Lesson video

Hello there.

My name is Mr. Goldie, and welcome to today's maths lesson.

And here is the learning outcome.

I can use column addition with regrouping in the ones and tens.

And here are our keywords for today's lesson.

So I'm going to say the keywords.

Can you repeat them back? So the first keywords are column addition.

And the next keyword is regroup.

Let's take a look at what those words mean.

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

The process of unitizing and exchanging between place values is known as regrouping.

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

And here's our lesson outline.

So the first part of the lesson is regrouping ones and tens, and the second part of the lesson is problem solving with regrouping.

And there's a few tricky problems in the second part of the lesson, so make sure you're listening really carefully.

Let's get started on the first part of the lesson.

In this lesson today, you will meet Jun and Laura, and they're going to be helping you with your maths and asking you some tricky questions.

Jun is thinking about adding two-digit numbers using column addition.

"What happens when the sums of the ones and the tens digits are both 10 or greater," asks Jun.

So here's an example of a calculation where the sums of the ones and the tens digits are both 10 or greater.

So we've got there the ones numbers, 4 and 7.

So 4 add 7 gives a sum greater than 10.

And if the tens digits are added together, they also have a sum greater than 10.

6 tens add 7 tens is greater than 10 tens.

60 add 70 gives a sum greater than 100.

Laura says we have to use regrouping in the ones and the tens.

So Laura shows Jun how to use column addition with regrouping in the ones and tens.

"I'm going to add together 64 and 77," says Laura.

here's our calculation.

64 add 77.

First of all, Laura starts off with numbers with the smallest place value first.

So 4 add 7 equals 11.

11 is regrouped into 1 ten and 1 one, and the 10 is moved into the tens column.

So the 10 is moved underneath the line in the tens column and the one is written in the ones column.

Next, Laura has to add together the tens.

6 tens add 7 tens add 1 ten.

60 add 70 add 10, 'cause remember to add that regrouped ten as well, equals 140.

140 is regrouped into 1 hundred and 4 tens, and the 100 is moved into the hundreds column.

So 60 add 70 add 10 equals 140.

The 100 is moved into the hundreds column, and the 4 tens is written in the tens column.

"There are no other hundreds except the regrouped hundred, so 1 is written in the hundreds column," says Laura.

There's a hundred, and 1 is written in the hundreds column.

There is 100.

Jun says, "64 add 77 equals 141." Jun thinks about adding three-digit numbers using column addition with regrouping in the ones and the tens.

So Jun's asked, "What's 176 add 176?" He's trying to think of two numbers that have to be added together so there's regrouping in the tens and the ones.

Now set it out as a column addition.

So 176 with 176 written below it.

And let's start off by adding the ones together first.

We always start with the smallest-place value numbers first.

And that's because of regrouping.

Because we can't add the tens until we've added the ones because we might have an extra 10 that we need to add on into the tens column.

"6 add 6 equals 12," says Laura.

12 is regrouped into 1 ten and 2 ones, and the 10 is moved into the tens column.

So there's our 10, it's written in the tens column, and 2, the 2 ones is written in the ones column.

Next we have to add the tens together.

So we've got 70 add 70 add 10 equals 150.

7 tens add 7 tens add 1 ten equals 15 tens.

150 is regrouped into 1 hundred and 5 tens.

The 100 is moved into the hundreds column, and the 5 tens, the 50 is written in the tens column.

Now we've got to add together the hundreds.

1 hundred add 1 hundred add the regrouped hundred equals 3 hundreds.

Put there 3 hundreds altogether.

So there is our answer.

There is our sum.

176 add 176 equals 352.

Use column addition to add together these numbers.

"What's 177 add 156," asks Jun.

So set it out as a column addition.

So you might want to have paper and pencil ready or a whiteboard and a pen, jot down that calculation, and have a go trying to work out the answer.

Don't forget to start with the ones numbers.

Always start with the smallest place-value numbers first.

So pause the video and see if you can work out what the answer to that question is.

And there is regrouping in the ones and the tens.

And welcome back.

How did you get on? Did you get the answer? Did you remember to regroup the ones and the tens? Did you remember to add the regrouped ten and the regrouped a hundred when you were calculating how many tens and hundreds there were? Let's take a look, see whether you were right.

So you have to start by adding the ones together first.

So we've got 7 ones add 6 ones.

7 add 6 equals 13, and 13 is regrouped into 1 ten and 3 ones.

And the 10 is moved into the tens column.

So we've got there our 10 and our 3 ones.

Next we have to get to the tens.

So we've got 70 add 50 add 10.

You've got to remember to add that regrouped ten as well.

That equals 130.

And 130 is regrouped into 1 hundred and 3 tens.

The 100 is moved into the hundreds column.

There's our 100 and there's our 30.

And lastly, I have to add together the hundreds.

