Lesson video

Hello, there.

My name is Mr. Tilstone.

I'm a teacher.

It's lovely to see you and lovely to be here with you today, teaching you a lesson all about unit conversions.

Today specifically, we are going to be looking at unit conversions to do with time.

And at the end of the lesson, we're going to play a fun game of Would You Rather? So if you are ready, I'm ready.

Let's begin.

The outcome of today's lesson is, I can solve problems involving converting between units of time.

In this lesson, we've got just one keyword and that is, my turn, convert, your turn- Can you remember what convert means? It's probably a word you've encountered quite a lot recently.

Well, let's have a reminder anyway.

To convert is to change of value or expression from one form to another, such as minutes to hours.

Can you think of another example? Maybe, hours to days for example.

Well, that's converting.

Our lesson is split into two cycles.

The first will be times in the day and the second beyond the clock.

So if you're ready, let's start by looking at times in the day.

In this lesson, you're going to meet Andeep.

Have you met him before? He's here today to give us a helping hand with our maths.

Let's have a little starter.

These are all time conversions, but only the initial letter of each unit of time has been used.

Can you work out what they are? So have a look at those, think about what you already know.

'Cause I think you already know most or all of these.

What do you think they short for? Well, let's have a look.

So we've got 60 minutes in one hour, 12 months in one year, seven days in one week, 24 hours in one day, 365 days in one year.

What about the 366 then? 366 days in one leap year.

You might want to write those down if you think you've not got them committed to memory, you might want to write them on a big sheet of paper or something like that.

So let's have a look.

So one hour equals 60 minutes.

I think you knew that already.

I'm confident you did.

The clock is showing 50 minutes past the hour.

We don't know which hour, it doesn't matter.

But it's showing 50 minutes past the hour.

Can you think of another way to say that? 50 plus something equals 60.

So a nice bit of hopefully, simple arithmetic for you there.

50 plus what, equals 60.

50 plus 10 equals 60.

50 minutes plus 10 minutes equals 60 minutes.

It is also showing 10 minutes to the next hour.

So it's 10 too.

Now what is the time 20 minutes later than 8:50? So we're going to put an hour in this time.

What's 20 minutes later than 8:50? Have a little go first and then we'll explore that.

Well, here's 8:50 on a number line and we're adding 20 minutes on.

What's the answer going to be? There are 60 minutes in an hour.

Adding 20 minutes to 8:50 would give 8:70, which doesn't make sense as a time.

You don't have a time 8:70 because they're only 60 minutes in an hour.

So that can't be right.

So we have to do something else.

The 20 minutes needs to be partitioned into the minutes to the o'clock, which remember we said was 10 and the minutes from the o'clock time.

This means you can bridge through the next hour.

So we're going to do some bridging.

So that 20 minutes, we're going to partition into 10 minutes and 10 minutes.

And 10 minutes later than nine o'clock is 9:10.

So that's called bridging and that's the correct answer.

Andeep, Izzy, and Alex start walking to school at hmm.

So some unspecified time.

It takes them hmm minutes.

We dunno how many yet.

What time do they arrive? Okay, that's a problem.

Let's have a look at a different problem.

See what you notice.

Andeep, Izzy, and Alex arrive at school at hmm? It took them hmm minutes to walk there.

What time do they set off? Was that the same? Was that similar? Was that different? What do you think? Let's have a look at one more.

Andeep, Izzy, and Alex set off for school at hmm and arrive at school at hmm? How long was their journey? Okay.

What have you noticed about those problems? Well, they're all quite similar.

They're all involve.

Andeep, Izzy, and Alex and walking to school, but they're slightly different too.

They're asking for different things, there's a different focus each time.

And that's been put in purple.

So what time did they arrive, what time did they set off, and how long was their journey? So they seem similar but each one is giving and asking for a different piece of information.

So think what information will the problem give us and what information will we need to calculate? So let's look at that first one.

Andeep, Izzy, and Alex start walking to school at hmm and it takes them hmm minutes.

What time do they arrive? So when there are values added to the blank bits, what will we be given and what will we need to calculate? Let's have a think.

So let's think about what's known and what's unknown.

So the start time, the finish time, and the duration.

Of each of those, which is known and which is unknown? Well, the start time will be known, will be given the starting time.

Andeep, Izzy, and Alex start walking school at hmm.

That's when they start walking and the duration will be known.

It takes them hmm minutes.

So duration is how long something takes.

What we don't know and what's going to need to be calculated is what time do they arrive.

So that's an unknown fact at the minute.

