Lesson video

(no audio) <v ->Hello, my name's Mrs. Hopper and I'm really happy</v> 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.

So today's lesson is about identifying the addends and sum in a column addition and it's part of the unit on column addition.

So by the end of today's lesson, you will be able to identify those addends and the sum in a column addition.

So let's see what's going to be in our lesson today.

We've got four key words here.

So things to look out for during our lesson.

So I'm going to say them and then it'll be your turn.

So my turn, addend.

Your turn.

My turn, sum.

Your turn.

My turn, equation.

Your turn.

My turn, column addition.

Your turn.

Now I suspect some of those words will be familiar to you.

Column addition might be a new one.

That's what we are learning all about today.

So let's see what those words mean.

So an addend is a number added to another number and you may well have come across that word before.

The sum is the total when numbers are added together, when addends are combined.

And you may well have come across the word sum before.

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

So you can see in the example here we've got two addends, 10 and six and they're being added together and they are equal to the sum of 16.

16 is also equal to 10 plus six.

So there's our equation showing our addends and our sum.

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

We're going to learn lots more about column addition in this lesson.

There are two parts to our lesson today.

We're going to start thinking about column addition and base ten blocks.

You may well have used those to represent your calculations before and then we'll move on to thinking about column addition with other representations.

So let's make a start.

And we've got Jun and Laura helping us with our work today.

So Jun is thinking about the different ways he can represent addition calculations.

Jun says, "I like using bar models and base ten blocks." I wonder if you've used bar models and base ten blocks? Do you have a favourite way of representing or do different things work better in different situations? Let's have a look at what Jun's got to share with us.

So here's Jun's bar model and you can see in his bar model he's shown the two addends and the sum and the addends combine to equal the sum.

He's also represented an addition using base ten blocks and we can see there that he's got 33 and he's adding 22.

So his addends are 33 and 22.

I wonder, you might be able to work that one out in your head, but we're not worried about the answer right now.

Jun says, "I also like writing addition equations." So let's have a look at an equation.

And there we are.

So he's represented his base ten blocks as an equation.

33 plus 22 is equal to 55.

If we combine those addends, we will have five tens and five ones.

So our answer will be 55.

Laura says, "I think you're ready to use column addition!" Ooh, so Jun's very confident with his bar model.

He's confident with the base ten blocks and he's confident using those equations.

He knows what's going on.

So Laura says you're ready for column addition.

Let's have a look.

Laura explains a bit more, 'cause Jun's not sure.

"What's column addition, Laura?" Laura says, "Column addition is a way of writing addition equations." Think of an addition equation we can use.

Hmm, let's see what Jun comes up with.

He thinks of this equation.

He thinks of 54 plus 30 is equal to 84.

We've got the answer.

He knows that the sum is 84, that if we combine those two addends, the sum will be 84.

Let's have a look at how Laura is going to write it down.

Laura says, "We would write it like this." 54 plus 30, one addend is written below the other.

So we've got the 54 at the top and we've got the 30 written underneath and you can see that we've got five tens and four ones in our 54 and we've got three tens in our 30.

So we can see that those tens are in the right place.

They're lined up together.

So we've written our addends one below the other.

Oh, what do those two lines remind you of I wonder? Does it looks like an equal sign? So the equal sign shows that this is an equation.

We're going to write the sum inside that equal sign.

And there it is.

The sum appears within the equal sign.

Again underneath our addends.

Jun is unsure about where the sum and the addends appear.

He says, "I'd like to see that again." I think I would too.

Let's have another look then.

Laura says, "Watch really carefully!" 54, which is one of our addends.

So we're going to write the addend 54.

Then the other addend is written below the first one.

So 30 is written underneath 54 and you can see we've got our addition sign.

It's a bit hiding behind the line at the moment.

Then we've got this equal sign showing that it's an equation and what we're going to write in there is equal to the sum of our addends and the sum appears within the equal sign.

So we've got our addends written one on top of the other above our equal sign and our sum within the equal sign.

Jun wants Laura to use column addition to represent addition using base ten blocks.

Remember, Jun liked using base ten blocks to represent addition.

I wonder what the column addition looks like alongside the base ten blocks.

He says, "Can you show me how you would represent the base ten blocks as column addition?" So here are some base ten blocks and what can we see there? We can see that we've got four tens and two ones, which is 42 and we're adding that to two tens and two ones which is 22.

So we've got 42 plus 22.

So Laura says, "42 is one of the addends." So we're gonna write that down.

"22 is the other addend." So we're going to write that one underneath our 42.

One addend is written below the other.

Then we've got our equal sign.

The equal sign shows that it is an equation.

If you imagine it written down as an equation, that will be our, there's our equal sign.

And Laura says, "The sum is 64." We know that, that's one we can do mentally.

We can work that out in our head by thinking about the tens and the ones.

