Lesson video

Hello everyone.

Welcome back to another maths lesson with me, Mrs. Pochciol.

As always, I can't wait to learn lots of new things and hopefully have lots of fun.

So let's get started.

This lesson is called add up to three four-digit numbers using column addition, and it comes from the unit column addition and subtraction with four-digit numbers.

By the end of this lesson, you should be able to add two or more four-digit numbers using column addition involving regrouping.

Here are this lesson's keywords.

Let's have a look at them.

Column addition, regrouping.

Let's practise.

My turn, column addition.

Your turn.

My turn, regrouping.

Your turn.

Wonderful.

Column addition is a way of adding numbers by writing a number below another, and the process of unitizing and exchanging between place values is known as regrouping.

For example, 10 tens can be regrouped as 100, and 100 can be regrouped as 10 tens.

These definitions are really gonna help us with our learning today.

So let's get started.

Let's have a look at our lesson outline.

In the first part of our learning, we're going to add four-digit numbers using column addition.

And in the second part of our learning, we're going to solve problems involving four-digit numbers.

Are we ready? Let's get started.

In this lesson, you are going to meet Sam, Sofia, Izzy, and Lucas.

They're going to help us with our learning today.

Are we ready guys? Are you ready to do some column addition? Let's start.

Izzy and Sofia are practising using column addition.

Izzy wants to use the column addition to add together 143 and 134.

They're going to start by using the base 10 blocks to represent the calculation.

143 can be partitioned into 100, 4 tens and 3 ones.

There we go.

Can you see them? And 134.

Hmm, what can we partition 134 into? 100, 3 tens and 4 ones.

Well done if you said that.

Hmm, right, so they've got the numbers now into their column addition, but how are they going to find the sum? We're going to start with the smallest place value numbers first.

So that's the ones.

3 ones add 4 ones is equal to? 7 ones.

Well done.

Now we're going to move on to which column? The tens column.

We have 4 tens and 3 tens, and we know that 4 tens add 3 tens is equal to 7 tens.

Well done if you said that.

And finally we move on to our hundreds column.

100 add 100 is equal to two hundreds.

Let's pop them in there.

Hmm, so what is our sum? Let's have a look.

143 plus 134 is equal to 277, because we have 2 hundreds, 7 tens and 7 ones.

Well done Izzy and Sofia.

Izzy and Sofia now look at a different problem.

Ooh.

Hmm.

What's different about this problem? Izzy thinks that we can still use column addition to solve this problem too.

Do you agree with Izzy? Sofia doesn't think that we can use column addition because they are four-digit numbers.

That's right, Sofia, we have 6,185 plus 2,738.

Let's have a think.

Who do you agree with? Do you think we can use column addition, or do you agree with Sofia that we can't use column addition because there's four-digits? Sofia decides to let Izzy have a go at using column addition to see if it will work.

So let's have a look.

Let's first create each number using the base 10.

We have 6,185.

That can be partitioned into 6 thousands, 1 hundred, 8 tens and 5 ones.

So let's have a look at our other four-digit number, 2,738.

We can see that that can be represented with 2 thousands, 7 hundreds, 3 tens, and 8 ones.

Well done if you said that.

So now they've represented them using the base 10, what are you going to do, girls? They're going to represent it in their column addition.

Let's create the column addition using base 10 blocks to represent our calculation.

We need a thousands column now though, because we have four-digit numbers, so let's add that in.

Can we see we've got our ones, our tens, our hundreds, and now our thousands column.

So let's pop our numbers in then, girls.

6,185.

And 2,738.

Can we see our numbers? Well done, girls.

So now what do we do to find the sum? We need to start with the smallest place value numbers.

Of course we do.

We start with our ones.

So 5 ones add 8 ones is equal to 13 ones.

You're right, Sofia, we do need to regroup 10 ones as 1 ten.

So let's do that.

Are we ready? There we go.

Can you see 10 of our ones have regrouped into 1 ten? Now we need to add the tens.

8 tens add 3 tens add our regrouped ten is equal to 12 tens.

We can now regroup 10 tens as 100.

Are we ready? There we go, look, 10 tens have regrouped and they're now in our hundreds column.

