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I can use column addition to add numbers by regrouping tens.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

When using column addition, start by adding the numbers with the smallest place value first.
If the sum of the tens digits is ten or greater, regrouping is needed.
Any complete hundreds are regrouped into the hundreds column.

Common misconception

Pupils may forget to add the 'regrouped' hundred when calculating the total for the hundreds column.

Model regrouping and finding column totals clearly, reminding pupils to add together all of the numbers in the column to get the total.

Keywords

Column addition - Column addition is a way of adding numbers by writing a number below another.
Regroup - The process of unitising and exchanging between place values is known as regrouping.

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Hello there.

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

And here is our learning outcome.

I can use column addition to add numbers by regrouping tens.

And you may want to have some paper and a pencil or a whiteboard and a whiteboard pen and maybe even some base 10 blocks to help you with learning today.

And here are the keywords.

So I'm going to say the keywords, can you repeat them back? So the first key words are column addition and the next keyword is regroup.

And 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 is our lesson outline.

So the first part of the lesson is regrouping tens with two-digit numbers.

And the second part of the lesson is regrouping tens with three-digit numbers.

Let's get started.

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

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

\"What happens when the sum of the tens digits is 10 or greater?\" asked Jun.

So here, we've got an example of a column addition where the sum of the tens numbers is greater than 10.

So 60 add 50 gives a sum greater than 100.

6 tens add 5 tens, it's more than 10 tens.

Laura says, \"We have to use regrouping to help get the answer.\" Laura uses base 10 blocks to represent the problem.

\"First, I'm going to represent 64 and 55 using base 10 blocks.\" So here, we've got 64 and 55.

Now, we always add the numbers with the smallest place value first.

So we've got there 4 add 5 equals 9.

No regrouping yet because the numbers are smaller than 10.

6 tens add 5 tens equals 11 tens.

So next, Laura adds the tens together.

We've got 6 tens, add 5 tens, and that equals 11 tens.

And this is where we got to use some regrouping.

The 11 tens can be regrouped as one hundred and one ten.

10 tens, of course, are equal to 100.

The 100 is moved into the hundreds column.

The tens get regrouped as 100 and 10, and that hundred gets moved into the hundreds column.

Jun says, \"64 add 55 equals 119.\" We got that 100, add a 10 and 9 ones, 119.

Laura represents the problem 73 add 65 using base 10 blocks.

So Laura's going to add together two different numbers using column addition, and she's going to represent the numbers using base 10 blocks.

So, \"First, I'm going to represent 73 and 65 using base 10 blocks,\" says Laura.

There's 73 and there is 65.

We always add the numbers with the smallest place value first.

3 add 5 equals 8.

So 3 ones add 5 ones equals 8 ones.

No regrouping yet.

Number isn't larger than 10.

7 tens add 6 tens equals 13 tens.

We now need to do some regrouping 'cause we've got more than 10 tens.

The 13 tens can be regrouped as one hundred and three tens.

The hundred is moved into the hundreds column.

Let's regroup them into a hundred and three tens.

And that 100 gets moved into the hundreds column.

And that gives us our answer.

73 add 65 equals 138.

One hundred, three tens, and eight ones.

Laura shows Jun how to add two-digit numbers using column addition.

\"I'm going to add together 65 and 63.\" So this time, Laura isn't going to use base 10 blocks to help her.

She's just going to write the numbers as column addition.

We've got 65, and underneath it, in the same columns, we've got 63.

And again, as always, we start with the numbers with the smallest place value first.

5 add 3 equals 8.

Then we've got to add together 6 tens and 6 tens, or 60 add 60.

And you probably know what double six is.

Wonder what double six is.

60 add 60 equals 120.

120 is regrouped into one hundred and two tens.

The hundred is moved into the hundreds column.

You write the two tens in the tens column and the hundred goes underneath the line in the hundreds column.

And we write it underneath because later, when you add together two three-digit numbers, you'll have some hundreds to add together as well.

Now, there are no hundreds except that regrouped 100.

1 is written in the hundreds column.

65 add 63 equals 128.

