Lesson video

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Hey everyone, nice to see you again.

My name is Mr. Ward.

Thank you for joining me once again, on Oak National Academy.

And today, we're on lesson nine of the unit line graphs and timetables, where we'll be looking at a series of transport tables and trying to record the information and answer a range of questions that are presented to us.

As always, it's good to be in a nice, quiet spot, free of distractions.

And when you're ready to start the lesson, and you've got all the equipment you need, we can get going.

Don't worry, everybody.

Before we make a start on our lesson, we of course have got time for our mathematical joke of the day.

For those that are new to Oak National Academy, today in my lesson taught by myself, Mr. Ward, I like to have a maths joke at the start of the day to get you smiling or groaning, but it gets you thinking mathematically.

I think it makes a nice warm up for the lesson.

So today the maths joke is simply this, what do you call a very fidgety number that won't stay in one place? A roamin' numeral! Now, if you think you can improve the standard of our jokes, there is an opportunity to share your own mathematical jokes with us here at Oak National Academy, details of which are shared at the end of the lesson.

So please keep watching to the end of the video.

Before we figure that one out, today's lesson; We introduce the new learning of the transport timetables.

Then you can have an opportunity to talk, test, and match number lines to the information presented.

We'll develop our understanding a bit further by using our skills.

So work out a variety of information from the tables presented, and then it'll be over to you as always.

You'll have an opportunity to interpret timetables and answer questions before having it go at the end of lesson quiz, just to show just how confident you are when you do timetables.

In order to make our lesson productive, We need to ensure we've got all the right equipment.

So if you've got a pencil, ruler, paper, or book or notebook that's been provided from school.

If you haven't got any of those things, you do need to go and get them.

So please pause the video.

Go and get exactly what you need.

And then when you're ready to resume the lesson, we can continue.

Okay, let's make a start on our main lesson today.

And we're going to be introducing the concept of using transport tables.

So using timetable in context is the real reason why we have timetables in everyday life.

It allows us to find the right information and to plan ahead or to identify what might be happening in the future.

So on, so forth.

So we use timetables for transport.

We use timetables when we look at events and schedules.

We use timetables when we're planning events in our calendars or diaries.

Just before I introduce the transport tables, I think it will be a good idea to get our brains warmed up by having another go at the missing information in the table ahead of you.

So those that have watched previous lessons in this unit, especially lesson eight will know how useful a number line can be to help us find timetables.

If you haven't gotten that, you should use any strategy that you think would be effective to complete these tasks.

So pause the video.

Spend a couple of minutes filling in the information so you can complete that table.

And then we'll briefly share the answers.

Good luck, speak to you in a few minutes.

Okay, we'll quickly share our answers.

Like I said, you may have decided to use a number line like we discussed previously, or you may have used mental arithmetic to work out the different duration of events or the start and finish time.

And of course you would have probably have had to convert between 12 and 24 hour analogue digital type.

So there are your answers on the board.

I'm sorry, I do say board.

I know it's a screen.

It's the same thing, quite old-fashioned.

I'm a teacher.

We have boards.

I miss those boards.

And now we can have a stance on today's transport timetables.

Again, lots of information.

As you can see, this is something you may see actually, every bus stop.

When you know, out and about in town, you know, you go to a bus stop, you'll probably see hidden beyond the plastic perspect, so it's protected from the weather.

The information it often gives you details about the stop, the bus stop, the time that that- so I'm coming across here- the time that the bus leaves that stop, and then the time it arrives at the next stop and so on and so forth.

So, here we have five bus stops on the route and there are three different buses that leave different times to get to the point.

Of course, I want to find out which bus completes the bus route in the quickest time.

So nice and even, what I'm going take is, I'm going to find the time it arrives at the last stop.

We'll do Sway Retail Park.

And I'm going to take the time and I'm going to take away the time it stops to compare the journey at High Road.

So I'm going to do 09:22 I'm going to take away 08:40.

I'm going to do that with column subtraction on time.

And that's going to give me the answer for the time interval between the journey.

And there we are, as you can see two take away zero is two, I can't take two so I have to exchange one.

So I'm exchanging it over here to come back over, coming over.

So now I've got 12 take away four, which is eight, and then I can just take eight take away eight, zero.

