Lesson video

Hello, my name's Mrs. Hopper and I'm really happy that we are going to be working together in our maths lesson today.

We're gonna work hard, we're going to do lots of thinking about our maths, but I'm really looking forward to sharing this learning with you.

So let's see what's in today's lesson.

Hello and welcome to this lesson in our unit on column addition.

And in this lesson we're going to be thinking about using place value to lay out column additions correctly.

So by the end of the lesson, you'll be laying out column additions correctly, using your place value knowledge to help you.

We've got a couple of keywords, which you may well have come across before.

So our keywords today are addend and column addition.

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

My turn first and then your turn.

So my turn, addend.

Your turn.

My turn, column addition.

Your turn.

Well done.

Let's have a think about what those words mean.

So an addend is a number added to another number.

So in this equation here we can see that our addends are 10 and 6, and together they combine to equal the sum of 16.

Column addition is a way of adding numbers by writing a number below another.

You may have come across column addition and we're going to think today about how we can make sure that we record the numbers in our column additions correctly using our place value understanding.

Two parts to our lesson today.

We're going to think about place value using base 10 blocks in the first part of our lesson, and then we're going to move on to thinking about three digit numbers and place value in three digit numbers.

So let's make a start.

And we've got Jun and Laura helping us with our learning today.

So Laura and Jun are using base 10 block representations to show place value and you may well have done that as well.

Let's have a look at what they've been up to.

So they've got, ooh some tens and some ones here, so what have they got? Oh, Jun says this representation shows 3 tens and 6 ones.

Can you see the 3 ten sticks and the 6 one blocks? Laura says we could show this using a place value chart.

So here she's got her tens and her ones, she's not got space for all the base 10 blocks this time, we're going to represent them using digits so let's have a look.

So Laura says we've got 3 tens and the tens have a value of 30 and we've got 6 ones with a value of six.

And if we look at our base 10 blocks, we can see that, we can see our 3 tens with a value of 30 and our 6 ones with a value of six, giving us 36.

Laura and Jun represent another two digit number.

Let's have a look.

What can we see this time? Jun says this representation shows 5 tens and 4 ones.

Laura says, we can show this using a place value chart.

So here's our place value chart with our tens and ones, and we can see that we've got 5, 5 tens with a value of 50, matching our base 10 blocks and 4 ones with a value of four, matching our base 10 block ones.

So we can see that we've represented the number 54 using the base 10 blocks and using a place value chart.

Now it's time to check your understanding.

Jun represents a two digit number using base 10 blocks.

And here it is.

Jun says how many tens are there? Laura says, how many ones are there? Complete the place value grid and think about the number that's been represented.

Okay, pause the video, have a go and then we'll discuss it together.

How did you get on? Did you notice anything? Did you notice that the way the base 10 blocks are arranged, you've got the ones first and then the tens.

Let's see, how many tens have we got? Well, there are 4 tens blocks there.

4 tens have a value of 40 and there are 8 ones, and 8 ones have a value of eight.

So Laura says the base 10 blocks represent 48.

So in column addition one addend is laid out below the other.

So if the first addend is 43, there are 4 tens and 3 ones.

The second addend is 24 and it's laid out under the first addend.

So then we can see the 24, there are 2 tens and 4 ones, and we can see that all the ones are lined up underneath each other and the tens are lined up underneath each other.

So we've used our place value to think about how we are organising the addends in our column addition.

Jun uses base 10 blocks to represent column addition.

He says I'm going to add together 43 and 24.

So here he has his tens and his ones, and we can see that one addend is going to be underneath the other one.

So he's laid out, his 43, 4 tens and 3 ones, and his 24, 2 tens and 4 ones.

And Laura says we could also show this as column addition with numerals.

So let's see how she's going to lay it out.

We need to use place value, she says, to help us to lay it out correctly.

So there are 4 tens, so we've recorded that with the numeral 4 and there are 3 ones and we record that with the numeral 3 in the ones column.

And then in our 24 there are 2 tens and we record that with a numeral 2 and there are 4 ones and we record that with the numeral 4 in the ones column.

So we can see that the base 10 blocks are represented in the columns with numerals looking like column addition.

So Jun says again, he's going to use base 10 blocks to represent column addition.

He says I'm going to add together 35 and 30.

So he set out his 35 and 30, his base 10 blocks, as if they were looking like a column addition.

So he's got 3 tens and 5 ones.

and then underneath he's got his 3 tens to represent the 30.

And Laura says we could show this with column addition with new rules.

So let's have a look.