So the sum is 64 and we write the 64 inside the equal sign.

There it is, the sum appears within the equal sign.

So we've taken Jun's base ten blocks and we've represented that addition using column addition.

So this time Jun matches this column addition with a base ten block representation.

So here is the column addition.

So can we see, can we see what our addends are? Can we see where the sum is? Let's have a look.

Jun says, "I'm going to represent this equation using base ten blocks." So Laura represented the base ten blocks as an equation.

Jun's gonna do it the other way round.

He's going to create the base ten blocks that match this representation.

So Laura says, "Which numbers are the addends in the equation?" Can you see the addends in the equation? Jun says, "41 and 23 are the addends." The two addends that we've written one on top of the other or one underneath the other.

And there they are.

So Jun has made the base ten blocks to match.

So he's got 41 and to that he's adding 23.

And we can see the four tens and one one and the two tens and three ones representing 41 plus 23.

And Laura says, "They add together to equal the sum." There's our sum of 64 and if we imagine putting all of those base ten blocks together, we'd have six tens and four ones.

So we'd have 64.

And there they are.

So Jun's going to do that again.

He's going to match another column addition with a base ten block representation.

So here is our column addition.

Can you see the addends? Can you see the sum there? What do you think the base ten blocks are going to look like? Jun says, "I'm going to represent this equation using base ten blocks." Has he got it right? So our two addends are 33 and 16.

Has he represented those with the base ten blocks? Laura says, "Which numbers are the addends in the equation?" Jun says, "Well 33 and 16 are the addends." There they are.

Has he represented them with the base ten blocks? He has, hasn't he? The first set of base ten blocks is three tens and three ones, so our 33 and the second set is one ten and six ones, which is 16.

And Laura says, "They add together to equal the sum." And there is our sum written within those equal signs.

And if we put all of those base ten blocks together, we would have four tens and nine ones.

So we'd have 49 in total.

Laura sets Jun a challenge.

So Laura's asking, "Which representation of base ten blocks matches the column addition?" So let's have a look.

You are going to have a go at this one and check your understanding.

So here is our column addition and here are the base ten blocks.

Jun says, "Which one should I choose?" So is it A, B, or C? Which set of base ten blocks matches the column addition? Pause the video now and then we'll talk about it together.

How did you get on? Did you spot that C had the base ten blocks to match the column addition? So in the column addition we can see that the addends are 21 and 12.

And in C we can see that our first set of base ten blocks is two tens and one one, 21.

And the second set is one ten and two ones, which is 12.

So it's time for you to do some practise.

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

And Jun says you could use your own base ten blocks or you could draw some or you could use the ones provided in the additional resource.

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

And two more here.

So pause the video and have a go at representing these column additions using base ten blocks.

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

So you were given some column additions and you had to represent the addends using base ten blocks.

So in A our addends were 23 and 21 and you can see them there represented with the base ten blocks.

In B, the addends were 22 and 31 and you can see them again represented.

In C, our addends were 26 and 12.

And in D, our addends were 32 and 33.

Ooh, very close together.

32 and 33, only one, one separating those two.

So, I hope you represented those correctly using either some of these 10 blocks that you had by drawing them or by matching them to the ones on the sheet.

Okay, so well done.

You've worked hard in that first part of the lesson.

Let's move on and think about column addition with other representations.

So Jun wants Laura to use column addition to represent a bar model.

If you remember, Jun was quite, he liked using bar models to represent addition.

So now he wants to see how the bar model links to the column addition.

So he says, "Can you show me how you would represent the bar model as column addition?" So here's his bar model.

So his two addends are 33 and 20 and his sum is 53.

How's that going to look as a column addition? And Laura says, well, "33 is one of the addends." So we can record our 33.

"20 is the other addend." And remember with our column addition we write one addend below the other one.

So we're going to write our plus sign and our 20 is our other addend.

We're going to write it below the 33.

Can you remember what comes next? So one addend is written below the other and then we've got that big equal sign to show that this is an equation.

So the equal sign shows that it's an equation and the sum is 53 and we write the sum within the equal sign.

So can you see the addends in the bar model and the sum? And can you see the addends and the sum in the column addition? Laura asks Jun if he can represent the column addition as a bar model.

So this time he's going to go the other way.

So here is the column addition.

How would that look as a bar model? What do you think? Can you imagine? Can you visualise where the different numbers are going to go? Where the addends and the sum are going to appear? Laura says, "Where is the sum and where are the addends?" Can you spot those? Jun says, well, "43 is one of the addends." Because we record the addends in a column addition, one underneath the other one, above that equals sign.

And in our bar model, those are the two parts making up our whole.

So 43 is one of the addends and Jun says 23 is the other addend, and 66 is the sum.

So he's recorded his addends as the two parts in the bar model and 66 as the whole, the sum.