Laura shows Jun another example of adding together two two-digit numbers.

This time, Laura adds together 75 and 51.

And again, Laura sets it out with 75 above 51.

And as always, we start with the numbers with the smallest place value first, so five add one, first of all.

Five add one equals six.

And we've got to add together seven tens and five tens, 70 add 50.

70 add 50 equals 120.

And again, 120 is regrouped into one hundred and two tens.

The hundred is moved into the hundreds column.

So two tens is written in the tens column and the hundred is written underneath the line in the hundreds column.

And there are no hundreds except the regrouped hundred, so one is written in the hundreds column.

And that gives us the answer, 126.

Use column addition to add together these two digit numbers.

So add together 73 and 44.

How would you add those numbers together? I think there's going to be some regrouping required isn't there in the tens? But this is your time to get some paper and a pencil or a whiteboard and a pen or base 10 blocks and have a go trying to work out the answer to that question.

Pause the video, see if you can find the answer.

And welcome back.

How did you get on? Did you find the answer? Let's have a look to see if you did it correctly.

So let's start off by adding together three add four.

Three add four equals seven.

There's no grouping in the ones, number isn't above 10.

Then we go down together seven tens and four tens, 70 and 40.

70 and 40 equals 110.

110 is regrouped into one hundred and one ten.

And the hundred is moved into the hundreds column.

So one ten and one hundred.

That one hundred is written underneath the line in the hundreds column.

And then we've just gotta work out how many hundreds there are.

Now, there are no other hundreds except the regrouped 100, so one is written in the hundreds column.

The answer is 117.

73 add 44 equals 117.

Very well done if you got that as the answer.

Jun wonders what happens when there are exactly 10 tens.

Let's add together 83 and 26 as Laura may have put there as eight tens and two tens.

Adding those together, eight to two, of course, equals 10.

So Laura sets out the column addition of 83 above 26.

Start with the ones, first of all.

So three add six equals nine.

No regrouping.

And we've got to add together 80 and 20, eight tens and two tens.

80 of 20 equals 100.

The hundred is moved into the hundred column and zero is written in the tens column.

There are no extra tens, there is just a hundred.

And there are no other hundreds except the regrouped 100.

So one is written in the hundreds column that gives us the answer.

So 83 add 26 equals 109.

Use column addition to calculate 65 add 42.

There's 65 add 42 set out as a column addition.

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

You may want to use a whiteboard and pen.

You may want to use base 10 blocks.

Have a go at trying to work out the answer to 65 and 42.

Pause the video.

Can you find the answer? And welcome back.

Let's see how you got on.

So first of all, you should have added together five and two.

So five add two equals seven.

Seven ones.

Then you've got to add together 60 and 40, six tens add four tens.

60 add 40 equals 100.

So the hundred is moved into the hundred column and zero is written in the tens column.

So zero gets written here and the hundred gets moved across here.

There are no hundreds except the regrouped hundred.

So one is written in the hundreds column.

So 65 and 42 equals 107.

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

Let's move on to task A.

So in task A, you're going to calculate the sum of each pair of numbers.

And you probably have noticed there is some regrouping going on in those tens as part two of task A.

So calculate the sum of each pair of numbers.

And again, there's still regrouping in the tens, but it looks like there are 10 tens each time.

And then part three, choose any two of these numbers.

How many ways can you make a sum of 137? Choose two numbers.

Can you make them add up to be equal to 137? And there are three different ways to find the answer.

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

And welcome back.

And let's take a look to see how you got on.

So here are the answers for part one of task A.

So 65 add 62, the answer was 127.

71 add 56, the answer was also 127.

And 66 and 52, the answer was 118.

Well done if you completed part one of task A.

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

So this time, the tens numbers added to make 100 exactly.

So 41 add 62 equals 103.

92 add 17 is equal to 109.

Again, well done if you manage to complete part two of task B.

And here are the answers for part three of task B.

So this time, the target number was 137 and you had to choose two numbers to equal 137.

So 62 and 75, add together to equal 137.

91 add 46 is equal to 137.

