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I can add 3-digit numbers using column addition.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

When using column addition, start by adding numbers with the smallest place value first.
Use zero to show that there are no tens or ones in a 3-digit number.
Partition each number carefully into hundreds, tens and ones.

Common misconception

Pupils may not use zero to show that there are no tens or ones number in a 3-digit number. They may also use a zero to show that there are no hundreds when adding a 2-digit to a 3-digit number.

Emphasise with pupils that they need to use a zero only when needed. The number 75 would not be written as 075, so should not be written like this in column addition.

Keywords

Addend - An addend is a number added to another.
Sum - The sum is the the total when numbers are added together.
Column addition - Column addition is a way of adding numbers by writing a number below another.

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Hello, my name's Mrs. Hopper, and I'm really happy that we're 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.

So our lesson today is all about adding three-digit numbers using column addition, and it's part of our unit on column addition.

So let's get on, and see what's happening in today's lesson.

We've got three keywords, addend, sum, and column addition.

You may well have come across them before, but they're important words, so, good to look out for them.

Let's just have a practise at saying them.

I'll take my turn, and then your turn.

So my turn, addend.

Your turn.

My turn, sum.

Your turn.

My turn, column addition.

Your turn.

Let's look at what those words mean again.

So an addend is a number that is added to another one.

We've got lots of addends around today, 'cause we're looking at column addition.

The sum is the total when numbers are added together.

So when we combine our addends, we get our sum.

There'll be lots of sums floating around today as well.

And column addition is a way of adding numbers, by writing a number below another one.

It's a way of organising our numbers so that we can add them efficiently.

So let's get into today's lesson, and see what it's all about.

So today's lesson is all about three-digit numbers.

So we're going to be adding them using column addition, and we're going to be doing some column addition with some missing numbers.

So, really thinking about what column addition is all about, and what addition of three-digit numbers is all about as well.

So let's get going with some column addition for three-digit numbers.

And we've got Jun and Laura helping us in our lesson today.

Jun wants to add together three-digit numbers.

So he's set out a column addition chart with place value headings to help him to get his numbers organised in the correct way.

He says, \"I want to use column addition to add together 143 and 134.\" So can you help him to get his numbers in the right place? Laura says, \"Let's start by using base 10 blocks to represent a calculation.\" So we've got our place value chart there, let's use our base 10 blocks to represent the calculation.

So 143 can be partitioned into one hundred, four tens, and three ones, and there we've got that represented with our base 10 blocks.

And our other addend was 134, and 134 can be partitioned into one hundred, three tens, and four ones.

So there, we've got our two addends partitioned using our base 10 blocks.

And Laura says, \"When we use column addition, we start with the smallest place value numbers first.\" So we're going to start with our ones.

And she says, \"Three ones plus four ones is equal to seven ones.\" So there are our ones, three ones and four ones is equal to seven ones.

Now, we can move to our next lowest value column, or next highest value column, which is our tens.

Jun's saying that \"Four tens add three tens is equal to seven tens,\" and there are our seven tens.

And Laura says we can move on to our hundreds.

One hundred plus one hundred is equal to two hundreds.

So we've got our two hundreds in our hundreds column.

So our final answer is 277.

143 plus 134 is equal to 277.

Jun's going to use column addition to add 143 and 134, the same addends, but let's record this as a column addition this time.

So 143 can be partitioned into one hundred, four tens, and three ones.

And 134 can be partitioned into one hundred, three tens, and four ones.

So we used the base 10 blocks before, now we're using the numerals to represent our addends in our column addition.

Jun's remembered all of Laura's advice.

\"I start with the smallest place value numbers first.\" So three ones add four ones is equal to seven ones.

Then we can move to the tens, four tens add three tens is equal to seven tens.

And then finally one hundred add one hundred is equal to two hundreds.

And so we've recorded our column addition using our numerals, and we know that 143 add 134 is equal to 277.

Time to check your understanding.

Can you use column addition to add 215 and 151? Pause the video now and have a go, and then we'll talk about it together.

How did you get on? Did you remember that 215 can be partitioned into two hundreds, one ten, and five ones? And 151 can be partitioned into one hundred, five tens, and one one.

And then we need to remember to start with the smallest place value numbers first.

So starting with our ones, five ones add one one is equal to six ones, then move to our tens.

One ten add five tens is equal to six tens.

