End Times to the Nearest Five Minutes
In this video, we’re going to model how long something takes or its duration on analog clocks or number lines. And we’re going to count in fives to find the end times of events in minutes.
Here’s a bowl of cookie dough. Let’s imagine that we’ve done all the preparation and the mixing, and all that’s left now is to put the cookies in the oven. When will our cookies be ready? In other words, what’s the end time of the cooking activity? At what time will they have finished being baked? To find the answer, we need to know two things: we need to know the start time and the time taken.
In this example, when we say start time, what we mean is the time now, the time at which we’re about to start cooking. Let’s imagine that we look up at the kitchen clock and we can see that the time is five minutes past 3. We know this because we can see that the minute hand has made one jump of five minutes from an o’clock time. And because the hour hand looks like it’s pointing to the number three, it must have only just been 3 o’clock. Our start time, then, is five minutes past 3 or 3:05.
The second piece of information that we need to work out an end time is how long something’s going to take. We can use a special maths word here to help us, and that’s the word “duration.” Duration of something is just the time that it takes. So, in this example, we need to know the duration of baking the cookies. Now, let’s imagine that we’re following a recipe card. And on the card, it says, “Cooking time: 25 minutes.” So, we know the time it’s going to take to bake our cookies is 25 minutes.
We have the two pieces of information we need to be able to work out the end time when our cookies are going to be ready. We’ve got the start time and the time it is going to take. Now, how can we use these two pieces of information to help us? One way to find the answer is to use an analog clock to help. We can begin by showing our start time, five minutes past 3. As we’ve said already, at 5 past 3, the minute hand points to the number one because five minutes have gone by since an o’clock time. But where’s the minute hand going to be at the end of our cooking time? Where will it be in 25 minutes time?
We can count in jumps of five minutes to find out. Five, 10, 15, 20, 25. We’ve modeled the time that it takes or the duration on our analog clock. And we found out that after 25 minutes have gone by, the minute hand will be pointing to the number six. This is going to be a half past time, isn’t it? It’s going to be half past 3. So, we’d better draw the hour hand in the right place too, halfway between the numbers three and four. The end time for baking our cookies, in other words, when we’re going to open the oven and take them out, is going to be half past 3.
Another way we could find the same answer is by sketching a number line and using it to help. Do you remember how many minutes there are in one hour? There are 60 minutes, aren’t there? So, we can mark our number line from zero to 60. Now, because we’re going to be counting in fives here, we’d better mark all the halfway points too. There we go. Now, our number line is marked in fives. Now, where are we going to start counting from? Do you remember our start time? It was five past 3, wasn’t it? Or 3:05.
So, we need to start counting from the number five on our number line. And just like with the analog clock, we’re going to skip count in fives until we’ve counted on 25. Five, 10, 15, 20, 25. If we start with a time that’s five minutes past something and we count on 25 minutes, then we end with a time that’s 30 minutes past the hour. That’s another way to find out that the time we need to pull our cookies out of the oven is 3:30 or half past 3.
Let’s answer some questions now where we have to put into practice what we’ve learned. In each question, we’re going to be looking for the end time. And what are we going to use to help? We’re going to use the time that something starts and also how long it takes or the duration.
It is 2 o’clock. Pick the time it will be in one hour. 1 o’clock, 3 o’clock, or 12:15.
To begin with, we’re told that the time is 2 o’clock. How do we know this? Well, we can see that the minute hand on our clock face is pointing right up to the number 12; this tells us it’s an o’clock time. And then, the hour hand is pointing straight at the number two; it’s 2 o’clock. And the question asks us to pick what the time will be in one hour. Now, we’re given three different times to choose from, and these aren’t just any three times. One of them is going to end up being the right answer; we know that. But the other two clocks show times that we could choose by accident if we made certain mistakes.
Let’s go through our possible answers and keep an eye out for those mistakes. We don’t wanna make them, do we? If we look at our first clock face, we can see that it’s another o’clock time. The minute hand is pointing to the 12; this clock shows 1 o’clock. Now, this is one-hour difference from 2 o’clock, isn’t it? Is this the right answer? It’s not, is it? We know that it’s 2 o’clock now. So, 1 o’clock is an hour before this time; it’s been and gone. It was 1 o’clock one hour ago. We need to find the time that’s one hour in the future.
So this clock might be an easy mistake to make if you’re counting in the wrong direction. But we’re not going to make that mistake. We’re going to count onwards from 2 o’clock. In one hour’s time, the minute hand will have gone all the way around the clock back to another o’clock time. But the hour hand will have moved on to the next number. It’s going to be 3 o’clock. Now, here’s where we need to make sure we don’t make a second mistake. We know that when it’s 3 o’clock, one of the hands points to the number 12. That’s an o’clock time. And the other hand points to number three, 3 o’clock.
