Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you today in this lesson from our unit on comparing, ordering and partitioning two digit numbers.

Have you done lots of work with two digit numbers before? I wonder? Well, I hope you're ready to work hard and think hard today.

So let's make a start.

So in this lesson we're going to be representing, combining and partitioning of tens and ones with addition and subtraction equations.

So we're still going to be thinking about partitioning two digit numbers, but we're going to think about representing them with addition and subtraction equations this time.

We've got some key words in our lesson, so let's practise saying them.

We've got partition, combine, parts and whole.

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

So my turn, partition.

Your turn.

My turn, combine.

Your turn.

My turn, parts.

Your turn.

My turn, whole.

Your turn.

Well done.

I'm sure they're words you are familiar with, but they're going to be really useful so look out for them in our lesson today.

There are two parts to our lesson.

We're going to be representing tens and ones with addition equations in the first part, and then we're going to be representing tens and ones with subtraction equations in the second part of our lesson.

So let's make a start.

And we've got Izzy and Lucas with us in our lesson to help with our learning.

Lucas combines the parts of the part-part-whole model to make the whole.

He wonders which equations he could write to represent this.

He says, "I know when adding, we combine the parts to make the whole.

I can show I've combined the parts with an addition equation".

So which equations could he write? He says there are 7 tens, which is 70 and 6 ones, which is 6.

There is 76 altogether.

So he could write 70 add 6 is equal to 76.

What else could he write? He says, "We know if we change the order of the addends, the sum remains the same".

The addends are the numbers we're adding together, aren't they? And the sum is our total.

So we can change the order of the addends and the sum remains the same.

That means that 6 plus 70 must also be equal to 76.

6 plus 70 is also 76.

And he's remembering that a part plus a part is equal to the whole.

Izzy combines the parts of this part-part-whole model and completes the equation to represent it.

What mistake has been made? "Oh", Izzy says, "I forgot to look at the signs in the equation".

She didn't look carefully at the equals and the add sign, did she? The equals sign means that both sides of the equation have the same value and I don't think that's right there is it? The whole is equal to the two parts and the two parts are equal to the whole.

So has she got the whole on one side of her equation and the two parts on the other? I don't think she has, has she? She says "Part plus part is equal to whole.

So whole must be equal to part plus part.

That means that the whole amount must be on one side of the equation and the two parts must be on the other".

Ah, she's corrected it.

So 46 is equal to 40 plus 6.

And she also says, "The addends can be combined in any order, so I could also have written 46 is equal to 6 plus 40".

Izzy has learned from her mistake.

She combines the parts of her bar model and writes two different addition equations.

Let's help her to complete them.

She says, "Part plus part is equal to whole and whole is equal to part plus part".

Can you see which way round this one's been written? Izzy says, "I know that the equal sign means both sides of the equation have the same value".

So 76 is our whole and that's equal to 70 add 6.

And she says, "I know that the addends can be combined in any order".

So 76 is also equal to 6 add 70.

Time to check your understanding.

Can you write two equations that could represent the part-part-whole model? Think carefully about where the equal sign is.

Where is your whole going to be represented and where are your parts going to be represented? Pause the video and we'll come back for some feedback.

How did you get on? So there are 4 tens, which is 40, and 3 ones which is 3, so there's 43 altogether.

So 40 plus 3 is equal to 43.

We know the addends can be combined in any order.

That means 3 plus 40 must also be equal to 43.

We know that part plus part is equal to whole.

So whole is equal to part plus part.

We know the addends can be combined in any order.

So this way round or this way round.

That means 43 must be equal to 3 plus 40 or 40 plus 3.

Lucas is trying to solve this equation.

I wonder how he could find the missing number? He says, "I'll draw a bar model to help me".

So there's his bar model.

So what do we know? We know the parts, don't we? He says, "I know in addition that we combine the parts to make the whole.

There are 5 tens, which is 50 and 4 ones which is 4".

