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.

Welcome to this lesson.

We're going to be adding two-digit numbers using column addition.

You may have come across this before, so this will be a good chance to practise and remember things that you've learned in the past perhaps.

So let's have a look at the lesson.

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

I'm sure you know them already, but let's just practise them to make sure.

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

So my turn, addend.

Your turn.

My turn, sum.

Your turn, My turn, column addition.

Your turn.

Well done.

As I say, I am sure you're familiar with those words, but they're going to be really useful in our lesson today.

so let's have a look at what they mean just to remind ourselves.

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 one number below another so we can keep track of our calculation as we go through.

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

Well, we've got two parts to today's lesson.

We are going to be adding two-digit numbers using column addition, and we're going to be, in the second part, solving two-digit column addition problems. So let's make a start on Part 1, and we've got Alex and Lucas helping us in our lesson today.

Alex sets out column addition using base 10 blocks.

He says, "I'm going to find the sum of 42 and 26.

42 and 26 are both parts." They're addends as well, aren't they? 42 is the first addend.

There are four 10s and two 1s, and there they are.

26 is the second addend.

There are two 10s and six 1s, and there they are.

Lucas says, "Start by adding the numbers with the smallest place value first." So that's our 1s.

So Alex says, "Two 1s and six 1s is equal to eight 1s." And then, "Four 10s and two 10s is equal to six 10s." And Lucas says, "68 is the sum of 42 and 26.

68 is the whole." And we can see that there with our base 10 blocks.

Alex represents the same problem using digits, and you can see there he's got his column addition ready to go.

He says, "I'm going to use the base 10 blocks to help me with the column addition.

42 is the first addend.

There are four 10s and two 1s." So that's going to be our first addend in our column addition, and we can represent that with a four in the 10s and a two in the 1s, 42.

26 is the second addend.

There are two 10s and six 1s.

So that's going to be represented underneath our 42 as our second addend in our column addition, two 10s and six 1s, 26.

Lucas says again, "Start by adding the numbers with the smallest place value first." So that's our 1s.

So two 1s add six 1s is equal to eight 1s.

Two 1s and six 1s is equal to eight 1s.

And then four 10s and two 10s is equal to six 10s.

Four 10s and two 10s is equal to six 10s.

So we can see how the base 10 blocks are represented in the column addition and the other way round.

Alex uses column addition to calculate the sum of 35 and 43.

I wonder if you can picture what it's going to look like.

He says, "I'm going to write one addend above the other.

I need to write the 1s and the 10s in the correct column." Lucas says, "If it helps, you could use base 10 blocks to help you to represent this problem," but you might be ready to represent it without them.

Maybe you could picture the base 10 blocks as you go along.

So here we've got a bit of place value chart to help us to organise our numbers in our column addition.

So there's our first addend, 35, and our second addend, 43, is written underneath it.

And we can see that we've lined up the 1s, and we've lined up the 10s.

And Lucas says, "We always start by adding the numbers with the smallest place value first." It may not seem that important at the moment, but it will be when you come to adding slightly larger numbers together perhaps.

So we're gonna start with our 1s.

Five 1s and three 1s is equal to eight 1s.

And then we can move to our 10s.

Three 10s add four 10s equals seven 10s, and we can record our sum in that big equal sign at the bottom of our column addition.

So 35 plus 43 is equal to 78.

And there we go.

We could record it as an an equation in one line as well.

Time to check your understanding now.

Can you calculate the sum of 41 and 24 using a column addition? Remember Alex says, "Write one addend above the other." And then Lucas is reminding you, "Start by adding the numbers with the smallest place value first." So pause the video, have a go, and we'll come back and look at it together.

How did you get on? Did you write 41 as your first addend and then underneath it, 24 as your second addend? And then as Lucas says, starting with the numbers with the smallest place value, so are 1s, One 1 plus four 1s is equal to five 1s.

And then looking at our 10s, four 10s plus two 10s is equal to six 10s.

So our sum of 41 and 24 is 65.

41 plus 24 is equal to 65.

Well done if you got that right.

Alex is using column addition again to calculate 62 plus 12, but this time.

he hasn't got the place value chart to aid him.

So he's got to think really carefully about where he writes his digits.

He says, "I need to think carefully about place value." And he's going to imagine, he says, "This is the 1s column, and this is the 10s column." Now when you are writing out your column additions, you might have squares on your paper to help you, but Alex is doing it on plain paper.

So he's thinking really carefully about where his digits need to go.

So he's starting with, well, I'm not sure.

He's put his two there.

I think he's thinking of 62 as his first addend.

Yes, he is.

So 62, so he's got his two 1s in this 1s column and his six 10s in the 10s column, and he's adding 12.

So he needs to think about carefully writing those in the right places.