Time for you to have a go.

Can you represent the column addition equation as a bar model? So here is the column addition and Laura's saying, "Where's the sum and where are the addends?" So can you represent this column addition as a bar model? Pause the video and have a go.

How did you get on? Did you draw your bar model? And Jun's saying, well "25 is one of the addends." So we'll record the 25.

"22 is the other addend." So we'll record that as our other part of our whole and the sum is 47.

We can see inside the equal sign the sum is 47 and that represents our whole in our bar model.

So well done if you've got that right.

So Jun's looking at this column addition equation.

So can you see where the addends and the sum are? We've got 32 plus 25 and in our equal sign it's equal to 57.

And Jun says, "I'm going to complete the equations below using the same three numbers." So do you remember that Jun liked to use bar models? He liked to use base ten, but he also liked to record his additions as equations.

So we've sort of got an equation in our column addition, but how does that look in the way we might have recorded equations before? So here we've got some equations with some blanks in.

So let's have a look carefully at where the symbols are.

Laura says, "Two equations start with the sum and two start with the addends." Can you see that two of the equations start with mm equals mm plus mm? And the bottom two have mm plus mm is equal to mm.

So we've got the equal sign and the addition sign just moving around.

So think really carefully about where the addends and the sum are going to be placed to make these equations correct.

So Jun says, well I can do 57 is equal to 32 plus 25.

But he could also write 57 is equal to 25 plus 32 because we know that it doesn't matter which way round the addends are, which order we add the addends, the sum remains the same.

So I wonder what you think might happen in the next one.

So we've got 32 plus 25 is equal to 57.

And then because we know we can add the addends in any order, we can also say 25 plus 32 is equal to 57.

So all of those equations are other ways of representing that column addition equation.

So, we'll do one together and then it'll be your turn to have a think.

So Jun looks at this column addition.

36 plus 12 is equal to 48.

He completes the equations below using the same three numbers.

So we've got mm equals mm plus mm and mm equals mm plus mm.

So what's gonna be first? Is it going to be the sum or is it going to be the addends? Let's have a look.

Mm equals mm plus mm.

So I think we've got the sum coming first here, haven't we? So yes, Jun says, "The sum appears at the start of the equations." So we've got 48 is equal to 36 plus 12.

And then how can we write that in a different way? Ah yes, we can swap the order of the addends.

48 is equal to 12 plus 36.

So Jun's helped us with one.

Now it's your turn to have a look.

So use the column addition and you're going to complete the equations below using the same numbers.

And this time Laura's telling us that the sum this time appears at the end of the equations.

So pause the video and have a go at completing those equations.

How did you get on? So Laura reminded us this time that the sum was at the end of the equations this time.

So did you get that 28 plus 11 is equal to 39, but then we can change the order of the addends and the sum remains the same.

So 11 plus 28 is equal to 39.

Time for you to do some practise.

So can you represent each column addition as a bar model? So we've given you the column additions and you've got some bar models there to fill in.

Can you complete the bar models to match the column additions? And then this time you're going to look at each column addition and complete the equations using the same three numbers.

So look carefully, does the sum come first or do the addends come first? Look carefully at the way we've arranged the equations on the page.

And then finally you're going to use the column addition and you're going to represent the equation using base ten blocks, a bar model and addition equations.

So how many different ways can you represent that column addition? Using bar model, using base ten blocks, or using addition equations.

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

How did you get on? So here are the bar models created from those column additions.

So did you spot that 31 and 21 are the addends in A and 52 is the sum? In B, 15 and 32 are the addends and 47 is the sum.

And in C, 34 and 11 are the addends and 45 is the sum.

And we can also think about the parts and the wholes.

So you can see that the addends are the same as the parts in the bar model and the sum is the same as the whole.

So for part two you had to represent the column addition as equations.

And did you spot that for A and B the addends came first? And we know that we can swap the order of the addends and the sum remains the same.

But for C, the sum came first.

So we had 47 is equal to 24 plus 23 and then we can swap the addends.

So 47 is also equal to 23 plus 24.

And for the third part you were representing the column addition in lots of different ways, spotting that the addends are 32 and 36.

So they become the parts in the bar model.

They're the addends that we represent with the base ten blocks.

And then we could write those equations in lots of different ways.

We could start with the sum, we could start with the addends and we could remember that the addends could be written in either order, we can swap them round and the sum remains the same.

Well done, you've worked really hard.

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

So what have we been learning about today? Well, we've started to think about column addition and we've learned that in column addition one addend is written below the other one, the equal sign shows that it is an equation and the sum, the total appears within the equal sign.

So in the example on this slide, 54 plus 30 is equal to 84.

54 plus 30, those are our addends and they are equal to the sum of 84.

Thank you so much for your hard work today.

I've really enjoyed working with you, learning about column addition and I hope to see you again soon, bye.

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