1
00:00:00,000 --> 00:00:08,600
Thanks, Dr. Seisler, for that information.

2
00:00:08,600 --> 00:00:09,600
We look forward to it.

3
00:00:09,600 --> 00:00:14,960
Okay, students, let's learn a little bit more about rational numbers so you can determine

4
00:00:14,960 --> 00:00:17,480
your ratio of rest.

5
00:00:17,480 --> 00:00:21,600
Numbers can be written in different forms, depending on how they're being used.

6
00:00:21,600 --> 00:00:29,220
We're going to look at three forms of rational numbers, fractions, decimals, and percents.

7
00:00:29,220 --> 00:00:32,420
One way to write a rational number is as a fraction.

8
00:00:32,420 --> 00:00:35,540
A fraction has a numerator and a denominator.

9
00:00:35,540 --> 00:00:40,300
For a rational number, both of these must be whole numbers, and the denominator must

10
00:00:40,300 --> 00:00:42,580
not be zero.

11
00:00:42,580 --> 00:00:47,260
The denominator is the number of equal parts you divide the whole into.

12
00:00:47,260 --> 00:00:52,980
The numerator stands for the number of pieces you are considering out of the whole.

13
00:00:52,980 --> 00:00:55,460
For example, Norbert is going to eat a pizza.

14
00:00:55,460 --> 00:00:59,060
Now, the pizza is cut into ten equal pieces.

15
00:00:59,060 --> 00:01:06,380
He eats seven pieces out of the ten, so we can say he eats seven-tenths of the pizza.

16
00:01:06,380 --> 00:01:10,180
Even a whole number can be written as a fraction when you put it over the number one.

17
00:01:10,180 --> 00:01:15,780
Now, any fraction with the same numerator and denominator is equal to one.

18
00:01:15,780 --> 00:01:18,820
And if you think about it for a minute, it makes sense.

19
00:01:18,820 --> 00:01:23,140
If Norbert had ten slices in the whole pizza, that is the denominator.

20
00:01:23,140 --> 00:01:26,400
And if he ate ten of them, that is the numerator.

21
00:01:26,400 --> 00:01:32,240
The resulting fraction would be ten-tenths, or ten divided by ten, and that equals one

22
00:01:32,240 --> 00:01:33,760
whole pizza.

23
00:01:33,760 --> 00:01:38,040
Another way of describing how much pizza Norbert can eat is by using a decimal.

24
00:01:38,040 --> 00:01:42,880
To express a fraction as a decimal, we divide the numerator by the denominator.

25
00:01:42,880 --> 00:01:47,840
In Norbert's case, we divide seven by ten, like this.

26
00:01:47,840 --> 00:01:49,560
We call this seven-tenths.

27
00:01:50,560 --> 00:01:58,160
Now, we can say that Norbert has eaten seven-tenths, or seven-tenths of his pizza.

28
00:01:58,160 --> 00:02:01,960
There is still another way to express how much pizza Norbert has eaten, and that is

29
00:02:01,960 --> 00:02:03,960
using percent.

30
00:02:03,960 --> 00:02:07,480
Percent is a special fraction that is always based on one hundred.

31
00:02:07,480 --> 00:02:13,120
We can express any decimal number as a percent simply by multiplying by one hundred.

32
00:02:13,120 --> 00:02:18,040
Seven-tenths multiplied by one hundred is seventy percent.

33
00:02:18,040 --> 00:02:19,040
Let's review.

34
00:02:19,040 --> 00:02:25,320
Seven-tenths equals seven-tenths equals seventy percent.

35
00:02:25,320 --> 00:02:30,600
Now that you know how to express rational numbers as fractions, decimals, and percents,

36
00:02:30,600 --> 00:02:31,920
try this example.

37
00:02:31,920 --> 00:02:35,320
Don't forget to look for equivalent fractions, too.

38
00:02:35,320 --> 00:02:39,580
Norbert orders an eight-slice pizza and eats six of the slices.

39
00:02:39,580 --> 00:02:45,000
Show how much he ate using a fraction, a decimal, and a percent.

40
00:02:45,000 --> 00:02:51,880
Teachers, now might be a great time to stop the program as students work this out.

41
00:02:51,880 --> 00:02:52,880
Welcome back.

42
00:02:52,880 --> 00:02:54,680
How did you do?

43
00:02:54,680 --> 00:02:58,600
Norbert ordered an eight-slice pizza, so eight becomes the denominator.

44
00:02:58,600 --> 00:03:01,440
He ate six, so that is the numerator.

45
00:03:01,440 --> 00:03:04,160
Norbert ate six-eighths of the pizza.

46
00:03:04,160 --> 00:03:07,400
To find the decimal, we divide six by eight.

47
00:03:07,400 --> 00:03:11,320
The answer, in decimal notation, is seventy-five hundredths.

48
00:03:11,840 --> 00:03:18,200
Now to figure out the percentage, let's multiply seventy-five hundredths by one hundred.