So one part is 50 and the other part is 4.

Ah, "This is 54 altogether".

So 50 plus 4 is equal to 54.

And Izzy says, "I know we can combine the addends in any order and the sum remains the same.

That means that 4 plus 50 is equal to 54".

Izzy wants to use the bar model to help to complete this equation.

Let's help her.

"There's 37 altogether.

This is the whole.

Part plus part is equal to whole and whole is equal to part plus part".

And we know that one part is 30 so let's think about 37.

"There are 3 tens, which is 30 and 7 ones which is 7".

So there's our other part.

"The missing part must be 7".

And Izzy says, "I know we can combine the addends in any order and the sum remains the same.

That means that 37 is also equal to 7 plus 30".

Time to check your understanding.

Can you draw a part-part-whole model to help find the missing number in the equation? Pause the video, have a go, and we'll come back for some feedback.

How did you get on? Is this the part-part-whole model you drew? We knew that it was 40 plus 3 is equal to something, so 40 and 3 must have been our parts.

So our whole must have been 43.

There are 4 tens, which is 40, and 3 ones, which is 3 and this is 43 altogether.

Another check.

Can you use the part-part-whole model to help you to complete this equation? So we've got a part-part-whole model.

We've got one complete equation and one with a missing box.

Pause the video and try and work out what the missing value is in the second equation.

How did you get on? Did you spot that the whole is equal to the two parts? So there's 43 all together.

So we were missing a part.

There are 4 tens, which is 40, and 3 ones, which is 3 in 43.

So our missing part must have been 3.

And we could see that from the part-part-whole model.

We could see that the 43 was the whole, 40 was a part and 3 was a part.

So in our equation we were missing a part.

And the part we were missing was 3.

Time for you to do some practise.

Use the stem sentences there at the bottom of the screen to find the missing numbers in the equations.

We've got some missing wholes and we've got some missing parts.

And look carefully to see how the equation has been written.

Where is the whole in each case? And then you're going to pick three examples and draw a part-part-whole model or a bar model to show that you are right.

So pause the video, have a go, and we'll get back together for some feedback.

How did you get on? So here are some answers.

So for A, we had a lot of missing wholes.

We knew about the tens part and the ones part and we had to combine them.

So 20 plus 4 was equal to 24.

40 plus 2 was equal to 42.

60 plus 7 was equal to 67.

70 plus 6 was equal to 76.

And then for the last two, we have the ones first, but that doesn't matter.

We can combine the addends in any order, combine the parts in any order.

So 5 plus 30 was equal to 35 and 3 plus 50 was equal to 53.

So did you spot that in all of those answers we had pairs of answers with the same digits, but the digits swapped around? 24 and 42, 67 and 76, 35 and 53.

What about B? Did you spot that the whole came first? Whole is equal to part plus part.

So we had 4 and 20, which is equal to 24.

So 24 is equal to 4 and 20.

42 is equal to 2 plus 40.

Ah, can you see what's happening here as well? In fact, can you see a link between A and B? 67 is equal to 60 plus 7 and 76 is equal to 70 plus 6.

For our last two though, we've changed them.

So 91 is equal to 90 plus 1 and 81 is equal to 1 plus 80.

What about C? Well for the first two in C, we had a missing whole.

But can you see what's happened? We've just reversed the order of the addends.

We've reversed the parts.

So 6 plus 80 is equal to 86 and 80 plus 6 is equal to 86.

And what about the other two? Can you see that our whole is still 86, so we were missing a part.

So we had a known part of 80 in the first one, so our missing part must be 6.

And in the second one we had a known part of 6 so our missing part must have been 80.

And can you see that we've done something similar for D, but this time the whole has come first? So 43 is equal to 3 plus 40 and 34 is equal to 4 plus 30.

So we have changed the digits round there.

So let's look carefully at the next one.

43 is equal to something plus 40.

Well we know about the 4 tens, so our 3 ones are missing.