Now we can represent this on a number line just like before.

So we've got a number line.

On the left is a start time, on the right is a finish time, and the duration is the timing between those two times how long it takes.

Right.

So let's put some times in.

So let's say they start walking to school at 7:50 AM.

That's known.

And let's say, it takes them 20 minutes.

Now we've looked at that number quite recently, haven't we? So hopefully, this is ringing a bell.

So we know the duration.

So we've got to calculate 20 minutes later than 7:50.

Now I'm sure you know that it's not 7:70.

We need to do a bridge, don't we? We need to bridge through the o'clock, the next o'clock, which is eight o'clock to find that unknown time.

Time bridges o'clock.

So it needs to be partitioned into minutes to the hour and minutes past the hour.

So we need to do something to that 20 minutes, partition it, split it into two parts.

Okay.

So if we bridge to the next hour, the next hour is eight o'clock, that's 10 minutes, and then another 10 minutes makes 20 minutes.

So that 20 has been partitioned to 10 and 10.

10 minutes later than eight o'clock is 8:10.

That's what time they arrive.

Let's look at a different problem.

Andeep, Izzy, and Alex catch a bus at hmm.

It is a hmm minute journey.

What time do they arrive at their destination? You might notice that's a quite similar problem in terms of structure to the previous one.

Because just like last time, we know the start time.

It's a bit more specific this time though.

7:47 AM and bus times and train times and tram times usually are.

So 7:47 and it's a 24 minute journey.

So we know the duration, what time do they arrive at their destination? So we are looking at what's 24 minutes later than 7:47.

Remember, we can't simply add 24 onto 47 because it will take us past 60.

So we need to partition.

And that's unknown, the finished time.

The time it takes bridges eight o'clock.

So it needs to be partitioned into minutes to the hour and minutes past the hour just like before.

So 7:47 to eight o'clock.

So you need to use your knowledge of numbers to 60.

So 47 plus what, equals 60, 13.

So 13 minutes after 7:47 is eight o'clock.

So we've split that 24 minutes into 13 minutes.

And what? What goes with 13 to make 24? What do you add to 13 to get to 24? And the answer is 11.

So 11 minutes after eight o'clock is 8:11.

And that's called bridges.

And that's what time they arrive at their destination, 8:11 AM.

Andeep, Izzy, and Alex catch a bus at hmm, it's a hmm minute journey.

What time do they arrive at their destination? So 8:47, the start time is known.

This time though, it's a one hour and 24 minute journey.

So it's more than an hour this time.

What time do they arrive at their destination? Hmm, we don't know the finish time.

The time it takes is over an hour and bridges through either nine or 10 o'clock.

It needs to be partitioned into one hour and then minutes to the hour and minutes past the hour.

So we've just got one more step to do this time.

So let's start with that one hour.

So 8:47 plus one hour, what do you think is that? That's 9:47.

Hopefully, that was quite straightforward for you.

And then we're going to partition the 24 minutes into 13 minutes, because that will take us to the next hour, which is 10 o'clock.

So 13 plus what, equals 24.

13 plus, we've done this before, 11.

So another 11 minutes after 10 o'clock is 10, 11 or 11 minutes past 10.

And that's what time they arrive at their destination.

So it was just the same as before.

Only this time, we needed to add the hour on as well.

Let's have a little check.

Let's see if you can use those number line skills or those partitioning skills.

Class five start a math test at 10:50 AM.

It takes them 35 minutes.

What time do they finish? So just like before you know the start time, you know the duration, you don't know the end time.

You can calculate that using hopefully, a number line, pause a video and have a go.

Let's have a look.

So here's your number line, starting with 10:50.

You are adding 35 minutes on, but we can't do that or take us past 60.

We don't know the end time, so we're gonna partition.

Partition the 35 minutes into 10 minutes and 25 minutes to bridge through the 11 o'clock.

So we add that 10 minutes on to get to 11 and the other 25 minutes, making 35 in total and that takes us to 11:25.

So very well done.

If you said 11:25, that's the correct answer and you're on track.

Let's have a look at another one and see what you notice.

Andeep, Izzy, and Alex arrive at school at hmm and it took them hmm minutes to walk there.

What time do they set off? Okay.

That's slightly different isn't it? That's got different known information and a different focus, different unknown information.

So let's have a look.

What will we know? It's asking for a different piece of information that's the bit we don't know.

So if they arrive at school at 9:10, we know the finish time this time and it took them 20 minutes to walk there.

So we know the duration this time.

What time do they set off? So we're kind of going backwards a little bit here.