So his two 1s and his one 10 lined up carefully with the 1s and the 10s from 62.

And then Alex says, reminding him again, "Start with the smallest value digit." So two 1s and two 1s equals four 1s, and then six 10s and one 10 equals seven 10s.

So 62 plus 12 is equal to 74.

Lucas says, "I think I could have calculated 62 plus 12 mentally.

I didn't need to record this as a column addition." Alex says, "You're right Lucas It is quite an easy calculation." But when we're reminding ourselves of a new way of recording our work, a new way of representing addition, sometimes it's good to start with some numbers that aren't too challenging for us so that we can understand the way we're writing them out and the way we're working and not have to worry too much about the answer.

But something to think about.

You don't always need to use a column addition.

Lucas challenges Alex.

|It's difficult to add three two-digit numbers without using column addition." It's hard to keep track of it all in your head, isn't it? So we've got three two-digit numbers to add this time.

Alex says, "I'm not sure how to find the answer to this." Can you think how you could help Alex, do you think? Lucas says, "It's okay.

There's just an extra part to add.

We've got 34, 30 and 15 and they're all parts that add to make the whole," and you might be able to picture that as a bar model with three parts and one whole or maybe a part-part-whole model that's got three parts instead of two parts feeding into the one whole.

Lucas says, "You just start by adding the numbers with the smallest place value first." So we're gonna start in our 1s.

And Alex says, "Well, four 1s and zero 1s add five 1s is equal to nine 1s." And then for our 10s, three 10s add three 10s add one 10 is equal to seven 10s.

So 34 plus 30 plus 15 is equal to 79.

And there we have it written out as a calculation along one line, and there we have it written out as an equation along one line.

And Lucas says, "Column addition is really useful for adding more than two numbers." It helps us to keep a track of where we're up to with our adding.

So time for you to have a go.

Can you complete this column addition of three two-digit numbers? Alex says, "Start by adding the numbers with the smallest place value first." So pause the video, have a go, and then we'll come back together for the answer.

How did you get on? Did you remember to start with the 1s? So three 1s add five 1s add one 1 is equal to nine 1s, and then in our 10s, four 10s add two 10s add two 10s is equal to eight 10s and which we know is the same as 80.

So 43 add 25 add 21 is equal to 89.

Well done if you got that right.

Time for you to do some practise now.

So for Part 1, can you complete each column addition? And you've got the stem sentences there to remind you to start with the digits with the lowest value and think about what it is you're adding together so that you make sure that you keep those columns correct and your answer is accurate.

And then this time, you've got some additions to solve, and we're asking you to set them out as column additions there.

And for Part 3, we've got three two-digit numbers.

So find the sum of each of these sets of two-digit numbers.

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

How did you get on? Did you complete the column additions and the stem sentences? So for a, three 1s add four 1s equal seven 1s.

Four 10s add five 10s is equal to nine 10s.

So our sum was 97.

And in b, two 1s plus seven 1s is equal to nine 1s.

Three 10s add two 10s is equal to five 10s, so our sum was 59.

32 add 27 is equal to 59.

This time, you had to set the column additions out as well.

Did you work out how to do that? So we had 51 and 15, and you can see there that the columns make sure that we know that 51 is five 10s and one 1 and 15 is one 10 and five 1s.

Our sum is 66, six 10s and six 1s.

43 add 25 is equal to 68.

And then in c, Alex says, "30 needs a zero in the 1s column." Did you remember that? So 30 add 55 is equal to 85.

And again, for some of those, you might have been able to work out the answer in your head, but being able to set them out as a column addition and being really confident with how those numbers are set out will be really useful when you're handling maybe larger numbers or more numbers.

And for Part 3, you were finding the sum of each of these sets of two-digit numbers.

So you had three two-digit numbers to add each time.

So did you remember to use those stem sentences? So Alex is reminding us for a, "Zero 1s add five 1s add three 1s is equal to eight 1s," and Lucas took charge of the 10s, "Two 10s add one 10 add two 10s is equal to five 10s or 50," so our sum was 58.

So if we'd use the same way of thinking through b and c, the answer to b, the sum was 77, and for c, the sum was 68.

I hope you had fun doing those, and I hope you were successful.

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

So we're going to be solving two-digit column addition problems this time.

I wonder what that's going to look like.

Let's have a look.

Oh, we've got some missing digits here.

Alex is trying to find the missing 1s digit.

What do you think it's going to be? How could he work it out? He says, "The 1s digit to the first addend is missing.

How can I work out what it is?" Lucas to the rescue.

Lucas says, "The missing digit and three have a sum of eight." So something add three is equal to eight.

So we know one part ,and we know the whole, and we know, as Lucas is reminding us, that to find a missing part, we subtract the part that we know from the whole.