And then two hundreds plus one hundred is equal to three hundreds.

So we know that 215 plus 151 is equal to 366.

So Jun uses column addition to add 328 and 230.

So 328 can be partitioned into three hundreds, two tens, and eight ones.

And 230 can be partitioned into two hundreds, three tens, and zero ones.

Remembering we've got to have that zero there to show we've got zero ones, but we've got three tens and two hundreds.

Starting with the smallest place value numbers first, he's going to add his ones.

So eight ones plus zero ones is equal to eight ones.

Then moving to the tens, two tens add three tens is equal to five tens.

And then finally the hundreds, three hundreds plus two hundreds is equal to five hundreds.

So our answer 328 plus 230 is equal to 558.

Jun's gonna add some more numbers together.

Ooh, this time, he's going to add 505 and 84.

So he's adding a three-digit number to a two-digit number.

So he's gonna have to think carefully about where he positions his numbers in his column addition.

505 can be partitioned into five hundreds and five ones.

We've got no tens, have we, in this number? So we've got five hundreds, five ones, and no tens.

And Jun says, \"I need to write a zero in the tens column.\" 84 can be partitioned into eight tens and four ones, but we must remember to write our eight tens in the tens column and our four ones in the fours column.

There are no hundreds in this number.

And as Laura says, \"The hundreds is left empty\" because we've just got a two-digit number this time.

But Jun's right, we're still going to start with the smallest place value numbers first.

So he's going to add his ones.

Five ones and four ones is equal to nine ones.

Then the tens, zero tens add eight tens is equal to eight tens.

And then in the hundreds, five hundreds plus zero hundreds is equal to five hundreds.

So 505 plus 84 is equal to 589.

Time to check your understanding.

Can you use column addition to add 530 and 67? And Jun says, \"How would you lay out the calculation?\" And, \"What would the sum be?\" Pause the video, have a go, and then we'll talk about it together.

How did you get on? Did you see that our 530 is five hundreds, three tens, and zero ones? And then 67 is a two-digit number, six tens, and seven ones.

So, nothing in the hundreds column for our second addend because it's just a two-digit number.

And then remembering that we start with the smallest place value numbers first, so we're going to start with our ones.

So zero ones plus seven ones is equal to seven.

Then move to our tens, three tens add six tens is equal to nine tens.

And then in our hundreds, five hundreds plus zero hundreds is equal to five hundreds.

So 530 plus 67 is equal to 597.

Time for you to do some practise now.

We've got some columns here for you to complete and to record the sum, both in the column addition and in the equation.

And then for the second part, you're going to use the equations to complete each column addition.

So you're going to take the numbers from the equations and complete the column additions correctly, and there are four of those for you to have a go at.

So pause the video now, and then we'll look at the answers together.

How did you get on? Did you complete the column additions correctly? Did you remember to start with the digits with the lowest place value, so starting with the ones? So the answer to our first one, 223 plus 342 is equal to 565.

And for B, 313 plus 266 is equal to 579.

Well done if you used your column additions correctly there.

This time you had to complete the column additions, and then work out what the sum was.

So the first one, we had two three-digit numbers.

So we could record our numbers quite easily, and so we could work out that 523 plus 162 is equal to 685.

In B, we've got to remember that 530 has a zero in the ones, but we need to put that zero there when we're completing our column addition.

So we could work out that 530 plus 262 is equal to 792.

In part C, we have to be careful because our first addend is 308.

Three hundreds, zero tens, and eight ones.

So we had to record that correctly, so that we could work out that 308 add 471 is equal to 779.

And in part D, we were adding a two-digit number as our second addend.

So we had 625, but then we had to remember that our 64 is six tens and four ones.

So, nothing recorded in the hundreds column.

And we could then use the column addition to work out that 625 plus 64 is equal to 689.

Well done, let's move on to the second part of our lesson.

So we're going to think about missing numbers in column addition for the second part of our lesson.

Jun's gonna set out a column addition, and he's going to think about where the hundreds and tens and ones should go.

He's not got the place value chart around at this time, so let's have a think.

He says he's going to add together 352 and 127, and he's going to think about where those numbers need to go in his column addition.

So he's saying this is the ones column, so all my ones digits have got to be in this column.

So 352, that means there's a two, 127 is his second addend, which is underneath.