So now we can add our hundreds.

100 add 7 hundreds, add 1 more hundred, which is our regrouped hundred, is equal to 9 hundreds.

Can we see? And finally, we now move on to our thousands column.

So how many thousands do we have? We have 6 thousands.

We have 2 thousands.

So 6 thousands add 2 thousands is equal to 8 thousands.

So let's have a look at our sum.

We have 8 thousands, 9 hundreds, 2 tens, and 3 ones, so that is equal to 8,923.

So the sum of 6,185 and 2,738 is 8,923.

Wow, so we can use our column addition to add four-digit numbers.

Well done Izzy, and well done Sofia for helping.

Izzy now decides to try something.

Let's have a look.

Oh, what's Izzy done here? Hmm, she's represented each of the numbers using digits for this calculation.

Look, 6,185 and 2,738.

It's still the same calculation, but she's used digits this time, rather than fiddling with all those base 10.

Let's have a look.

Should we see if we still get the same sum using the digits instead of the base 10? Remember, we start with the smallest place value first, so that's the ones.

5 ones add 8 ones is equal to 13 ones.

We can regroup 10 ones as 1 ten.

So we have 3 ones and we have our regrouped 10.

Now let's add the tens.

8 tens, add 3 tens, add the regrouped 10 is equal to 12 tens, and we know that we can regroup 10 tens as 100.

So we have 2 tens and we have 1 regrouped hundred.

Now let's add the hundreds.

We have 1 hundred add 7 hundreds add 1 hundred, our regrouped one, which is equal to 9 hundreds.

And finally, let's look at our thousands column.

We have 6 thousands, add 2 thousands, which is equal to 8 thousands, 8,923.

It's still the same answer that we got when we used the base 10.

Now it's time for you to have a go.

So represent this calculation using your own column addition to find the sum.

Look out when you're adding for any regrouping.

Come on back once you found the sum.

Welcome back.

I'm hoping that you recognise that using four-digits in a column addition is just the same as using three digits.

It's just an extra column.

Shall we see how you got on? You should have represented your four-digit numbers like this, 3 thousands, 6 hundreds, 9 tens, and 8 ones, and 2 thousands, 8 hundreds, 4 tens and 3 ones.

Now we can add them together.

We're going to start with that smallest place value number first, our ones.

8 ones add 3 ones is equal to 11 ones, and we can regroup 10 ones as one 10.

Look, just like that.

Now let's look at our tens.

9 tens, add 4 tens, add the regrouped 10 is equal to 14 tens, and we can regroup 10 tens as 100.

So we have 4 tens and our regrouped 100.

Well done if you've got that bit.

Now let's add the hundreds.

6 hundreds, add 8 hundreds add the one regrouped hundred is equal to 1500.

Goodness me, there's lots of regrouping today, isn't there? So we can regroup 10 hundreds as 1000.

So we have 5 hundreds and we have our regrouped 1000.

Now finally, let's add our thousands.

3 thousands add 2 thousands add 1 thousand, the regrouped one, is equal to 6,000.

So I can see that the sum is 6,541.

So 3,698 plus 2,843 is equal to 6,541.

Well done to you if you got that.

Izzy and Sofia now look at this problem.

Hmm, what's different about this problem? What do you notice? Do you think we could still use our column addition to find the sum of this problem? Izzy has noticed that we now have to add three addends.

You're right, Izzy, that's what's different about this problem.

Sofia thinks that we could still use our column addition.

What do you think? Do you agree with Sofia? Do you think we could still use our column addition? Sofia's not sure if she can add together three numbers using our column addition, but the girls are going to have a try.

Are we ready? Let's go.

6,378 plus 2,553 plus 1,041.

Let's have a go at using our column addition.

To add together our three addends, we had to add another row into our column addition.

Can you see? We now have three rows.

6,378, 2,553 and 1041.

All of the numbers have now been put into their rows.

Now we can add them together.

So which column are going to start with first? The ones, well done.

8 ones add 3 ones add 1 one is equal to 12 ones.

And again, we can regroup 10 ones as 1 ten.

Now let's look at the tens.

7 tens plus 5 tens plus 4 tens plus one more ten that we regrouped is equal to 17 tens.

