Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in our maths lesson today from the unit "Reviewing column addition and subtraction".

Hopefully, there'll be things in here that are familiar to you, and you'll be able to revisit some ideas that you've learned about before.

So if you're ready, let's make a start.

So in this lesson, we're going to be thinking about adding 3-digit numbers using column addition.

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

I'll take my turn, then it'll be your turn.

So my turn, addend, your turn.

My turn, sum, your turn.

My turn, column addition, your turn.

I'm sure they're words you're familiar with, but let's just check what they mean, 'cause they're going to be useful to us in today's lesson.

So an addend is a number added to another.

The sum is the total when numbers are added together.

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

It's a way of organising our numbers and representing them in a way that makes it easy to add them together.

There are two parts to our lesson today.

In the first part, we're going to be adding 3-digit numbers using column addition.

And in the second part, we're going to be solving 3-digit column addition problems. So let's make a start with part one.

And we've got Alex and Lucas helping us with our work today.

Alex wants to add together two 3-digit numbers.

He says, "I want to add together 143 and 134".

Lucas says, "Let's start by using Base 10 blocks" "to represent a column addition." Alex says, "143 can be partitioned" "into 1 hundred, 4 tens, and 3 ones." And we can use the Base 10 blocks to represent that.

134 can be partitioned into 1 hundred, 3 tens, and 4 ones.

There they are.

Lucas says, "Start with the smallest place value numbers first." That's going to be really important to us as we go on and learn more about column addition.

So let's get used to doing that.

3 ones add 4 ones is equal to 7 ones, and then we move to the tens, 4 tens add 3 tens is equal to 7 tens.

1 hundred add 1 hundred is equal to 2 hundreds.

There are 2 hundreds.

So what have we got in our sum? We've got 277.

So we know that 143 add 134 is equal to 277.

Alex represents the same problem using digits.

He says, "143 can be partitioned" "into 1 hundred, 4 tens, and 3 ones." There they are.

And 134 can be partitioned into 1 hundred, 3 tens, and 4 ones.

And there they are.

He says, "I start by adding the numbers" "with the smallest place value first." So he's gonna start in the ones.

3 ones add 4 ones is equal to 7 ones.

4 tens, add 3 tens equals 7 tens.

1 hundred add 1 hundred equals 2 hundreds.

So you can see that we've now represented those Base 10 blocks with digits, and we can still see that we've got the same sum and we can see that 143 add 134 is equal to 277.

Alex uses column addition to add 223 and 72.

Can you spot something there? He says, "I'm adding a 3-digit number" "and a 2-digit number." "223 can be partitioned into 2 hundreds," "2 tens and 3 ones." "72 can be partitioned into 7 tens and 2 ones." Do think carefully about where he's going to write those digits? That's right, he's got to make sure that the 7 tens lines up with the 2 tens in 223.

So he's put his 72 in the correct place.

He says, "I start by adding the numbers" "with the smallest place value first", so he's starting in the ones.

3 ones add 2 ones equals 5 ones.

2 tens add 7 tens equals 9 tens.

And then, 2 hundreds, well, they're all on their own, there aren't any hundreds, 'cause we were adding a 2-digit number.

So 2 hundreds add no hundreds equals 2 hundreds, 223 add 72 is equal to 295.

Time to check your understanding.

Can you use column addition to add 133 and 235? Alex says, "Start with the smallest place value numbers first." So pause the video, have a go, and we'll get together for some feedback.

How did you get on? So 133 can be partitioned into 1 hundred, 3 tens, and 3 ones.

There they are.

And 235 can be partitioned into 2 hundreds, 3 tens, and 5 ones.

And we've recorded those underneath as our second addend.

We're gonna start with that smallest place value column first, which is the ones.

So 3 ones add 5 ones equals 8 ones.

And then to the tens, 3 tens add 3 tens equals 6 tens.

And then in our hundreds, 1 hundred add 2 hundreds equals 3 hundreds.

So our sum is 368.

133 add 235 equals 368.

I hope you got that one right.

Alex uses column addition to add 343 and 244.

But this time he's not got the place value grid to work in, so he's got to think carefully.

He says, "I need to write the hundreds," "tens, and ones in the right columns." "This time, there isn't a place value grid," "so I need to set it out carefully." So he's written his first addend, at the top, 343.

And his second addend, at the bottom, 244.

Did you notice he started with the ones in both cases? So he made sure he got them lined up correctly.

So that's right, isn't it? His ones are in the right column, his tens are in the right column, and his hundreds are in the right column.

So this is the ones column, this is the tens column, and this is the hundreds column.

He's going to start with that smallest value digit column first, which is the ones.