So he's going to line up his two and his seven, the ones digits from his two addends.

And then moving along, he's got the tens column.

So let's look at the tens values of his addends.

352, that's five tens and 127, that's two tens.

So he knows he's got his tens digits in the correct columns, in the correct place in his column addition.

Now, this is the hundreds column, so let's look at those hundreds values.

So his addends are 352, so that's a three in the hundreds.

And 127, so that's a one in the hundreds.

So by thinking carefully about where those columns are on his page, Jun has correctly written 352 plus 127, and laid it out as a column addition.

Laura is stepping in to help now.

\"Two ones add seven ones is equal to nine ones,\" she says.

Five tens add two tens is equal to seven tens, and three hundreds plus one hundred is equal to four hundreds.

So 352 plus 127 is equal to 479.

Well, Jun's gonna try and find some missing numbers now.

He's got a three-digit plus a three-digit column addition.

So two three-digit addends, and he knows that the sum is 657, but he's missing some numbers.

So Jun says, \"One addend has a missing tens number and the other has a missing one's number.\" So his first addend, his top addend, has a missing one.

And his second addend, the one underneath, has a missing ten.

Laura says that, thinking about these parts and holes, so she says, \"To find a missing part, we subtract the other part from the hole.\" Our addends are like our parts in a bar model, aren't they? And our sum is like the whole.

But if we sort of think about each column as a part and a whole, we know we've got seven ones in our sum.

So our two addend ones must combine to equal seven.

So something plus two is equal to seven.

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

So seven subtract two is equal to five.

So we know that the missing ones digit in our first addend must be five, and we can check that by saying, five ones at two ones is equal to seven ones.

What about the missing ten then? We know that four tens plus hmm tens is equal to five tens.

So four plus something is equal to five.

Subtract the part we know from the whole.

We know that the five tens are worth 50, subtract four tens, 40, is going to leave us with one ten, which is 10.

So our missing tens digit must be a one, four tens plus one 10 is equal to five tens, or 40 plus 10 is equal to 50.

Jun's got some different missing numbers here.

He says, \"One addend has a missing tens number.\" That's his top addend, his first addend.

And one addend has a missing hundreds number, his second addend, the one recorded below.

This time, we know all about the ones.

So we know that three ones plus six ones is equal to nine ones.

And Laura is reminding us again, to find a missing part, we subtract the other part from the whole.

And the missing numbers are a missing part of our tens and a missing part of our hundreds.

So something plus three is equal to seven.

If we want to find the missing part, we're going to subtract the three from the seven, but remembering this is tens.

So 70 subtract 30 is equal to 40.

So we know that that missing number represents 40, which is four tens, so it must be a four.

And we can check it by doing the addition, four tens plus three tens is equal to seven tens.

What about our missing hundreds number? So we know that two hundreds plus hmm hundreds equals five hundreds, or 200 plus something equals 500.

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

So 500 subtract 200 is equal to 300.

So we know that our missing hundred must be 300, which is a three in the hundreds column.

And we can check it by saying two hundreds plus three hundreds is equal to five hundreds.

Time to check your understanding now.

Can you find the missing numbers in this column addition? Now, Jun says, \"Find the missing ones number in the first addend, \"And the missing hundreds number\" in the second addend.

And Laura's reminding us that to find a missing part, we subtract the other part from the whole.

So pause the video, have a go, and then we'll look at the answer together.

How did you get on? Did you spot in the ones that we need, something plus three is equal to eight? So to find our missing part, we're going to subtract the part we know from the whole.

So eight subtract three is equal to five.

So we know our missing ones digit must be five.

And we can check it by saying five ones plus three ones is equal to eight ones, we know we're correct.

In our hundreds, we've got five hundreds plus hmm hundreds is equal to eight hundreds.

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

So 800 subtract 500 is equal to 300.

So we know our missing part represents 300, and we know that that is a three in the hundreds column.

And we can check it, five hundreds plus three hundreds is equal to eight hundreds.

Did you spot there that we've used the same fact? Pretty much, five plus three is equal to eight, eight minus three is equal to five, eight minus five is equal to three.

So we had a missing five in the ones, and a missing three in the hundreds.

Laura gives Jun a challenge, we've got three missing numbers this time.

Laura says, \"Can find all of the missing numbers?\" And Jun says, \"Well, to find a missing part, subtract the other part from the whole.\" So I know that we've got a missing part in the ones of our first addend, and in the tens of our second addend.