Again, we can regroup 10 tens as 100.

Now let's look at our hundreds.

3 hundreds plus 5 hundreds plus our regrouped hundred is equal to 9 hundreds.

And finally our thousands column, 6 thousands plus 2 thousands, that's 8 thousands, plus one more thousands, that is 9 thousands.

So we can see that our sum is 9,972.

Wow, so we can use our column addition to add three addends together.

Well done, girls.

That's gonna really help us, isn't it, with our learning.

Over to you then for your turn.

Represent this calculation using your own column addition to find the sum.

2,347 plus 1,573 plus 3,672.

Pause this video, represent those three numbers onto your column addition and find the sum, and come on back once you found the sum.

Welcome back.

Let's have a look then at how you got on.

The first thing we needed to do was to place our numbers onto our column addition.

So there we go, there we go, and there we go.

Well done.

Now we start with our ones, remember, so let's have a look.

7 ones plus 3 ones is equal to 10 ones, plus two more, that's equal to 12 ones, and we need to regroup 10 of those ones as 1 ten.

Now let's move on to our tens.

We can see that we have 19 tens altogether, and we've regrouped 10 tens as 100.

Let's have a look at our hundreds.

We can see that we have 15 hundreds altogether, and 10 of those hundreds are regrouped as 1000.

Now let's move on to our thousands.

Let's have a look.

I can see I've got three plus three, that's six, plus one more, that is 7 thousands.

We can now see that 2,347 plus 1,573 plus 3,672 is equal to 7,592.

Well done to you if you got that one correct.

Sofia and.

Izzy and Sofia now look at one final problem.

Let's have a look then, girls.

Hmm, what do you notice? Izzy has noticed that we now have a four-digit number and a three digit number.

We do, 4,349 and 662.

Hmm, do you think we can still use column addition? Sofia thinks that we can still use column addition, but she's not sure about adding two numbers with different numbers of digits.

What do you think? Do you think we could still use column addition? I think we should have a try.

Are we ready? Let's first put our numbers onto our column addition, 5,214 and 738.

Hmm, I'm not sure about that, Izzy.

Sofia, what do you think? Sofia has noticed that 738 doesn't have any thousands, so Izzy's put them in the wrong columns.

Oh, I see, look, we've put the seven in the thousands column, that means 7 thousands, but we don't, we have 7 hundreds, so we need to place 738 here because it has 7 hundreds, 3 tens, and 8 ones.

Well done, Sofia.

Thank you for noticing that.

First we're going to add together our ones then.

4 ones add 8 ones is equal to 12 ones.

We've regrouped 10 of those ones as 1 ten, so it's going to look like this.

Now we can add our tens.

1 ten add 3 tens add that regrouped 10 is equal to 5 tens.

2 hundreds add 7 hundreds is equal to 9 hundreds.

And 5 thousands plus zero thousands, because remember, 738 doesn't have any thousands, is equal to 5 thousands.

So we can see that 5,214 plus 738 is equal to 5,952.

Well done to Izzy and well done to Sofia.

Let's have a go at this for ourselves.

Over to you for your check.

Represent this calculation using your own column addition to find the sum of 359 and 4,385.

Remember to represent each number in the correct columns to ensure that your sum is accurate.

Pause this video, find the sum, and come on back when you're ready to see how you've got on.

Welcome back.

Let's see how you got on then.

359 doesn't have any thousands, so that's only going to be in our hundreds, tens, and ones column.

3 hundreds, 5 tens, and 9 ones.

4,385 has thousands, hundreds, tens and ones, so that can be placed in there.

Then we can place 4,385 into our column.

Now we can add them together.

9 ones plus 5 ones is equal to 14 ones.

We can regroup.

5 tens plus 8 tens plus one 10 is equal to 14 tens.

3 hundreds plus 3 hundreds plus 100 is equal to 7 hundreds.

And finally, 4 thousands plus zero thousands, because remember, 359 doesn't have any, is equal to 4 thousands.

So we can see that the sum of 359 and 4,385 is 4,744.

Well done to you if you got that correct.

Over to you then with task A.