There's our column addition laid out with the place value headings to help us, and we need to use that place value to help us to lay it out correctly to make sure we've got the numbers lined up, so we're adding the tens together and the ones together.

So there are 3 tens in the 35, so we represent that with the numeral 3 and there are 5 ones.

And then for 30 there are 3 tens, but there are 0 ones, there are no extra ones.

We've just got the 3 tens representing 30, but we need a 0 to show that we've got no ones.

Time for you to have a check.

But again, we are going to use base 10 blocks and column addition to represent a calculation.

So can we help Jun? So here there are the base 10 blocks and Jun says I'm adding these two numbers together.

Laura says, has Jun laid out the column addition correctly? So let's have a look.

He's used his base 10 blocks and he's used a column addition recording as well with the numerals.

So pause the video and have a check.

Has Jun laid this out correctly? What did you think? Has Jun laid out the calculation correctly? So in the base 10 blocks we can see we've got, 5 tens and 3 ones, 53.

So that top number's correct, isn't it? And then in the base 10 blocks, we can see 2 tens and 5 ones, 20, oh, I can see a problem.

Can you? Jun's made a mistake with the number of tens in the second addend.

He's only recorded 1 ten in his column addition with the numerals, but there are 2 tens in his base 10, so he'd need to correct that to make sure that he used the column addition correctly.

Time for you to have a go now.

So some things for you to practise.

So first of all, can you use the base 10 block representations to correctly lay out each column addition.

So can you represent those base 10 layouts as column addition using the numeral, so you've got a, b, and then you've got c and d as well.

And then once you've had a go at that, Jun has had a go at doing some as well, he's completed some column additions from his base 10 blocks.

Has he made any mistakes though? Have a look and check Jun's work really carefully to see if he's made any mistakes.

So pause the video now and then we'll come back and discuss them later.

How did you get on? Did you manage to use the base 10 blocks to lay out the column additions? So we can see in a here, our first addend, our top addend was 4 tens and 6 ones, 46.

And so we've represented that using the numerals.

And our second addend was 3 tens and 3 ones, 33, and we've represented that as well.

In b, our first addend was 23 and our second addend we can see, was 31.

And we've recorded those correctly in the place value charts using those to help us to set out our column addition.

C and d, we had 63 plus 11, and 78 plus 20.

So I hope you got all those correct.

Now moving on, Jun had made some mistakes I'm afraid.

So when we had a look in the base 10 blocks, we can see that our first addend in a is 43 and Jun had recorded 44, so we had to correct that to make sure he's records 4 tens and 3 ones.

And then he made another mistake, didn't he? I think he might've got them the wrong way round, so our bottom number is 34, 3 tens and 4 ones, but he'd recorded 3 tens and 3 ones, hmm.

He'd got those ones the wrong way round when he turned the base 10 blocks into a column addition.

So let's have a look at b.

And he'd made a couple of mistakes there as well, hadn't he? He hadn't recorded the 0 ones from his 60.

So even though there are no ones, we know we have to put a 0 there to show that there are no ones, and our 6 is representing 6 tens, so he needed to put the 0 in the ones column.

And then the second addend in b is 1 ten and 9 ones, it's 19 and not 29.

So he'd put the wrong number of tens for the second addend.

I hope you spotted all of those mistakes.

So into the second part of our lesson and we're going to be thinking about place value with three digit numbers.

So Jun uses base 10 blocks to represent a two digit and a three digit number.

And Jun says I'm going to add together 145 and 34, going to add them together.

So he's recorded his addition of his three digit and his two digit number, thinking about the place value.

So he's got a 145, 1 hundred, 4 tens, and 5 ones, and then 34, 3 tens and 4 ones.

There are no hundreds in that because it's a two digit number, isn't it? Laura says we could show this with column addition with numerals.

Hmm, wonder what that's going to look like.

She says we need to use place value to help us to lay it out.

So this time she's got hundreds, tens, and ones in her place value so that we've got enough space to lay out our three digit numbers.

So she says there's 1 hundred, so we're going to have a 1 in our hundreds column.

There are 4 tens in our first addend, so we're going to put a 4 in our tens column, and there are 5 ones, so we're going to put a 5 in our ones column.

What about our second addend, which is 34? There are 0 hundreds, it's a two digit number.

We've got no hundreds, so we can leave the column empty in the second addend, we don't need to record anything in our hundreds.

There are 3 tens, so we record a 3 in our tens and there are 4 ones, so we record a 4 in our ones column.