So we could think about eight subtract three to find out what our missing part is.

And Alex says, "Eight subtract three is equal to five.

The missing 1s digit is five." He says, "I actually knew that five add three is equal to eight, so I didn't really need to subtract." And if we know our number facts, we can use them either way round to help us to find these missing numbers.

We're going to think a lot about the subtraction to find the missing part.

But if you can do it by thinking about your known facts that have that sum, then you could think about it that way as well.

So here, five was our missing number.

Five 1s and three 1s is equal to eight 1s.

And you might have done that by subtracting, or you might've known that if eight is the whole and three is a part, then five is the other part.

So our whole equation looks like 45 plus 23 is equal to 68.

Alex is trying to complete this column addition.

What do you notice this time? Hmm.

There are two missing parts, aren't there? Alex says, "The 10s digit of the first addend and the 1s number of the second addend are missing." So we've got two to find here.

Have we got enough information? And Lucas is reminding us, if we're not sure of our number facts, then to find a missing part, we subtract the part we know from the whole.

So Alex says, "Seven 1s," if we're looking at the 1s column, "Seven 1s subtract two 1s is equal to five 1s.

So the missing digit must be five." Now you might have looked at that and thought, "Two add something equals seven.

Two add five equals seven." That's absolutely fine as well if you know your number facts.

So then for the 10s, four 10s is our sum.

So that's our whole.

we subtract the one 10 we know about, and we are left with three 10s.

So the missing 10s digit must be three because three 10s add one 10 is equal to four 10s.

So in these calculations, the digits in our sum within our equal sign in our column addition, those are our whole, and our parts are the two addends, aren't they? So we can use that information to help us to work out those missing values.

And our equation as a whole, 32 add 15 is equal to 47.

Right, now, Alex completes a column addition where three two-digit numbers are added to make a sum, but again, we've got some missing values.

Alex says, "Two of the addends have missing parts." And Lucas says again, "To find a missing part, subtract the known part from the whole." So in our 1s, our whole is five 1s, and we know that we've got four 1s and one 1.

So we can subtract those known parts from the whole.

So five subtract four subtract another one, well, that's equal to zero.

So our missing 1s digit is actually zero.

What about the 10s? Well, our whole is six.

So six subtract three subtract two 'cause three and two are known numbers of 10s.

So six 10s subtract three 10s subtract two 10s is equal to one 10.

And Alex said, I also can think of this as 60 subtract 30 subtract 20 is equal to 10.

So the missing 10s digit is one representing that one 10.

So our whole equation is 14 add 30 add 21 is equal to 65/ Time to check your understanding now.

Can you find the missing digits in this column addition of three two-digit numbers? Alex says, "Two of the add-ins have missing parts." And Lucas says, "To find a missing part, subtract the known part from the whole." So use your knowledge of number facts and your understanding of column addition to find those missing digits.

Pause the video.

and we'll come back to talk about the answers.

How did you get on? Alex says, "For our 1s, our eight was our whole number of 1s and we knew about two 1s and another two 1s.

So eight subtract two subtract two is equal to four." So we had four altogether, and our missing number must be four as well.

So two 1s plus two 1s plus another four 1s is equal to eight 1s.

What about the 10s? Well, this time, our whole was four 10s and we knew about one 10 and another 10.

So four subtract one subtract one is equal to two.

The missing 10s digit is two.

And we can check that, one 10 plus two 10s plus another one 10 is equal to four 10s.

So our full equation was 12 add 22 add 14 is equal to 48.

Well done if you've got that right.

Now Alex says he's going to use three of these two-digit numbers to complete this column addition.

He says, "I'm going to find the three addends that add together to equal the sum," and the sum is 58.

So I wonder which three of these two-digit numbers he's going to use.

Lucas says, "I've noticed that the 1s digit of the sum is eight." So in 58, we've got eight 1s.

Alex says, "That's really helpful.

I know that three add three add two is equal to eight." And can you see, he's got quite a lot of threes and twos in the 1s digits of his numbers that he's got to choose from? So what's he going to choose? He says, "I'm going to use 13 and 22 and 33." So he knows that he's got that three plus two plus three to equal eight.

So let's put those in, 13 plus 22 plus 33.

Now does that equal 58? Let's check.

Three 1s add two 1s add three 1s is equal to eight 1s.

So it works in the 1s.

What about the 10s? One 10 add two 10s add three 10s is equal to six 10s.

But Lucas says, "Your sum only has five 10s, so your sum is too large." So it doesn't work in the 10s.

Hmm, I wonder if there's a way he could change that.

What do you think he could do? So can you change Alex's choice of numbers to make the equation correct, to make that column addition of three two-digit numbers have a sum of 58? So which three of these numbers have a sum of 58? And remember that Alex added 13, 22 and 33, and got a sum of 68.

