Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today.

We are going to be thinking all about place value, numbers up to a hundred, and how we can apply that another strategies to adding and subtracting.

So I hope you're ready to work hard and have some fun in our maths lesson today.

So today's lesson in our unit, securing place value to a hundred and applying to addition and subtraction, is all about using place value knowledge to write addition and subtraction equations.

So by the end of the lesson today, you'll be able to use your place value knowledge to write addition and subtraction equations.

So we've got some keywords in our lesson today and those keywords are part, whole, and bar model.

So let's have a go at just saying those.

So I'll take my turn and then it'll be your turn.

So my turn, part, your turn.

My turn, whole, your turn.

My turn, bar model, your turn.

Well done.

Now you might well have come across those words before, but they're key words for us.

They're important in what we are going to be learning in our lesson today.

So let's have a look at what they mean.

So let's start with that bar model.

So one of the most effective ways, one of the best ways to represent a problem is to use a bar model.

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

And you've got a couple of examples there.

One whole made from two parts and one whole made from three parts.

So a part is a piece or a section of the whole.

And the whole is all of a group or number.

When you have the whole, you have all of something.

So look out for those words as we go through our lesson today.

So there are two parts to our lesson.

We're going to use addition and subtraction to compose three digit multiples of 10.

And then we're going to use place value to solve problems. So let's have a look into this first part of our lesson.

And we've got lots of helpers today.

We've got Sophie, Andeep, Jacob, and Izzy helping us in our lesson today.

So Izzy says, "What do the base 10 blocks represent?" What can you see there? I can see one block representing a hundred and then four blocks representing tens.

So let's have a look.

Jacob says "There is 140 represented in base 10 blocks.

100 and 40." So there's our 100, and there's our 40.

Izzy says, "There are 14 tens represented in base 10 blocks.

There are 10 tens and 4 tens." So yeah, we can see that our 100 is composed of 10 tens, and then we've got 4 more tens.

So you may have come across this before that we can represent our number as 100 and 4 more tens, or we can represent it as 14 tens.

Izzy says, "We can use addition to represent 140." Jacob says, "140 = 100 + 40." And you can see the 100 and the 40 there clearly in the representation.

Jacob also says, "14 tens is the same as 10 tens and 4 tens." It's equal, and we can see that equal sign there.

14 tens is equal to 10 tens and 4 tens.

Izzy says, "We can also use subtraction to show how 140 is composed." I wonder what that's gonna look like.

Let's have a look.

So Jacob says, "140 - 100 = 40." So I've got my 140 represented there.

If I remove, take away my 100, I'm left with my 40.

So there are my 140 represented.

If I take away the 40, I'm left with the 100.

So we can use addition and subtraction to think about how those numbers are composed.

And our place value helps us to see that we can take away a hundred or we can take away a group of tens quite easily from a three digit number.

Jacob says we can think about this a different way.

He says 14 tens - 10 tens = 4 tens.

So we are thinking about that number as a number of tens.

So we can see that there are 14 tens altogether.

If I subtract 10 of those tens, I will be left with 4 tens.

I wonder if we can think about that a different way.

Yes, Jacob says if we think of our 14 tens, and this time we take away 4 of the tens, we can see we are left with 10 tens.

So is he saying we can use subtraction to think about that composition? We can think about our place value 140, or we can think about it in terms of how many tens we've got and thinking that we know that 10 tens is equal to 100.

Izzy says we can also represent this in a bar model.

So here's our bar model.

Our whole is 140 and the two parts we can see is a 100 and 40.

140 is the whole, 100 is a part, and 40 is a part.

And we can also use a part part whole model.

So this is another way of representing that whole and those parts.

So we can see the two parts and the whole again.

So again, 140 is the whole, 100 is a part, and 40 is a part.

So we can represent this as a bar model or as a part part whole model.

And Izzy says, "We add the parts to find the whole." So a part plus a part is equal to the whole.

Jacob says 100 plus 40, the two parts, is equal to 140.

So our parts combine to make our whole part plus part is equal to whole.

Oh, Izzy says though, if we subtract a part from the whole, we find the other part.

So let's have a think about that.

A whole subtract a part is equal to the other part.

140 - 100 = 40.

And we can see that in the bar model and in the part part whole model.

Or if we think 140 - 40, that's equal to 100.