And 83 add 54 is also equal to 137.

Very well done if you completed part three of task A.

That was quite tricky.

And let's move on to the second part of the lesson.

So the second part of the lesson is regrouping tens with three digit numbers.

Laura uses column addition with three-digit numbers.

\"I'm going to add together 183 and 164,\" says Laura.

So she writes 183, and underneath, she writes 164, making sure she writes the numbers in the correct columns.

She starts by adding together the ones numbers first, so three add four equals seven.

So three add four equals seven.

There are seven ones.

Eight tens add six tens equals 14 tens.

Four is written in the tens column.

So four is put into the tens column.

And 10 of the tens are regrouped into one hundred and moved into the hundreds column.

And this is why it was important.

We practised writing that one underneath the line because this time, there are more than 100.

One hundred at one hundred add the regrouped hundred equals three hundreds.

So altogether, there are three hundreds.

So 183 add 164 is equal to 347.

Let's take a look at another example.

So again, Laura is going to use column addition to add together two three-digit numbers.

This time, she's going to add together 285 and 171.

So again, Laura sets it out very carefully, making sure she writes the numbers underneath each other in the correct columns.

Starts off by adding the numbers with the smallest place value first.

Five add one equals six.

Then Laura has got to add together the tens and here is where she's got to do some regrouping.

We've got there eight tens add seven tens.

Eight tens add seven tens equals 15 tens.

So five is written in the tens column.

10 tens are regrouped into one hundred and moved into the hundreds column.

So 100 is written in the hundreds column.

\"Two hundreds add one hundreds, add the regrouped 100, equals four hundreds,\" says Jun.

Altogether, we've got four hundreds.

So 285 add 171 equals 456.

Now, it's time for you to have a go at adding together two three-digit numbers.

So Laura says, \"Add together 273 and 273.\" So make sure when you write it out, sit down really carefully, make sure you write the numbers in the right columns.

The ones, the tens and the hundreds, all in the right places.

And you've gotta add the numbers together.

So use paper and pencil or a whiteboard and a whiteboard pen.

See if you can work out the answer to 273 add 273.

Pause the video.

Can you find the answer? And welcome back.

Let's take a look at the answer, see if you've got it right.

So hopefully, started off by adding together the ones numbers.

So three add three equals six.

No regrouping there at all.

And then you had to add together seven tens and seven tens.

Seven tens add seven tens equals 14 tens.

70 add 70 equals 140.

So four is written in the tens column.

10 tens are regrouped into one hundred and moved into the hundreds column.

So 70 add 70 equals 140.

The hundred is written in the hundreds column.

And the 40 is written in the tens column.

Two hundreds add two hundreds, add the regrouped hundred, equals five hundreds.

So altogether, there are five hundreds.

So 273 add 273 is equal to 546.

Excellent work if you've got the right answer.

Laura challenges Jun with this puzzle.

\"What's the missing tens number?\" asks Laura.

Jun looks carefully and he says, \"There's a hundred regrouped in the hundreds column.

There are 12 tens altogether.\" So altogether, there are 12 tens or 120.

\"So a number add 30 equals 120,\" says John.

To find a missing part, subtract the other part from the whole.

So Jun thinks I start with 120 and I subtract 30, I will get the answer, I'll get the missing number.

So 120 subtract 30 is 90.

So the missing number there must be 90.

30 add 90 equals 120.

Three tens add nine tens is equal to 12 tens.

Pat on Jun for finding the missing number.

132 add 192 equals 324.

Oh dear.

Laura's challenges get more difficult, don't they? So Laura challenges Jun with another puzzle.

What are the missing numbers? So Jun's gotta find a missing hundreds number.

He's also gotta find a missing tens number.

And again, John looks really carefully and he says, \"There's a hundred regrouped into the hundreds column.

There are 16 tens altogether.\" So we've got there a hundred regroup from the tens and we've got another six tens as well.

So there are 16 tens altogether.

Now, one of the numbers is eight in the tens column.

So eight tens add how many tens equals 16 tens.