So you can see that we've recorded our two addends of 145 and we've recorded our addend of 34, but we've been really careful where we've positioned that 34 so that we keep all our tens together and all our ones together.

Jun uses base 10 blocks to represent 2 three digit numbers.

So 2 three digit numbers this time, let's have a look.

He says, I'm going to add these numbers together.

Now what numbers has he represented? Laura says we could show this with column addition with numerals.

Have you spotted something though? What's that first addend in that top number? We've got 1 hundred, 0 tens, and 3 ones, we've got 103, haven't we? Hmm, that's gonna be interesting when we put it into our column addition, let's have a look.

As Laura says, we need to use place value to help us lay it out correctly.

So we've got our three digit numbers, so we've got hundreds, tens, and ones.

So in our first addend we've got 1 hundred, but we've got no tens.

So can we just ignore it? We don't, we need to record that there are no tens.

So we're going to use a 0 if a three digit number has no tens or ones.

And do you remember that was a mistake that Jun had made earlier on in the lesson, hadn't he? So we need to record that 0 in the tens to show that there are no tens in this particular number.

Let's have a look at the ones.

We've got 3 ones, so we're going to record a 3 in the ones column.

So what about our second addend? Well again, we've got 1 hundred, so we're going to record our 1 hundred, but this time we've got 3 tens, so we're going to record our 3 tens in our tens column, and we're going to record the 4 ones in the ones column.

So we need to be really careful when we've got three digit numbers where there are no additional tens or no additional units to make sure that we record those zeros so that we keep all our hundreds together, all our tens together and all our ones together in the correct columns.

Time for you to check.

So you are going to write these 2 three digit numbers as a column addition and think carefully about what we've just talked about.

We're going to write these 2 three digit numbers as a column addition.

So there are our three digit numbers represented with base 10 blocks and we're going to use place value to lay it out correctly, using a place value grid using the numerals to represent our 2 three digit numbers in a column addition.

So pause the video and then we'll have a talk about it.

How did you get on? So did you spot that this time there's 1 hundred in our first addend.

There are 6 tens in our first addend and there are two ones.

So we've got 162 and in our second addend there is also 1 hundred, and there are 2 tens, and there are 6 ones.

So we've got 126.

Did you spot that we've got some same numbers in there, so we have to be really careful to make sure we know whether we're representing tens or ones with our numerals.

So our addition is 162 plus 126.

So Jun and Laura setting out another calculation as a column addition, let's have a look.

Ooh this time we're going straight from the equation calculation into our column addition.

We haven't got our base 10 blocks this time to help us.

So what numbers have we got? We've got 304 plus 275 and we're going to set this out as a column addition.

Let's have a look.

So there are hundreds, tens and ones because we've got 2 three digit numbers here.

And Jun says I'm going to write 304 in the correct columns.

Can you see what he's got to be careful with? 304 is equal to 3 hundreds, 0 tens, and 4 ones.

So he's going to record a 3 in the hundreds, a 0 in the tens, and a 4 in the ones, to record his 304 in the correct columns.

And Laura's going to do the 275 in the correct columns.

275 is equal to 2 hundreds, 7 tens, and 5 ones.

So she's got a 2 in the hundreds column, a 7 in the tens column, and a 5 in the ones column.

So we've recorded 304 plus 275 as a column addition.

Right, time for you to have a check.

We've got an expression here, 213 plus 450.

Which column addition shows this correctly set out.

So we've got three choices there.

So have a look, see which column addition shows that addition represented correctly.

Pause the video and then we'll have a talk about it together.

How did you get on? Did you spot the right one? Look carefully at the number of hundreds, tens, and ones, Jun says.

And we can see that that's not right, is it? That top addend doesn't show 213, it shows 231.

So yes, the first addend is incorrect.

It's 213, it should be not the 231 that we've got in that column addition.

What about the next one? Ooh, that one's not correct either.

Jun says the 450 has been written in the wrong columns.

The 4 represents 4 hundred and not 4 tens.

So because we've got a 0 in there, we can't just squash the number down, we've still got to record it as 4 hundreds, 5 tens, and 0 ones.

So that must mean surely that our last one is correct.

Yes it is.

And we can see that this, in this addition, the digits are in the correct columns and we can see 213 plus 450 correctly represented in the column addition.

Jun wants to add together 120 and 67.

Gosh, this is in words this time, isn't it? Hmm, I wonder what he's going to do to help him here.

Jun says, I'm going to write both addends' numerals.

So, he says, he's got 120, which he knows is going to be represented as 1 hundred, 2 tens, and 0 ones, and 67, which is just 6 tens and 7 ones.