And in 34 we know about our 4 ones so the missing part is our 3 tens, 30.

So I hope you used the stem sentences to help you.

So which did you choose to represent with a bar model or a part-part-whole model? So we've chosen 5 plus 30 is equal to something.

So we've got a missing whole.

So there are 3 tens, which is 30 and 5 ones which is 5, so there is 35 altogether.

We knew the parts and we could combine them to work out the whole.

So in the second example we've chosen, we've put the whole first.

So we are still missing a whole, but it comes at the beginning of our equation.

So we still know about our parts.

9 tens, which is 90, and 1 one, which is 1.

So there's 91 altogether, our whole is 91.

And in the third example, we are missing apart.

So we knew this time that our whole was 86.

There are 8 tens, which is 80.

That was our known part.

And so there are 6 ones, which is 6, there's 86 altogether.

So 6 was our missing part.

And let's move on to the second part of our lesson.

We're going to represent tens and ones with subtraction equations this time.

Lucas partitions the whole amount into the parts.

So our whole is 76 and he's partitioned it into 7 tens, or 70, and the 6 ones.

What equations should he write to represent this? He says, "When we know the whole and we know one part, we can subtract to find the other part.

I can write a subtraction equation", he says.

So his whole is 76, that's what we're going to subtract from.

And there we've represented it with base 10 blocks.

So 76, subtract 6 is one of our parts, is equal to 70, our other part.

And we can also say 76 subtract 70 is equal to 6.

Izzy wants to complete the subtraction equation here.

She's got a part-part-whole model.

Her whole is 54 and her parts are 50 and 4.

Let's use the bar model to help us.

"There's 54, which is 5 tens or 50, and 4 ones which is 4.

If 54 is the whole and 4 is a part, then the other part must be 50".

So 54, subtract 4 is equal to 50.

Izzy says, "I think I can write a different subtraction equation.

If 54 is the whole and 50 is a part, then the other part must be 4".

So she can write 54 subtract 50 is equal to 4.

Over to you to check your understanding.

Can you use a bar model to find which of the following will complete the equation? So we've got an equation with a missing part and you need to find the missing part.

So there's a bar model to help you.

Pause the video and have a go, see if you can find the missing part.

How did you get on? So we knew that 72 was our whole, that was the number we were subtracting our parts from.

So 72 was the whole and 2 was a part.

There are 7 tens, which is 70, and 2 ones, which is 2.

So this is 72 altogether.

So our missing part must be the 70.

Izzy wants to complete these subtraction equations to show how she partitioned her number.

Let's find out what's different about these equations.

Izzy says, "The equal sign is the first symbol in the equation.

In subtraction, we know that we partition one part from the whole to find the other part.

We know that whole minus part is equal to part.

So part must equal whole minus the part".

Ooh, that's interesting.

So before the equal sign, we're going to have one of our parts.

So if one of our parts is 6, how can we complete the equation? Well, 6 must be equal to 76.

Subtract our other part, which is 70.

Or, 70 is a part, and that's equal to our whole, which is 76.

Subtract our other part, which is 6.

Over to you now to check your understanding.

Which of the following numbers A, B, or C, completes the equation correctly.

Use a bar model to help you find out.

Remember to think carefully about what's a whole and what is a part.

To pause the video, have a go, and we'll come back for some feedback.

How did you get on? Did you use the bar model to help you? We knew that our whole was 34 and one part was 4.

In subtraction, we subtract one part from the whole to find the other part.

Whole subtract part is equal to part, so part is equal to whole subtract part.

There's 34 altogether.

This is the same as 4 ones, which is 4, and 3 tens, which is 30.

So our missing part was 30 and that completed our equation.

So B was the correct answer.

30 is equal to 34 subtract 4.

The children are trying to find the missing number in these equations.

Lucas says, "I will draw a part-part-whole model to help me".

