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.

And in this lesson, we're going to be adding two digit numbers using column addition.

And this is part of the unit column addition.

So let's get on and see what we're going to be learning about today.

We've got three key words to look out for in this lesson, and you may well have come across them before.

They are addend, sum and column addition.

So let's have a go at saying them.

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

So my turn, addend, your turn.

My turn sum, your turn.

My turn, column addition, your turn.

Well done.

Let's just check what those mean.

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 one.

So let's get into today's lesson.

There are two parts to today's lesson.

The first one is adding using column addition.

And then we're going to move on and think about missing numbers in some column additions and how we might be able to work out what those are.

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

So Jun uses base 10 blocks to help him to understand column addition.

He says I'm going to add together 35 and 32.

So he's used his base 10 blocks and he's laid them out as he has learned about column addition with the first addend on top and the second addend underneath it.

So we can see the 35 and the 32.

Laura says we could show this column addition with numerals.

So she set it out using place value to help her to get the numbers in the right places.

And we can see that the first addend is 35 and then underneath it we've recorded the second addend of 32.

We want to work out the answer to this and Laura says, we always start column addition by adding the numbers with the smallest place value first.

So the smallest place value we can see there is the ones.

So we're going to start with the ones.

So we can see that we've got five ones and two ones in our base 10 blocks.

So five ones add two ones equals seven ones.

So we could see that if we put those together, we'd get seven ones.

And we can record that five ones plus two ones is equal to seven ones.

And record that seven in the ones column of our column addition.

Then we can move on to the tens.

So after adding the ones, we add the tens.

And we can see here that we've got three tens, add three tens or 30 add 30.

So three tens add three tens is equal to six tens.

And we can see those six tens together with our base 10 blocks.

So we're going to record three tens plus three tens is equal to six tens.

And so we've completed our column addition and we know that 35 plus 32 is equal to 67, and we can record that as an equation as well if we want to.

So Jun's gonna have another go.

So this time he says I'm going to add together 24 and 44.

And you can see that he's recorded his 24 as his first addend using his base 10 blocks and underneath it his second addend of 44 using base 10 blocks.

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

And she's recorded that for us.

So we can see that that first addend is 24, two tens and four ones.

We can see matching our base 10 blocks and our second addend of 44, four tens and four ones.

But we want to work out the answer.

And Laura's reminding us, we always start by adding the numbers with the smallest place value first.

So we're gonna start with those ones.

So we've got four ones and another four ones.

Four ones add four ones is equal to eight ones.

We could record that with our base 10, but we can also record four ones plus four ones with an eight in our ones column.

And now we can add the tens.

And we can see that we've got two tens and four tens, which is equal to six tens, two tens add four tens equals six tens.

And we can see those six tens with our base 10 blocks.

But if we look at our column addition, we can see that two tens plus four tens is equal to six tens and we can record that six in our tens column of our column addition.

And we can also record the whole thing as an equation, 24 plus 44 is equal to 68.

And you might have known that already.

You might have worked it out, but it's interesting to see how it looks when we work it out using the column addition 'cause we might get to a point where the numbers we can't work out in our head and the column addition will be very useful.

Time to check your understanding.

Can you use the base 10 blocks and the column addition to help you to find the sum.

Think about what we'd be doing, where have we started? Which column have we looked at first? Can you work out the sum using the column addition using the base 10 blocks and using the numerals.

So Jun says, what is the sum of 53 and 25? And Laura says, start by adding the numbers with the smallest place value first.

So pause the video, work out the sum, and then we'll talk it through together.

How did you get on? Did you spot that we had three ones plus five ones equaling eight ones, which we can record as with our base 10 blocks and we can also record in our column addition.

And then we can move to the tens and we can see that we've got five tens and another two tens.

Five tens add two tens is equal to seven tens.

And we can record that with our base 10 blocks, but we can also see that in our column addition we've got five tens and two tens with equaling seven tens.

So we can see that 53 plus 25 is equal to 78 and we can record that with an equation as well.