And there you have the answer.

It's 82 minutes, isn't it? No? Excellent.

I'm really glad that you're pointing out my mistakes.

Using column subtraction, strong as it may be, does not really work when we're looking at time, because of course, when we use column subtraction, when you imagine that, you know, nine is the most amount of units and it moves on to the next column, so nine and then 10 and then, and so on and so forth.

We are using 60, no, 100 when we think about limited time.

So column addition or column subtraction, doesn't really generally work and we tend not to encourage people to use it.

We try to use other methods of finding the time.

Okay, well, I'm going to do some modelling for you again.

Now those, again, that are familiar with lesson eight, you may have seen me use this method.

If you haven't, it's absolutely fine.

I'm introducing it again.

If you have seen this method before, why don't you have a go while I'm doing it and we'll show you several ways of doing this.

So first of all, you can see on screen, I actually want to find the interval between bus B leaving High Road and arriving at Sway Retail Park.

So I'm going to use a blank number line.

I'm going to start with my starting point, which I know is 09:05.

And I'm going to get to 09:47.

Now we can do this in multiple ways.

First of all, I can do the intermediary stop if I want to.

So it's a new lane.

I'm adding seven minutes because I get there at 09:12, and then I'm adding 09:21, 09:21.

Well, I know that that's an extra nine.

So together that's 16, that's important for me.

And then for Main Street to Blue Road, I'm going to jump 13 minutes and that's going to take me to 09:34 and then 34 to 47 or 47 take away 34 is 13.

So I know that I'm adding 13 as well.

And again, these two here are worth 26, 13, 13, we've 26, and then I've got 16, which is seven and nine.

So if I add my 26 and 16 together mentally, I know I can get 42 minutes.

Sorry, that was an accident.

So I did that.

I did it mentally, but I also did it just to show you that if you want to be confident with your mental you can add that with your columns.

Okay, now.

Of course, what I noticed here was that I could have done it a far simpler way depending how comfortable you are.

I could have started simply with knowing five and I could have made one big jump of 42 minutes because I knew that five and 47, the difference was 42 minutes.

Now the question originally was which bus was the quickest, and we know that the bus being able to take 42 minutes, I'm losing you again.

There we go.

42 minutes.

So let's try something else, then.

We may see some patterns here.

So obviously, mentally, you might look at, say 08:14, 09:22, and actually you might be able to work out at the interval level.

We're just going to do this method here to help.

So Bus A again, 08:40.

And it's going to get, I'm going to show you this one, it's very interesting.

I want to go to Main Street, okay? At Main Street, it rides at 08:56.

So from Near Lane and Main Street, 08:56.

And actually, that difference there is 16.

If we go back to our original one at the top here, just change it, you'll notice that the first two stops took 16 minutes.

They're starting to tell me something, that actually they're very similar.

And then 56 to 22, if I add four.

If I add four, that would take me to nine o'clock.

And then I add 22, and that would take me to 09:22.

So four and 22 makes 26.

So actually I can jump 26 minutes here.


And I can get to there.

So if I looked at the top one, the two thirteens, the two other stops, Main Street and the Blue Road, was 26 minutes.

So actually here, it's also 42 minutes in total.

So Bus A is also 42, and I'm starting to see some patterns here.

So it's both of them 42.

So I'm going to expect Bus C to be the same, okay? And now I can do a number line, if I want to, okay? I'm going to show you a number line backwards, but actually you might mentally think, but if I add 35 to 25, I'm going to get 10, 25, 35 makes 60 minutes.

So I'm going to get to 10 o'clock and then I'm going to add seven.

So you're going to add 35 and seven, which we know is 42, but I'm just going to show you a number line.

You don't need to use the number line if you're comfortable with your mental arithmetic, but you know, it's good to have to just double check.

Well, actually, I'm going to jump back seven.

Like I just did here mentally.

And then from seven, we take it to 10, I'm going to jump all the way to 09:25.

Well, I know that's at 60 because that's to the hour.

60 minutes take away 35 takes to me to 09:25.

So 35 and seven together makes 42, 42.

Let me see if you can see it.

So yes, it is true.

I thought so.

I suspected it, Bus A, B, and C are actually the same amount of time in the journeys.