100 add 100 add the regrouped 100 equals 300.

There is our answer, our sum.

So 177 add 156 equals 333.

Very well done if you've got the right answer.

Now, sometimes the ones or tens digits add to 10.

Jun says, "What's 289 add 271?" Let's write the calculation out.

289 add 271.

And we always start, of course, by adding the ones numbers together the first.

So 9 add 1.

Well, you probably know that 9 add 1 is a number pair that adds together to make 10.

So 9 add 1 equals 10.

Now, 10 is regrouped into 1 ten, and the 10 is moved into the tens column, and zero is written in the ones column.

9 add 1 makes 10 exactly, so it makes 1 ten, and there are no ones left over.

There are no extra ones.

Zero is written in the ones column.

Next we've got to add together the tens.

So we've got 80 add 70 add the regrouped 10.

80 add 70 add 10 equals 160.

160 is regrouped into 1 hundred and 6 tens.

The 100 is moved into the hundreds column.

So again, we've got there 160, so 6 tens in the tens column and the 100 goes in the hundreds column.

And lastly, in some ways the easiest bit, add together those hundreds.

Two hundreds add two hundreds add the regrouped hundred equals 5 hundreds.

289 add 271 equals 560.

Sometimes regrouping the ones means regrouping in the tens.

Let's take a look at an example.

So Jun's saying, "What's 257 add 446?" Let's take a look at that calculation.

And we can see straight away, 7 add 6, that's going to make a number larger than 10.

So we definitely got more than 10 ones.

And then we've got a tens column.

We've got 5 tens add 4 tens.

Well, 5 tens add 4 tens is only 9 tens.

So is there regrouping in the tens as well? Well, let's take a look.

Let's start off with our ones.

So we got 7 add 6.

7 add 6 equals 13.

And 13 is regrouped into 1 ten and 3 ones.

And the 10 is moved into the tens column.

So we've got here our 10 and our 3 ones.

Ah, can you see what's happened? So when we add the tens together, we've no longer got 9 tens, we have now got 10 tens.

50 add 40 add 10 equals 100.

The regrouping in the tens only happens because there were more than 10 ones.

So sometimes because you've regrouped in a different column, that means another column has to be regrouped as well.

50 add 40 add 10 equals 100.

We put the 100 in the hundreds column, and zero is written in the tens column.

There are no extra tens, there's just that 100.

And then lastly, add those hundreds together.

2 hundreds add 4 hundreds add the regrouped hundred equals 7 hundreds.

257 add 446 equals 703.

So here's a question for you to try on your own.

Use column addition to add together these numbers.

"So what's 228 add 175," says Jun.

So again, you might want to use paper and pencil.

You might want to use a whiteboard and a whiteboard pen to work out the answer.

Have a go at jotting down that calculation, see if you can work out the answer, and look really carefully at where you have to regroup.

So pause the video and have a go at that calculation.

And welcome back.

How did you get on? Did you get the right answer? Did you spot anything in that calculation? Let's take a look.

So let's start off by adding the ones numbers together first.

So 8 and 5 equals 13, and 13 is regrouped into 1 ten and 3 ones.

And the 10 is moved into the tens column.

So 10's put into the tens column and 3 is written in the ones column.

Next we've got to add together 20 and 70 and the extra 10.

So 20 add 70 add 10 equals 100.

And again the regrouping in the tens only happens because there were more than 10 ones.

So we add together our tens, we get 100, and zero is written in the tens column.

And lastly, let's look at those hundreds.

So 100 add 200 add the regrouped hundred equals 4 hundreds.

So 228 add 175 equals 403.

Very well done if you got the right answer and you spotted the regrouping in the tens only happens because we regrouped those ones.

Let's move on to task A.

So task A, calculate the sum of each pair of numbers.

And I think there should be regrouping in the tens and the ones in each of those.

So look really carefully, add those numbers carefully together.

And don't forget to add the regrouped ten and hundreds when you're calculating the sum of the tens and hundreds columns.

Here's part two of task A.

So again, calculate the sum of each pair of numbers.

Let's take a look at B quickly.

So we've got 157 add 144, and you can see there's regrouping in the ones.

7 add 4 equals 11.

So there will be a regrouped 10 as well.

In the tens column, we've got 50 and 40.

50 add 40 on its own equals 90, but we've got that regrouped 10 as well, so be really, really careful when you're calculating the sum of each pair of numbers there.

And then part three of task A.

So choose any two of these numbers, add them together.

How close to 500 can you make the sums? You're trying to get the sum as close to 500 as you possibly can.

You choose any two of those numbers? So pause the video and have a go at task A.

And welcome back.

Let's take a look at those answers.

So we've got here the answers for the first part of task A.

So 166 add 166 is equal to 332.

And there is some grouping there in the tens and the ones.

