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 welcome to our lesson, this is from our unit on reviewing column addition and subtraction.

And in this lesson, we're going to be looking at the addends and the sum in a column addition.

So by the end of the lesson, you should be able to identify the addends and the sum in column addition.

Now, column addition may be something you've seen before.

So this is all about reviewing, reminding ourselves about it, and making sure that we are really confident.

So let's make a start.

We've got four keywords today.

We've got addend, sum, equation, and column addition.

So I'll take my turn to say them and then you can have a go.

So my turn, addend, your turn.

My turn, sum, your turn.

My turn, equation, your turn.

My turn, column addition, your turn.

Well done, I'm sure they're words you're familiar with, but let's just remind ourselves what they mean, 'cause they're going to be really useful to us in this lesson and in some of the others to follow.

So an addend is a number added to another one.

The sum is the total when numbers are added together.

An equation shows that one number or calculation is equal to another.

And you can see here, we've got addends and a sum in an equation.

So 15 add seven, those are our addends, 15 and seven.

And they are equal to 22, and 22 is the sum.

And the whole thing is an equation that shows us that 15 plus seven is equal to 22.

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

So keeping those columns of place value lined up so that we can easily see the numbers that we're adding together, and we can keep a track of what we've added together and what our sum is.

So let's get into this lesson.

There are two parts to our lesson today.

We're going to be identifying addends and sum in column addition, and we're going to be linking column addition to known representations.

So let's make a start by identifying addends and sum in column addition.

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

So Alex represents 54 plus 25 in different ways, let's have a look at what he does.

Alex says 54 and 25 are both addends, they add together to make a sum.

54 and 25 are both parts, they add together to make a whole.

Oh, you may have come across part, part, and whole as well in different ways.

Let's have a look at how Alex represents 54 plus 25.

Ah, Alex uses base 10 blocks.

Can you see the 54 and the 25 in his base 10 blocks? He also uses a bar model.

Can you see that 54 and 25 are the parts? And we've got a whole there, I wonder what the whole would represent.

And he uses a part-part-whole model.

So there are two parts, 54 and 25.

Alex says, all these help me represent the problem, but I cannot easily work out the sum.

Yes, we've not got the sum there yet, have we? And those show us what the parts are, but they don't really help us to work out the sum.

So let's have a think about how we can help ourselves to work out the sum of 54 and 25.

Oh, Lucas says, have you tried using column addition? I wonder if he has.

Alex is keen to know more.

So am I, should we have a look? He says, I remember learning about column addition in year three, but I've forgotten how to set it out.

Oh, I Alex, I hope we can help you.

Lucas says, column addition is a way of writing addition equations.

So this is how we would set out 54 plus 25, one addend is written below the other.

So there's 54 and there's 25, and we can see that our ones are together, four ones and five ones.

And our tens are together, the five tens and the two tens.

Then underneath it, we write an equal sign to show that it's an equation.

It's that big equal sign underneath our two addends.

And then the sum appears within the equal sign.

So the sum of our ones and the sum of our tens gives us a sum of 79.

Four ones plus five ones is equal to nine, and five tens plus two tens is equal to seven tens, so 79 is our sum.

Alex is unsure where the sum and the addends appear, so he still needs a bit more practise.

Let's have another look.

He says, I'd like to see that again.

Now, Lucas says, let's set out 45 plus 32 as a column addition.

So 45, one addend appears here, so we write our first addend down.

And then we're going to add 32, which is our second addend.

So we write the other addend below the first one, making sure that our ones and our tens line up correctly so that we are adding in the right columns.

Can you remember what that was? That's right, that's our equal sign to show that we've got an equation.

And then the sum appears within the equal sign.

And this time, five ones plus two ones is equal to seven ones, and four tens plus three tens is equal to seven tens.

So our sum is 77.

There it is.

Lucas uses column addition to represent an addition of base 10 blocks.

So he is got his base 10 blocks there, and he's going to write this out as a column addition.

So what can you see in those base 10 blocks? And Alex is asking another question, where are the addends and the sum? So Lucas says, well, 53 is an addend, it's one of the parts.

So you can see that that first set of base 10 blocks is five tens and three ones, which is 53.

So Lucas is going to record it, the first of our addends.

Did you spot that the second addend is 34, three tens and four ones? So 34 is the other addend, Lucas says, it's one of the parts.

And he's going to record it underneath the first addend.

So we've got 53 plus 34.

One addend is written below the other.

Then the equal sign to show it's an equation.

And where's our sum going to go? So the sum is 87, and the sum is the whole.

And it's going to go inside the equal sign to show that it's an equation.

So three ones plus four ones is equal to seven ones, and five tens plus three tens is equal to eight tens.

So our sum appears within the equal sign, and it is 87.

Alex represents this column addition using base 10 blocks, Alex's turn to have a go.