So Jun's going to use column addition this time to calculate the sum of 43 and 22, which I think he's gonna use his base 10 blocks this time.

Let's see how he gets on.

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

So he's using his place value to help him.

So he's going to record his 43, four tens and three one, and underneath his other addend of 22, two tens and two ones.

And Laura is reminding him, we always start adding the numbers with the smallest place value first.

So where are we going to start? That's right, we're gonna start with the ones.

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

And we're going to record our five in our ones column.

Remember the equal sign there where we record the sum inside the equal sign.

Now we can move to our tens and we can see that we've got four tens and two tens.

And four tens add two tens is equal to six tens.

And we can record our six in our tens column of our column addition.

And we can then record the equation as a whole, 43 plus 22 is equal to 65.

And we used our column addition to help us to partition really to add the ones first and then the tens, and then we can see the number recombining as well.

Jun's going to use column addition again to calculate the sum of 65 and 30.

And he says again, I'm going to write one addend above the other.

So he's using his place value to help him.

So he's written his first addend of 65, six tens and what, five ones, and his second addend of 30, three tens and zero ones.

What's Laura going to remind us about? That's right, we always start with the numbers with the smallest place value first.

So we're going to start in the ones.

Oh well this time that's quite straightforward isn't it? We've got five ones plus zero ones, five add zero is equal to five.

So five ones add zero ones is equal to five ones.

So we're going to record a five in our ones column and then we're going to look at our tens and we've got six tens, add three tens, which is equal to nine tens.

So we can record our nine in our tens column and we can see that 65 plus 30 is equal to 95, and we can record that as an equation to show the answer to Jun's addition.

Time for you to have a go.

Can you calculate the sum of 13 and 25 and can you set it out as a column addition? Jun's reminding you to write one addend above the other.

And here's a place value chart to help you.

So use it to record your column addition to calculate the sum of 13 and 25.

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

How did you get on? Did you remember, as Jun said, to write one addend above the other? So our first addend was 13, our second addend was 25, and we write that one underneath the 13.

And then remembering that Laura always reminds us that we need to start with the numbers of the smallest place value first.

We can add our three ones and our five ones, which equals eight ones, and then our one 10 and our two tens, which equals three tens, and record that.

So we can see that 13 plus 25 is equal to 38 and we can record that with an equation as well.

Well done.

Time for a bit to practise here.

Can you complete each column addition and can you use those stem sentences, bit like the ones we've been using, hmm ones add hmm ones.

So we've given you the first one here, 23 add 14, three ones add four ones is equal to seven ones.

So can you use those stem sentences as you are working with your column additions to make sure that we are always starting with the digits with the smallest place value first and then moving on to our tens in this case.

So complete the calculations and complete the stem sentences.

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

So this time you are going to arrange the numbers in the column addition, use that to complete the calculation and then record the sum.

And you've got six of those to have a go at.

So pause the video now, have a go at your practise tasks and then we'll look at the answers together.

How did you get on? Did you use the stem sentences? We've just completed the stem sentences here.

I expect you might have completed the additions as well.

So for A, three ones plus four ones is equal to seven ones, and two tens plus one 10 is equal to three tens.

So that gives us 37 as the sum of our two add-ins.

In B, one one plus eight ones is equal to nine ones, and six tens plus one 10 is equal to seven tens.

So we had a sum of 79.

So this time we were using the equations to complete the column additions.

So did you manage to record your tens and ones in the correct column? Did you always remember to start with the digits with the smallest place value, so starting in the ones.

That will become more important the more column addition we do, but it's important to get into a good habit with that and we'll understand why that's really important a little bit later on.

So hopefully you managed to transfer those equations into the column additions and work out that the answers were A was 65, B was 48, and C had a sum of 58.

And then for the final three we had D had a sum of 59, E had a sum of 93 and F had a sum of 76.

Well done.

Let's move on and see what else we can do with column addition.

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

So Jun's gonna set out a column addition and he's really gonna think about where the tens and ones should go.

Do you notice this time he hasn't got a sort of place value chart around it this time.