You're going to roll a dice to create your own addition to solve using column addition.

Sofia, can you show us how to do it? Sofia first rolls a four so she can see that that represents 2,941 and 3,548.

She then rolls a six, so now she's going to look at the second column.

That represents 3,256.

She now has to solve 2,941 plus 3,548 plus 3,256.

So we can see that that's a three addend edition, because in the first row, there are two numbers.

She's then going to use her column addition to solve this problem, and we'll see how she gets on with it later.

So pause this video, grab your dice, and get creating your own additions to solve using column addition.

We'll see you soon.

Welcome back.

Let's have a look at how Sofia used column addition to solve her problem.

So the sum of 2,941, 3,548 and 3,256 is 9,745.

Well done Sofia.

And well done to you for completing task A.

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

Now we've practised using column addition, we're going to solve some problems involving four-digit numbers.

Are we ready? Izzy, Sofia, Sam and Lucas visit their local arcade for a fun day out.

They first have a go at one of the computer games.

Izzy scored 4,673 points, and Sofia scored 4,834 points.

They want to know how many points they scored altogether.

They're going to use a column addition to find the sum of both of their scores, 4,673 and 4,834.

Let's get adding then.

First we start with our ones.

3 ones and 4 ones is equal to 7 ones.

7 tens plus 3 tens is equal to 10 tens.

We can regroup 10 tens as 1 hundreds.

Now we add the hundreds.

6 hundreds, add 8 hundreds add 100 is equal to 15 hundreds, and we regroup 10 hundreds as 1,000, and 4,000 plus 4,000 plus 1,000 is equal to 9,000.

So we can see that they scored 9,507 points all together.

Wow, so close to 10,000 girls.

Well done.

Lucas tried to calculate his and Sam's scores combined, but he does not think he's right.

Lucas used rounding to estimate his score, and he thinks that their combined score should be closer to 8,000.

Have a look at Lucas's column addition.

What has he missed? Pause this video and come on back when you've got some advice for him.

Welcome back.

I hope you enjoyed exploring Lucas's column addition there.

Did we find what he'd missed? Let's have a look.

You might have noticed that Lucas saw that 8 and 2 was equal to 10, but he forgot to show the regrouping.

He forgot to regroup the 10 ones as a 10, and the 10 hundreds as a thousand.

Lucas realised what he missed.

Come on then, Lucas, see if you can fix your column addition.

We need one more ten and one more thousand, so the sum is 8,050.

Yes, you were right Lucas.

It should have been closer to 8,000.

Well done to Lucas, well done to Sofia, and well done to you.

Let's move on.

To find Lucas's final score, the points he scored in each of the three rounds are added together.

So what was Lucas's final score? In round one, he scores 2,879 points.

In round two, he scores 1033 points, and in round three, it was against a really hard boss, so he only scored 137 points.

Lucas uses column addition to find the sum of his three scores.

First we add the ones.

9 ones plus 3 ones plus 7 ones is equal to 19 ones.

7 tens plus 3 tens plus 3 tens plus 1 more ten is equal to 14.

8 hundreds plus 1 hundred plus that regrouped hundred is equal to 10 hundreds, which we can regroup as 1,000.

And 2,000 add 1,000 plus 1 more thousand is equal to 4,000.

So we can see that altogether, Lucas scored 4,049 points.

Wow, Lucas, well done.

I love how you added together those three addends there using the column addition.

On the next game, Izzy, Sofia, Lucas and Sam have a competition to see which team can get the closest score to 9,000.

Sofia and Izzy pair up, and Sam and Lucas pair up.

Which team has the closest score to 9,000? Let's have a look.

Each pair calculate their totals using a column addition.

Let's have a look then.

Sofia has noticed that it's going to be really close, because when we round to estimate, both the totals are very close to 9,000.

So let's have a look.

We have 18 ones, so we regroup 10 of them into a 10.

We now have 11 tens.

We can regroup 10 of those tens into 100.

We have 1700, so we regroup 10 of those hundreds into a thousand, and we have 8,000 altogether.

So Sofia and Izzy have scored 8,718.

That's very close to 9,000.

Let's have a look at Sam and Lucas.

15 ones.