So here, we've got the column addition, and Alex is going to use base 10 blocks to represent the addends.

So we've got 55 plus 13 is equal to 68, five ones plus three ones is equal to eight ones.

Five tens plus one ten is equal to six tens, and the 68 is written inside the equals sign.

Well done, Alex, yes, 55 is one of the addends, it is a part.

So he's represented that with five tens and five ones.

And he says 13 is the other addend, and it's also a part.

So how would we represent the 13? That's right, with one ten and three ones.

The two addends add together to equal the sum.

So there we've got our addition sign, and we can see that 55 plus 13 is equal to that sum of 68, and there's our 68.

If we combine all our tens and ones with our base 10 blocks, we've got six tens and eight ones, 68.

Lucas sets Alex a challenge, which base 10 block representation matches the column addition? So we've got some base 10 block representations there, and we've got a column addition.

So your turn to have a go, you're going to pause the video and decide, which of the base 10 representations matches the column addition? Pause the video and we'll come back for some feedback.

How did you get on? Which of the base 10 blocks represented our column addition, which shows 43 plus 34 is equal to 77? Alex says, A represents 44 plus 33.

Hmm, that's interesting isn't it? There are 77 blocks there, but it's not quite the equation that's been represented in our column addition.

So it's not quite right, gives the same sum, but it's not quite the right representation.

Alex says, B represents 43 plus 34, four tens and three ones, and then three tens and four ones.

So that one is correct.

What about C? Ah, too many ones there.

We had 34 and 44, so that wasn't the right representation.

A was very close though, but we just had those ones swapped around in the addends.

B was the correct answer.

Time for you to do some practise now.

You're going to represent the addends in these column additions using base 10 blocks.

So you can see the space underneath for you, either to draw your own base 10 blocks, or there are some base 10 blocks you could cut out and use as an additional resource.

So we've got the column additions written out here and space for you to draw those base 10 blocks, two here and two more here.

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

So let's have a look, how did you get on? So the first column addition was 52 plus 43 is equal to 95.

And our first addend was 52, five tens and two ones.

And our second addend was 43, four tens and three ones.

And when we combine those, we get nine tens and five ones, 95.

Part B, we had 41 plus 32.

So four tens and one one added to three tens and two ones, and that gave us seven tens and three ones, 73.

And Alex says, 41 is one of the addends, so I found four tens and one one.

And Lucas says, 32 is the other addend, so I found three tens and two ones.

I hope that's the sort of thing you were talking about as you were working on your answers as well.

Let's have a look at the final two.

So for C, our addends were 45 and 23, so four tens and five ones, two tens and three ones.

And that gave us a sum of 68.

And for D, 35 plus 42, so 35 was one addend, three tens and five ones.

And 42 was the other addend, four tens and two ones.

And when we combined those to make our whole, or our sum, we had seven tens and seven ones, which was 77.

Okay, onto the second part of our lesson.

And here, we're going to be linking column addition to known representations.

We've done a bit of that, but let's have a look at some more.

So Alex sets out the parts and the whole from the bar model in a column addition.

He says 33 and 22 are the parts and 55 is the whole.

And there's the bar model that shows it.

33 is a part, 22 is a part, and 55 is a whole.

And Lucas says, 33 is one of the addends, it's one of the parts.

So our addends and our parts are the same.

So there's 33.

What about the other addend? Ah, yes, well done, Lucas.

22 is the other addend, it's also one of the parts.

And when we use our column addition, we write one addend underneath the other one.

And then what happens? That's right, we write that equal sign to show that we've got an equation here.

And Lucas says, the sum is 55, this is the whole.

So in our bar model, we can see that 55 is the whole.

And in our column addition, we can see that 55 is the sum.

The sum and the whole are the same.

And the sum appears within the equal sign.

Lucas asks Alex if he can represent the column addition as a bar model, so can he go the other way round? So what are the parts and what's the whole in our column addition? What do you think? Lucas says, where's the sum? Where are the addends? So where are the parts and where's the whole? Alex says, 37 is one of the addends, it's one of the parts.

So he can write that one in.

31 is the other addend, it's one of the parts as well.

So there's our other part.

And the sum is 68, so 68 is the whole.

So we can see how the addends and the sum in our column addition relate to the parts and the whole in the bar model.

And that's really useful, sometimes we might have some information that we can make sense of and represent in a bar model and that will help us to identify the numbers that we need to add together.

And then we might use a column addition to add them together.

So it's really useful to be able to go between the different representations.

Your turn to have a go.

So can you represent the column addition equation as a bar model? You've got the column addition equation there, 36 plus 23 is equal to 59.

Can you put those values into the bar model so that it represents the same equation? Pause the video and have a go, and then we'll come back for some feedback.

How did you get on? Did you answer those questions? Where's the sum, and where are the addends? So yeah, 36 is one of the addends, so it's also one of the parts.