He's just got the addition sign and that big equals sign that where his sum is going to go.

So let's have a think.

He says I'm going to add together 31 and 45.

He's going to imagine where that ones column is.

And he's got one one from his 31 and five ones from his 45.

So he is sort of mixed and matched how he's recorded them.

This time he's recorded the ones digits first and then he is going to imagine this is the tens column.

So remember he's adding 31 and 45.

So 31 that's going to need a three in the tens column and 45 will need a four in the tens column.

So he's recorded his addends of 31 and 45 correctly, but this time he's really thought about where the digits go without using the place value charts ahead to help him.

So now he can go ahead and add.

And Laura's gonna help him.

One one add five ones is equal to six ones, and three tens add four tens is equal to seven tens.

So 31 add plus 45 is equal to 76 and they've recorded it as an equation as well.

This time Jun has spotted a missing number.

He's trying to find the missing ones number.

He says the ones number of the first addend is missing.

I need to work out what it is.

I wonder if you can think how you'd work out what it is.

Laura says the missing number and four have a sum of seven.

Oh, let's just think about that.

Remember we're going to combine our addends to equal our sum.

We can see our sum is 37.

It's written there within that big equal sign.

And we know that we've done, hmm ones plus four ones is equal to seven ones.

So something plus four is equal to seven.

Hmm plus four is equal to seven.

Laura says, well that's a missing part.

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

So if you can picture that as a bar model that we've got a missing part plus four is equal to seven.

If we subtract four from seven, we'll find the missing part.

So let's rearrange that so we can work out the missing part.

So seven subtract four is equal to hmm, our missing part.

And we know that seven subtract four is equal to three.

So our missing number must be three.

And we can do a quick check.

Three ones plus four ones is equal to seven ones, that's right.

And then two tens plus one 10 is equal to three tens.

So we've correctly worked out the missing number in our column addition.

And 23 plus 14 is equal to 37.

This time Jun's got a missing tens number to find.

He says the second addend, he says the tens number of the second addend is missing and I need to work out what it is.

So let's have a think.

Laura says the missing number and 20 have a sum of 50.

So we can think about it as a number of tens.

We could think about it as two tens add hmm tens equals five tens.

Or we could think about it as 20 add hmm is equal to 50.

So 20 plus something is equal to 50.

Again, let's picture that bar model.

We are missing a part, aren't we? And if we know one part is missing, we know that to find the missing part, we subtract the other part from the whole,, so we can rearrange that calculation to help us.

So 50 subtract 20 is equal to hmm, which is our missing part.

And 50 subtract 20 or five tens subtract two tens is equal to three tens or 30.

So we know that that missing number must be three.

So let's just double check to make sure we've got it right.

Four ones plus two ones is equal to six ones, two tens plus three tens is equal to five tens.

So 24 plus 32 must be equal to 56.

So the missing number is three in the tens or 30.

Oh Jun's trying to complete this column addition.

He's got two missing numbers this time.

Gosh, this is gonna take a bit of thinking about, isn't it? So Jun says both addends have a missing part, either a ones number or a tens number.

Laura is reminding us to find a missing part, we subtract the other part from the whole, but we've got to do that twice this time.

So we know that six plus something is equal to seven.

So in order to work out the missing part, we subtract the part we know from the whole.

So seven, subtract six equals one.

So our missing ones number in the second addend must be a one.

And let's just check that, six plus six ones plus one one equals seven ones.

That's correct.

Let's have a look at the tens then.

We know that hmm tens plus two tens is equal to eight tens.

So something plus two must be equal to eight or something plus 20 is equal to 80.

And thinking about what Laura says, to find a missing part, we subtract the part we know from the whole.

So 80 subtract 20 or eight 10 subtract two tens equals 60 or six tens.

So our missing number must be six.

So should we double check, six ones plus one one equals seven ones, six tens plus two tens is equal to eight tens.

So 66 plus 21 must be equal to 87.

And we've successfully worked out our missing numbers.