Can you see what’s similar about our two remaining answers? They both have hands pointing to the 12 and to the three. It would be very easy to choose the wrong clock here. Now, we’ve got digital times written underneath each clock, so we can see which one is 3 o’clock. But even if the digital time wasn’t there, we could tell which clock was correct by looking for the one where the minute hand — that’s the longest hand — is pointing to the 12 and the hour hand — that’s the shorter hand — is pointing to the three. On our last clock, those hands are pointing the other way around, and so it shows 12:15 and not 3 o’clock. If it’s 2 o’clock, the time it will be in one hour will be 3 o’clock.
It is 25 minutes after 9. Pick the time it will be in 10 minutes. 9:15, 9:30, or 9:35.
In this question, we’re being asked to find the end time, in other words, the time that it’s going to be. And to help us, we’re told the time that it is now, which is 25 minutes after 9, and also the duration or the time that’s going to go by, which is 10 minutes. So, we’re being asked if it’s 25 past 9 now, what will the clock look like in another 10 minutes time? Let’s sketch some clocks to help us here.
We know that when the time is 25 minutes after nine, the minute hand points to the number five and the hour hand is almost halfway between the numbers nine and 10. This is our start time, and we also know the time that goes by or the duration. The minute hand is pointing to the number five, but 10 minutes need to go by. Remember, the gap between two numbers that are next door to each other on a clock face is five minutes. So, we can skip count in fives to count 10 minutes. Five, 10. After 10 minutes have gone by, the minute hand is going to move so that it is pointing to the number seven.
Now, we know the end time we’re looking for. The minute hand is going to be pointing to the seven. And because it’s just past half past nine, we’d expect the hour hand to be just a little bit more than halfway between nine and 10. And if we look at our answers, we can see that only one of the clocks looks the way we wanted to. It’s this one, isn’t it? We know that 25 plus 10 is 35. And so, 9:25 plus 10 minutes is 9:35. The time that it will be in 10 minutes is 9:35.
Emma leaves her house to walk to the library at 10:30. The walk takes her 15 minutes. What time does she arrive?
This question describes Emma who’s walking from her house to the library. And the question asks us to find out what time she gets there. What time does she arrive? Now, we’re given two pieces of information to help us. We’re told the start time of Emma’s walk. She leaves her house at 10:30 and we’re also told the duration or how long it takes her. The walk takes her 15 minutes. Now, we can use the start time and the duration to help us find the end time. We need to start at 10:30 and count on 15 minutes.
We could use a number line to help us. We know that there are 60 minutes in an hour, so we can label our number line from zero to 60. This shows a whole hour. Now, Emma starts walking at half past 10 or 10:30. So, we can mark the start time on our number line, 30 minutes past 10. Now, let’s show the duration. We need to count on 15 minutes, and we’re going to do this by skip counting in fives. Five, 10, 15. How many minutes past 10 is it now? We’ve ended up halfway between the numbers 40 and 50. This shows the number 45, doesn’t it? It’s 45 minutes past 10.
To work out the end time or the time that Emma arrives at the library, we’ve used the time that she starts her journey and how long it takes. If we count on 15 minutes from 10:30, the end time will be 10:45.
Jennifer leaves to take her dog for a walk at 7:05. They walk for 20 minutes. What time do they return?
This question describes Jennifer who’s taking her dog for a walk. And we’re asked what time they both get back from their walk, in other words, what time their walk ends. And to help us know what time their walk ends, we’ve got two pieces of information to help us. Firstly, we know what time their walk starts. The start time for their walk is 7:05 or five past seven. This is going to be important to us, so let’s sketch it on a clock. Now, we know at 7 o’clock, the minute hand would be pointing directly to the number 12 and the hour hand would be pointing straight at the number seven.
Now, at 7:05, five minutes have gone by. And because we know the gap between one number and the next number on a clock face is worth five minutes, we know the minute hand at five past seven is pointing to the number one. And because it’s still quite near to 7 o’clock, the hour hand won’t have moved very much. This is what the clock looks like when Jennifer and the dog leave.
The other piece of information that we’re going to use here to help us is how long it takes them. We’re told that they walk for 20 minutes. What will happen to the hands of a clock in 20 minutes? At five past 7, the minute hand is pointing to the number one as we’ve said. Let’s count on another 20 minutes. And we’re going to skip count in fives to help us do this. Five, 10, 15, 20.
We can see then that when Jennifer returns home, the minute hand is going to be pointing to the number five. We know that when it points to a six, it is a half past time. And at that point, the hour hand will be halfway between the seven and the eight. So, at the moment, it’s almost half past 7. So, we could draw the hour hand about here. So, how would we read this time? We know that it’s still 7 something, that if the minute hand was pointing to the number six, it would be 7:30. At the moment, it’s one number before the six, isn’t it? So, this is five minutes before 30. We know that 30 take away five is 25. And so, the time that Jennifer and her dog return home is 7:25.
What’ve we learned in this video? We’ve learned to model the time that something takes or its duration on analog clocks or number lines. And we’ve skip counted in fives to find the end times of events in minutes.