So Lucas says, "3 ones add 4 ones is equal to 7 ones." And then moving to the tens, 4 tens add 4 tens is equal to 8 tens.

And then in the hundreds, 3 hundreds, add 2 hundreds is equal to 5 hundreds.

So what's our sum? That's right.

343 add 244 is equal to 587.

Time to check your understanding now.

Can you use column addition to add 225 and 223? And Alex says, "Write the hundreds, tens, and ones in the right columns." So pause the video, have a go, and we'll get together to find out if we laid our column addition out correctly.

How did you get on? Did you lay out your columns correctly? Let's have a look at how Alex did his.

So he started with his ones.

So 225 add 223.

He's got his 5 and his 3 in his ones lined up correctly.

And then it was all twos, 2 tens and 2 tens, 2 hundreds and 2 hundreds.

So yes, that's laid out correctly.

And where's he going to start? He's got the ones column, the tens column, and the hundreds column.

And we're going to start adding in the ones column, 'cause it's the smallest value digits.

So 5 ones add 3 ones is equal to 8 ones.

2 tens add 2 tens is equal to 4 tens.

And, 2 hundreds add 2 hundreds is equal to 4 hundreds.

So our sum is 448, 225 add 223 is equal to 448.

Well done if you got that right.

And well done for setting out your column addition neatly.

Time for you to do some practise.

Can you complete each column addition, and then fill in the answer in the equation above it.

And we've laid out the column addition for you in this case.

For the second part, you're going to use the equations to complete the column addition, so you are going to set out the column addition.

And Alex says, "Look carefully at the number of 100s," "10s, and 1s in each number." And then for the second part of two, you've just got the equation and you're going to set out the column addition yourself.

And again, look carefully at the number of 100s, 10s, and 1s in each number.

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

How did you get on? So here are the answers to the first one.

And we gave you the column addition this time.

So it was making sure you were adding your columns.

Did you all start at the ones? So the answer to A was that 231 add 154 is equal to 385, that's our sum.

And for b, 314 add 75 is equal to 389.

And that's our sum.

And as Alex points out, that hundreds column is left empty when we've only got a 2-digit number to add.

So for part two you had to put the numbers in to make the column additions.

So hopefully you worked out that the sum for a was 459, and the sum for b was 588.

And as Alex says "235", he was thinking about that partitioning for the first addend in a, "235 can be partitioned into 2 hundreds, 3 tens, and 5 ones.

And maybe you use that sort of language to help you to make sure that you'd got your numbers and your digits in the right columns.

And for the second part of three you had to create the column additions for yourself.

And did you spot in d that there was a 2-digit number to add there? So the sum for c was 481 and the sum for d was 379.

And Alex spotted as well that 250 has 0 ones, so he needed to write a 0 in the ones column.

It's really important to spot where you've got a different number of digits or where you've got a really important zero that you need to make sure is part of the calculation.

It shows us that we've got 2 hundreds, 5 tens, and 0 ones.

So it's a really important zero.

Well done, I hope you got all of those correct.

Let's move on to part two.

So in the second part of our lesson we're going to be solving 3-digit column addition problems. Let's have a look.

Ah, we've got some missing digits.

Alex is trying to find the missing numbers in this column addition.

He says, "One addend has a missing tens digit," "and the other has a missing ones digit." And Lucas is reminding us that, "To find a missing part, we can subtract" "the known part from the whole." So what's the whole in this case? So the whole is the sum written between the equal signs.

So our sum is 584.

We know that the sum in the ones column is 4 ones.

The sum in the tens column is 8 tens.

And the sum in the hundreds column is 5 hundreds.

And we can use that to help us work out those missing values.

So Alex says, "4 ones subtract one is equal to 3 ones." So he knows that the whole of our ones is 4 ones.

And if he takes away the known 1, he knows that the missing part is 3.

He might have known that 1 add 3 is equal to 4 as well.

But however he thought about it, the missing ones digit in that addend is 3 ones.

We know that our whole is 8 tens.

So Alex says, "8 tens subtract 3 tens is equal to 5 tens." So our missing tens digit in the first addend must be a five.

Alex said, "I actually knew that 5 + 3 = 8, "so I didn't need to do the subtraction." And we can do that if we know the known fact.

We sometimes don't need to do the subtraction, because we know if 8 is a whole and 3 is a part, then 5 must be the other part.

There it is.

So 351 add 233 is equal to 584.

He's going to find the missing digits again here.

So he says, "One addend has a missing ones digit," "the other has a missing tens digit." "And the sum has a missing hundreds digit." So we're missing the parts for two of them, and we're missing the whole for one.