So what's the whole and what are the parts? Oh, and Izzy's going to use the stem sentences.

So 28 was our whole, so this is 28.

And Izzy's stem sentence says this is the same as 2 tens, which is 20, so that's one of our parts.

And 8 ones which is 8, so that's our other part.

So the missing part in our equation must be 20.

28 subtract 20 is equal to 8.

What about this missing number? So this time our missing number is the whole.

So this is, hmm, we don't know what.

This is the same as 2 tens, which is 2o, one of our parts, and 8 ones which is 8, the other part.

So we knew that the number we were subtracting was one of our parts and the number we were left with, so after the equal sign, was our other part, because we know that whole subtract part is equal to part.

So we knew the two parts.

And Izzy says, "The whole is missing this time.

And the missing number is 28".

Because 2 tens and 8 ones is equal to 28.

Time to check your understanding.

Can you match the equation to the correct missing number? Pause the video, have a go, and then we'll look at the answers together.

How did you get on? Did you spot that 7 was missing from our first equation? 47 subtract 7 is equal to 40, so we were missing a part.

What about the second one? Something subtract 7 is equal to 40.

Well this time we were missing the whole.

Whole subtract part is equal to part.

So our whole is 47.

47 subtract 7 is equal to 40.

What was missing in the third one? It was a whole again, wasn't it? Part is equal to whole subtract part.

So 4 is equal to 74, subtract 70.

I hope you got those right.

The children think they can use the inequality symbols to compare tens and ones with two digit numbers.

Ooh, this is interesting.

So we're going to think about things that are greater than and less than.

Izzy says, "I know that 30 plus 6 is 3 tens plus 6 ones.

And 63 has 6 tens and 3 ones.

So 30 plus 6 is less than 63".

Great thinking Izzy.

She was using her knowledge about comparing two digit numbers, but one of our two digit numbers had been partitioned into tens and ones.

Really good thinking there, Izzy.

Well done.

What about this one? Lucas says, "Each side has 5 ones, but I know that 60 is greater than 50.

So 5 plus 60 must be greater than 5 plus 50".

Great thinking there Lucas, as well.

This time both our numbers have been partitioned and one of them have the ones digit first in the addition.

But Lucas remembered that if a number has more tens, then it will be larger.

Over to you for some practise.

Can you use the stem sentences to find the missing numbers in the equations? So you've got missing wholes, missing parts, you've got equations written in different orders.

And then you're going to pick three examples and draw a part-part-whole model or a bar model to show that you are right.

So in question two, you're going to use the inequality symbols to compare these expressions and two digit numbers, and there are the stem sentences that you can use to help you.

Pause the video, have a go at your tasks, and we'll get together and look at the answers.

How did you get on? Lots to look at here.

So let's start with A.

So 36 subtract 30 was equal to 6.

36 is equal to 3 tens or 30 and 6 ones.

So if we knew about the 30, our missing part was 6.

In the next one, 46 subtract 40.

This time we're taking away the tens, so we're left with the ones.

So again, we've got 6 left.

Oh, can you see something happening here? 56, subtract 50.

Again, we've taken away all the tens and we're left with our ones.

So what's gonna happen here? 66 subtract something is equal to 60.

So 66 is our whole, 60 is a part.

So the part we subtracted must be 6 as well.

Something subtract 70 is equal to 6.

This time we've got a missing whole.

So we combine our parts.

So we must have started with 76.

And then 76 subtract 6 is equal to? That must be 70, mustn't it? There were a lot of 6's around there, weren't there? There were 6 ones in all of those examples.

What about B? So this time we've got our part as our first missing number here.

Part is equal to whole subtract part.

So something is equal to 15, subtract 5.

10 is equal to 15, subtract 5.

If 15 is the whole and 5 is one part, then 10 must be the other part.

So again, we're looking for a part in this next one.

Something is equal to 58, subtract 8.

Well, if I start with 58 and I subtract 8, I'm left with 50.