If we subtract the 40 part, we are left with the 100 part.

If we subtract the 100 part, we are left with the 40 part.

And there's our 100 if we subtract the 40.

So we subtract a part from the whole to find the other part.

Whole - part = part.

Okay, time to check your understanding here.

So we've got a bar model and we've got a part part whole model.

So what I'd like you to do is to write two addition calculations and two subtraction calculations, remembering that we add the parts to find the whole and we subtract one part from the whole to find the other part.

So pause the video and see if you can complete those four calculations based on the bar model and the part part whole models you can see on the slide.

How did you get on then? So I completed the calculations.

So our whole in this case was 160 and our parts were 100 and 60.

And we know that we add the parts to find the whole.

So 100 + 60 = 160.

And because we know we can swap our add ends around and add in any order, we can also say that 60 + 100 = 160.

I should be careful with our subtraction 'cause we're always going to be starting with our whole, which in this case is 160.

So 160 - 100 = 60.

If I subtract one part from the whole, I'm left with the other part.

This time I subtracted the other part.

I subtracted the 60 from the 160 and I was left with the 100.

So you can see if I take away the hundred, I'm left with the tens.

If I take away the tens, I'm left with the hundred.

Now here we can see that we can use our understanding of parts and the whole to work out what is missing.

So what's missing in this case? Jacob says the whole is missing.

So how did we work out the whole? Izzy says, "We add the parts to find the whole." So we've got to add our parts together to work out what our whole is.

So Jacob says 100 + 30 = 130.

So our whole, our missing whole, was 130.

Oh, Jacob says, now we've got a part missing.

And Izzy says, well, we subtract a part from the whole to find the other parts.

So we know about one of the parts, we know that one of the parts is 30.

So if we subtract the part we know from the whole, we can find out what the other part is.

So we have to do 130 - 30, and we know that that is equal to 100.

If we subtract the tens, all the tens, we are left with the hundred value.

So 130 - 30 = 100.

So we can use our knowledge of parts and wholes to help us work out missing numbers.

A missing part, as Jacob says, is 100.

Okay, so we've got a two part one here.

We're gonna have a go at the left hand side of the screen together and then you are going to have a go at the right hand side.

So we've got information presented in different ways here.

We've got a bar model and then we've got some calculations and we're going to use all the information to sort of fill in the gaps.

So can we see with the bar model what's our whole going to be? Well, we dunno the whole but we know the parts, and we know that we have to combine the parts or add the parts to find the whole.

So 100 + 20 = 120.

So I know my whole here is 120.

Let's see if we can fill in the gaps in the calculations.

I've got 100 plus hmm is equal to 120.

So I've got one part, I've got a missing part.

I can see from the bar model that my other part is 20.

So 100 + 20 = 120.

And then I've got a hmm plus 100 equals 120.

I've just swapped those add ends around, haven't I? So I know that 20 + 100 = 120.

So let's have a look at the subtractions.

Do you remember Izzy telling us that if we want to find a part, we subtract the other part from the whole? So 120 subtract hmm is equal to 100.

Well, I can see my two parts of 120.

So 120 - 20 = 100 and 120 - 100, while I'm taking away one of my parts, I'm going to be left with my other parts, so that must be equal to 20.

So using the bar model and what you know about parts and wholes, pause the video and have a go filling in the gaps for the other side of the screen.

How did you get on? Did you spot that we knew the two parts again when we were trying to work out the whole? So if you remember, we had to add the parts to find out the whole.

So 100 plus another 40 is equal to 140.

So we know our whole is 140.

Let's look at the gaps in the calculations.

So we've got 100 plus hmm equals 140.

So I know that 100 is one of my parts.

My other part is 40.

So 100 + 40 = 140.

So now I've got hmm plus 100 is equal to 140.

Oh, that's another missing part, isn't it? And if I look at the calculation above, I can see that I've swapped my add ends around again.

So I know that 40 + 100 = 140.

Let's look at those subtractions.

140 subtract hmm equals 100.

Well, I know one of my parts is a hundred, and if I subtract the 100 from the whole, I'm left with 40.

So it must be 140 - 40.

I've taken away my tens.

I'm left with my number of hundreds.

And the final one, 140 subtract to 100 is equal to, well, I've subtracted one of my parts, so I'm going to be left with my other part.

So my answer is 40.

140 - 100 = 40.