And Lucas says, "To find a missing part," "subtract the known part from the whole." Or you could use a number fact like Alex did on the last question.

So this time he knows in the ones that 7 ones is our whole.

So if we subtract the 2 ones, we'll find the missing part, which is equal to 5 ones, 7 subtract 2 is equal to 5.

Now this one's interesting, isn't it? Because our whole is seven tens, and we've got a known part of 0 tens.

So we've got nothing to subtract, have we? 7 tens subtract zero tens, well, it's 7 tens.

So we know our missing tens must be 7.

Now, for the missing hundreds digit in the sum, this time we are missing the whole.

And to find a missing whole, we add the parts together.

So 4 hundreds plus 3 hundreds is equal to 7 hundreds.

So our missing hundredth digit in our sum is 7.

Oh, so 405 add 372 is equal to 777.

Time for you to have a go.

Can you find the missing digits in this column addition? Alex is reminding us that to find a missing part, we can subtract the other part from the whole.

And Lucas is reminding us that to find a missing whole, we add the parts together.

So pause the video, have a go at working out those missing parts and wholes, and we'll look at them together in a moment.

How did you get on? Where did you start? Alex started with the ones, he knew that the whole was 7 ones, and that one part was 4 ones, so he could subtract the 4 ones.

So 7 ones, subtract 4 ones, is equal to 3 ones.

So the missing ones digit in our addend end was 3.

Lucas has gone for the missing whole, the missing number of tens in our sum.

And he said that 3 tens add 6 tens is equal to 9 tens or 90.

And 90 is represented with a 9 in the tens.

So our missing digit in our sum must be 9 tens.

What about our hundreds? Well, again, this time we know the whole is 5, so we need to subtract the part we know, which is the 2 hundreds.

So 5 hundreds subtract 2 hundreds is equal to 3 hundreds.

So our missing hundreds digit must be three.

So 334 add 263 is equal to 597.

And we could do the addition to check.

Alex has got some digit cards here.

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

He tries to make the sum as close to 300 as possible.

So he is going to use the digit cards to form two 3-digit numbers and he's going to add them together and see how close he can get to 300.

Hmm, you've got any thoughts on where he might start? Alex says, "I'm going to arrange the cards" "into two 3-digit numbers," "and then add them using column addition." So he's gonna start with a 1 in the hundreds, and a 2 in the hundreds.

Well, 100 plus 200 equals 300, so we're doing quite well there.

What's he going to do next do you think? Ah, he's gone for the next smallest value of numbers.

So 300 plus zero.

Ah, so 3 in the tens plus 0 tens is 30.

So we're at 330 now.

And he's got the 4 and the 5 left in the one, so they're not worth as much.

So what is his sum going to be? Let's help him work it out.

4 ones add 5 ones is equal to 9 ones.

3 tens add 0 tens is equal to 3 tens And 1 hundred plus 2 hundreds is equal to 3 hundreds.

So what's he got? He's got 339.

He says, "339 and 300 have a difference of 39", so he is only 39 away.

Over to you now.

Can you use all six digit cards? I wonder if you can get closer to 300.

So 339 was Alex's first sum.

Can you get a sum that is even closer to 300? See if you can arrange the six cards as two 3-digit numbers, add them together and get a sum that is closer to 300 than Alex got with 339.

Pause the video, have a go, and then we'll get together for some feedback.

How did you get on? Alex said, "I'm going to make a sum" "of less than 300 this time." "I'll use a 2 and a 0 in the hundreds column." Oh, that's an interesting start, isn't it? So he's used a 2 and a 0 in his hundreds.

I wonder what he's going to use next.

He wants to get as close as possible to 300.

Hmm, what do you think? He's used the 5 and the 4? 'Cause 5 tens add 4 tens is 9 tens, so he's got 290 now.

What's he got left? He's got the 3 and the 1 left.

So he's used the 3 and the 1 in the ones.

Now you wouldn't usually write a zero here, but it shows that the card has been used, and it's used to represent 0 hundreds.

So he's starting in the ones to do his addition, 3 ones add 1 one is equal to 4 ones.

5 tens add 4 tens is equal to 9 tens.

And he said he used the largest digits to get close to 300.

So he's got that 94.

And then, 2 hundreds add 0 hundreds is equal to 2 hundreds.

294.

He says, "294 and 300 only have a difference of six".

It's possible to get closer by making a sum less than 300.

It's a lot closer than he got when he went over 300, isn't it? I wonder if you got the 294 as well.

I hope you had fun trying.

Time for you to do some practise.

So can you find the missing digits in these 3-digit column additions? Remember, think about whether you're trying to find a part or whether you're trying to find the whole.