So it works.

And now, again, just to reiterate, I've used number lines, black number lines, because I think they're really effective.

I did find intervals and it actually allowed me to spot patterns and to estimate that actually each bus was the same amount of time.

And with my number line, I've gone in small jumps.

I've been comfortable doing a large jump 'cause I'm good with my mental arithmetic.

And I've also shown that you can actually go backwards if you want to.

Judging how familiar you are with number lines.

Okay? Let me put my pen down and let's carry on with lesson.

So I think we're ready for our talk task now.

Just a reminder that talk tasks generally happen in groups or pairs or even a whole class discussions.

Of course, some of you may be working on your own, but it does not mean that you can't take part as always.

You should pause the video, spend some time reflecting on information and have it go with the task at hand, and then we can share the answers back together.

But if you do happen to have somebody nearby, a parent, carer, guardian, sibling, even a pet dog.

Get them over, have a chat about the maps, discuss it- it's quite a verbal activity- and then check your answers on the slide.

And your talk task today involves a train time table.

And the question is what, or rather the task is, what question could be asked to result in the number line given? I know what you're thinking, there's not a number line there.

It's coming up in a minute.

Just have a quick look at that trend time table.

You can see the columns and rows, the information that might be presented to you.

I don't want to give you too much information at the moment.

And then there'll be a series of number lines.

Here's an example.

There's a number line here, if I look at that number line, I can see the starting point, 10:40, and I can see the end point is 15:49 with a jump for five hours and nine minutes.

Actually I've modelled how to do a number line, so you will know how to use one.

And the task is to create a question that could be asked as a result of the number line.

You know, what is the question that was being asked that gave you that answer? So obviously I identified that it was Train B that was leaving London Paddington at 10:40 and it arrived in Penzance at 15:49.

That's a whopper of a train journey.

Five hours, nine minutes.

I hope they've got lots of books or an iPad, or maybe they just want to sleep.

That's a long time to sit in a carriage.

I transgress.

So let's go back to the math.

So here's what I said.

I gave some explanation and I'd like you to discuss it.

So if you're able to talk about this at home, I want you to have a conversation and you should say something like this in your verbal reasoning.

The number line starts at 10:40, which I identified as being Train B from London Paddington.

It also ends at 15:49, which I also identified as being the final stop in Penzance.

The total travel time shown on the number line is five hours and nine minutes.

So the question I came up with was this, "How long does it take for Train B to travel from London Paddington to Penzance?" Nice and simple.

So the task is actually just identifying the correct information within that timetable.

And then thinking about what possible question it could be that would generate that number line as part of your answer.

So I'd like you to pause the video and spend a few moments doing that, really think about, identify the task, identify the information, consider what would you use that number line for and think of a question that could be generated that involves the answer involving that number line.

Okay, so pause the video.

I'll see you in a few minutes to share some possible examples together.

Okay, we won't drawl too long.

I hope you enjoyed that and you gave full answers.

And if you did have conversations with somebody, fantastic, I hope you were listening to each other and you're using the right mathematical vocabulary.

Here is some example answers that I came up with.

Obviously I can't see what you came up with, but if you've got something very similar, that's great.

It's an open task, there's so many different varieties you could have come up with the questions.

So for this one, This number line says two hours and six minutes, I could see that it was 13:01, So I identified it as Newton Abbot on Train B and I identified that it landed, or rather, it's arrived in Truro at 15:07.

So my question was this: "If the journey time from Train B from Newton Abbot to Truro is two hours, six minutes, what time did the train depart?" Obviously the answer would be 13:01.

For this number line, I noticed that it started at 01:23.

So again, I converted 01:23, which is in analogue, and I added 12 to make it 24 hours, So one plus 12 makes it 13:23.

Removed the PM so I knew that's when it was.

So I did find it as being Exeter St David's.

And then I saw that 02:35.

Again, I did the same, two plus 12, makes 14:35, remove the PM.

I've got my 24 hour clock.

So I've got my two times I identified.

So the times were 37 35 together.

So my question was this, "Train C does not depart from Newton Abbot for Plymouth until 14:00, which is 2:00 PM.

How long was it standing still at Newton Abbot after arriving?" Well, obviously I could tell that it doesn't leave until two, but it arrived in Newton Abbot at 13:44.