23 is the other addend, it's one of the parts as well.

And the sum was 59, so 59 was the whole.

So there we go, our completed bar model, which represents the same as our column addition equation.

Lucas looks at this column addition equation.

He says, I'm going to complete the equations below using the same three numbers.

Ooh, this is interesting.

Ah, so Lucas is going from a column addition to an equation that's written in one line.

So how are those numbers going to translate? And Alex has spotted, two equations start with an addend, and two of the equations start with the sum.

And we know that it doesn't matter which way round we write them, it's an equation, so both sides of the equal sign have exactly the same value.

So Lucas says, well, you could write the first one as 33 plus 41 is equal to 74.

How else could we write it though? Ah, that's right, do you remember that addition is commutative? So it doesn't matter which order we add the addends, the sum will be the same.

So 41 plus 33 is also equal to 74.

And then we've got the two that Alex spotted that start with the sum.

So this time we're going to start with our 74, with our whole, with our sum.

So 74 is equal to 33 plus 41.

And then because of the commutativity of addition, we can swap those addends around and the sum will remain the same.

74 is equal to 41 plus 33.

So we can write all those different equations based on our column addition.

Alex looks at this column addition.

So 36 plus 42 is equal to 78.

And he completes the equations below using the same three numbers.

So what do you spot? Yes, we've got that sum first, our whole is first in both of the equations.

So what are they going to look like? Alex says, the sum appears at the start of the equations.

So our sum was 78.

So 78 is equal to 36 plus 42, and 78 is also equal to 42 plus 36.

Okay, time for you to have a go.

Use the column addition, there we are, and complete the equations using the same three numbers.

And this time, Lucas says, the sum appears at the end of the equations.

So there are the two equations.

So pause the video, complete those equations, and then we'll have a look at them together.

How did you get on? Did you spot that we could write, 37 plus 22 is equal to 59? And then because addition is commutative, we can also write 22 plus 37 is equal to 59.

Well done if you've got those.

Time for you to do some practise.

So in this first part, you're going to represent each column addition as a bar model, and you've got three there to have a go at.

And then in second part, you're going to look at each column addition and you're going to complete the equations underneath using the same three numbers.

And remember to look carefully, do the addends come first? Or does the sum come first? And in part three, you're going to represent the column addition using base 10 blocks, using a bar model, and using addition equations.

So thinking about all the different ways that we can represent that column addition.

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

How did you get on? Let's have a look at some of the answers together.

So in A, we had 44 plus 15 is equal to 59.

44 and 15 are both addends, so they're the parts in our bar model.

59 is the sum, so it's the whole, so can we use that same thinking for B and C? So in B, 55 plus 23 is equal to 78.

55 and 23 are both the addends, so they are the parts in our bar model.

78 is the sum, and it is the whole in our bar model.

And then for C, 21 and 47 are our addends and our parts.

68 is the sum, so it represents the whole in the bar model.

So for the second part, you were asked to complete the equations underneath our column additions.

So let's have a think, 36 plus 53 equals 89.

So we can record that, we have the sum at the end this time, and the parts or the addends at the beginning.

And we can write those addends in any order because addition is commutative.

So 36 and 53 are the addends, and they are the parts.

89 is the sum and it's the whole.

In B, we could do the same because our addends came first.

So 13 and 64 were our addends, so we added those together to get the sum of 77, which was our whole.

And then in C, just the same 27 and 72 are our addends, so they are the parts, and 99 is the whole or the sum.

But this time, you had to spot that the sum came first in our equation.

So 99 was equal to 27 plus 72, and 99 was equal to 72 plus 27.

And here, you had to represent the column addition in different ways.

So we had 43 plus 32, those were our addends, 75 was our sum.

So using the base 10 blocks, we can see we've got four tens and three ones, 43, added to three tens and two ones, 32.

And if we combine our base 10 blocks, we'll get our sum of 75.

In the bar model, 43 and 32 were our parts, and 75 is the whole.

And with those addition equations, we started off here, we've got 75 as our sum, is equal to the two addends together.

And for the second two, the addends combined are equal to the sum of 75.

So we've come to the end of our lesson, reviewing column addition and identifying the addends and the sum when we set out our additions as a column addition.

So what have we learned about today? Well, we've learned about or reminded ourselves that the addends when we use a column addition are written in columns with the same value digits in the same column.

So one addend is written above the other one, with the ones lined up and the tens lined up, in our lesson today.

And that the sum is recorded underneath the addends, again, with the same value digits in the same column.

Thank you for all your hard work today.

I hope you've enjoyed going back and looking at column addition again, and reminding yourself of how we set it out.

And how column addition links to other representations, base 10 blocks, bar models, part-part-whole models, and equations written in a line rather than in a column.

I've really enjoyed working with you today and I hope we get to work together again soon, bye-bye.