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Rational Numbers - Student Activity - Contenido educativo

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Subido el 28 de mayo de 2007 por EducaMadrid

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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.

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Thanks, Dr. Seisler, for that information. 00:00:00
We look forward to it. 00:00:08
Okay, students, let's learn a little bit more about rational numbers so you can determine 00:00:09
your ratio of rest. 00:00:14
Numbers can be written in different forms, depending on how they're being used. 00:00:17
We're going to look at three forms of rational numbers, fractions, decimals, and percents. 00:00:21
One way to write a rational number is as a fraction. 00:00:29
A fraction has a numerator and a denominator. 00:00:32
For a rational number, both of these must be whole numbers, and the denominator must 00:00:35
not be zero. 00:00:40
The denominator is the number of equal parts you divide the whole into. 00:00:42
The numerator stands for the number of pieces you are considering out of the whole. 00:00:47
For example, Norbert is going to eat a pizza. 00:00:52
Now, the pizza is cut into ten equal pieces. 00:00:55
He eats seven pieces out of the ten, so we can say he eats seven-tenths of the pizza. 00:00:59
Even a whole number can be written as a fraction when you put it over the number one. 00:01:06
Now, any fraction with the same numerator and denominator is equal to one. 00:01:10
And if you think about it for a minute, it makes sense. 00:01:15
If Norbert had ten slices in the whole pizza, that is the denominator. 00:01:18
And if he ate ten of them, that is the numerator. 00:01:23
The resulting fraction would be ten-tenths, or ten divided by ten, and that equals one 00:01:26
whole pizza. 00:01:32
Another way of describing how much pizza Norbert can eat is by using a decimal. 00:01:33
To express a fraction as a decimal, we divide the numerator by the denominator. 00:01:38
In Norbert's case, we divide seven by ten, like this. 00:01:42
We call this seven-tenths. 00:01:47
Now, we can say that Norbert has eaten seven-tenths, or seven-tenths of his pizza. 00:01:50
There is still another way to express how much pizza Norbert has eaten, and that is 00:01:58
using percent. 00:02:01
Percent is a special fraction that is always based on one hundred. 00:02:03
We can express any decimal number as a percent simply by multiplying by one hundred. 00:02:07
Seven-tenths multiplied by one hundred is seventy percent. 00:02:13
Let's review. 00:02:18
Seven-tenths equals seven-tenths equals seventy percent. 00:02:19
Now that you know how to express rational numbers as fractions, decimals, and percents, 00:02:25
try this example. 00:02:30
Don't forget to look for equivalent fractions, too. 00:02:31
Norbert orders an eight-slice pizza and eats six of the slices. 00:02:35
Show how much he ate using a fraction, a decimal, and a percent. 00:02:39
Teachers, now might be a great time to stop the program as students work this out. 00:02:45
Welcome back. 00:02:51
How did you do? 00:02:52
Norbert ordered an eight-slice pizza, so eight becomes the denominator. 00:02:54
He ate six, so that is the numerator. 00:02:58
Norbert ate six-eighths of the pizza. 00:03:01
To find the decimal, we divide six by eight. 00:03:04
The answer, in decimal notation, is seventy-five hundredths. 00:03:07
Now to figure out the percentage, let's multiply seventy-five hundredths by one hundred. 00:03:11
Norbert ate seventy-five percent of his pizza. 00:03:18
Now let's look at ratios. 00:03:21
A ratio is a comparison of two quantities by division. 00:03:24
Because we know that Norbert ate six slices of pizza from the total number of slices, 00:03:28
eight, we would write this ratio as six eaten to eight total. 00:03:33
Ratios can also be written as fractions, like this, six over eight. 00:03:39
Now let's look at proportions. 00:03:44
A proportion is an equation stating that two ratios are equivalent. 00:03:46
Let's compare how much pizza Norbert ate compared to how much Zot ate. 00:03:51
The unit is a slice. 00:03:55
Now we know that Norbert ordered an eight-slice pizza, but Zot wanted his pizza cut into twelve 00:03:57
slices. 00:04:03
We know that Norbert ate six slices. 00:04:04
Norbert eats nine of his twelve. 00:04:07
Norbert's ratio of eaten slices to total slices was six to eight. 00:04:09
What will Zot's be? 00:04:14
That's right, nine to twelve. 00:04:16
To see if these ratios form a proportion, we set them up like this. 00:04:19
Six-eighths equals nine-twelfths. 00:04:23
Next, we cross-multiply the denominators and numerators like this. 00:04:26
If the answers on either side of the equal sign are the same, then the two ratios are 00:04:32
proportional. 00:04:37
Now that we know Norbert has been well-fed, let's visit with students from Cole Middle 00:04:38
School in Oakland, California. 00:04:44
They're doing a classroom activity on decimals and percentages, along with some scientific 00:04:46
observations on their sleep. 00:04:50
Hello. 00:04:53
Welcome to Cole Middle School. 00:04:54
We're about to show you a cool activity that you can try with your class. 00:04:56