And if I start with 32 and subtract 2, I'm going to be left with 30.

This time we knew about our part, 40, and that was equal to 46 subtract something.

So if 40 is a part and 46 is the whole, the other part must be 6.

Now in this one we've got 20 is equal to something subtract 1.

So we're missing that whole.

Part is equal to whole subtract part.

So 20 and 1 are our parts.

So 21 must be our whole.

And for the final one, we knew our whole was 76.

We subtracted one part, which is 6, so our part remaining must be 70.

For C, let's have a look at what's happening here.

We've got 41, 42, 43, 44, 45 as our wholes and we're subtracting a part each time.

So 41 subtract 1 is equal to 40.

42 subtract 2 is equal to 40.

43 subtract 3 is equal to 40.

And 44 subtract 4 is equal to 40.

Each time we'd remove the ones part of our two digit number.

So what about the next one? 45 subtract something is equal to 40.

Well if 45 is our whole and 40 is a part we know the other part must be 5.

And then let's have a think.

Oh, I can see what's happening here.

Something subtract 5 is equal to 40.

So 5 and 40 are our parts, so 45 must be our whole.

And what about D? Again, we've got some missing parts.

Part is equal to whole subtract part.

So 3 is equal to 63 subtract 60.

7 is equal to 47, subtract 70.

And 9 is equal to 89 subtract 80.

We've taken away the tens number each time so we were left with the ones digit.

6 is equal to 36, subtract? 30, that's right.

If 6 is a part, 36 is the whole, then 30 must be our other part.

And 5 is equal to something subtract 40.

Oh, that must be 45, mustn't it? I hope you did good thinking about parts and wholes to work out those missing numbers.

And then here we were looking at comparing the expressions and the two digit numbers to see which were greater, which were less, and which perhaps were equal.

So 30 plus 6 and 63.

Well there are more tens in 63 so 63 must be greater.

30 plus 6 and 36.

Well they're equal, aren't they? 3 tens and 6 ones in each.

5 plus 50 and 60 plus 5.

Well, there are more tens in 60 plus 5.

So 60 plus 5 must be greater.

Now we've got some with subtractions.

43 subtract 3, so 4 tens and 3 ones.

Subtract the 3 ones, that must be 40.

And 54 subtract 4.

Well, I've got more tens there and I'm only subtracting the ones.

So 54, subtract 4 is greater.

Let's have a look at the next one.

71 subtract 70.

I'm subtracting all my tens so I'm left with one.

And 43 subtract 40.

Again, I've subtracted all my tens, so I'm just left with my ones.

And we know that 1 is less than 3.

Let's look at B.

18, and 1 plus 80.

Oh now 1 plus 80, that's 8 tens and 1 one.

And we've got 1 ten and 8 ones.

So 18 is less than 1 plus 80.

But what about 1 plus 80 and 81? They're the same, aren't they? 8 tens and 1 one.

3 plus 70 and 70 plus 3.

Again, we've got 7 tens and 3 ones in both.

So those are equal.

We've got another one with subtractions here.

93 subtract 3.

So we've taken away all the ones so we're left with 90.

95 subtract 5.

Again, we've taken away all the ones so we're left with 90.

Those are equal as well.

27 subtract 20.

We're taking away the tens so we're left with 7.

28 subtract 20.

Again we've taken away all the tens, so we're just left with the ones, and 7 is less than 8.

I hope you did some good thinking and used your stem sentences to think about how those numbers were made up of tens and ones.

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

We've been representing addition and subtraction of tens and ones with equations.

What have we learned about? We've learned that when tens and ones are combined to make a two digit number, this can be represented as an addition equation.

And when a two digit number is partitioned into tens and ones, this can be represented as a subtraction equation.

And we've also thought really hard about where the parts and wholes are in our equations, haven't we? Thank you for your hard work and all your great mathematical thinking today, and I hope we get to work together again soon.

Bye-bye.