So Jun says, \"Nine subtract five is equal to four.\" So the missing ones digit must be a four, four ones plus five ones is equal to nine ones.

What about the tens then? We know that our whole number of tens is seven tens, one part is five, and there's a missing part.

So seven tens is 70, subtract five tens, which is 50, which equals 20.

So we know that our missing part must be 20, or two tens.

Five tens plus two tens is equal to seven tens.

Jun then says, \"To find a missing hole, we add the parts together.\" When we've got a missing number in our sum, that represents the whole.

So this time, we're not going to do a subtraction, we're going to add our parts.

Two hundreds plus six hundreds is equal to eight hundreds.

600 plus 200 is equal to 800, and an 800 is eight in the hundreds column.

So our missing hundreds digit must be eight.

Time to check your understanding.

You've got three missing numbers in this column addition now.

Can you work out, when is it that you're finding a missing part, and when are you finding a missing hole? And what do you need to do? Laura says, \"To find a missing part, subtract the other part from the hole.\" And Jun says, \"To find a missing hole, add the parts together.\" So can you work out, which missing number means you're missing a part, and which means you're missing a whole? Pause the video, have a go, and then we'll look at the answers together.

How did you get on? Did you spot that that first addend is missing a ones digit? So we're missing a part there, aren't we? So we know the whole is six ones.

Six ones subtract three ones is equal to three ones, so our missing part must be three.

Three ones plus three ones is equal to six ones.

Our next missing number is in the tens, but this time it's the missing sum.

It's the 10 of the sum that's missing.

So we know that we have to combine the parts to equal the whole.

So we've got two tens, or 20, plus one ten, 10, and 20 plus 10 is equal to 30.

And we represent that with a three in the tens column, two tens plus one 10 is equal to three tens.

In the hundreds, we're missing a part again, aren't we? We've got one hundred plus hmm hundreds is equal to nine hundreds.

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

So 900, which is our nine in our sum, subtract 100, which is our known part, gives us 800.

So we know that we are missing an eight in that hundreds.

So one hundred plus eight hundreds is equal to nine hundreds.

And we found the values of the three missing parts.

Now, Laura's playing a game with some digit cards here.

She's going to use all six of the digit cards.

She tries to make the sum as close to 900 as possible.

Ooh, gosh, I wonder where she's gonna start with that.

She says, \"I'm going to arrange the cards into two three-digit numbers, and add them using column addition.\" So there are her spaces for her cards in her column addition.

I wonder what she's going to choose.

She's decided to put five in the hundreds.

I wonder what she would add to that five in the hundreds to get as close to 900 as possible.

Oh, she's gone with the four hundreds.

So five hundreds plus four hundreds is equal to nine hundreds.

She doesn't want to get too much above 900, does she? So she's decided to put the zero in the tens column, that's the smallest value she can have.

So she's put the zero in the tens column with the 500.

I wonder what else she's going to choose as a tens value.

Did you get that? Yes, she's chosen a one.

500 plus 400 is equal to 900, and she wants to be as close to 900 as possible.

So she's chosen the smallest values that she can for her tens.

What about the ones? She's got the two and the three left.

So she's put the three ones with her 500, to make 503.

And the two ones with her 400 and one ten, to make 412.

Now, she's going to use column addition to add them.

So where she's going to start? She's going to start with the smallest digits for the place value, which is our ones.

So three ones plus two ones is equal to five ones.

Zero tens plus one 10 is equal to one tens, and five hundreds plus four hundreds is equal to 900.

So she's found 915.

Hmm, I wonder if we could find anything closer to 900.

So we've got six digit cards for you.

This time, you're going to use all of them to create a three-digit plus a three-digit column addition.

And you're going to try and make the sum as close as possible to 400 this time.

So, set out your cards to make two three-digit numbers.

Add them using column addition, and see if you can get your sum as close to 400 as possible.

Pause the video, have a go, and then we'll come back and talk about it.

How did you get on? How close did you get to 400? Laura's going to share her solution, and she's wondering if you've got as close to 400 as she did.

She decided to start with 100 and 200.

Oh, that's interesting, isn't it? So she didn't go with 100 and 300 to make 400.

Maybe she realised she'd have to have some bigger numbers after that.

