### Video Transcript

The Number of Hours in a Day

In this video, we’re going to learn
how to model the number of hours in a day. And we’re also going to calculate
times and dates that are 24 hours earlier or later. Let’s start with a question.

If you pointed to one of the
numbers on an analog clock face, how many jumps from number to number would you need
to make to get back to where you began?

Let’s find out. Let’s start with the number eight,
shall we? One, two, three, four, five, six,
seven, eight, nine, 10, 11, 12 jumps from number to number, and we’ve arrived back
where we began. This is true whatever number we
start from. And because we know that when the
hour hand on a clock face moves from one number to the next, an hour has gone
by. We can say that it takes 12 hours
for the hour hand to make a journey once around the clock face. 12 hours take us back to a time
that looks exactly the same as the time we started with.

Although we’ve used 8 o’clock in
this example, this is true of any time. If it’s half past 3, 12 hours
later, it’ll be half past 3 again. If it’s quarter past 11, in 12
hours time, it’ll be quarter past 11 again. So the hour hand goes once all the
way around the clock face in 12 hours. But how many times does the hour
hand go around the clock face in a day? And how many hours are there in the
day?

Let’s draw a timeline to help
us. At the very beginning of our
timeline, we’ll show the start of a new day. What day should we call it? Let’s choose Monday. Now, at what time of day does
Monday begin? Perhaps, you think the day begins
when you open your book at school at 9 o’clock and you have to write the date. Or did the day begin at 7 o’clock
when your alarm went off and you jumped out of bed? Or what about 6 o’clock when the
sun came up and the bird started singing outside? Surely, that’s the start of a new
day, isn’t it?

Well, you know, to find the start
of a new day, we’re going to have to keep pushing that hour hand backwards right
through the time when you’re asleep until we get to 12 o’clock. Now, often, when we think of 12
o’clock, we think of lunchtime, the middle of the day. But did you know there’s a 12
o’clock in the middle of the night, too? Even though it’s dark outside and
you’re probably curled up in bed sleeping away, this is when a new day begins at 12
o’clock in the middle of the night. And we call this 12 o’clock time
midnight. Here’s something else
interesting. Even though it’s the middle of the
night, we call this time 12 o’clock in the morning.

Let’s make the time 12 o’clock, and
we’re going to count through all the hours of the day to see how long Monday
lasts. And every time we count a new hour,
we’re going to move a counter along the number line. One; this takes us to start 1
o’clock in the morning. Two, three, four, five, six hours
have gone by, and it’s now 6 o’clock on Monday morning. Now, depending on where you live
and the time of year, perhaps the sun is starting to come up. The birds are singing outside. Although we might think this is the
time the day begins, the day’s already six hours old.

Let’s keep counting. Seven, eight. It’s 8 o’clock in the morning
now. Perhaps, you’re eating your
breakfast at this time. What time does your school they
begin? For many children, it might be
around 9 o’clock, nine hours after the day begins. 10, 11 o’clock in the morning,
12. This is interesting. On our clock face, it looks like
exactly the same time we began with. This is what we talked about at the
start of the video, isn’t it? After 12 hours, we get to a time
that looks exactly the same as the one we started with except we don’t call this
time 12 o’clock in the morning. As we said already, 12 o’clock in
the morning is midnight.

This is 12 o’clock in the
afternoon, and we call this time midday. It’s the middle of the day. And many people all around the
world might stop what they’re doing and eat some lunch. At 12 o’clock midday, the hour hand
has gone one turn around the clock, and 12 hours have gone by, but it’s still not
the end of the day yet. Let’s keep counting. 13; it’s now 1 o’clock in the
afternoon. 14, 15, 16. It’s now 4 o’clock in the
afternoon. Perhaps, school has finished for
the day in your home. 17, 18, 19, 20. It’s now 8 o’clock at night.

Depending on the time of the year
and where you are in the world, perhaps the sun is going down. It’s starting to get dark. Maybe, it’s even time to go to bed
for the night. Where were we up to, 20? 21, 22, 23, 24. We know that another lot of 12
hours have gone by because we’ve gone from 12 midday once around the clock again to
12 o’clock midnight or 12 o’clock in the morning. And you remember what we said about
12 o’clock midnight. It’s when a new day begins, and we
go from Monday into Tuesday.

So, how many hours are there in a
day? We counted 24, didn’t we? There are 12 hours in the morning
from midnight to midday, and there are 12 hours in the afternoon in the night from
midday through to midnight. And so, we can say that every day
is 24 hours long. And because there are 24 hours in a
whole day, we can use this to help us jump from one day to another. To get from midnight Monday to
midnight Tuesday is 24 hours. To get from half past 4 on a Friday
afternoon to half past 4 on a Saturday afternoon is also 24 hours. In fact, to get from any time of
the day to exactly the same time the next day is always 24 hours.

Now that may have seemed like a
long introduction, but it’s important that we understand where 24 hours in a day
comes from. Let’s try answering some quick
questions now where we put into practice what we’ve learned.

How many times a day does the clock
show the given time?

The clock that the question’s
talking about is shown in the picture. We know that at an o’clock time,
the minute hand points to the number 12, but in this picture it’s pointing to the
number three. It’s moved a quarter of the way
around the clock face. This is a quarter past time. And if we look at the hour hand, we
can see what hour of the day it is. The hour hand is on its way from
the number six to the number seven. We know that at 6 o’clock, it
would’ve been pointing exactly to the number six. And so, we can read this time as
quarter past 6.

