Lesson video

Hello, everyone, and welcome to today's maths lesson.

In today's maths lesson, we're going to be learning about how we can represent comparison word problems and bar models.

Don't worry.

That sounds a bit complicated at the moment.

We'll go through exactly what it means together in a minute.

Are you having a good day? I hope you are.

Would you, if you can, please turn off any notifications on your phone, tablet, or whatever device you're using to access today's lesson on? And then, if you can, try and find somewhere nice and quiet in your home where we're not going to be disturbed in our learning today.

When you're ready, let's begin.

Okay, then.

We're going to start off by going through today's lesson agenda.

So we'll start off by creating a word problem.

Then, we're going to do Let's Explore, which will be bar models on word problems. Then we're going to be looking at word problems, how do we create a bar model? And then, your independent task today will be representing a problem.

So, before we get started today, can you please make sure you've got yourself a pencil and some paper? Please pause your video now to go and get those things if you haven't got them already.

Okay, welcome back, and let's begin.

So I'm just going to move myself down here a tiny bit so that you can see these two different bar models.

Now, my question today is what's the same and what is different between these two bar models? And that is what we're going to be looking at this, not this morning, during this lesson, sorry.

So what do you notice about these two different bar models? Well, I notice that the whole is the same on both of them.

I noticed that I've got one part value, which is 1,767.

The same in both.

And I notice that there's a question mark in both of them.

But I do notice something different and that just here, that bar goes all the way across and there's a bar underneath it here, whereas here there's just one bar.

There isn't two bars next to each other.

I'm just going to move myself between the bar models.

So, I know that each bar model here, this bar module, sorry, has two bars.

And this is what we're going to be looking at today, when bar models have two bars.

Each bar represents a quantity, so an amount, and what we're looking at today is the relationship between them.

So you can see here that, that big jump, tells me that that bar represents 1,915.

And you can see here that this bottom bar represents 1,767.

So I know that there are two separate bars, but what I don't know is the relationship between them, because I don't know what that gap is here.

I don't know the difference between this part here and this part, and the two parts.

So we're going to find out exactly how we can do that and what we'll use to find out that difference today.

So I'm going to move myself out of the picture of Paris.

Now, I'm thinking.

Here is a picture of Paris.

It's not a actual picture.

It's a cartoon version of the picture.

And you can see the Eiffel Tower in the background and you can see lots of people getting up to go and buy their baked goods from our French baker here.

See bus stalls.

Can see a boat in the background, and we can see a taxi.

Now we're going to look at our bar model here.

Now, using that bar model, that comparison bar model, you can clearly see there are two bars.

Each of the bars have been marked.

So I know the top bar represents 300, not 300, sorry, 3,965.

And I know my bottom bar represents 2,524.

What I don't know is that gap, that different part here, which is our question mark.

So, as I said, I don't know the difference between them, and that's what we want to find out today.

So how would we usually find out the difference between them? Well, maybe we could write a word problem so that it might explain the bar model a little bit more clearly.

So let's think what could our word problem be? Well, my word problem could be, yours could be completely different, so if you've thought of something completely different, that's absolutely fine.

Mine's going to be though, 3,965 people travelled to the Eiffel Tower, there it is, by boat, and 2,524 people travelled by coach.

So it could have been like a bus tour on a coach.

How many more people travelled by boat, here's our boat, than by our coach? So we have the values.

We know how many people travelled by the boat.

We know how many people travelled by the coach.

What we don't know is how many more people travelled on our boat than on our coach, that relationship, what that gap is, that difference between them.

So in order to find that out, we needed to do an equation to work it out.

So I needed to do some subtracting.

So I'm going to take my largest number and I'm going to subtract my smaller number from it to work out what the difference is between those two numbers, to find out how many more travelled by that boat than by the coach.

So when I'm subtracting, which column do I start with? Absolutely, I always start with my ones column.

So five subtract four is equal to one.

Six subtract two is equal to four.

Nine subtract five is equal to four.

And three subtract two is equal to one.

So I know there are 1,441 more people travelled by boat than by coach.