You can view and download this activity from the NASA Connect website. 00:05:00
Our teacher gave us data sheets to collect information about the way we and our family 00:05:10
sleep at night. 00:05:14
On the data sheet, we recorded when we went to bed, when we woke up, and how many hours 00:05:16
we slept. 00:05:20
Some of us also kept track of other members in our family. 00:05:21
We collected this data for at least one week. 00:05:25
We also recorded some observations about how we felt throughout each day. 00:05:27
Using the logs, we made graphs to see if any patterns occurred in our data. 00:05:32
Next, using the data, we figured out the average number of hours each person slept. 00:05:36
Some of us noticed that younger kids in our families sleep a lot more than we do. 00:05:41
We also noticed that some days we felt really tired and had a hard time getting out of bed. 00:05:46
Next, we created another representation of our data called fraction wheels. 00:05:51
To make our graph, these wheels showed how much of our day was spent sleeping. 00:05:56
Write this portion as a fraction and convert this to percent and then decimal. 00:06:01
To make our fraction wheels, we used colored construction paper, pencils, compass, protractor, 00:06:06
and scissors. 00:06:12
We drew two circles and cut them out. 00:06:13
One entire circle represents 24 hours in an Earth day. 00:06:15
Remember the length of any planet's day is the number of hours it takes to rotate once 00:06:20
on its axis. 00:06:24
Because there are 24 hours in one day, we divided one of our circles into 24 equal pieces. 00:06:27
We used a vision to figure out how many degrees were in each piece. 00:06:33
Can you think of another way of making 24 equal pieces? 00:06:37
Next, we needed to make the slits that let us split the two circles together, like this. 00:06:41
Now we could see what fraction of our day was spent sleeping, and it was easy to see 00:06:46
how fractions, percents, and decimals are the same. 00:06:50
Now we must also research the length of a day on other planets. 00:06:54
For more information about this and other student activities, visit the NASA Connect 00:06:57
website. 00:07:01
Awesome job. 00:07:02
Well, we've seen how Cole Middle School conducted the activity. 00:07:07
Let's return to Derek's challenge, take it a step further, and see if we can help Norbert 00:07:11
out. 00:07:15
Oh, my hands are talking to me. 00:07:16
Thanks, Jen. 00:07:18
Okay, kids. 00:07:20
You have learned how to set up ratios. 00:07:21
Let's apply what we have learned to Norbert and Zot as they explore the other bodies of 00:07:23
our solar system. 00:07:26
We want to make sure Norbert and Zot get the right ratio of rest. 00:07:28
On Earth, Norbert feels pretty good when he sleeps about 9 out of 24 hours, or three-eighths 00:07:31
of the day. 00:07:36
A lot like you. 00:07:37
But if he wants to get the same ratio of rest when he visits Neptune, how much should he 00:07:38
sleep? 00:07:42
First, you will need to find out how many hours are in a whole day on Neptune. 00:07:43
Next, we need to apply ratios and proportions. 00:07:48
Remember, a ratio is a comparison of two numbers by division. 00:07:51
In this case, we are comparing hours on Earth to hours on Neptune. 00:07:55
The unit of measure is an hour, and a proportion is a statement that two ratios are equivalent. 00:07:59
How many hours of sleep are needed on Neptune in order to create a proportion with the same 00:08:05
Earth rest ratio? 00:08:10
Teachers, now is a good time to pause the program. 00:08:11
Let's see what you came up with. 00:08:16
You should have set up a proportion that states 9 over 24 hours on Earth is equivalent 00:08:18
to X over 16 hours. 00:08:23
We use the variable X for the amount of sleep hours since we don't know the value yet. 00:08:25
Next, we will cross-multiply like this. 00:08:30
Find the products on both sides of the equation and solve for X. 00:08:34
X equals 6. 00:08:38
In order for Norbert to sleep three-eighths, or 9 twenty-fourths of his day while on Neptune, 00:08:40
he should sleep about six hours while on Neptune. 00:08:45
Don't worry if you got this answer wrong. 00:08:48
You can always try again. 00:08:49
Wow. 00:08:51
You know, six hours of sleep a night isn't enough to keep me healthy and performing at 00:08:52
the top of my game. 00:09:05
I know. 00:09:08
Let's check back with RJ and see if he's found out any information on the circadian clock 00:09:09
that might help Norbert in his travels around our solar system. 00:09:14
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Idioma/s:
en
Materias:
Matemáticas
Niveles educativos:
▼ Mostrar / ocultar niveles
      • Nivel Intermedio
Autor/es:
NASA LaRC Office of Education
Subido por:
EducaMadrid
Licencia:
Reconocimiento - No comercial - Sin obra derivada
Visualizaciones:
3001
Fecha:
28 de mayo de 2007 - 16:54
Visibilidad:
Público
Enlace Relacionado:
NASAs center for distance learning
Duración:
09′ 17″
Relación de aspecto:
4:3 Hasta 2009 fue el estándar utilizado en la televisión PAL; muchas pantallas de ordenador y televisores usan este estándar, erróneamente llamado cuadrado, cuando en la realidad es rectangular o wide.
Resolución:
480x360 píxeles
Tamaño:
55.80 MBytes

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