or 7/10,
of his pizza.

There is still another way
to express
how much pizza
Norbert has eaten,
and that is using percent.

Percent is a special fraction
that is always based on 100.

We can express
any decimal number as a percent
simply by multiplying by 100.

0.7 multiplied by 100 is 70%.

Let's review.

7/10 equals 0.7 equals 70%.

Now that you know how
to express rational numbers
as fractions, decimals,
and percents,
try this example.

Don't forget to look
for equivalent fractions too.

Norbert orders an 8-slice pizza
and eats 6 of the slices.

Show how much he ate
using a fraction, a decimal,
and a percent.

Teachers, now might be
a great time
to stop the program
as students work this out.

Welcome back.

How did you do?

Norbert ordered
an 8-slice pizza,
so 8 becomes the denominator.

He ate 6,
so that is the numerator.

Norbert ate 6/8 of the pizza.

To find the decimal,
we divide 6 by 8.

The answer, in decimal notation,
is 0.75.

Now to figure out
the percentage,
let's multiply 0.75 by 100.

Norbert ate 75% of his pizza.

Now let's look at ratios.

A ratio is a comparison
of two quantities by division.

Because we know that Norbert ate
6 slices of pizza
from the total number
of slices, 8,
we would write this ratio
as 6 eaten to 8 total.

Ratios can also be written
as fractions like this:

Now let's look at proportions.

A proportion is an equation
stating that two ratios
are equivalent.

Let's compare
how much pizza Norbert ate
compared to how much Zot ate.

The unit is a slice.

Now, we know that Norbert
ordered an 8-slice pizza,
but Zot wanted his pizza cut
into 12 slices.

We know that Norbert ate
6 slices.

Zot eats 9 of his 12.

Norbert's ratio of eaten slices
to total slices was 6:8.

What will Zot's be?

That's right, 9:12.

To see if these ratios form
a proportion,
we set them up like this:

Next we cross multiply
the denominators and numerators
like this.

If the answers
on either side
of the equals sign are the same,
then the two ratios
are proportional.

Now that we know Norbert
has been well fed,
let's visit with students
from Cole Middle School
in Oakland, California.

They're doing
a classroom activity
on decimals and percentages,
along with
some scientific observations
on their sleep.

Hello, welcome
to Cole Middle School.

We are about to show you
a cool activity
that you can try
with your class.

You can view and download
this activity
from the NASA Connect website.

Our teacher gave us data sheets
to collect information
about the way we and
our families sleep at night.

(Bianca)
On the data sheet,
we recorded when we went to bed,
when we woke up,
and how many hours we slept.

Some of us also kept track
of other members in our family.

We collected this data
for at least one week.

We also recorded
some observations
about how we felt
throughout each day.

Using the logs, we made graphs
to see if any patterns occurred
in our data.

Next, using the data,
we figured out
the average number of hours
each person slept.

Some of us noticed that
younger kids in our families
sleep a lot more than we do.

We also noticed that some days,
we felt really tired
and had a hard time
getting out of bed.

Next, we created another
representation of our data
called fraction wheels.

Like our graph,
these wheels showed
how much of our day
was spent sleeping.

Write this portion
as a fraction,
and convert this to percent
and then decimal.

To make our fraction wheels,
we used colored
construction paper, pencils,
compass, protractor,
and scissors.

We drew two circles
and cut them out.

One entire circle represents
24 hours in an Earth day.

Remember, the length
of any planet's day
is the number of hours it takes
to rotate once on its axis.

(Bianca)
Because there are 24 hours
in one day,
we divided one of our circles
into 24 equal pieces.

We used division to figure out
how many degrees
were in each piece.

Can you think of another way
of making 24 equal pieces?

(Bianca)
Next, we needed
to make the slits
that let us slip the two circles
together, like this.

Now we could see what fraction
of our day was spent sleeping,
and it was easy to see
how fractions, percents,
and decimals are the same.

Some of us also researched
the length of a day
on other planets.

(Bianca)
For more information about this
and other student activities,
visit the NASA Connect website.

Awesome job.

Well, we've seen how
Cole Middle School
conducted the activity.

Let's return
to Derek's challenge,
take it a step further,
and see if we can
help Norbert out.

Oh, my hams are talking to me.

Thanks, Jen.

Okay, kids, you have learned
how to set up ratios.

Let's apply what we have learned
to Norbert and Zot
as they explore the other bodies
of our solar system.

We want to make sure
Norbert and Zot get
the right ratio of rest.

On Earth,
Norbert feels pretty good
when he sleeps about 9
out of 24 hours,
or 3/8 of the day--
a lot like you.

But if he wants to get
the same ratio of rest
when he visits Neptune,
how much should he sleep?

First you will need to find out
how many hours are
in a whole day on Neptune.

Next, we need to apply ratios
and proportions.

Remember,
a ratio is a comparison
of two numbers by division.

In this case,
we are comparing hours on Earth
to hours on Neptune.

The unit of measure is an hour,
and a proportion is a statement
that two ratios are equivalent.

How many hours of sleep
are needed on Neptune
in order to create a proportion
with the same Earth rest ratio?

Teachers, now is a good time
to pause the program.

Let's see what you came up with.

You should have set up
a proportion
that states:

We use the variable X
for the amount of sleep hours
since we don't know
the value yet.

Next, we will cross-multiply
like this.

Find the products on both sides
of the equation,
and solve for X.

X equals 6.

In order for Norbert
to sleep 3/8, or 9/24,
of his day while on Neptune,
he should sleep about 6 hours
while on Neptune.

Don't worry
if you got this answer wrong;
you can always try again.

snore!
flap!

snore!
flap!

snore!

Wow.

You know, six hours
of sleep a night isn't enough
to keep me healthy
and performing
at the top of my game.

I know; let's check back with RJ
and see if he's found out
any information
on the circadian clock
that might help Norbert
in his travels
around our solar system.

Virginia Standards

6th Grade SOLs » Mathematics » 6.1
6th Grade SOLs » Mathematics » 6.4
6th Grade SOLs » Mathematics » 6.6
6th Grade SOLs » Mathematics » 6.7
7th Grade SOLs » Mathematics » 7.6
7th Grade SOLs » Mathematics » 7.11
8th Grade SOLs » Mathematics » 8.3