To check that, I can use the inverse operation, if I would like to.

So I can do 1,441, the more amount, and I'm going to add how many people travelled by coach to find out if it gives me this value here.

So one add four is? Fantastic, it's five.

Four add two? Yup, it's six.

Four add five, nine.

And one add two, three.

Brilliant.

Is it the same number? Fantastic.

It is, so I haven't gone wrong with my subtracting.

So that shows me, sorry, before we go on to the next question, I'm just going to quickly recap.

That shows me that my answer is correct and that I've worked out that relationship between them.

I know that 1,441 more people travelled by boat than by coach to the Eiffel Tower.

Now let's have a look at our second equation.

If you're feeling really, really confident, how about you have a go at writing your own word problem, using these values, thinking about what that relationship is between the two different values.

And then, can you solve it? Can you work out what our question mark is? If you're not feeling super confident, absolutely fine because we're going to go through it together now.

Now, so, I'm going to carry on using my Paris theme today.

And I'm going to think about what our word problem could be first before we have a go at solving it.

So, what do you think our word problem could be? Well, I've been thinking, and I think our work problem could be this.

4,673 people, using that number from one of my bars, travelled to Notre Dame, a very famous landmark in Paris, by boat, can't actually see it in this picture, but here's our boat, and 1,562 people travelled by coach.

Now, I can clearly see more people travelled by boat to Notre Dame than by coach, but I don't know how many more.

So my question is how many more people travelled by boat than coach.

So, how are we going to work it out? Well, we need to subtract how many people travelled by coach from how many people travelled by boat to find out how many more people travelled by boat.

So three subtract two, can I do that? Yes, I can, and it gives me one.

Seven subtract six.

Yup, one.

Six subtract five, yes, I can do that.

It gives me one.

And four subtract one is equal to three.

So I know that 3,111 more people travelled by boat than coach.

So if I was a coach company, I would be thinking, What can I do to lure some of the boat customers onto my coaches because I'm not making as much money as them.

But if I owned the boat company, I'd be thinking, yes, I'm getting lots of different people travelling on my boats, so I'm doing quite a good job here.

Could we check our answer? Could we use the inverse? Absolutely.

So I'm going to take my answer, which is 3,111, I'm going to add one of my values here.

I'm going the part here, which was how many people travel by coach, to find out if it gives us the same amount as the people who travelled by boat.

So, one add two is? Fantastic, it's three.

One add six, it's seven.

One add five, it's six.

And three add one, it's four.

So my answer is 4,673.

Okay then, it's now time for your Let's Explore today.

And for your Let's Explore today, we're going to be looking at bar models and word problems. So, here you've got two different bar models.

What I would like you to do today is have a go at creating a word problem.

Now, think about these different sentence starters here to help you.

So, I know the smaller quantity is.

Have a look at your bar model.

Choose one of them.

You don't have to choose both.

If you really want to challenge yourself, you could choose both of them.

You don't have to.

I know the other quantity is.

And what is the other quantity? I don't know the gap.

So where our question mark is, what is that gap? And then think about using that to help you create your own word problem.

You can use the Paris theme if you would like to.

But if you want to write a word problem about something else, that is absolutely fine, too.

Please pause the video now to have a go at today's Let's Explore.

Okay, and welcome back.

Let's have a look then.

I'm just going to move myself so that we can see really clearly here our question.

So, Pierre travels 4,345 miles from his home to Paris.

Jean travels 1,467 miles more to get to Paris from his home.

How many miles did Jean travel to get to Paris? So, let's think about how we could represent that on a bar model.

So, like we did before, we had the bar model first, and then we wrote the problem.

This time, we've got the problem, we need to use a bar model to represent it, to see exactly what it needs to look like before we solve it.

So just going to move myself out of the way here now because we know that all I'm hiding is the word Jean.

So here you can see Pierre's travels.

Here's Pierre's travels.

He's travelling 4,345 miles.

Jean travels 1,467 miles more than Pierre.

We don't know the actual amount that Jean travels, so Jean's travel is a question mark.