We're starting at the end.

So we're going to go back 20 minutes this time.

Now just like before, it's not as simple as just taking 20 from 10, we're going to have to bridge, going to have to partition that 20 minutes into two different parts.

We're going to have to go back to the o'clock.

So that's nine o'clock and that's 10 minutes, and then another 10 minutes making 20.

Altogether, we'll take us two.

What's 10 minutes before nine o'clock? That's 8:50.

So that's what time they set off, 8:50.

So it was very similar to before, but just going the other way round this time.

Well, let's do another check.

Class five finish a maths test at 2:15 PM.

It took them 40 minutes.

What time did they start? So just like before, we know the end time, we know the duration, we don't know the start time.

See if you can use a number line to work that one out.

Pause the video and have a go.

Did you manage to get an answer? Let's have a look.

So we start with the 2:15 this time and we're partitioning that 40 into 15, taking us to two o'clock and 25, taking us to 1:35.

So well done if you said 1:35 PM.

You are correct.

What about this question? What do you notice this time? Andeep, Izzy, and Alex set off for school at hmm and arrive at school at hmm.

How long was their journey? Now did you notice that slightly similar and slightly different as well to before? It's asking for a different piece of information and the information it's asking for, is how long was their journey? But this time, we know the start time.

They set off a school at 7:50.

That's when they start.

This time we also know the finish time.

That's 8:10.

What we don't know is the duration, how long the journey was.

That's what we're going to have to calculate.

And just like before you guessed it, we can use a number line.

So 7:50 is when we start.

8:10 is the end time and we've gotta work out what that duration is.

Just like before, we are going to bridge and partition.

So if we bridge to eight o'clock and from eight o'clock, it's 10 minutes to eight o'clock from 7:50 and it's 10 minutes from eight o'clock to get to 8:10.

At 10 equals to 20, so it is 20 minutes, that's a 20 minute duration.

Let's have a look at this one.

Andeep, Izzy, and Alex catch a bus at hmm and gets off the bus at hmm.

How long was their journey? A bit similar to the last one won't you say? We know the start time and we will know it and we will know the finish time, we won't know the duration.

That's what we'll have to calculate.

So let's put some numbers in, let's some put some times in.

So 8:33 AM is what time the journey starts.

9:18 AM is what time it finishes, don't know the duration.

So let's work it out.

So again, just like before, the numbers are a little bit trickier this time, but it's the same structure, same concept.

So you are working out 8:33 to nine, and then nine to 9:18, and that's the easier part, the last part.

So from 8:33 to nine, it's a 27 minute duration.

And then from nine to 9:18, it's an 18 minute duration.

What do I do with those two numbers, the 27 and the 18? We add them together and you can use any strategy you like.

I think that's one that you could do mentally I would add 20 and take two.

But whatever you want to do, it gives you 45 minutes.

So that was a 45 minute journey.

Let's do another check.

Class five start a math test at 11:35 AM and finish it at 12:15 PM.

How long was the test? So just like the last question, we know the start time, we know the finish time, we don't know the duration.

Use a number line to work it out.

Pause the video and have a go.

Let's see, here's your number line.

We know the start and end times.

Gotta bridge through 12 o'clock.

So first of all, 11:35 to 12.

So what do you add to 35 to get to 60? That's 25, so 25 minutes.

And then the easy part, I think getting from 12 to 12:15, that's 15 minutes.

And then adding those two numbers together, they're fairly friendly numbers.

They go together pretty well.

You should hopefully able to do that mentally.

That is 40 minutes.

The test was 40 minutes long.

Well done, if you got that.

It's time for some practise.

Look at the following problems. Write ST next to the ones where the start time, ST for start time is unknown.

So when you don't know the start time when that's going to be your focus, write ST.

FT next to the ones where the finish time is unknown and D next to the ones where the duration is unknown, so how long it is.

And when you've done that, solve each one using a number line to support your calculation.

So the questions are as follows and you're going to write ST, FT or D, next to each one.

A, Sophia has to leave for school at 8:05 and it's now 7:53 AM.

How long has she got left at home? B, Izzy has just woken up.

The time is 7:40 and mom tells her she needs to leave school in half an hour.

What time does she need to leave? Playtime at to academy starts at quarter to 11 and finishes at five minutes past 11.

How long does it last? D, home time at Oak Academy is quarter past three.

The afternoon session starts straight after lunch and lasts for two and a half hours.

What time does the afternoon session start? So that one involves a time of more than an hour.

E, lunch lasts for 50 minutes, what time does it start? And you'll need to use your answer to D as your starting point for that.

