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.

And welcome to this lesson.

So in the lesson today, we're going to be thinking about how we can use place value to lay out column addition correctly.

So column addition may be something that you've used before, so it's always good though to have a chance to remind ourselves how to lay it out correctly to make sure that we use it really accurately.

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

You may well be familiar with them, but let's just have a practise 'cause they're going to be useful in our lesson.

I'll say it and then it'll be your turn.

So my turn, addend.

Your turn.

My turn, column addition.

Your turn.

My turn, sum.

Your turn.

Okay, words you've probably used before, but let's just remind ourselves what they mean 'cause they're going to be used a lot in our lesson today.

So an addend is a number added to another one.

So here in 10 + 6 = 16.

Our addends are 10 and six.

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

So it's a way of organising our numbers so that we can keep track of them and we can keep track of how we're getting through our calculation.

And the sum is the total when numbers are added together.

So in our 10 + 6 = 16, our sum would be 16.

There are two parts to our lesson today.

We're going to be setting out 2-digit column addition and then we're going to be setting out 3-digit column addition.

So let's make a start on part one.

And we've got Alex and Lucas helping us out today.

So Alex is using base 10 blocks.

So can you see he's set some base 10 blocks out.

He's got his tens all together and his ones together.

What's he got there? What can you see? He says this representation shows four 10s and six 1s.

And Lucas says we could show this using a place value chart.

So there are tens and ones again, this time we're just going to write a numeral, a digit to represent the numbers.

Four 10s have a value of 40, so that's a four in the tens column.

And six 1s have a value of six, so that's a six in the ones column.

So our four 10s and six 1s, we can write as 46.

Alex says the base 10 blocks can help me to understand how to lay out a column addition.

They can, because Alex can see when he's collecting his tens together and his ones together.

He says I can easily see the tens and ones because they show the value of each digit.

So we remember that in column addition one addend is laid out below the other one keeping those columns lined up so we know what we're adding together.

So let's have a look.

Alex says I'm going to lay out 33 add 23.

So the first addend is 33.

There are three 10s and three 1s.

There they are.

We can see the three 10s and the three 1s.

The second addend Lucas says is 23.

It's laid out under the first addend.

So there are two 10s and three 1s.

And there they are two 10s and three 1s.

33 and 23 have a sum of 56.

So we can see that there are six 1s altogether and five 10s altogether.

So five 10s and six 1s gives us a sum of 56.

Alex is going to write a column addition to go with the base 10 representations.

He says I'm going to use the base 10 block representation to help me.

So there he is setting out his column addition.

So he's keeping his tens and his ones together.

33 is the first addend.

There are three 10s and three 1s.

So there they are.

And now we're going to represent them in the column addition, three 10s and three 1s.

It's really important to know which are the tens and which are the ones, isn't it? Because the digit is the same.

We've got a three for three 10s and a three for three 1s, but the three for three 10s represents 30 if we are using the base 10 blocks.

Lucas says 23 is the second addend.

There are two 10s and three 1s and there we can see them.

So now we're going to transfer them to the column addition, two 10s and three 1s giving us our 23.

And Lucas says 33 and 23 have a sum of 56.

There's our sum of 56 and we can see we've combined the ones.

Three 1s plus three 1s is equal to six 1s and we've combined the tens.

Three 10s plus two 10s is equal to five 10s.

And we've got our sum of 56.

Time to check your understanding.

Alex is laying out a column addition and there it is.

He's used the base 10 blocks and he says, does the base 10 block representation exactly match the column addition? There's the column addition.

Okay, so you're gonna pause the video and check to see whether the base 10 blocks and the column addition match exactly.

So pause the video and we'll come back for some feedback.

What did you think? Oh, Lucas says it's not right Alex, the base 10 blocks represent 43 + 15 = 58.

But what about the column addition? Lucas says the column addition represents the equation 45 + 13 = 58.

Hmm, what do you notice? Oh, Alex says if I changed the ones then this would be correct.

Let's have a look.

That's right.

The sum was the same.

We still had three 1s plus five 1s.

But in the base 10 representation, the three 1s were with the four 10s and in the first column addition, the three 1s were with the one 10.

So we had the same sum, but the ones digits had been swapped around in the column addition.

Now they're correct and they match.

So the base 10 blocks match the column addition.

Well done if you spotted that.

Now Alex is going to use arrow cards to lay out a column addition.

Lucas sets him a challenge.

Can you set out the equation 43 + 24 = 67? He's going to use these arrow cards.

I wonder if you've used them before.

So Alex says 43 is the first addend.

There are four 10s and three 1s.

So there's our arrow card for 40 and then we can put the three on top to show that we've got 43, four 10s and three 1s.

24 is the second addend.

There are two 10s and four 1s.

So two 10s, which is we know is worth 20 and four 1s to give us 24.

Now what was the sum? That's right, the sum is 67.

So this is six 10s and seven 1s.

So 67.

So another way to represent our numbers within our column addition and we can really see how we can partition into tens and ones using the arrow cards.

Alex uses arrow cards to lay out another column addition.

And Lucas challenges him.