We know that amount more than Pierre's, but we don't know the total.

So in order for us to work out the total, we need to add them together.

So if you can see here, we need to add these two digits together to give us the total amount that Jean travelled to get to Paris.

So let's get started then by adding five and seven.

Oh, what do I notice about numbers five and seven? Are they going to create a bond that is 10 or greater? Absolutely, they are.

They're going to create the number 12, so I need to do some regrouping.

Four add six, add one, again, I'm going to need to do some regrouping to give me 11.

Three add four, add one, I don't need to regroup this time because my answer's eight.

Four add one is five.

So my answer is 5,812 miles.

To check it, we can use the inverse and we can take our whole, the amount that Jean travelled, and we can take away the amount more that he travelled than Pierre to find out if it gives us the amount Pierre travelled.

So, two take away seven, what do you notice? We need to regroup.

So I'm going to regroup here and I'm going to be left with zero tens, and 10 ones with the two ones gives me 12 ones.

12 take away seven is equal to five.

Nothing take away six.

I can't do that, so I need to put a line through my eight to give me seven tens, sorry, not tens, seven hundreds.

I was going to say seven eights, but that doesn't make any sense at all.

And 10 tens.

So 10 take away six, I can do.

That gives me four.

Seven take away four gives me three.

Five takeaway one gives me four.

So my answer, 4,345.

Is that the same amount of miles that Pierre travelled in total? Absolutely, it is.

So I know I haven't gone wrong anywhere.

I'm just going to move myself down here for a moment.

The next question then.

Sorry, if you're feeling confident, once I've read the question, you can pause the video to begin drawing your own bar model and solving the problem.

So the Louvre museum had some visitors on Monday.

In the afternoon, they had 1,283 less visitors than the morning.

In the morning, there were 2,349 visitors.

So, how many people visited? How many visitors visited in the afternoon? Wow, let's think.

Let's have a look at our bar model.

I'm just going to cover that question slightly so I can show you the bar model.

So, we can see here that this was how many, just move this, in the morning, here, with 2,349 visitors.

We could see here that there were 1,283 less visitors in the afternoon.

This was the amount of visitors there were in the afternoon.

We just don't know what that actual value is.

We it's a question mark.

We know it's that.

This number here take away this number here is going to give us the amount of visitors that there were in the afternoon.

So let's work it out then.

We need to do 2,349 subtract 1,283.

Which column do I need to start with? Fantastic.

I start with my ones column.

So nine subtract three is equal to six.

Four subtract eight.

Can I do that without regrouping? No, I can't.

So I need to regroup from my hundreds column, leaving me with two hundreds and 10 tens, remembering I've still got that four tens there.

14 subtract eight, can I do that now? Absolutely, I can, and it gives me six.

Two subtract two gives me zero.

Do I need to write a zero in? I do, indeed.

That zero's a really important place holder.

It shows me that there are no hundreds here.

But if I didn't use it, it would throw my place value out completely.

Two subtract one is equal to one, so my number is 1,066.

Again, could I check my answer? I could use the inverse.

So I'm going to take both of my parts to see if they equal my whole.

So I'm going to take this part here and this part here, and add them together to see if they equal the total amount of visitors in the morning.

Now, three add six is nine.

Eight add six, I know I going to need to regroup because I know they create a bond that is 10 or greater.

They create the bond 14.

Two add nothing, add one is three.

Why is it important I add that one? Absolutely.

It's been regrouped.

You cannot forget to add it on.

One add one is two.

Have I got the same number? 2,349, absolutely, I did.

Right, then, it's now time for your independent task today, which is going to be your turn at representing a word problem.

I'm going to hide myself again, for a moment.

So, you have got four word problems here.

What I would like you to do is represent each problem using a bar model and then calculate the solution.

Remember, label the values that you have been given.

Work through the problems that are here.

Please pause the video now to complete your task.

Don't forget to resume once you're finished, and we'll go through the answers together.

Hello, everyone.

My name is Miss.

Jones and I'm going to be taking you through today's answers.