So he's got a three digit number and a two digit number.

He's going to record his addition as a column addition.

So he says 120 is equal to 1 hundred, 2 tens, and 0 ones, 1 hundred, 2 tens, and 0 ones, and 67 is equal to 6 tens and 7 ones.

So we can see we've got a three digit number and a two digit number, but we've got everything in the right column.

So the ones are with the ones, and the tens are with the tens, and the hundred there is on its own 'cause it's the only one that has a hundred.

Time to check your understanding.

Which column addition shows 105 add 40.

So think carefully about those, think about what Jun did in using numerals to represent those numbers before he put them into the column addition.

So there are three possibilities.

So which column addition shows correctly 105 add 40? Pause the video and then we'll have a chat about it.

How did you get on? Which one represents 105 add 40? Hmm, Jun says it helps to write the equation in numerals.

And so Laura says the calculation is 105 plus 40.

So can we see that correctly represented in one of those column additions? Well that first one shows 150, doesn't it? Not 1 hundred and 5 ones, but they've put 1 hundred and 5 tens, so that's not the correct representation.

And that's not the correct representation, the third one.

Jun says the 40 has been written in the wrong columns, so they've put, instead of 4 tens, they've recorded 4 hundreds.

So that's not correct either, is it? But the middle one is correct.

105, 1 hundred, no tens, and 5 ones, plus 40, 4 tens and 0 ones.

So thinking really carefully about the zeros and where they go and making sure that our digits are recorded, our numerals are recorded in the correct columns is going to be really important as we move on with our column addition.

Time for you to do some practise.

Use the base 10 blocks to lay out the column addition correctly.

So think about what's represented in the base 10 blocks and how can you transfer that and represent it as a column addition.

Here we're going to lay out each column addition correctly based on these expressions that we've been given.

So we were given the numbers written as numerals, so we're going to transfer those and write the additions as column additions.

And then finally we're going to think about those numbers represented as words.

So we've got three here to have a go out where the numbers are represented as words, and remember Jun's advice about taking those words and turning them into numbers represented as numerals to help you.

So pause the video, have a go at those tasks and then we'll talk through them.

How did you get on? So our first one, we had some base 10 blocks and we could see that we had 1 hundred, 5 tens, and 4 ones, and to that we were adding 1 hundred, 4 tens, and 3 ones.

So 154 plus 143, 2 three digit numbers to add together.

This time we went from the numbers themselves and transferred them into the place value charts to help us to lay out our column additions correctly.

So the first one we had 234 add 122.

So 2 three digit numbers, no zeros to to make us think on that one.

So that one was a fairly straightforward one.

The next one, 350 plus 503.

Oh gosh, there's lots of similar digits in there and lots of zeros.

So 350 is 3 hundreds, 5 tens and 0 ones.

503, we need to be careful.

That's 5 hundreds, 0 tens, and 3 ones.

So we needed that 0 in the tens column there of the second addend to make sure that we had put our our numbers into the column addition correctly.

And then in the final example, 313 plus 44, we've got a three digit number plus a two digit number.

So our first addend is 3 hundreds, 1 ten, and 3 ones for 313.

Our second addend is 44, 4 tens and 4 ones.

So we need to remember that we record those in the, 4 tens and the 4 ones, and our hundreds column is blank because we don't have any hundreds in a two digit number.

And for question three, you were turning those numbers written out as words into numerals in a column addition.

I wonder if you wrote out the numbers with the digits, with the numerals before you put them into the column addition.

So we had 325 plus 131, 408 add 71, and then 440 add 505.

So quite a few zeros floating around there to make sure we had 0 tens in the 408 and the 505 in the second and third examples.

And in the second example, we had a three digit number plus a two digit number.

So remembering that for 71, we are recording that in the tens and the ones column and that we have nothing in the hundreds column because it's a two digit number.

Well done.

You've worked hard on those.

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

So what have we been learning about today? So we've been thinking about writing digits in the correct column, when we lay out an addition as a column addition.

We thought about using a zero to show when there are no hundreds, tens, or ones.

If it's a two digit number, we don't have to put the zero in the hundreds column.

It's not wrong if we do, but we don't have to.

But if there are 0 tens in a three digit number or 0 ones in a two or a three digit number, we need that zero to show that we have 0 tens or 0 ones, but we do have some of the other values of the digits.

And if numbers are written in words, writing them in numerals can really help you to set them out as a column addition.

Thank you for working so hard today.

It's been a pleasure to work with you and I hope I'll see you again.

Goodbye.