Well done.

Time for some practise.

So I've got a couple of questions for you to have a look at.

So what calculations do you need to find the missing numbers? Don't just want the numbers this time.

What calculations are you writing down? Are you combining parts to make the whole or are you subtracting a part from the whole? So you're gonna write down the calculations you need to find those missing numbers in these bar models.

And then you're going to fill in some missing numbers in some calculations there.

We've got some additions, we've got some subtractions, and we've got a couple of bar models to work with.

So pause the video, have a go at your practise tasks, and then we'll look at the answers together.

Okay, how did you get on? So what calculations did you need to find the missing numbers? So here we had a missing whole and we needed to do 100 + 70 and combine those parts to find our missing whole, which was equal to 170.

So in B, this time we had a missing part.

So if we remember what Izzy was telling us, to find a missing part, we subtract the part we know.

So 110 - 100 = 10.

Our missing part was 10.

We needed to do a subtraction.

What about C? Again, we had a missing part.

So we knew that the whole was 13 tens and we knew that one part was 10 tens.

So this time we're thinking about this as a number of tens.

So we need to those subtract one part from the whole to find the other part.

So 13 tens - 10 tens = 3 tens.

So our missing part was 3 tens.

And in D, again, we had a missing whole.

But again, it was thinking about how many tens have we got? So this time we knew that one of the parts was 10 tens and the other part was 9 tens.

So if we add those together, 10 tens + 9 tens = 19 tens.

So I hope you recorded those calculations and thought about the parts and the wholes and how they relate to each other to work out how to find those missing values.

So in the second part, we asked you to fill in those missing numbers.

So in part A, we had a part part whole model with a missing part.

So we had to subtract one part from the whole to find the other part, and our missing part was 50.

150 - 100 = 50.

In B, again, we had a missing part.

This time we needed to use our knowledge of some number bonds here, didn't we? So we knew that our whole was 13 tens and one part was 8 tens.

13 tens - 8 tens = 5 tens, so our missing part was 5 tens.

And then you can see there we had some missing numbers to fill in.

We didn't have the bar models here.

I wonder if you were thinking about those gaps as whether we were missing a part or a whole.

So take a moment and make sure that you filled in those answers correctly.

So time to move on to the second part of our lesson and we're going to be using place value in addition and subtraction to solve some problems. So let's have a look.

So Year 3 is having a cake sale.

That cake looks rather delicious, doesn't it? They've got 140 cakes and they've sold 40 cakes.

So how many cakes are left? Hmm, I wonder what we can do here.

Jacob says, "I can show this on a bar model." Okay, so I wonder how we're gonna represent this on a bar model.

So there is Jacob's bar model, how does that relate to our problem, I wonder? So there are 140 cakes and they've sold 40 cakes, how many are left? So Izzy says, "140 is the whole.

It's all the cakes." Remember that whole was about the whole of something.

If we'd got the whole, we had all of it.

So they started with 140 cakes.

So the whole is 140 cakes.

Jacob says, "40 is a part." So they've sold some of the cakes.

They've sold part of the cakes.

So he's written 40 in as one of the parts.

And Izzy says, "40 is the part of the cakes they have sold." So Jacob says, "We have to subtract a part from the whole to find the other part." And Izzy says, "The missing part is how many cakes are left." So what calculation are we gonna have to do? Jacob says we've got to do 140 - 40 to find out the value of our missing part.

So we've represented our 140 using our base 10 blocks and we can use some place value knowledge here, can't we? So this time we're subtracting the tens.

So 140 - 40 is equal to, there's our whole, 140, and we're gonna subtract the 40, and we are left with 100.

That's right.

140 - 40 = 100.

There are 100 cakes left.

So we've represented our problem as a bar model.

We used our knowledge of parts and wholes to work out the calculation and then we used our place value understanding of 100 and hmm more tens to help us to solve that calculation and work out the answer.

Sophia and Andeep and Jacob are selling the cakes at the Year 3 cake sale and they have all sold some cakes and they've sold 140 cakes altogether.

Well, that was our whole number of cakes.

So they've sold all the cakes, which is really good news.

So we've drawn a bar model here to show that Sophia, Andeep, and Jacob have sold the cakes together.

So what else do we need to know? Ah, so we've got some numbers here.