We regroup.

9 tens.

17 hundreds, so we regroup.

And we have 8 thousands, 8,795.

Oh, let's have a look.

We have 8,795 for Lucas and Sam.

We can see that Sam and Lucas have more tens, so that means that their score is closer to 9,000.

Well done for spotting that, Sofia.

So that means Sam and Lucas were the winners.

Over to you then.

So which two children have a score of 6,866? Hmm, what strategies could you use to work out which two children have that score combined? Pause this video, have an explore, and come on back to see how you got on.

Welcome back.

Let's have a look at how Izzy solved this problem.

Izzy used estimation to help her to work out which two scores could combine to equal 6,866.

She noticed that this score is around 7,000, and Sofia and Lucas's scores are close to 4,000 and 3,000.

She then uses column addition to double check if she's correct.

So let's have a look.

9 ones plus 7 ones is equal to 16 ones.

7 tens plus 8 tens plus 1 ten is equal to 16 tens.

8 hundreds plus 9 hundreds plus 100 is equal to 18 hundreds.

And 3 thousands plus 2 thousands plus 1000 is equal to 6,000.

So yes, Sofia and Lucas's scores do add up to 6,866.

Well done to you if you said Sofia and Lucas's scores would add up to 6,866.

Over to you then with task B.

Find a solution to each of these problems. A, what was the total score of the two highest scoring children? B, which two children together had a score of 4,426? C, what was Sam's, Lucas's and Sofia's total score? And D, which team scored the closest to 5,000 points? Sofia and Izzy, or Lucas and Sam? Pause this video, find a solution to A, B, C, and D, and come on back when you're ready to complete the learning.

Welcome back.

I hope you enjoyed exploring those problems there.

Let's have a look at how you got on.

A, so what was the total score of the two highest scoring children? We can see that 5,408 and 3,839 were the highest scores, so let's add them together.

17 ones, 4 tens, 12 hundreds, regroup.

We have 9 thousands.

9,247 is the score of the two highest scoring children.

Well done if you got that one.

B, which two children had a score of 4,426? Izzy's score and a three digit score would result in this score.

Izzy noticed that 587 would keep the sum closer to 4,000 than 876 would, so she adds them together.

Let's have a look.

16 ones, 12 tens, 14 hundreds, we regroup, and 3 plus 1 is equal to 4 thousands.

So yes, Izzy and Lucas' score do sum to 4,426.

So well done if you said Izzy and Lucas.

And over to C.

So what was the total score of Sam, Lucas and Sofia? Sam scored 5,408, Lucas scored 587, and Sofia scored 872.

Let's add them together to find out their total score.

We have 17 ones, so we need to regroup.

We have 16 tens.

Let's regroup.

We have 18 hundreds, so let's regroup.

And we have 6 thousands, so we can see that altogether, Sam, Sofia, and Lucas scored 6,867.

Well done if you got that one.

And part D, which team scored closest to 5,000 points? Sofia and Izzy, or Lucas and Sam? Let's have a look.

Ooh, let's add them together.

Then we can see 11 ones and they have 15 ones.

Hmm.

We have 11 tens, let's regroup, and there's only 9 tens there.

Let's have a look.

8 tens, 8 hundreds plus 8 hundreds plus 1.

Here we have 17 hundreds, and over here we have 9 hundreds, and 3 thousands plus 1000, that's 4,000, and over here we have 5,000, that big score from Sam there.

Now we've added them together, so let's see who is closest to 5,000 points.

Izzy and Sofia scored 4,711 points, and Lucas and Sam scored 5,995 points, but who is closer to 5,000? 5,995 is nearly 1,000 more than 5,000, whereas 4,711 is only about 300 less than 5,000.

So that means that 4,711 is closest to 5,000, so Izzy and Sofia were the closest.

They are the winners.

Let's have a look at what we've learned today.

We can use column addition to add four-digit numbers.

We can regroup 10 hundreds as 1000.

Make sure that any regrouped thousands are added with the values in the thousands column.

Make sure that all regrouped values are added in the correct column.

Welcome for completing this lesson, and thank you for all of your hard work today.

I hope to see you again soon for some more maths.

Goodbye!.