I wonder if you can use that information to help you.

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

How did you get on? Did you use Alex's three numbers to help you to adjust it to find the correct three numbers, I wonder? Alex says, "My answer was 10 more than 58.

The numbers 13, 22 and 23 have a sum 10 less than mine." Let's just check.

He had 13, 22 and 33.

So he swapped the 33 for 23 to give him a sum that is 10 smaller than the sum he had before.

So let's double check.

13, 22.

and 23.

So let's have a look at the 1s.

Three 1s add two 1s add three 1s is equal to eight 1s.

We knew that was right.

Those 1s digits haven't changed, so that's correct.

And now let's look at the 10s.

One 10 add two 10s add two 10s is equal to five 10s.

So we've got it correct this time.

Well done if you managed to spot that and well done if you've used Alex's answer to help you to adjust the numbers you added to make sure that the sum was correct.

Time for you to do some practise.

You're going to have a go at finding the missing numbers in these column additions.

So can you use your knowledge of parts and wholes and the idea of if we know the whole, we can take away the known parts to find the missing parts? Can you fill in the missing numbers? The missing numbers here in when we're adding three two-digit numbers.

But you'll notice a, there's something slightly different about a, isn't there? And then Part 3, use any three of the two-digit numbers, add them together to make each of the sums below.

So in a, you've got to find a sum of 78.

In b, you've got to find a sum of 87.

And in c, you've got to find a sum of 97.

So use the two-digit numbers to make the sums below.

And Alex is reminding you, "Look carefully at the 1s and 10s digits." So pause the video, have a go at your tasks, and we'll come back for some feedback.

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

So Alex is saying, "For a, the 1s digits add up to nine." So something plus four is equal to nine, or we can think of nine subtract four, which will give us that answer of five because five 1s plus four 1s is equal to nine 1s.

So for b, we've got two 1s plus six 1s is equal to eight 1s.

And Lucas is reminding us of that thinking/ For the 10s digits, they added up to seven, and he knew that five plus two was equal to seven, so the missing digit was two.

So he used his number facts and thought about the addition rather than doing a subtraction.

You can do it either way, whichever works best for you.

So whichever way you thought about c, our missing 10s digit in the first addend was 3, 36.

And in the second addend, the missing 1s digit was zero because six plus zero is equal to six.

So we had 36 add 40 for c.

In Part 2 we had three two-digit numbers to think about.

And for a, we worked out that the 1s digits added up to eight.

So Alex used a subtraction, eight subtract two subtract one is equal to five 'cause we knew about the two 1s and the one 1, and we can check that, two 1s plus five 1s plus one 1 is equal to eight 1s.

And the other missing digit was actually in the sum, wasn't it? So one 10 plus one 10 plus three 10s is equal to five 10.

So our sum is 58.

So in b, our missing 1s digit was a one, six plus one is equal to seven and one more is equal to eight.

And Lucas talks about the 10s digits.

He said, "The 10s digits adds up to six.

He says, "I know that three plus two plus one equals six, so the missing digit is a one." So they were both 1s in this case, a missing one 10 in the first addend and a missing one 1 in the second addend.

And in c, however you thought about it, our missing 10s digit in the first addend was two, so for 21, and our missing 1s digit in the second addend was a three, giving us 23.

And in 3, you had to choose from the two-digit numbers to make the sums givens.

So here are the answers to these, the three two-digit numbers that made the sum correct in each case.

So have a look and check.

I wonder how you thought about those.

Where did you start with your thinking? And Alex says, "For a, the 1s digits add up to eight.

So two plus three plus three equals eight." So he said, "You have to use the 22 in this," because you need to have that two to add to the threes to give you a sum of eight in the 1s.

And Lucas says, "For b and c, the 1s digits add up to seven." So you had to use three plus three plus one in the 1s to equal seven.

So you had to use the 41 in this case.

Interesting about the reasoning they used to work out that you had to use the 22 to get a sum of eight in the 1s, and you had to use the 41 to get a sum of seven in the 1s.

I wonder if you had that thinking as well.

But well done.

You've worked hard.

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

So we've been reviewing adding two-digit numbers using column addition without regrouping.

And if you're not sure what that means, don't worry, we'll come to that in another lesson.

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, and that it's really important to make sure that line up so that we add the correct parts of the numbers together.

In column addition, we start by adding the numbers with the smallest place value first.

And as we move on through our learning about column addition, you'll see where that's really important.

We record the sum below the addends in that sort of giant equals sign at the bottom.

And we've reminded ourselves that to find a missing part, we subtract the known part from the whole, and that helps us to solve those problems with the missing digits in our additions.

Thank you very much for all your hard work today, and I hope I get to work with you again soon.

Buh-bye.