Can you set out a column addition using the arrow cards? So he's given him the arrow cards this time.

Can he set them out as a column addition? Hmm.

Alex says 78 is the largest number, so it must be the sum in this example.

So he is going to put the 78 in as the sum.

He says, I'm going to use 45 as the first addend.

So his four 10s and five 1s, I'm going to use 33 as the second addend.

There we go.

Three 10s and three 1s.

Is that correct? Can we have a look? Well if we think about the ones, we've got five 1s plus three 1s is equal to eight 1s.

And in the tens, four 10s plus three 10s is equal to seven 10s.

So yeah, I think that's work that works.

Doesn't it? Time to check your understanding.

Alex has used the cards to set out a column addition in one way, but Lucas says, how else can you use the cards to make this column addition correct? Can you find another way to do it? Pause the video, have a go and we'll come back for some feedback.

How did you get on? Did you find another way? Alex says, 78 is the largest number.

So again, it's got to still be the sum in this example.

So 78 needs to go there, but he says you can use 33 as the first addend because we know that addition is commutative.

It doesn't matter which order we add the addends, the sum will be the same.

So 33 could be the first addend and you can use 45 as the second addend and the sum will remain the same.

Well done if you've got that right.

Time for you to do some practise.

You are going to use base 10 block representations to correctly lay out each column addition.

So can you represent the column additions that have been laid out using base 10 blocks as column additions using digits and you've got two to have a go at there.

And then for part two you're going to use the arrow cards.

Can you find two ways to complete each column addition like Alex was doing just before? And then you've got some things to look at in task three.

So can you use each arrow card once in each column addition, combine the tens and the ones to make three 2-digit numbers and then use them to make a column addition? And Alex says, I've made these 2-digit numbers.

There they are.

Can I use them to make the column addition correct? And then you're gonna have a go as well.

Can you find different ways to complete a column addition using those arrow cards given? So lots to have a think about there, pause the video and we'll come back for some feedback.

How did you get on? So for the first question, you were representing the additions set out with base 10 blocks as column additions.

So Alex says the base 10 blocks represent 25 + 32 = 57.

So if we write that out as a column addition, we've got 25 as our first addend 32 as our second addend, 57 is our sum, and we can see that we've got the columns lined up, so all the ones digits line up and all the tens digits line up.

And for B, 21 and 22 were our addends and 43 was our sum.

And so again, we've set that out as a column addition.

So here we had to use the arrow cards to complete the column additions.

And Alex says, in these examples, the sum is the largest number, but the order of the addends can be changed.

So 68 had to be our sum, but we could have 51 + 17 or we could have 17 + 51.

And for B, again our largest number was our sum for these examples.

So 86 was our sum in both occasions, but then our addends of 62 and 24 could be switched around because we can add the addends in either order and the sum remains the same.

Then Alex asked if he could use the 2-digit numbers that he made to make the column addition correct.

And if you looked at it, I'm afraid he couldn't, sorry, Alex.

Alex can't use these numbers to make the column addition correct as the ones digits of the addends sum to more than 10.

So the sum would not be 83.

The sum in these examples is always the largest number.

So that would be 83.

And if we look we'd have then our addends would be 38 and 55.

And we know that eight 1s plus five 1s is equal to 13 ones, which would give us an extra 10.

So the sum would not be correct.

Sorry Alex, those don't work this time.

But you can use those arrow cards to create correct equations.

We've just got to think carefully about where we position each of them.

So as long as we've got five 1s and three 1s equaling eight 1s and five 10s and three 10s equaling eight 10s, we can have four different column additions that sum to 88.

And Alex says, remember in these examples, you can swap around the tens and ones digits of each addend.

So you can move the tens and you can move the ones digits and the sum will remain the same.

So we can have 33 and 55 in either order and we could have 35 and 53 in either order.

So four different ways we could complete those column additions.

Well done if you got all of those right.

So time for the second part of our lesson and we're going to be setting out 3-digit column additions this time.

So Lucas asks Alex to represent this equation, 233 + 64 = 297.

And Lucas says, use arrow cards to lay this out as a column addition.

And Alex says 233 is the first addend.

There are two 100s, three 10s and three 1s.

So we've got 200, three 10s and three 1s.

So a 3-digit number.

64 is the second addend.

There are zero 100s, six 10s and four 1s.

So there we can see our six 10s and our four 1s.

And Alex has been very careful to make sure that the correct digits are in the correct column.

And the arrow cards have helped him to do that because he can see that he's got his tens and his ones lined up.

There are some hundreds in the first addend, but there are no hundreds in the second addend.

And Alex says, 297 is the sum.

So there are two 100s, nine 10s and seven 1s and there's our 297.

And you can see if you look down the ones, three 1s plus four 1s is equal to seven 1s.

Three 10s plus six 10s is equal to nine 10s.

And our two 100s plus no hundreds is equal to two 100s.

Alex represents this equation, 585 = 262 + 323.

Have you noticed anything there? That's right, yes.

This time the sum appears first in our equation.

So we need to think about that as we are laying it out as a column addition.