Okay? So have a good look at those answers for B and C as well.

And then let's move on to part two of task A.

So for some of these, there was only regrouping in the tens because there was regrouping in the ones.

So 157 add 144, because there are more than 10 ones, we end up having to regroup in the tens as well.

So 5 tens add 4 tens add that extra regrouped ten equals 10 tens altogether, so we end up putting a zero in that tens column and regrouping those 10 tens into 100, and that goes into the hundreds column.

So have a good look at those answers, see if you've got them right.

And then let's move on to part three of task A.

And very well done if you've got on to part three.

And here is the sum closest to 500 you could possibly make.

So it was 501.

And the two numbers you should have added together to get 501 were 243 and 258.

So very well done if you got close to 500, and excellent work if you got 501.

That was very, very well spotted indeed.

Let's move on to the second part of the lesson.

So the second part of the lesson is problem-solving with regrouping.

Done a little bit of problem solving already.

We've got a bit more to do in the second part of the lesson.

So Laura gives Jun a problem.

You may have spotted what is missing from the problem that Laura has given Jun already.

"What digits are missing from this column addition," says Laura.

There are two digits missing.

So Jun has to try and work out what the missing numbers are.

So let's start off by looking at the ones number first of all.

So we've got there 3 add something equals 10.

So the two numbers in the ones column have a sum of 10.

And Jun says, "The missing number must be 7." You can see there we've got 1 ten and zero ones.

And the two ones numbers add together to equal 10.

Jun knows the number pairs that equal 10, so he knows the missing number must be 7.

So 3 add 7 equals 10.

Well done, Jun.

Good start.

Now he's got to work out that missing tens number.

So we've got a 5 in 157.

We don't know what the tens number is in that first three-digit number.

Let's take a look.

So we've got there the two numbers add together to get a sum of 120.

We've got a regrouped 100 from the tens column, and we've also got the two extra tens as well.

So we've got 120, or 12 tens.

Jun says the tens numbers have a sum of 120.

50 add the regrouped 10, you've got to remember that regrouped 10 from the ones as well, is equal to 60.

So the missing tens digit is 6.

It must be 6 tens.

6 tens add 5 tens add 1 ten equals 12 tens.

60 add 50 add 10 equals 120.

So 263 add 157 equals 420.

Excellent work, Jun.

That's very well worked out.

And here's a problem for you to try on your own.

Calculate the missing digits.

Laura says, "What digits are missing from this column addition?" Pause the video and see if you can work out what ones number is missing and what tens number is missing.

And welcome back.

Did you manage to work out both missing numbers? Let's take a look, see if you've got them right.

So let's start off with the ones number first of all.

So we've got there the two ones numbers add together to make a total of 10.

Jun says, "The two numbers in the ones column have a sum of 10.

The missing number must be 5." There's a regrouped 10, isn't there, at the bottom of the column addition.

And there's a zero in the ones column.

So the missing number must be 5.

5 add 5 equals 10.

Let's take a look at the tens numbers next.

So we've got there a sum of 140.

We've got a regrouped 100 plus 4 tens, 140, or 14 tens altogether.

So the tens numbers have a sum of 140.

80 add the regrouped 10 is equal to 90.

We've got to remember there's a regrouped 10 from the ones as well.

So Jun says, "The missing tens digit is 5." 5 tens add 8 tens add 1 ten is equal to 14 tens.

Our missing digit is 5.

Very well done if you worked out both missing numbers.

Jun uses these number cards to make two three-digit numbers.

He uses column addition to add them together.

Jun says, "The sum of the two addends is 603." There's our sum, 603.

"I'm going to work out how Jun arranged the cards," says Laura.

So Laura is trying to work out what two three-digit numbers Jun made to get a sum of 603.

Laura starts by trying to complete the ones column.

There aren't two numbers with a sum of 3, so the sum must be 13.

and Laura says, "6 add 7 equals 13." So Laura's realised, of course, there aren't two numbers that Jun could have used to equal 3.

Laura jots down that regrouped 10 that she's going to make.

And she uses 6 and 7 in the ones column.

6 add 7 equals 13.

We've got a regrouped 10 and 3 ones.

The tens digits have a sum of 10.

So the digits she could use are 4 and 5, add the extra regrouped 1 equals 10 tens altogether.

Remember this number of tens that Laura is working out here.

So altogether that must equal 100.

So she jots down that regrouped 100 in the hundreds column.

And she uses the number cards 4 and 5 in the tens column.

4 tens add 5 tens add the regrouped ten equals 10 tens altogether, equals 100.

That means I can use 2 and 3 as the hundreds digits.

So 2 and 3 she puts in the hundreds column.

Add the regrouped 100 equals 600.

So 246 add 357 equals 603.

"Excellent work, Laura," says Jun.