And F, Sam goes to bed at 8:55 PM and sleeps for nine and a half hours.

What time does she wake up? Pause the video.

Good luck with that if you can work with somebody else and compare answers and strategies, and what have you.

Good luck and I'll see you soon.

Welcome back.

How did you get on with those? How did you find that? Let's have a look.

Sophia has to leave the school at 8:05.

It's now 7:53.

How long has she got left at home? So what was the focus of that? That was a D.

We're looking for the duration, we don't know that.

And using a number line, we go from 7:53 to 8:05.

So that means we need to bridge to eight.

So seven minutes will take us to eight, five minutes to 8:05.

Add them together and you've got 12 minutes.

Well then if you've got that one, this is just woken up.

The time is 7:40 AM.

Her mom tells us, she needs to leave for school in half an hour.

What time does she need to leave? So what don't we know this time? What's the focus? The finish time.

We're looking to work at the finish time.

We know the start time.

We know the duration.

So that's the start time and we're going to bridge through eight o'clock this time for the duration.

So 20 minutes and 30 minutes which make half an hour.

Well done if you knew that, takes us to 8:10.

So that time is the finish time.

Playtime at Oak Academy starts at quarter to 11 and finishes at five minutes past 11.

How long does it last? So for this one, you need knowledge of what quarter two means.

Hopefully, you knew that.

And the duration is what we're looking for here.

So 10:45 is quarter to 11.

So we're going to bridge through the 11.

So 15 minutes takes us to 11 and five minutes takes us to 11:05.

Add them together and you've got 20 minutes.

And home time at Oak Academy is quarter past three.

So again, you're going to need to know what quarter past is.

I'm sure you do, that's 3:15.

The afternoon session starts straight after lunch and last for two and a half hours.

What time does the afternoon session start? Don't we know this time? We don't know the start time.

So we have to start at the end.

So 3:15 going back two hours to start with.

So two hours before 3:15 is 1:15.

So that's a two hour part covered and we need to get the half an hour bit covered now.

That's 30 minutes and we're gonna split that into 15 minutes to take us back to one and 15 minutes to take us back to 12:45.

Well then if you've got that, there's quite a lot to know and to do in that one.

So well then if you've got it, 12:45.

Lunch lasts for 15 minutes, what time does it start? Use your answer to D as a starting point.

We're looking for the start time.

Okay.

So we've got 12:45, we know that already.

And we're going to go back to 12, that's 45 minutes and it lasts for 15 minutes.

So another five minutes is needed.

Five minutes before 12 o'clock is 11:55.

11:55.

And if Sam goes to bed at 8:55 PM and sleep for nine and a half hours.

What time does she wake up? We don't know the finish time this time.

We know the start time though, 8:55.

Let's put that nine hours in.

Now that was tricky because that goes past midnight.

There's quite a lot to do here, but nine hours later than 8:55 is 5:55 and then we need another half an hour on top of that.

So going to have to partition that into five minutes and 25 minutes.

So there's your five minutes taking you to six and the other 25 minutes takes you to 6:25.

Well done if you've got that.

Again, lots going on there.

So big well done if you've got that.

Right.

Are you ready for the second cycle? This is beyond the clock.

We're going to play a game of Would You Rather? Have you played this before? You've gotta get two options.

You've gotta say which one you'd rather do but you've gotta justify it.

So, would you rather go on holiday for three full weeks or for 20 days? I'm presuming you like holidays, I certainly do.

So we've gotta work out which is the better deal there.

Three, four weeks or 20 days? We need to do a bit of a unit conversion here that's there are seven days in one week.

So seven days times three, gives us 21 days.

So three full weeks is 21 days, which is slightly greater than 20 days.

Andeep says, and I agree with him, I would rather go on holiday for three, four weeks.

Me too, because you're getting one extra day.

So, definitely.

Seven times three says Andeep, is a times table's fact, which I knew off by heart.

Yes, me too.

It was instant.

I didn't need to do much thinking for that.

It was there already.

Let's do another one.

Would you rather play your favourite video game every day for 40 months or every day for three years? It's gotta be a good video game, hasn't it? But hmm, and you've gotta like video games I guess.

But what would you rather do? So let's have a think.

Every day for 40 months, every day for three years.

We need to do another unit conversion and we need to know that there are 12 months in one year, which I bet you did know that already, 12 months in a year.

Now it said three years.

So 12 months times three is 36 months.

40 months is greater than 36 months.

So if I've got those choices.