So Sophia has sold 70 cakes, Andeep has sold 30 cakes, but we don't know how many cakes Jacob has sold.

So this time we've got three parts in our bar model.

So we've got Sophia's part, Andeep's part, and Jacob's part.

And we know about Sophia's and Andeep's, but we dunno about Jacob's part.

So let's put that information into the bar model.

Jacob says how can we do that? Well, we've got our three parts, I think we'll be all right, let's have a look.

So there we go.

Sophia sold 70 cakes, that's her part of the bar, and Andeep sold 30 cakes, so that's his part of the bar model.

But we don't know how many cakes Jacob has sold.

Okay, Jacob says to find a missing part, we subtract the other part from the whole, but we've got two other parts.

Hmm, I wonder what we're going to do.

Well, I spot something about those two parts, about Sophia's part and Andeep's part.

Something familiar about 70 and 30.

Have you spotted anything? Let's have a look.

Sophia says, "I know that 70 + 30 = 100.

So Andeep and I have sold 100 cakes." So if we combine those two parts, we can now make our bar into just two parts.

And so Jacob telling us we can subtract one part to find the missing part.

That's now going to work, isn't it? Because we know that together, Andeep and Sophia have sold 100 cakes.

So now we can work out how many Jacob has sold.

140 - 100 = 40.

Jacob says, "I can use place value to work that out.

I know that if I take away 100 from 140, I'm left with the 40, I'm left with my value of my tens.

So I'm left with 40." So Jacob has sold 40 cakes.

Okay, time to check your understanding.

So we've got some information here.

Jacob has 100 football stickers and Izzy has 20 football stickers.

How many stickers do they have together? And what I'd like you to do is to draw a bar model to decide if you know about the parts or the whole in the problem.

So pause the video and have a go at drawing that bar model.

So is that the bar model you drew? So Jacob had 100 football stickers and Izzy has 20.

How many stickers do they have all together? So the bit we don't know is the whole.

We know about the two parts.

So Jacob has 100 stickers, Izzy has 20 stickers.

"These are the parts," Jacob says.

And Izzy says, "To find the whole we need to add the parts." So we know that 100 + 20 = 120.

So they have 120 stickers together.

Oh, now this looks a bit different, doesn't it? So we know that Sophia is 130 centimetres tall and Jacob is 100 centimetres.

How much shorter is Jacob? Hmm.

Izzy says I can represent this on a bar model.

I wonder what's the whole and what are the parts in this story do you think? Let's have a look, see what Izzy thinks.

Izzy says Sophia's height is the whole and Jacob's height is a part.

So we can see that Sophia is the taller one, isn't she? Her height is our whole in this problem and Jacob's height is a part.

So what's the other part then? Izzy says the other part is how much shorter Jacob is.

And if you look at the bar model, you can sort of see that.

If you imagine that that 130 in the whole is Sophia's height, may be drawn as a line this time, and then Jacob's height is drawn as the 100, the bit missing is how much shorter Jacob is or how much taller Sophia is, whichever way round you want to look at it.

So what's the calculation we're gonna have to do? Izzy says, "To find a missing part, we subtract the other part from the whole." So we need to subtract 100 from 130.

So 130 - 100 = 30.

So Jacob is 30 centimetres shorter.

Time for you to have a go.

So we've got another pair of characters here.

It says Andeep is 150 centimetres tall and Jacob is 100 centimetres.

How much shorter is Jacob? So can you draw the bar model and solve this problem? Pause the video and we'll talk about it afterwards.

So here's Izzy's bar model.

She says Andeep's height is the whole and Jacob's height is a part.

So she's drawn her bar model with 150 as the whole and 100 as one of the part.

So what was that missing part? Well, she says to find a part, you subtract the other part from the whole.

So the part we're trying to find is the part that says how much shorter Jacob is than Andeep.

So what calculation are we going to have to do? We're going to do 150 subtract 100 and that equals 50.

So Jacob is 50 centimetres shorter than Andeep.

Time for you to have a go at some questions.

So we've got some problems here and like you to solve the problems, but I'd like you to draw a bar model to represent each problem.

So think about what's the whole and what are the parts in these problems. So A is about Sophia buying an incredibly long fruit string that's 170 centimetres long.

She's giving 70 centimetres to Andeep.

So how much does she have left? And part B, Andeep has 10 bags of 10 marbles.