Okay, time for you to have a go.

So you've got a missing 10 in the first addend and a missing one in the second addend.

Can you work out what the missing numbers are to complete this calculation? So Jun says both addends have a part missing, either a one's number or a tens number.

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

So pause the video and see if you can work out what those missing numbers are to complete the column addition.

How did you get on? So the first one was interesting.

We had three subtract hmm equals three.

So our whole and our part are both three.

So we know that three subtract three is zero.

So our missing number there must be zero, three ones plus zero ones is equal to three ones.

What about the tens? Hmm plus three is equal to five.

So we know that if missing, we subtract the part we know from the whole.

So five subtract three or five tens subtract three tens, 50 subtract 30 is equal to 20.

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

Now double check that, two tens plus three tens is equal to five tens.

So our calculation is 23 plus 30 is equal to 53.

Oh, this is interesting.

Jun wants to add three two digit numbers using column addition.

Do you think he can do that? He says, I'm not sure how to find the answer.

There are three, two digit numbers.

Laura says it's okay.

Start by adding the numbers with the smallest place value first.

So those are all ones.

So we're going to say one one plus two ones plus six ones is equal to nine, nine ones.

And then moving to our tens, four tens plus two tens plus one 10.

So four plus two plus one is equal to, same as 40 plus 20 plus 10.

So we can think of it as a number of tens or we can think of the tens themselves.

40 plus 20 plus 10 is equal to 70 or seven tens.

So our answer is 79.

41 plus 22 plus 16 is equal to 79.

So can you have a go to complete this column addition with three two digit numbers? Jen's reminding us, start by adding the numbers with the smallest place value first.

So pause the video, have a go and we'll talk about it together.

How did you get on? Did you start with the ones? So did you start by thinking about four ones plus two ones plus one one.

Four plus two plus one is equal to seven.

So there are seven ones.

And then moving to our tens, one 10 plus two tens plus two tens or 10 plus 20 plus 20.

This time we've written it the other way around, 20 plus 20 plus 10 is equal to 50, which is five tens.

So our answer is 57.

14 plus 22 plus 21 is equal to 57.

Oh, we've got some missing numbers with our three two digit addends.

So Jun's gonna try and find the missing numbers in this column addition.

He says two of the addends have parts missing.

So we've got a missing tens number in the first addend and a missing one's number in the second addend.

So Laura says let's start with the numbers on the right first with our ones.

So we can see that we've got three plus hmm plus one is equal to eight.

We can rearrange things and we can subtract the parts we know from the whole.

So to find out what our missing part is, we can think about subtracting the parts we know from the whole.

So we can rearrange this to say eight subtract three subtract another one is equal to, it's equal to four.

Eight subtract three is five.

Five subtract one is four.

So our missing ones digit must be four.

Let's check it the other way round.

Three ones plus fou ones plus one one is equal to eight ones.

Three ones plus four ones is equal to seven ones add another one is eight.

Or we could have said three plus one equals four.

And four plus four is equal to eight.

So we can change the order of the add-ins and the sum remains the same.

Let's have a look at the tens.

This time we've got hmm plus two tens plus three tens is equal to seven tens, or something plus 20 plus 30 is equal to 70.

So something plus 20 plus 30 is equal to 70.

Again, Laura's statement is true.

We can subtract the parts we know from the whole, so we can say 70 subtract 30, subtract 20 is equal to 20.

70 subtract 30 is equal to 40, subtract another 20 is equal to 20.

20 is two tens.

So our missing number must be two for two tens.

Two tens plus two tens plus three tens is equal to seven tens.

So we know that 23 plus 24 plus 31 is equal to 78.

Time for you to have a go.

Just one missing number this time.

Can you find the missing number to complete this column addition with three two digit addends.

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

So pause the video and have a go at completing this column addition.

How did you get on? Did you think about two plus one plus hmm is equal to eight? And did you rearrange it? So we know that the whole is eight and we can subtract the parts we know.

So eight subtract two subtract one must equal five.

Eight subtract two is six.

