Lesson video

Hello, how are you today? My name is Dr.

Shorrock and I'm really happy that you have chosen to do your math learning with me today.

We are gonna have a lot of fun as we move through the learning together.

Today's lesson is from the unit measuring length and recording in tables.

This lesson is called solve problems about length and heights.

As we move through the learning today, we are going to learn all about how it's really useful to visualise a word problem and then to represent it.

And if we can represent it, it will help us form a calculation and then be able to solve it.

Sometimes learning can be a little bit tricky, but we can work really hard together and I know that we will be successful.

So how do we solve problems about length and heights? These are the key words that we will be using throughout the course of the learning today.

We've got bar model, part and whole, and I'm sure you've probably heard those words before, but just in case, shall we practise them? So my turn, bar model, your turn.

Lovely.

My turn, part.

Your turn.

Fantastic.

My turn, whole.

Your turn.

Well done.

So the bar model is one of the strategies that we are going to be using today.

It helps us represent a problem and when we represent the problem, we make it visual.

We can then see the maths a bit clearer and it helps us to identify a strategy that we can use to then solve the problem.

We usually use bar models to solve number problems to do with addition and subtraction or multiplication and division.

You can see I've got a picture of a whole pizza.

So when we talk about the whole, we mean all of something.

It's complete.

This is a whole pizza.

You can also see I've shown a picture of part of a pizza.

So it's not all of the pizza, it's an amount or part of the pizza.

When you combine it with others, it could make up the whole.

So today we're going to start by thinking about how we represent a problem as a bar model and then we will move on to identifying the calculation and solving the problem.

These are the characters who are going to help us with our learning today.

We've got Izzy, Laura, Jacob and Andeep.

When we are given a word problem to solve, first it's important that we can visualise it to show that we can actually see it happening in the real world.

We then need to represent the word problem mathematically because that's what helps us to find out how to solve it.

Let's look at this word problem.

Izzy had one metre of ribbon, she used 20 centimetres of it.

Hmm.

Jacob wonders what the question could be.

What do you think? Yes, they might ask us what colour the ribbon is.

Hmm, although that's not very mathematical, is it? Usually word problems in maths have something to do with numbers.

Let's have a look at what the question is.

How much ribbon does she have left? And Jacob is asking us how would we solve the problem? And Izzy very sensible.

She's saying, "I would stop and see what I notice first." Jacob asks, "Well, what do you notice?" I wonder if you've noticed something.

Ah, Izzy has noticed that the units are different.

We've got one metre of ribbon, but 20 centimetres have been used.

So we've got different units, we've got metres and we've got centimetres.

So what do we need to do first? That's right Izzy.

First we need to represent this.

So hopefully you have visualised this problem.

You can see that you could have a length of ribbon and you could use 20 centimetres of it.

Now we need to represent this so that we can find the answer to the question and we can represent problems in many ways.

One of the most effective ways is to draw a bar model.

And a bar model is made up of parts and holes.

And if we can identify the parts and holes in our problem, it helps us understand the structure of the maths, the structure of the problem, and it helps us to solve it because it tells us which operation we need to use.

So we've got our word problem, Izzy he had a metre ribbon, this is our whole.

How do we know it's our whole? Because she's used 20 centimetres of it, so she hasn't added anything to it.

She's used.

So that 20 centimetres is a part of our whole.

How much ribbon does she have left? Well that will be the missing part.

So once we have our bar model, we can then use it to help us know what to calculate and how.

Let's check your understanding.

Can you represent this word problem in a bar model? Izzy had one metre of string, she used 40 centimetres of it.

How much string does she have left? Press pause.

And when you've represented it as a bar model, press play.

How did you get on? Did you notice that Izzy had one metre of string? So that is the whole amount.

We know it's the whole amount because she uses 40 centimetres of it.

So that must be a part.

How much string does she have left? This is the other part.

How did you get on? Well done.

Let's look at a new problem.

A black cat walks 60 metres.

Can you visualise that? Can you see a black cat in your head? Can you see it walking? A white cat walks 30 metres further than the black cat.

Oh again, Jacob is wondering what the question could be.

I like the way he tries to think of the question before it comes out.

Hmm? What do you think the question could be? It could be how far does the grey cat walk? But there isn't a grey cat mentioned in the problem.

We've got a black cat and a white cat.

So let's use the information in the question to help us think about what the question could be.

Ah.

How far does the white cat walk? What do we need to do first? That's right, Izzy knows.