So actually it was 16 minutes.

Then it goes 44, plus 16, take you to the next hour, 60 minutes.

There was 16 minutes it went to the station, the train stayed in the station.

Could have either got there very early and it was waiting 'til its depart.

And finally again, for this number line I identified 12:06 and I saw that it was from Exeter St.

David's and I noticed that it was for three hours five minutes and the exact time interval to get to 15:11.

So I know that was Penzance.

So we're looking at a journey of Exeter St.

Davis to Penzance.

My question,.

Train A arrived at its final destination in Penzance five minutes earlier than scheduled, so it's scheduled for 1511.

What time did it arrive, and how long was the length of the total journey? Well, so then I use this number line in the following context.

It arrives five minutes early, so I took five minutes away, 15:06, and then I jumped back three hours from 15 to 12.

I could've jumped forward, exactly, if I'm honest, but either way.

So therefore the journey length falls three hours, wasn't it? Cause I got there a little bit earlier.

So I'm just going a little bit, I think, creative with my questions and trying to think of something a little bit outside the box with those number lines.

I got to say, check your answers, hope you came up with some really good questions that demonstrate and interpret the information from those number lines.

Okay, we're going to take our learning a little bit further now with a bit of extra information using timetables Now I circled that spot on the timetable, that blank spot.

Think for a moment.

Why have I seen that little question symbol? Why have I circled that spot? There's nothing in it.

Why? Of course, because that represents a part of the time when the bus does not stop.

So it's Bus J does not stop at Near Lane, so there's no need for any information.

It hasn't been missed off it, because the bus doesn't stop there.

Now, it doesn't necessarily mean it was on a different journey.

It will be still on the same journey or just continue past Near Lane and arrive at Main Street to 11:46.

So it would just, in a sense, skip by.

This happens quite often with faster buses or because of different times of day.

It happens to happen quite a lot of times in real life as well.

Buses, trains, those sort of things.

It doesn't always stop at those bus stops.

And that's why it's really important that you check timetables and don't just assume that every bus, even on the same journey, every bus will stop at every stop.

But we're going to look at a series of questions about timetables that are presented to us.

And sometimes we're going to need mental arithmetic and sometimes we'll be able to identify or estimate.

And other times we're going to need the strategies that we've learned before.

So again, I'm just going to demonstrate once again, how a number line might help with certain questions.

So the question is, it's there on your page, how long does it take each bus to travel from High Road to Sway Retail Park? Now looking at High Road, there are three buses.

So we're going to make it a black number line, Bus J, 11:35.

And it gets there 12:26.

So the first thing we're going to do, 11:35.

I'm going to add 25 to get to the next hour.

'Cause 35 and 25 makes 12, next hour, 60 minutes.

So I added 25 mins and then I added 12 here.

So 25 and 12 altogether makes 37 minutes.

So that is Bus J, got a little cross there.


I'm not going to assume that they're all the same.

Like I said before, sometimes buses do go at slightly different paces.

So this time Bus K starts at 11:50.

Don't forget my colon, I forgot my colons when I was up there, but we are in 24 hour clock here.

So it has to be colons, my mistake.

Let me go back and put those colons in so I can demonstrate.

Okay, 11:50 and it arrives at 12:25.

So this time I'm going to add those 10 minutes, cause 50 and 10 makes 60, like the hour.

So I've added my 10 and then at 12, I'm going to add 25.


So I've got 10 and I've got 25.

So altogether I've got 35 minutes.

So K is slightly faster.

And then I'm just going to check Bus L, that could be the same time, could be faster.

It could be shorter.

Who knows? I don't know.

I don't know, it doesn't say what is the fastest bus.

It doesn't give you a note on it, sometimes they will tell you, they'll have a little asterisk or star saying this track, this is going the fastest one, but this doesn't tell us that.

So again, I'm going to start here at 12:30.

Again, you can go either way on the number line.

I could start actually at 13:05.

Yeah, let's do that.

Let's do it this way.

So let's take five back.

So I'm taking five off.

I just went to 13, one o'clock and then half an hour there.

'Cause I know that 30 and 30 makes 60.

So I go back 30 and like I said, 13:05 gives me 35 minutes.