Six subtract one is five.

So our missing part must be five, two ones plus one one plus five ones is equal to eight ones.

So we can say that 32 plus 41 plus 25 is equal to 98.

Time for you to have some practise now.

You're going to find some missing numbers in some column additions.

So you've got three here to have a look at.

You've got a missing one in the first question.

You've got a missing 10 in B, and in C you've got a missing 10 and a missing one.

So think about what Laura was saying about subtracting the parts we know from the whole.

For question two, you're going to find the sum of each set of two digit numbers.

No missing numbers here, just a missing answer.

So you're gonna have a go at finding the sum of each set of two digit numbers.

Then you've got some missing numbers to find again, this time when we've got three addends.

So can you find the missing numbers in this? And if you look carefully at A, we've actually got a missing part of the sum there.

So we've got a bit of a mixture.

And finally a challenge for you.

You can use any four of the digit cards each time and you're going to use column addition and you're going to arrange the cards.

So you're gonna pick four of the cards, arrange them into two two digit numbers.

And there's some challenges for you.

Can you make the smallest sum possible choosing four cards? Can you make the largest sum possible using four cards? And can you make the sum that gets you nearest to 50 using four of the cards? Lots to think about there.

So pause the video, have a go at your tasks and then we'll talk about them together.

How did you get on? Did you find the missing numbers? Did you spot that that first missing number was three? You might have thought, hmm plus six is equal to nine.

What do I know that I have to add to six to equal nine? Or you might have said nine subtract six is equal to three to find your missing number.

In B, we had a missing 10.

So six tens plus hmm tens is equal to seven tens.

And again, you might have known that six plus one is equal to seven.

You might not have needed to do the subtraction there.

And then in C, our missing numbers were five tens in our first addend and eight ones in our second addend.

51 plus 38 is equal to 89.

Then you had to find the sum of each set of two digit numbers.

You had three, two digit numbers each time.

So A, the sum was 87, B, the sum was 66 and C, the sum was 79.

Then you had some more missing numbers to find.

And again, you might have used subtraction or you might have used your own number facts with addition to be able to work it out.

So for A, the missing ones number was three because six ones plus three ones is equal to nine ones.

And for the second missing number in A, we didn't need to do any subtraction, did we? We just had to work out what the sum was for our tens digits.

So one 10 plus two tens plus four tens is equal to seven tens.

And for B, your missing tens number in the first addend was three.

So making 31.

And the missing ones number in the second addend was a six for 36.

And in C, again, we had a missing tens number in the first addend.

And that was a five, five tens, so 52.

And our second addend had a missing ones number and that addend was 24.

And the missing ones digit was a four.

I wonder how you got on with the picking the cards activity.

Here are some sums you should have made.

You may have arranged the cards differently.

That would be interesting.

Did you arrange them differently but still get the same sum? So the smallest sum that was possible was 37, and you might have had 13 plus 24.

But I wonder if any of you had 14 plus 23.

Hmm.

That's something to think about.

Why did they both work? What do we know about addition that means that that will work.

For the largest sum possible, we've got 43 plus 52.

But again, you might, I wonder if you had 42 plus 53.

And again, have a think about how that might have worked.

And then for the sum closest to 50, we've got 14 plus 35, but I wonder if you had 15 plus 34.

But it gives you a sum of 49, which is pretty close to 50, isn't it? Well done.

And I hope you had fun discussing your different possibilities.

And we've come to the end of our lesson, adding two digit numbers using column addition.

What have we learned about? Well, we've learned about writing one addend above the other or one below the other and making sure that our place value columns are lined up.

So we are always adding our ones together in one column.

our tens together in another column.

And in column addition we start by adding numbers with the smallest place value first.

So we've been starting with the ones digits.

And we've also been thinking about solving problems finding missing numbers.

So to find a missing part, we subtract the other part or the other parts we know from the whole and then we can find our missing part.

Thank you so much for all your hard work today.

I've really enjoyed exploring column addition with you.

And I hope to see you again soon.

Bye-Bye.