We need to represent this.

We visualise it.

We can see that black cat walking.

We can see that white cat walking 30 metres further than the black cat.

Now we've got to represent it.

We can represent our problem using a bar model.

A black cat walks 60 metres.

This is a part.

How do we know it's a part? Because the white cat walks 30 metres further than the black cat.

So the 60 metres can't have been the whole.

And the question, how far does the white cat walk? Well that's the whole amount because it's what the black cat walked and the white cat walked 30 metres further than that.

So the whole amount is how far the white cat walked.

Once we've got our bar model, we can use it to help us decide how to solve the problem.

Your turn to have a go at drawing another bar model.

Can you represent this word problem? Izzy kicks a ball 20 metres.

So visualise that.

Can you see her kicking a ball 20 metres? Jacob kicks a ball 35 metres further than this.

How far does Jacob kick the ball? I'd like you to pause the video, have a go at representing that in a bar model.

And when you are ready, press play.

How did you get on? So Izzy kicking the ball 20 metres.

That's a part.

We know it's a part because Jacob kicks his ball 35 metres further than this.

So that's the other part.

How far does Jacob kick the ball in total? Well that's the whole.

That's because he's got what Izzy has done and 35 metres more than that.

So how far he kicks the ball is the whole.

Let's look at this new problem.

Hmm.

Again, Jacob is saying, I wonder what the question could be.

I wonder if you've got any ideas.

How much taller is the first stick than the second stick? So what do we need to do first? That's right.

First we need to represent this.

I wonder if you could guess that's what she was going to say.

So we can represent our problem as a bar model.

The first stick is 50 centimetres and that's our whole.

The second stick is 90 millimetres.

This is a part.

I wonder if you've noticed those units are different, aren't they? Hmm.

How much taller is the first stick than the second stick? So because the first stick is taller, that must be the whole amount.

The second stick is a part of that whole amount and how much taller is the other part.

And once we've got our bar model, we can then use it to help us decide how to solve the problem.

But we're not worried about that now.

At the moment, we just want to practise representing the problem as a bar model.

So it is time for you to have another go.

Can you identify the parts and whole and then represent this word problem as a bar model? We've got Izzy is 130 centimetres tall.

Jacob is 150 centimetres tall.

How much taller is Jacob than Izzy? I'd like you to pause the video, have a go.

And when you've done that, press play.

How did you get on? Were you able to represent that word problem as a bar model? So Izzy's 130 centimetres tall, that's a part.

Jacob is 150 centimetres tall.

That's the whole.

It wasn't the other part because we're not adding their heights together.

We were working out how much taller Jacob is than Izzy.

So that's the other part.

That's the difference between his height and Izzy's height.

Your turn to practise now.

For task A question one, I'd like you to represent these problems as a bar model.

To help you do that, it's always worth visualising these problems first.

Can you see it happening in real life inside your head? And then that will help you draw the bar model.

But don't worry about finding the answers to these problems. I want you to do the bar model to show me that you really understand the structure of the maths that is being asked.

So question A, Izzy lays two sticks end to end.

The first stick is 30 centimetres long and the second stick is 20 millimetres long.

How long is her length of sticks? Part B, Laura competes in the triple jump.

She hops one metre, skips two metres and jumps another 200 centimetres.

How far has she travelled in total? Part C, Andeep has 90 centimetres of wool.

He cuts off 50 millimetres.

How much wool does he have left? And part D Jacob jumps 140 centimetres.

Izzy jumps one metre.

How much further does Jacob jump than Izzy? For question two, we're gonna do the opposite.

I want you to write a word problem that could be represented by these bar models.

So have a look at these bar models.

Think are they parts, are they wholes? What have you got? And what word problem could you write that matches them? Press pause on the video.

When you've had to go at both questions, press play.

So how did you get on? For question one, you were asked to represent these problems as a bar model.

For part A, you can see you were given two parts, so you've got 30 centimetres and 20 millimetres.

For part B, you were given three parts.

For part C, you were given the whole and one part.

And for part D, you were given the whole and one part.

For question two, these are some problems that you might have written.

For part A, I wrote one snail moves 40 centimetres, then rests, it then moves another 10 millimetres.

How far does it move in total? So I had the two parts there.

The missing bit was my whole.

Part B, I wrote Izzy had 41 centimetres of string.

She cuts off 40 centimetres.

How much string is left? So the 41 centimetres was my whole.