Lucas says again, use arrow cards to lay this out as a column addition.

So Alex says 585 is the sum.

This time there are five 100s, eight 10s, and five 1s.

So we're going to fill in our sum first.

262 is the first addend, so that's two 100s, six 10s and two 1s.

And 323 is the second addend.

Three 100s, two 10s, and three 1s.

There it is.

So we've used our arrow cards to lay out the column addition.

This time we had 3-digit numbers each time.

So our column addition is sort of full.

We've got numbers in the hundreds and the tens and the ones for all of our addends.

And for our sum.

Time for you to have a go.

Alex is going to have a go at representing this equation.

Can you help him? So here is our equation.

And Alex says, have I set it out correctly? Pause the video and see if you can work out whether Alex has set this out correctly or not.

What did you think? Well, Alex has set it out.

He's written the addends in a different order, but the equation will still be correct because it doesn't matter which order we add the addends, the sum will be the same.

So he has got 520 and 334, but he's put the 520 as the first addend in the column addition.

So it is correct, just written in a slightly different order.

Alex is going to represent another equation using arrow cards.

Oh this time Lucas is going to give it to him in words, one hundred and forty-seven add one hundred and twenty is equal to two hundred and sixty-seven.

Hmm, let's have a think about that.

Alex says 147 is the first addend.

There's one hundred, four 10s and seven 1s.

So there they are with our arrow cards.

120 is the second addend.

There is one hundred, two 10s and no ones.

So no extra ones in that calculation.

So we've got 120.

And Alex says, 267 is the sum.

There are two 100s, six 10s, and seven 1s.

So there we go.

Well done.

Alex worked out from Lucas telling him the numbers, he was able to think about what they looked like and then represent them with the arrow cards to correctly set out his column addition.

Alex lays out another one.

Oh, Lucas says, use these three numbers.

And he's given them in words.

Three hundred and sixty.

Seven hundred and eighty-nine.

Four hundred and twenty-nine.

Ooh, I wonder if you can think about what those are going to look like.

Alex says, well, 789 must be the sum because it's the largest number.

And in our examples the sum is the largest number.

So there is 789.

And Alex says, I'm going to use 360 as the first addend.

Can you think about what that's going to look like in our column addition? That's right, three 100s, six 10s and no ones or no extra ones.

And he says, I'm going to use 429 as the second addend.

If you notice, Alex has written them down using the digits.

Well, he's put them in his speech as the digits to help him to pick out the right arrow cards to represent the numbers.

And there's 429 our second addend.

So does that work? Well, Yes.

We can see a sum of nine 1s, eight 10s and seven 100s.

So 360 + 429 = 789.

Time for you to do some checking.

Alex is laying out another column addition.

He's using these three numbers and there they are.

And again, Alex asks you, has he set it out correctly? Here's Alex's go.

So pause the video and decide whether Alex has set out his column addition correctly using the numbers that Lucas gave him.

How did you get on? Was Alex correct? Did you spot that he'd got the wrong arrow cards out to represent 330? He's represented it as 303 instead.

He's perhaps muddled up the tens and the ones at this point.

So the column addition is going to be incorrect.

It doesn't give the right answer because he used a three instead of a 30.

Time for you to have a go.

Can you lay out each calculation using column addition and just be careful, do the addends come first or does the sum come first? And you're going to use the three numbers and you're gonna find two different ways to set out a column addition.

And then for part three, you are going to combine the hundreds, the tens and the ones to make three 3-digit numbers and find different ways to lay out a column addition.

So pause the video, have a go at your tasks and we'll get together for some feedback.

How did you get on? Here are some possible answers.

So we had 455 + 222 = 677.

So we could have had the 455 as the first addend, but we could have had it as the second addend as well.

And for B, did you spot this time that the sum came first? So our sum was 673, and again, you could have had the addends in different orders to make the equation still correct and to set out the column addition correctly.

And there we go, Alex, reminding us for B, the sum is given first, but it needs to appear below the addends in the column addition in that equal sign at the bottom.

And again, for part two, here are the possible answers.

So for the first one, we could have had 461 + 525 + 986 or we could have had 525 + 461 = 986.

And Alex reminds us, the addends can be added in a different order and still give the same sum.

And for part three, you had lots of different possibilities of the answers that you could have given here.

So have a look and see if your answers matched the ones that we've got here or whether you had some different ones.

And Alex says, the largest hundreds, tens and ones digits have to be used to make the sum in these examples.

So our five and our three had to be the sum because they gave us the largest value of hundreds.

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

Thank you for all your hard work.

I hope you've enjoyed exploring two and three-digit column additions, setting them out correctly, perhaps using some arrow cards yourself to have a go.

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.

One addend is written above the other one and the sum is recorded underneath the addends with the same value digits in the same column.

And in part two of our lesson, we also learned that we have to be careful because sometimes there'll be a different number of digits in the addends.

And so you have to make sure that you really have lined your columns up correctly and also being very careful with those zeros.

Do you remember Alex and his 330 and 303 mistake? Really important to check where your zeros are going if you've got them in your number.

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

Bye-Bye.