She worked it out first time.

Jun gives Laura another challenge, this time the sum is 711.

And again, Jun has arranged those number cards into two three-digit numbers, added them together and has got a sum of 711.

Laura is going to try to work out how he's arranged those cards.

So Laura starts off by thinking, "Can't make one, can't just be 1 one, so it's got to be 11 ones altogether." So she's going to jot down that extra 10, that regrouped 10 in the tens column to remind herself there's an extra 10 as well.

And she's going to put 6 and 5 in the ones column.

6 add 5 equals 11, equals a 10 and a 1.

7 tens add 3 tens add the regrouped ten is equal to 11 tens.

So Laura jots down that hundred, and she uses the number card 7 and 3 in the tens column.

70 add 30 add the regrouped 10 is equal to 110.

And that means Laura can use 4 and 2 in the hundreds column.

4 hundreds add 2 hundreds add the regrouped hundred is equal to 7 hundreds.

4 hundreds add 2 hundreds add the regrouped hundred, of course, we've got from adding the tens together, and that equals 7 hundreds.

475 add 236 equals 711.

Excellent work again, Laura.

Work out the missing numbers.

So here's one for you to try on your own.

Jun says, "This time the sum is 630." How could Jun have arranged the number cards to get a sum of 630? So it might be helpful to have the number cards 2, 3, 4, 5, 6, and 7 to help you.

And you might want to play around with those, manipulate those cards, see if you can work out how Jun arranged them.

So pause the video and see if you can work out the answer.

And welcome back.

Did you manage to solve the problem? Let's take a look.

So here is one solution.

You may have solved the problem in a slightly different way 'cause there's different ways you could have rearranged those numbers.

So Laura says, "4 and 6 equals 10." So we could use the number cards 4 and 6 in the ones column.

7 tens add 5 tens add the regrouped 10 is equal to 13 tens.

So there are 13 tens, 10 of those tens are regrouped as 100 and moved into the hundreds column.

7 tens add 5 tens add the regrouped ten is equal to 13 tens, or 130.

And that means you could have used 2 and 3 in the hundreds column.

2 hundreds add 3 hundreds add the regrouped hundred is equal to 6 hundreds.

274 add 356 equals 630.

Very well done if you solved that problem.

And of course there is more than one solution, so your answer may have looked slightly different to that one, but very well done if you managed to get a sum of 630.

And let's move on to task B.

So first part of task B, you're going to calculate the missing digits.

You've got to find what digits are missing from each calculation.

So in A, there's a tens number missing and a ones number missing.

And look carefully to see if there are any regrouped tens or 1 hundred 'cause that will help you work out what the missing number is.

Here's part two of task B.

So find three ways to make this correct.

Look carefully to see whether you need to regroup.

So you can use any numbers in these at all, but you've got to make that sum correct.

So A, B and C are all exactly the same, but you've got to look for three different solutions.

So in that first number, we've got the tens digit missing.

And in the second number we've got the tens and the ones missing.

And in the sum, the ones number is missing.

And finally, use these number cards, see all the number cards there, 2 to 7.

And it might be really helpful to have the number cards actually available so you can move them around.

Make each of the sums below using each number card only once each time.

So you've got to make the sum 801 and 612 and 900.

So pause the video and have a go at task B.

And welcome back.

It's quite a lot of work to do there.

Lots of thinking, lots of problem solving.

But let's take a look to see if you got them right.

So here are the answers for the first part of task B.

So the first calculation, the answer was 166 add 145.

And those two numbers have a sum of 311.

For B, the missing digits were 8 and 7.

278 add 172 gives you a sum of 450.

So very well done if you managed to complete part one of task B.

Let's take a look at part two of task B.

Now, here are some possible answers.

You may have the cards in a different order.

Your answer could have been 399 add 356.

That would give you a sum of 755.

You may have done 379 add 371.

That would give you a sum of 750.

So very well done if you completed part two of task B.

And here are some possible answers for part three of task B.

And again, you may have solved these problems in a slightly different way.

To get a sum of 801, you could have added together the numbers 264 and 537.

To get a sum of 612, you could have used 245 add 367.

So very well done if you've got onto to part three of task B and you managed to solve some of those problems as well.

Excellent work.

And very, very well done on today's lesson.

Lots and lots of thinking going on, and you've worked really, really hard to answer questions where you've had to regroup ones and tens using column addition.

And very well done on the second part of the lesson as well, all those problems you had to solve, all those missing numbers, all those numbers you had to move around to try and find a sum.

Very well done today.

And finally, let's move on to our lesson summary.

So when using column addition, start by adding the numbers with the smallest place-value first.

If the sum of the ones or tens numbers is 10 or greater, regrouping is needed.

Any complete tens are regrouped into the tens column and any complete hundreds are regrouped into the hundreds column.