49
00:03:18,200 --> 00:03:21,960
Norbert ate seventy-five percent of his pizza.

50
00:03:21,960 --> 00:03:24,600
Now let's look at ratios.

51
00:03:24,600 --> 00:03:28,920
A ratio is a comparison of two quantities by division.

52
00:03:28,920 --> 00:03:33,680
Because we know that Norbert ate six slices of pizza from the total number of slices,

53
00:03:33,680 --> 00:03:39,560
eight, we would write this ratio as six eaten to eight total.

54
00:03:39,560 --> 00:03:44,640
Ratios can also be written as fractions, like this, six over eight.

55
00:03:44,640 --> 00:03:46,520
Now let's look at proportions.

56
00:03:46,520 --> 00:03:51,320
A proportion is an equation stating that two ratios are equivalent.

57
00:03:51,320 --> 00:03:55,800
Let's compare how much pizza Norbert ate compared to how much Zot ate.

58
00:03:55,800 --> 00:03:57,200
The unit is a slice.

59
00:03:57,200 --> 00:04:03,360
Now we know that Norbert ordered an eight-slice pizza, but Zot wanted his pizza cut into twelve

60
00:04:03,360 --> 00:04:04,360
slices.

61
00:04:04,360 --> 00:04:07,000
We know that Norbert ate six slices.

62
00:04:07,440 --> 00:04:09,680
Norbert eats nine of his twelve.

63
00:04:09,680 --> 00:04:14,480
Norbert's ratio of eaten slices to total slices was six to eight.

64
00:04:14,480 --> 00:04:16,240
What will Zot's be?

65
00:04:16,240 --> 00:04:19,000
That's right, nine to twelve.

66
00:04:19,000 --> 00:04:23,360
To see if these ratios form a proportion, we set them up like this.

67
00:04:23,360 --> 00:04:26,000
Six-eighths equals nine-twelfths.

68
00:04:26,000 --> 00:04:32,320
Next, we cross-multiply the denominators and numerators like this.

69
00:04:32,320 --> 00:04:37,680
If the answers on either side of the equal sign are the same, then the two ratios are

70
00:04:37,680 --> 00:04:38,680
proportional.

71
00:04:38,680 --> 00:04:44,000
Now that we know Norbert has been well-fed, let's visit with students from Cole Middle

72
00:04:44,000 --> 00:04:46,160
School in Oakland, California.

73
00:04:46,160 --> 00:04:50,960
They're doing a classroom activity on decimals and percentages, along with some scientific

74
00:04:50,960 --> 00:04:53,400
observations on their sleep.

75
00:04:53,400 --> 00:04:54,400
Hello.

76
00:04:54,400 --> 00:04:56,680
Welcome to Cole Middle School.

77
00:04:56,680 --> 00:05:00,880
We're about to show you a cool activity that you can try with your class.

78
00:05:00,880 --> 00:05:05,080
You can view and download this activity from the NASA Connect website.

79
00:05:10,440 --> 00:05:14,400
Our teacher gave us data sheets to collect information about the way we and our family

80
00:05:14,400 --> 00:05:16,000
sleep at night.

81
00:05:16,000 --> 00:05:20,520
On the data sheet, we recorded when we went to bed, when we woke up, and how many hours

82
00:05:20,520 --> 00:05:21,520
we slept.

83
00:05:21,520 --> 00:05:25,080
Some of us also kept track of other members in our family.

84
00:05:25,080 --> 00:05:27,920
We collected this data for at least one week.

85
00:05:27,920 --> 00:05:32,400
We also recorded some observations about how we felt throughout each day.

86
00:05:32,400 --> 00:05:36,600
Using the logs, we made graphs to see if any patterns occurred in our data.

87
00:05:36,600 --> 00:05:41,720
Next, using the data, we figured out the average number of hours each person slept.

88
00:05:41,720 --> 00:05:46,360
Some of us noticed that younger kids in our families sleep a lot more than we do.

89
00:05:46,360 --> 00:05:51,720
We also noticed that some days we felt really tired and had a hard time getting out of bed.

90
00:05:51,720 --> 00:05:56,880
Next, we created another representation of our data called fraction wheels.

91
00:05:56,880 --> 00:06:01,120
To make our graph, these wheels showed how much of our day was spent sleeping.

92
00:06:01,120 --> 00:06:06,480
Write this portion as a fraction and convert this to percent and then decimal.

93
00:06:06,480 --> 00:06:12,320
To make our fraction wheels, we used colored construction paper, pencils, compass, protractor,

94
00:06:12,320 --> 00:06:13,480
and scissors.

95
00:06:13,480 --> 00:06:15,920
We drew two circles and cut them out.

96
00:06:15,920 --> 00:06:20,440
One entire circle represents 24 hours in an Earth day.

97
00:06:20,440 --> 00:06:24,560
Remember the length of any planet's day is the number of hours it takes to rotate once

98
00:06:24,560 --> 00:06:27,440
on its axis.