And the bit that was cut off is a part.

Part C, I wrote Jacob collected three pebbles and he lined them up.

One pebble was 30 centimetres, another was 20 centimetres and the smallest was 10 millimetres.

How long was his line of pebbles? So my three pebbles are the three parts and the total length was the whole.

Part D, Andeep kicked a football 30 metres.

Jacob threw a football 200 centimetres.

How much further did Andeep's football go than Jacob's? I wonder how you got on.

Well done.

I'm sure you did really well.

Fantastic.

You are making such a lot of progress in your understanding about solving problems about length and heights.

And I can see how much confidence you've got now in representing your problems as bar models.

We're gonna now move on to the second part of the learning where we're gonna look at using those bar models to identify the calculation and then solve the problem.

So let's revisit our first problem.

We're gonna identify the calculation needed and then we're going to solve it.

So Izzy had one metre of ribbon, if you remember she used 20 centimetres of it.

Can you remember that? Can you visualise that? How much ribbon does she have left? So we did a bar model for it.

We showed the one metre as the whole and the 20 centimetres was a part of the whole and we needed to find that missing part, the amount of ribbon that was left.

So from that bar model, we can see the parts and the wholes and that's why it's really important to represent words as a bar model because we can see the bit that we're looking for is a part.

It is a missing part and we need to find that part.

To find a missing part, we need to subtract the part we know from the whole.

And that's a really key piece of learning.

So I think we should say that together.

Are you ready to say that sentence with me? Good.

Let's go.

To find a missing part we need to subtract the part we know from the whole.

So which part do we know and what's the whole? That's right, we've got one metre is our whole and we're gonna subtract from it that 20 centimetres.

Oh, what's Izzy remembered? That's right.

Stop! Izzy's noticed that the units are different.

We've got metres and we've got centimetres, so we are gonna have to convert them to the same unit.

We know one metre is equal to 100 centimetres.

So instead of using one metre, we can use 100 centimetres.

So we know one metre is the same as 100 centimetres and we can use that in our calculation.

We've got 100 centimetres and we're gonna subtract that part.

The 20 centimetres.

If we do 100, subtract 20, we get 80 centimetres.

And that is our missing part.

She has 80 centimetres of ribbon left.

Let's check your understanding.

We're gonna revisit this problem that we looked at earlier.

Identify the calculation and solve it.

The problem was Izzy had one metre of string, she used 40 centimetres of it.

How much string does she have left? And you can see this represented in the bar model and I've given you a stem sentence to help you.

To find a missing part, we need to mm and if you remember, we just said that out loud together.

And Izzy is reminding us to remember to change the units when you do the calculation so that they are the same and it will make the calculation easier for you.

Press pause on the video, have a go.

And when you're ready, press play.

How did you get on? Did you remember to change the units at one metre is the same as 100 centimetres.

And did you remember that sentence? To find the missing part, we need to subtract the part we know from the whole.

We know one metre is equal to 100 centimetres, so we can use that in our calculation.

We've got 100 centimetres, we're gonna subtract the part we know the 40 centimetres and that gives us 60 centimetres.

So she had 60 centimetres of string left.

Let's revisit our second problem.

We're gonna identify the calculation and then solve it.

Remember we had a black cat walked 60 metres, the white cat walks 30 metres further than the black cat.

How far does the white cat walk? We did this bar model.

We represented those words as a bar model.

And from the bar model we can see we have two parts this time and we need to find the whole.

To find the whole.

We need to add parts together.

It's a very key piece of learning here.

So let's practise that.

My turn.

To find the whole, we need to add parts together.

Your turn.

Fantastic.

So let's have a go.

60 metres and 30 metres.

Well they're both metres this time so we don't have to worry about any converting of the unit.

60 and 30 is equal to 90.

So the white cat walked 90 metres, which is that 60 metres that the black cat walked and another 30 metres.

Let's check your understanding.

We're gonna revisit this problem.

I would like you to identify the calculation and then solve it.

The problem was Izzy kicks the ball 20 metres, Jacob kicks the ball 35 metres further than this.

How far does Jacob kick the ball? We represented it in a bar model and we could see that we needed to find the whole and I've given you part of the stem sentence there to help you to find the whole.

We need to mm, to have a think about that.

What do we need to do to find the whole? Pause the video, have a go.

Identifying the calculation and solving it.

And when you're ready, press play.

How did you get on? Did you remember that to find the whole, we need to add the parts together.