So it actually, Bus L and K take the same amount of time.

Bus K and Bus L took the same amount of time, they take 35 minutes.

And J is slightly longer because it takes 37 minutes for that journey.

Okay, now we'll look at the second question.

She takes the fastest bus from Main Street to the retail park.

Which bus does she take? Well, let's look at Main Street.

Now, you'll notice there's a big blank in the middle of Bus K and as we said, that means the bus doesn't stop there.

So she cannot get to Bus K.

She can only get Bush J or Bus L and she'd go into the retail park.

So again, I'm going to use a number line just to demonstrate, just to see, not too quickly.

So she gets the 11:46 here, put my colons in and she gets there at 12:12.

Okay, so this is J.

So again, I'm going to have 14, that's a big jump.

14, that takes me to 12 midday.

And then I'm going to add my 12 and I'm going to add those two together.

So 14 to 12 minutes makes 26 minutes.

So 26 minutes for Bus J.

And now I'm just going to do one more.

Cause I just want to check that the L, which she can also catch.

So this time, she can catch the one at 12:46.

Very similar, of course, I think, but we don't know for sure.

And this time it gets in Sway at 13:05.

So again, I'm going to add those 14 minutes.

'Cause that takes me to the next hour, which is one o'clock, but then it's only at five minutes.

Okay, and so when I add 14 and five, this gives me 19 minutes.

So actually that is much quicker, isn't it, actually, although she does have to wait an extra hour.

So it's 19 minutes on the bus.

So Bus L is the quickest bus that she can take to go from Main Street to Sway Retail Park.

And that's how we worked the answer out and proved it.

As we said earlier on, you don't necessarily need to use the same strategy every time and you can be efficient by picking out the right strategy to use the right time.

So we'll look at a few questions now, which I wouldn't necessarily use a number line in order to solve.

I would use for mental arithmetic and process of elimination.

So the question, Lisa has an appointment at Blue Road at 12:30.

What time must she depart from High Road to arrive in time for her appointment? Hmm.


Well, first of all, I have to identify that it needs to be at Blue Road by 12:30.

As you see Bus L, never actually arrives at Blue Road.

So the latest she can get there is 12:12 or the earliest you can get there.

There's no bus after that, okay? So she wants to get there by 12:30, 12:12 is the earliest she can get there or the latest she can get there on time.

So therefore she would be taking the 11:50 from High Road in order to get there on time.

There's no point getting 12:30, like I said, because the Bus L, 12:30, does not actually a stop at Blue Road.

Finn arrives at High Road at 11:45 and takes the next bus to Main Street.

What time does he arrive at Main Street? Well, let's have a look, shall we? He wants to arrive at High Road at 11:45.

Well, I can see that if he arrives at 11:45, he's already missed out on Bus J, and therefore he's got to climb to catch 11:50 Bus K or 12:30 Bus L.

And he wants to take the next bus to Main Street.

However, there's a problem, isn't there, if he gets Bus K, 11:50? Can you spot the problem? Of course you have, 'cause you are switched on and you're focused, aren't you? You've noticed that if he gets 11:50, he won't actually be able to get to Main Street, he'll have to get off at Near Lane or Blue Road and walk back.

So that's not going to do him any good at all, is it? So he cannot get Bus K and that leaves him with only one option.

You'll have to get Bus L at 12:30 and arrive at Main Street at 12:46.

Obviously that means a little bit of a wait at High Road, but I'm sure it's a nice day, sun's out.

He can just relax and hopefully listen some music or read a book, which is always a good way to pass the time.

So we've come to the part of the lesson now where I hand over the reins to you and you have a go at an independent task and try to demonstrate some of the learning that's taken place today.

Now over the course of this lesson and all the lessons within the unit of line graphs and timetables, we've looked at a number of different strategies that we can use to identify the correct information within the table, to identify the missing time intervals and to make sure we locate the right information within a tight timetable.

Feel free to use any of the strategies we've looked at or choose the strategy that you feel most comfortable with when answering the question.

As you can see on your screen, you've been presented with a train timetable and your task today is to use that timetable, interpret it carefully and answer the questions below.

Now try to provide your answers in full sentences, please, to show your understanding and to show your skill in interpreting that information.