Just like Andeep, I'd rather play my favourite video game every day for 40 months, 'cause you're getting four extra months.

Definitely.

And he says 12 times three is another times tables fact.

So I knew that automatically.

So if you know all your times tables facts, specifically the 12 ones is time, you don't need to do much calculation.

So important to know those tables facts.

Would you rather have superpowers for 75 hours or three full days? So what do you think is a unit conversion we need to do this time? Is that three full days? So what we're going to do with that.

24 hours in a day, I bet you knew that.

24 hours times three equals 72 hours.

That wasn't a times tables fact was it? We'll come back to that in a second.

75 hours is slightly greater than 72 hours by three hours.

So Andeep says, I'd rather have superpowers for 75 hours.

What could you do with those extra three hours if you had superpowers? I don't know, but I'll definitely take that deal.

This time it says, I used a written method of short multiplication, because he couldn't do 24 times three in his head.

You might be able to.

Andeep couldn't, so he used something else.

He used a short multiplication.

Let's do another one.

Would you rather receive this money every day for three years or every day for 1000 days? Hmm.

I'm confident you want the money, I'm sure.

Let's have a look.

So every day for three years or every day for 1000 days? Well, there are 365 days in one year.

Apart from leap years, of course.

365 days times three equals 1,095 days.

And I would have to use a written calculation like that to calculate that, but whatever way, it gives you 1,095.

1,095 is greater than 1000 days.

You'd be getting that money every day for 95 extra days.

So that's definitely the one worth taking.

Andeep agrees, he says I'd rather have that money every day for three years.

Definitely.

He says, so I had a quicker way to answer this one.

Oh okay, I like that.

That's called being fluent.

1000 divided by three is just over 333.

So three lots of 365 had to be more than 1000.

Oh yes, that's true.

So he didn't even use a calculation at all.

He didn't have to.

Good work, Andeep.

You really thought your way around that one.

Let's have a check.

Would you rather have superpowers for 10 days or 250 hours? Think about what unit conversion you are going to need for that one and have a go, pause the video.

Again, presuming you want to have superpowers, but who wouldn't? So there are 24 hours in one day.

So 24 hours times 10 is 240 hours.

Now for me, that's not a calculation I need to do a lot of thinking about.

I know that to multiply number by 10, you move all the digits one place to the left, so that was pretty straightforward.

240 hours is less than 250 hours.

So Andeep says and I agree, I'd rather have superpowers for 250 hours, definitely.

And he said, I can quickly multiply numbers by 10 in my head easily.

It is time for some practise.

Circle the option you'd rather have or do and explain why.

Good luck with that.

Have some fun and I'll see you soon for some feedback.

Welcome back.

So what would you rather do? Again, this is a matter of opinion and preference, but as long as you can justify it.

That is fine.

I would rather eat what I want for 50 hours, 24 times two equals 48 and 48 to less than 50.

I'd rather be a celebrity for five weeks, because seven times five equals 35 and 35 days is greater than 30 days.

I'd rather live for 100 years because 365 times a hundred is 36,500, which is greater than by a long way in fact, 25,000.

I'd rather have a daily wish granted by a genie for 3000 days.

Although, I think I'd struggle by the end to think about what I wanted, but I'll take that deal.

So 365 times 80 equals 2,920 and I would've used short multiplication for that one.

And 2,920 days is less than 3000 days.

I would rather receive a piece of gold every month for nine years.

12 times nine is 108.

That's a times tables fact.

So hopefully that was instant and 108 months is greater than a hundred months.

The last one was a bit of a trick one, 'cause it was the same, half a day equals 12 hours.

12 times six equals 72.

So 12 times 60 minutes equals 720 minutes.

So wearing a cloak of invisibility for half a day is exactly the same as wearing a cloak of invisibility for 720 minutes.

I wonder what you'd do with a cloak of invisibility.

Sound like a good story? Maybe you could write that story.

We've come to the end of the lesson and I've had great fun.

We've been solving problems involving converting between units of time.

When time problems involve bridging our clock.

It is helpful to partition the time going to the hour and then from the hour.

The key conversion fact that 60 minutes equals one hour can be used when bridging to the hour.

Other time conversion facts do exist as well, such as 24 hours equals one day, seven days equals one week, 365 or 366 days equals one year and 12 months equals one year.

And these can be used as a basis for other conversions.

It's been a lot of fun working with you today.

I've really enjoyed it.

Hopefully, I get the chance to work with you again soon and do some more maths with you soon.

But until then, enjoy the rest of your day, whatever you've got in store.

Take care and goodbye.