Now, our question asks us, “how
many times a day does the clock show this time?” Now, it’s easy to make a mistake
here. We might look at the time and just
say, “Well, there’s only one-quarter past 6 every day.” But let’s use some facts to help
us. Firstly, we know that 24 hours are
the same as one day. When we say a day, we don’t just
mean the daytime when the sun is up; we mean a whole day, for example, Monday or
Tuesday. So this includes the daytime and
the nighttime.

Another fact we can use to help us
here is that the hour hand goes round the clock face once every 12 hours. It doesn’t matter what time of day
it is. It takes 12 hours for it to go all
the way around back to where it was. So if we look at our clock face and
we think that our hour hand is in the exact position for quarter past 6, if 12 hours
go by, it’s going to show quarter past 6 again. But there aren’t 12 hours in a
day. There are 24 hours in a day. This is where we can use a number
fact to help us. We know that 12 plus another 12
make 24.

And so, in a whole day, the hour
hand doesn’t just go once around the clock; it goes twice. This clock is going to show the
time quarter past 6 twice a day, quarter past 6 in the morning and then quarter past
6 in the evening. We know that the hour hand makes
two journeys around the clock face in a day. And you know, it doesn’t really
matter what time this clock shows. The number of times every day that
a clock shows any time is always two.

A business woman went to her
company on Wednesday morning at the time shown below. She had a lot of work, and it took
her 12 hours to finish it. At what time did she finish?

And we can see that we’ve got four
different answers to choose from here. Let’s go through the question
carefully and try to pick out the important information. To begin with, we’re told that a
business woman went to her company on Wednesday morning. This is important because three of
our answers show times on Wednesday, and one shows a time on Thursday. So, the day and the time of day are
important here. But we’re also given more
information than this. We’re told the exact time that this
lady goes to her company. It’s the time on the clock.

What time did she go to work? The minute hand on this clock face
is pointing to the six. It’s gone half the way around the
clock face, and so we know it’s a half past time. The hour hand is halfway between
the number eight and nine. And so, we know it’s half the way
past 8 o’clock on its way to 9 o’clock. The time is half past 8. So, we’re told that this lady goes
to work at half past 8 in the morning.

We’re then told that she had a lot
of work to do, and it took her 12 hours to finish it. That’s quite a long workday. Now, this amount of time, 12 hours,
is important. What do we know about 12 hours? We know that 12 hours is the length
of time it takes for the hour hand to start from a position on the clock face and go
all the way around back to where it started. And we can use this fact to help
us. As we’ve said already at half past
8 in the morning, the hour hand is halfway between the number eight and nine. And so, 12 hours later, when this
lady finishes her work, it’s going to be halfway between the eight and the nine
again. The time will be half past 8
again.

If we look at our first possible
answer, we can see that the clock shows half past 8 on Wednesday. And if we look at the window, we
can see the sun is up in the sky. It looks like it’s Wednesday
morning, doesn’t it? This lady doesn’t finish her work
on Wednesday morning at half past 8; this is when she starts work. So this isn’t the right answer. But you know, we’ve got another
morning time in our answers too. This one shows Thursday morning at
half past 8. Now, if it only took 12 hours to
get from Wednesday morning at half past 8 to Thursday morning at half past 8, then
we could say that there are 12 hours in a day, but we know there are 24 hours in a
day. So if this lady was to finish our
work at half past 8 in the morning the next day, that would mean she’d spent 24
hours on it, not 12.

So, we’re left with two possible
answers. We know that we’re looking for a
half past 8 time. And both of these pictures show
Wednesday night. We can see that because the moon’s
out in the sky. Now, which one of our clocks shows
half past 8? It’s this one, isn’t it? The minute hand is pointing to the
six, and the hour hand is halfway between the eight and the nine. Let’s not make the mistake of
choosing this answer. If you look at this clock, we can
see that the minute and the hour hand have been swapped around. We don’t wanna get them muddled up,
do we? The time that is 12 hours later
from Wednesday morning at half past 8 is Wednesday evening at half past 8.

Noah was studying math, for the
final exam, on Sunday morning at the time shown below. After he looked at his watch, he
said, “There are exactly two days till I start the final exam.” At what time will he start the
exam?

We’re given four possible answers
to choose from here. But before we look at those, let’s
look at the question itself. There’s a lot of words to get
through. Firstly, we’re told that Noah was
studying math for a final exam. It’s not really important what exam
he was studying for, but what is important is when he was studying. We’re told that it was on Sunday
morning at the time shown below. This is talking about the clock
face we can see. And if we read the time on the
clock, we can see that it shows 9 o’clock. So, the first piece of information
we know is that Noah starts studying on Sunday morning at 9 o’clock.

We’re then told that he looks at
his watch. And after he done so, he says,
“There are exactly two days till I start the final exam.” We can use this information to help
us work out the time that he starts his exam. If we start at 9 o’clock on Sunday,
one day later would be 9 o’clock in the morning on Monday, the next day. But Noah’s math exam is not the
next day. It’s two days later. So, if we count on another day, we
get to choose day morning at 9 o’clock. Now, only two of our answers show
Tuesday, and they both show in the morning. But which one shows 9 o’clock?

This is tricky because both clock
faces show a hand pointing to the 12 and another hand pointing to the nine, but the
hands are swapped around. Which one is correct? We know that at 9 o’clock, it’s the
minute hand that points to the 12 and the hour hand, which is the shorter hand, that
points to the nine. Exactly two days after Sunday
morning at 9 o’clock, it will be Tuesday morning at 9 o’clock.

What have we learned in this
video? We’ve learned that there are 24
hours in a day, and we’ve learned how to model this fact. We’ve also learned how to calculate
times and dates that are 24 hours earlier or later.