So, looking at this first question, what I've done is already created my bar model for you on the slides.

I'll talk you through how I created it and then we'll work out the answers together.

So I knew that Pat walked 3,138 metres on Thursday.

So this bar represents what she walked on Thursday, and this bar represents what she walked on Friday.

Now, the unknown here is the difference.

We need to find out how much further this is compared to this.

So in order to do that, we need to find this amount here.

Now, are we going to use addition here or subtraction? We're going to need to use subtraction to find the difference here.

So let's use column subtraction here to work it out.

We'll start with our ones and we'll work our way through.

So eight subtract six is going to leave us with two.

Three subtract four.

We're going to need to regroup.

So then if we have 13 subtract four, we're left with nine.

Zero subtract three in our hundreds column, again, we're going to need to regroup in order to do that.

So this time now I've got 10 subtract three, which will get me seven.

And then two subtract two, which is equal to zero.

So I know that this missing amount is 792.

Okay, and I need to remember when I'm articulating that because I'm talking about metres.

So if I was saying my answer out loud, I would say 792 metres.

Let's look at the next one.

Okay, so again, I'm going to think about what I know and what is unknown.

Here we're working in euros.

So this sign here is a symbol for euros, which is a currency, the amount of money they use in European, certain European countries.

So John bought a week-long holiday to Paris for 3,325, but Ahmed paid 5,496 euros for the same holiday.

Now, I think this is really important because we want to make sure that we're thinking about which deal is better by finding the difference.

So how much did John save? So again, we're looking for the difference between these two amounts.

So here, I've got my amounts here that Ahmed paid and my amount that John paid.

And again, I'm going to have to use subtraction to find the difference between the two.

Okay, so here's my column subtraction.

Again, we'll start with the ones.

Six take away five is one.

Nine take away two in my tens is seven tens.

Four hundreds take away three hundreds will give us 100.

And five thousands take away three thousands will give us two thousands.

So he saved a huge amount of 2,171.

What are we talking about here? Euros.

Okay, a baker's making some brown and white baguettes.

I know that there are fewer brown baguettes than white ones.

So on my bars here, I know that brown baguettes will be the smaller one.

White will be the larger one.

I know how many brown baguettes there are, but I don't know how many whites baguettes there are.

What I do know at this time is that there is 1,549 fewer brown.

So this time I know the difference, but I do not know the value of one of my amounts, the amount of white baguettes.

So this time, let's think about which operation we need.

If we know the difference already, we can add that on to our first amount to find out our second amount.

So instead of subtraction, this time, we're going to be doing some addition.

So let's take our two amounts and add them together.

So we've got a 14 in our ones, so we'll regroup our one 10 here.

And then we've got eight add four is equal to 12, add on our one is equal to 13.

So again, we need to regroup into our hundreds.

Seven and five is equal to 12, add on our one again is equal to 13.

And we've got six add one, and added to our final one in the thousands there, we should end up with 8,333.

That's a lot of baguettes.

Let's look at our final problem.

On Friday, I know that 1,273 people decided to take a bus trip.

And on Saturday there were more, so this is my larger bar, 2,276.

How many more people went on the bus on Saturday compared to the day before? So again, we're working out the difference again, so we're going to need to do a subtraction.

So I've got my column subtraction here.

So six subtract three.

Seven subtract seven is equal to zero.

Two subtract two is equal to zero hundreds, as well.

And two subtract one is equal to 1,000.

Remembering that I'm going to need the zeros in there to hold the place and to make sure that this sits in the thousands column.

So my missing difference here is 1,003.

Okay, I'm going to pass you back over to your teacher to end the lesson.

If you'd like to, please ask your parent or carer to share your work from today on Twitter, by tagging @OakNational and using the #LearnwithOak.

I've been so impressed with your work today.

It's been fantastic.

Don't forget to go and complete your quiz now to show off all that fantastic learning you've been doing about comparison bar models.

Hopefully, I'll see you again soon for some more maths.

Thank you.

Have a great day, and bye-bye.