99
00:06:27,440 --> 00:06:33,240
Because there are 24 hours in one day, we divided one of our circles into 24 equal pieces.

100
00:06:33,240 --> 00:06:37,400
We used a vision to figure out how many degrees were in each piece.

101
00:06:37,400 --> 00:06:41,000
Can you think of another way of making 24 equal pieces?

102
00:06:41,000 --> 00:06:46,800
Next, we needed to make the slits that let us split the two circles together, like this.

103
00:06:46,800 --> 00:06:50,680
Now we could see what fraction of our day was spent sleeping, and it was easy to see

104
00:06:50,680 --> 00:06:54,120
how fractions, percents, and decimals are the same.

105
00:06:54,120 --> 00:06:57,680
Now we must also research the length of a day on other planets.

106
00:06:57,680 --> 00:07:01,880
For more information about this and other student activities, visit the NASA Connect

107
00:07:01,880 --> 00:07:02,880
website.

108
00:07:02,880 --> 00:07:07,760
Awesome job.

109
00:07:07,760 --> 00:07:11,040
Well, we've seen how Cole Middle School conducted the activity.

110
00:07:11,040 --> 00:07:15,440
Let's return to Derek's challenge, take it a step further, and see if we can help Norbert

111
00:07:15,440 --> 00:07:16,440
out.

112
00:07:16,440 --> 00:07:18,400
Oh, my hands are talking to me.

113
00:07:18,400 --> 00:07:20,080
Thanks, Jen.

114
00:07:20,080 --> 00:07:21,360
Okay, kids.

115
00:07:21,360 --> 00:07:23,200
You have learned how to set up ratios.

116
00:07:23,200 --> 00:07:26,600
Let's apply what we have learned to Norbert and Zot as they explore the other bodies of

117
00:07:26,600 --> 00:07:28,000
our solar system.

118
00:07:28,000 --> 00:07:31,560
We want to make sure Norbert and Zot get the right ratio of rest.

119
00:07:31,560 --> 00:07:36,320
On Earth, Norbert feels pretty good when he sleeps about 9 out of 24 hours, or three-eighths

120
00:07:36,320 --> 00:07:37,320
of the day.

121
00:07:37,320 --> 00:07:38,320
A lot like you.

122
00:07:38,320 --> 00:07:42,840
But if he wants to get the same ratio of rest when he visits Neptune, how much should he

123
00:07:42,840 --> 00:07:43,840
sleep?

124
00:07:43,840 --> 00:07:48,000
First, you will need to find out how many hours are in a whole day on Neptune.

125
00:07:48,000 --> 00:07:51,240
Next, we need to apply ratios and proportions.

126
00:07:51,280 --> 00:07:55,400
Remember, a ratio is a comparison of two numbers by division.

127
00:07:55,400 --> 00:07:59,400
In this case, we are comparing hours on Earth to hours on Neptune.

128
00:07:59,400 --> 00:08:05,560
The unit of measure is an hour, and a proportion is a statement that two ratios are equivalent.

129
00:08:05,560 --> 00:08:10,160
How many hours of sleep are needed on Neptune in order to create a proportion with the same

130
00:08:10,160 --> 00:08:11,920
Earth rest ratio?

131
00:08:11,920 --> 00:08:16,400
Teachers, now is a good time to pause the program.

132
00:08:16,400 --> 00:08:18,080
Let's see what you came up with.

133
00:08:18,080 --> 00:08:23,280
You should have set up a proportion that states 9 over 24 hours on Earth is equivalent

134
00:08:23,280 --> 00:08:25,960
to X over 16 hours.

135
00:08:25,960 --> 00:08:30,720
We use the variable X for the amount of sleep hours since we don't know the value yet.

136
00:08:30,720 --> 00:08:34,240
Next, we will cross-multiply like this.

137
00:08:34,240 --> 00:08:38,240
Find the products on both sides of the equation and solve for X.

138
00:08:38,240 --> 00:08:40,920
X equals 6.

139
00:08:40,920 --> 00:08:45,320
In order for Norbert to sleep three-eighths, or 9 twenty-fourths of his day while on Neptune,

140
00:08:45,320 --> 00:08:48,360
he should sleep about six hours while on Neptune.

141
00:08:48,360 --> 00:08:49,760
Don't worry if you got this answer wrong.

142
00:08:49,760 --> 00:08:51,760
You can always try again.

143
00:08:51,760 --> 00:08:52,760
Wow.

144
00:08:52,760 --> 00:09:05,320
You know, six hours of sleep a night isn't enough to keep me healthy and performing at

145
00:09:05,320 --> 00:09:08,760
the top of my game.

146
00:09:08,760 --> 00:09:09,760
I know.

147
00:09:09,760 --> 00:09:14,320
Let's check back with RJ and see if he's found out any information on the circadian clock

148
00:09:14,320 --> 00:09:17,560
that might help Norbert in his travels around our solar system.