Lesson Video: The Number of Hours in a Day | Nagwa Lesson Video: The Number of Hours in a Day | Nagwa

# Lesson Video: The Number of Hours in a Day Mathematics

In this video, we will learn how to model the number of hours in a day and calculate times and dates that are 24 hours earlier or later.

15:24

### 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.