Let's have a go.

We've got 20 metres and 35 metres to add together.

The units are the same, so we do not need to worry about converting 20 metres and 35 metres is equal to 55 metres.

So Jacob kicked the ball 55 metres.

Let's revisit our third problem.

Identify the calculation and solve it.

The problem was how much taller is the first stick than the second stick? And we represented it in a bar model.

Once we've got the bar model, we can then use it to help us decide how to solve it.

We need to find a missing part and we know to find a missing part, we need to subtract the part we know from the whole.

Stop! Izzy is saying, what do we notice? Yes, the units are different.

We've got centimetres and millimetres.

We need to do 50 centimetres and subtract that known part, 90 millimetres.

We can't do 50, subtract 90.

Ah, that's because the units are different.

So we need to make sure our units are the same.

We need to convert to the same unit.

We know 90 millimetres is equal to nine centimetres, so we can use nine centimetres.

So we know we need to subtract the part we know from the whole and we're going to use nine centimetres instead of 90 millimetres.

50 centimetres subtract nine centimetres.

The units are now the same.

We can do the subtraction, which equals 41 centimetres.

The first stick is 41 centimetres taller than the second stick.

Let's check your understanding.

I want you to revisit this problem.

Can you identify the calculation and solve it? Izzy is 130 centimetres tall.

Jacob is 150 centimetres tall.

How much taller is Jacob than Izzy? And we represented that as a bar model and we can see that we need to find the missing part and I've given you that stem sentence with a part missing.

To find a missing part, we need to, mm.

Have a go.

Pause the video and when you're ready, press play.

How did you get on? Did you remember that to find a missing part, we need to subtract the part we know from the whole? So we've got 150 centimetres and we're gonna subtract the part we know, 130 centimetres.

The units are the same so we can just subtract 150.

Subtract 130 equals 20.

Jacob is 20 centimetres taller than Izzy.

Your turn to have a go.

For task B, I would like you to look at the questions from task A where you represented them as a bar model, but this time I would like you to identify the calculation and solve the problems. For question, two again I would like you to look at the word problems that you wrote for task A part two and have a go identifying the calculation and solving them.

For question three, I'd like you to make up your own word problem related to length or height and represent it in a bar model.

Identify the calculation and solve it.

Pause the video and when you finished all three questions, press play.

How did you get on? For question one, you were asked to identify the calculation and solve the problems. So for part A, I identified that we had to add the parts.

I could see the units were different, so I chose to convert 20 millimetres to two centimetres.

When I added them together, I got 32 centimetres.

A length of six was 32 centimetres.

For part B, again, I noticed the units were different.

I chose to convert the 200 centimetres to two metres and when I added those three parts together, I got five metres.

Laura had travelled five metres in total.

For part C, again, I noticed different units.

I chose to convert 50 millimetres to five centimetres and when I did the subtraction, I was left with 85 centimetres.

Andeep has 85 centimetres of wool left.

For Part D, again, I had different units.

I chose to convert one metre to 100 centimetres.

When I did the subtraction, I could see that Jacob jumped 40 centimetres further than Izzy.

Well done.

For question two, you had to identify the calculations, solve the problems. We had different units, so we had to convert.

I did 40 centimetres at one centimetre was 41 centimetres.

For part B we could subtract.

I was left with one centimetre.

For part C, again, different units, so I had to convert.

I chose to convert 10 millimetres to one centimetre.

When I added them all together, I got 51 centimetres.

For Part D, again, different units.

I chose to convert 200 centimetres to two metres.

When I did the subtraction, I was left with 28 metres.

For question three, you might have made up a problem like this.

Izzy's stride length is 110 centimetres, Andeep's stride length is 130 centimetres.

How much longer is Andeep's stride? You might then have represented it in a bar model.

I identified my whole and my part.

I could see I needed to find a missing part and then I might have solved it because I'm finding a missing part I had to subtract.

So my answer was 20 centimetres.

I wonder how you got on there.

Wonder what you wrote.

Fantastic learning today, everybody.

Really well done.

I can see how much progress you have made about solving problems with lengths and height.

You now know that we can represent word problems as a bar model.

When we identify those parts in the whole and that when we have represented in a bar model, it really helps us understand the structure of the maths and helps us form that calculation.

We know to find the whole, we need to add the parts together and we know that to find a part, we need to subtract the part we know from the whole.

Fantastic learning everybody, and I will see you again soon.