Here's the timetable, I've made it slightly bigger so you can get all the information that you need to answer those questions.

And remember, please answers in full sentences where appropriate.

So pause the video now, take as long as you need.

There's no rush whatsoever.

And when you're ready to resume the video, we can check our answers together.

I look forward to speaking to you all in a few minutes time, best of luck, speak to you soon.

Right, so let's just take a few moments to check our answers.

If you do happen to spot any mistakes that you make or misconceptions, that's perfectly fine.

You either go back, have a go again, see if you can spot where you went wrong with the information I'm providing to you now, and that hopefully you will spot- it's usually just a small misstep somewhere- and then you can correct yourself and you can get to the right answer.

So using that timetable in front of me, I can answer the following questions.

Question A, how long does each train take to travel from Bristol to Reading? You see I've worked out the exact timings in hours and minutes.

The fastest train from Reading is, rather from Bristol to Reading, is going to be Train A which takes 59 minutes.

Question B, Jasmine needs to be in Bristol by 12:30 PM.

What time must she depart from Swansea? I said she can catch the fast train from Swansea, which is Train B.

And that leaves Swansea at 10:58 and arrives in Bristol at 12 o'clock midday.

Sacha wants to take the train from Britain to Swindon and arrive by 1:00 PM.

What are his options? I said he only actually has two options available to him.

After leaving Bristol, he can arrive at 12:39 or he can work with 12:57.

As you can see, there's no other- Train A and Train B don't actually stop at Swindon so there's only these two options here.

Claire, D.

Claire is travelling from Bristol to Reading at midday.

So we can look on our timetable Bristol to Reading, there's midday.

Is Train B the best choice? But it would be better to actually catch Number A, Train A because although it leaves three minutes after Train B at 12:03, it actually arrives six minutes earlier so it's a quicker train from those two locations.

And finally, Adam gets the fastest train from Cardiff to Bristol, which train does he get? He got Train D because that takes 36 minutes and is actually one minute faster than Train A and Train C.

Of course, we didn't go to Train B because you will notice Train B does not depart or stop at Cardiff.

So he wouldn't be able to get on that train.

So there are our answers.

I hope you did really well.

Again, if you did spot any mistakes, just go back, double check, and see where you did go slightly off course.

But those of you who're not quite ready to put away your equipment just yet, I have included an additional challenge slide once again for you to continue with.

You have to pause the video, read the instructions carefully, and take your time providing your answers.

By all means, take as long as you need for the challenge slide.

And feel free to come back to it any point during the day.

Best of luck with the challenge.

And so we're almost at the end of our lesson.

This slide usually indicates that you need to be reminded to do the end of lesson quiz.

That was a lot of information that we shared.

Once again today, I'm hoping that a lot of that has been absorbed and embedded, and this will be your opportunity to demonstrate what you know, but as always, if you feel a little bit unfamiliar, or un-confident or you're not quite so sure of some of the questions and you need to revisit the video at any point, feel free to go back to any part of the video you need to review the learning and the stages that you require.

Now, obviously there's no way of beating my Roman joke from today because that was top dollar.

However, if you feel you have your own math joke, which will be just as good, and it's just as funny, you can of course share that along with any fantastic work that you've produced during the unit.

So to share your work with Oak National, all we ask is for you to ask your parent or carer to share your work on Twitter, tag it at Oak National and hashtag LearnwithOak.

As always, I have really enjoyed seeing some of the work that's been coming in and I'm looking forward to seeing even more as the lessons go by.

And that brings us to the end of another fantastic lesson here on Oak National Academy with me, Mr. Ward.

I'm really impressed, once again, with you guys today, you've really stayed focused.

There's a lot of information there to interpret.

Now, I hope taking away from this lesson, you'll remember to use blank number lines because they're really good, either to identify missing number intervals, to help identify the duration of a time or an event, or even just to convert between 24 and 12 hour clock.

There's a number of reasons you might use a blank number line to jot them down on your page.

So hopefully that's the main learning you'll take from today's lesson.

So I'm going to go off now and have a little rest.

I've worked very hard today.

I know you have too, and I hope see you very soon again here at Oak National Academy.

So from me, Mr. Ward, bye for now and have a great rest of the day.

Bye bye.