So you've got four to have a go at.

And then you've got a bit of a challenge.

You're going to use column addition, you're going to arrange the cards into two, 3-digit numbers and you're going to use all six cards each time.

And so for part a, you've got to make a sum nearest to 600.

For b, you've got to make a sum nearest to 700.

And for c, can you make the sum nearest to 800? I wonder if you'll go higher or lower to get your sum as close as possible.

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

How did you get on? Let's have a look at these first ones with the missing numbers.

Alex says, "For a, I can see" "that the missing tens digit must be a 0." Because 8 add 0 is equal to 8.

And I wonder, did you know that 4 plus 2 is equal to 6, or did you do 6 subtract 4? And take away the known part from the whole? Anyway, 304 add 282 is equal to 586.

And Lucas says "For b, I can see" "that the missing hundreds digit must be a 1." 3 + 1 = 4.

For the missing tens digit in the sum.

We could add the tens digits of the addends, so that was a 9, and we might have known that 2 plus 6 equals 8, or we might have done a subtraction.

Our whole is 8, known party's 2, 8 subtract two is equal to 6, however you worked it out, 362 add 136 is equal to 498.

So here, "For c", Alex says, "the missing tens digit is a 3," the whole is 7, the known part is 4, so 7 subtract 4 equals 3.

We had a missing whole in the ones, 7 add 0 equals 7.

And then, for the hundreds digit, we had a known part of 5 and the whole was 7.

And you might have known that 5 and another 2 is equal to 7, so 537 add 240 is equal to 777.

And Lucas says, "For d, the missing ones digit is 5," "7 - 2 = 5".

So the whole was 7, the known part was 2.

We could subtract the known part from the whole to find the missing part.

You might have used the same strategy to find the missing tens digit of 2, or you might have known that if we had 6, we'd need another 2 to make the sum of 8.

And 3 plus 0 is equal to 3.

So that was a straightforward one to find the missing whole in the hundreds.

322 add 65 is equal to 387.

Now, here are some examples of the sums that you could have made and you may have arranged the cards differently.

Remember, that we can sort of swap around the the the tens and the ones digits with our hundreds digits.

And because of the way that addition works, that won't change the sum.

So to get close to 600, we could do 351 add 240, or you might have had 250 add 341 or 241 add 350.

Lots of different ways to arrange the digits, but we wanted to make a 5 in the hundreds, and 9 in the tens, and a 1 in the ones to get that 591, just nine away from 600.

And Alex says, "It's possible to get closer to 600" "by making a number less than 600," "rather than greater than 600." Lucas says, "I used 3 hundreds and 2 hundreds" "to make 5 hundreds," "and I used the 5 tens and the 4 tens to make 9 tens." That strategy that Alex had used earlier.

So for b, to get close to 700, you could have gone less than or above 700.

You're gonna get slightly closer though if you go above 700 this time.

Alex says, "It's possible to get closer to 700" "by making a number greater than 700 instead" "of a number less than 700." And Lucas says, "681 and 700 have a difference of 19," "whereas 717 and 700 only have a difference of 17." So it was close.

And again, your numbers may look slightly different, but however you arrange them, you'd have used the same numbers in the same columns.

So if you went for 681, you'd have used a 4 and a 2 in the hundreds, a 5 and a 3 in the tens, and a 1 and a 0 in the ones.

And if you went above to 717, you'd have used a 5 and a 2 in the hundreds, a 1 and a 0 in the tens, and a 3 and a 4 in the ones.

But your numbers may have looked slightly different.

What about c? What about the closest to 900? Is that what you got? Or, did your numbers look slightly different? Alex says, "It's possible to get closer to 900" "by making a number greater than 900" "instead of a number less than 900." And Lucas says, "I used 5 hundreds and 4 hundreds to make 9 hundreds." "I used 0 tens and 1 tens to make 1 ten." And then the remain digits to make the ones.

So just 15 away from 900.

I hope you had lots of fun rearranging your digits to try and get those sums as close as you could to 700, 800, and 900.

I'm sure you did lots of really good thinking.

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

Thank you for all your hard work, thinking about, reviewing, adding 3-digit numbers using column addition.

There's no regrouping at the moment.

So what have we learned about today? We've learned that the addends are written in columns with the same value digits in the same column.

The sum is recorded underneath the addends with the same value digits in the same column again.

We can use a zero to show that there are no tens or ones in a 3-digit number.

And when using column addition, we always start by adding the numbers with the smallest place value first.

Again, thank you for all your hard work and all your great mathematical thinking today, and I hope I get to work with you again soon.

Bye-Bye.