Oh, we're thinking about groups of 10 there, aren't we? And Jacob has 20 marbles.

Oh, now Jacob's counted his in tens.

Think carefully about how you are going to represent that on your bar model.

We want to know how many marbles they have altogether.

And similar things in C, think about the bags of 10 sweets and the number of sweets.

So draw bar models to represent each problem for number one.

And then in part two, we've given you some bar models here and I'd like you to write your own problems. What might these bar models be representing if they were a problem? So pause the video and then we'll talk through the answers together.

Okay, so how did you get on? Let's have a look at the bar models that you were going to draw to solve the problems in part one.

So Sophia's incredibly long fruit string is 170 centimetres long.

She gives 70 centimetres to Andeep, how much does she have left? So the 170 centimetres is the whole.

That's how much fruit string she's got altogether.

She gives 70 centimetres to Andeep, so that's one part, and we need to work out what the other part is.

So we know that to find a missing part, we subtract the part we know from the whole.

So 170 - 70 = 100.

There is 100 centimetres of fruit string left over.

So plenty for Sophia.

Part B was about marbles.

Andeep has 10 bags of 10 marbles and Jacob has 20 marbles.

How many marbles do they have together? So this time we don't know the whole, the whole is was missing, wasn't it? And one of the parts was Andeep's 10 bags of 10 marbles and the other part was Jacob's 20 marbles.

But we need to have a think about how we can combine those because we've got some bags of 10 marbles and then some marbles.

So I know that 10 bags of 10 marbles is equal to 100 marbles.

So Andeep has 100 marbles and Jacob has 20 marbles.

So we need to add the parts to find the whole.

So 100 marbles + 20 marbles = 120 marbles.

So they have 120 marbles together.

And part C, this time, I think we knew about the whole, didn't we? So Jacob has 13 bags of 10 sweets.

30 of the sweets are mints, how many sweets are not mint sweets? So we know that part of the sweets are mints and part of them are not mints.

So we are finding a missing part here, and we know that the whole is these 13 bags of 10 sweets.

But again, we've got that mixture.

We've got some counting in tens and we've got some counting the groups of 10.

So let's have a think about those 13 bags of 10 sweets.

13 bags of 10 sweets is 130 sweets.

13 groups of 10 is equal to 130.

So we know that 30 of them are mints and we know that to find a missing part, we subtract the part we know from the whole.

So 130 - 30 = 100.

So 100 sweets are not mint sweets.

I wonder what flavour they were.

What flavour would you like them to be? And then in part two, well, I wonder what problems you came up with.

I thought about Izzy and Jacob doing some running.

So in our first one, we had two parts of 100 and 50 and we had a whole of 150.

So I thought about the fact that Izzy ran 100 metres and Jacob ran 50 metres further.

Oh, that's an interesting one.

So my two parts were Izzy's 100 metres and Jacob's extra 50 metres, how many metres did Jacob run? Well, he ran the 100 metres and another 50 metres, so he ran 150 metres.

And then I thought about pencils.

So Class 3 had 140 pencils.

But by half term 100 had been used and 20 had been lost.

How many pencils were left? So I can represent that by whole is 140.

One part, the used pencils, is 100.

The lost pencils were 20.

But what's my missing part? Well, to find a missing part, I subtract the part I know from the whole.

Well, I can do the 100 bit quite easily.

140 - 100 = 40 pencils.

So that's 40 pencils that haven't been used, but I know that 20 of them have been lost.

So now I've got this sort of other part.

So if I know that 20 have been lost, I know that 40 - 20 = 20.

So there must be 20 pencils left.

I hope they look after their 20 pencils.

And we've come to the end of our lesson today.

Thank you so much for all your hard work.

So what have we learned about today? We've learned that place value knowledge helps us to use number facts to add and subtract multiples of 10, crossing the hundreds.

So we know that we can take away the hundreds and be left with the tens, or we can take away the tens and be left with the hundreds.

We know that the bar model can help us to understand the structure of the maths and to form a calculation to help solve a problem.

So a bar model can be a really useful way of representing a word problem.

So we can represent word problems in a bar model by identifying the parts and the whole.

And then we know that when we find the whole, we need to add the parts.

And when we find a part, we need to subtract the part we know from the whole.

So I hope you'll remember those and use them in your problem solving.

And I also hope I'll get to see you again soon.

Thank you.