So she's decided to go with 100 plus 200, which will give her 300.

So now she needs quite a big value in her tens, doesn't she? Ah, she's chosen five tens and four tens.

So that would give her, five tens plus four tens is nine tens.

so that would give her 390 something.

What's she got left? She's used one, two, four, and five.

Well, she's only got the three and the zero left, hasn't she? So she adds those together, three plus zero is equal to three ones.

Five tens plus four tens is equal to nine tens.

One hundred plus two hundred is equal to three hundreds.

So she's made 393 as her total, and she'd only need seven more to make 400, so that's pretty close to 400.

I wonder how close you got, was it possible to get any closer? Time for you to have some practise.

So you're going to find the missing numbers in these column additions, working out whether it is you're finding a missing part, or a missing hole because it's part of the sum.

So you've got four of those to have a go at, and then there's a challenge.

You're going to use all six of the digit cards each time to make two three-digit numbers.

And you're going to use column addition to add them up to see if you can find the smallest sum you can make, the largest sum you can make, and the sum nearest to 500.

So have fun playing with your number cards in creating your column additions, pause the video, and we'll talk through the answers afterwards.

How did you get on? Did you find the missing numbers? So in A, we were looking for two missing parts.

We were looking for a missing part in the tens, which was three tens, and a missing part in the ones, which was one one.

So our missing addends created 335 and 441.

B was interesting 'cause we were missing two parts of the same addend, we were missing the hundreds and the ones, and they both ended up being five.

So our missing addend was 515.

The third missing number this time was in the sum.

So we were looking for a missing whole, so we had to combine the tens, six tens plus one ten is equal to seven tens to find our missing hole, which was the tens value in our sum.

In C, we were looking for, again, a missing hole as the ones digit in our sum and then two missing parts.

The tens in our first addend, and the hundreds in our second addend.

And we ended up with 734 plus 142 is equal to 876.

And D was interesting, we had a three-digit plus a two-digit number.

So we had a missing part in our ones, which was three, giving us a second addend of 83.

The missing part in our first addend though ended up being a zero missing, so it was something plus eight is equal to eight.

So zero plus eight is equal to eight.

And then zero kind of came into play with the other missing number as well.

This missing number was the hundreds value of our sum, so we were missing a whole.

So three plus something is equal to three, three plus zero.

There were no hundreds in our second addend.

So I wonder how you got on with this.

Did you get as close as you could to these highest and lowest sums? So these were the highest and lowest that are possible.

I wonder if you made them, and I wonder if you made them slightly differently.

So we got 124 plus 35.

Now, you wouldn't usually write a zero there, but we've put the card in to show which card has been used because we have the cards zero, one, two, three, four, and five.

So 124 plus 35, it gives you 159, which is the smallest possible sum.

Now, you may have had 135 plus 24, or you may have had another combination.

But I would imagine that if you made 159, you must have had a four and a five in the ones, and you must have had a two and a three in the tens.

But your numbers may have been slightly differently organised.

And the largest sum possible was 951.

So a five and a four is your hundreds digits, three and a two is your tens digits, and the one and the zero is your ones digits.

And that would give you, in any different combination of those numbers, the largest possible sum.

I wonder how close you got to 500.

Interestingly, Laura and Jun came up with two different options here.

Laura said she made a number larger than 500, so she made a sum of 519.

But Jun says, well, my number is even closer to 500, but it was smaller.

He managed to make the sum of 492, which is only eight away from 500, whereas Laura's was 19 more than 500.

I wonder if you managed to make the sum of 492.

Did your numbers look the same as Jun's, or did you have your digits in a different combination? I hope you've had lots of fun playing with those and getting numbers close to, or larger or smaller, than anybody else's, so well done.

We've come to the end of our lesson on adding three-digit numbers using column addition.

What have we learned about in today's lesson? Well, we've learned to partition each number carefully into hundreds, tens, and ones when we're arranging them into column additions.

We've learned about using a zero to show that there are no tens or no ones in a three-digit number.

And we've also thought about, in our column addition, that when we are using column addition to add, we always start by adding the numbers with the smallest place value first.

And as we move on and learn more about column addition, you'll see why that is all the more important.

Thank you ever so much for your hard work, and all your careful thinking about those missing numbers today.

It's been a pleasure working with you and I hope to see you again soon, bye bye.

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