So what number add 80 equals 160? Jun says, \"I know eight add eight equals 16.

So 80 add 80 equals 160.\" Eight tens add eight tens equals 16 tens.

So missing number there is eight.

This parts have the tens number.

He's now gotta work out the hundreds number that's missing.

I think that's actually easier to work out.

\"There are six hundreds altogether,\" says Jun.

One add two add something equals six.

So we've gotta regrouped hundred.

And there's also two hundreds in the 287.

And added to the missing number, that makes six hundreds altogether.

So the missing digit must be three.

Three hundreds add two hundreds add one hundred equals six hundreds.

Pat on Jun for finding both missing numbers.

381 add 287 equals 668.

And here's one to try on your own.

So calculate the missing numbers.

There's a hundred number missing.

There's also a missing tens number.

\"What are the missing numbers?\" says Laura.

So have a good think.

Have a good look at that column addition.

Can you work out what the missing numbers are? You might want to use paper and pencil or a whiteboard or whiteboard pen to help you work out the answer.

But pause the video and see if you can work out what the missing numbers are.

And welcome back.

Did you manage to find the missing numbers? Let's take a look to see whether you were right.

So Jun says, \"There's a hundred regrouped in the hundreds column.

There are 11 tens altogether.\" So I hope you spotted that.

So we've got there a hundred's been regrouped from the tens, and there's another 10 there as well, so altogether there are 11 tens or 110.

So 70 at what number equals 110 or seven tens add how many tens equals 11 tens.

Jun says, \"Seven tens add four tens is equal to 11 tens.\" So there are four tens missing.

And then Jun says, \"There are five hundreds altogether.

One add two add our missing number equals five.

The missing digit is two.\" Two hundreds add two hundreds add one hundred is equal to five hundreds.

273 add 242 equals 515.

Very well done if you've managed to find both missing digits in that column addition, because that was quite a tricky problem.

And let's move on to task B.

So the first part of task B, you've got to calculate the sum of each pair of numbers.

And again, look really carefully to see where you need to regroup.

Part two, gotta calculate the missing numbers.

So that first one, we've got a tens number missing.

And B, there's another tens number missing.

And in C, there's a tens number missing and a hundred number missing.

So really carefully have a really good think and see if you can work out what the missing number is.

And then lastly, find three different ways to make these calculations correct using different digits each time.

So we've got two hundreds and two ones add two hundreds and two ones, what could the tens numbers be? Have really good think and look really carefully at each column addition and see if you can work out what the tens numbers could be.

There are at least three different ways of working out the answer.

And there's a second part two, part three as well.

So there are three different column additions.

Can you work out three different ways to make them correct using different digits each time? They've all got the same number of hundreds and ones in them.

Can you work out what the tens numbers could be? And again, have a really, really good look.

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

And welcome back.

Let's take a look at those answers.

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

So calculate the sum of each pair of numbers.

So 162 add 165, the answer was 327.

Add those six tens add six tens are equal to 12 tens, or 120.

So you had to regroup 10 of those tens into 100.

Well, I don't know if you've managed to answer part one of task B correctly.

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

So in this one, you had to calculate the missing numbers.

So in A, the missing number was four, four tens.

Four tens add nine tens is equal to 13 tens.

B, we've got two tens was the missing number.

80 add 20 is equal to 100.

We've got their 10 tens altogether.

And then C, there were four tens missing.

40 add 60 equals 10 tens or 100.

We got there a hundred be regrouped into the tens column.

And then there were six hundreds missing altogether.

Six hundreds add one hundred add one hundred is equal to 800.

Very well done if you got onto to part two and managed to solve those problems. Let's take a look at part three.

So we've got there three different solutions.

We've got 272 add 272 is equal to 544.

You could have had 282 add 262.

You could have had 292 add 252.

Here are the answers for part three B.

So you may have done 374 add 161, that is equal to 535.

384 add 151, that is equal to 535.

And 394 add 141, that is also equal to 535.

And each time, there were 13 tens altogether.

So the number of tens you put in had to be equal to 130.

So very well done if you've got onto to part three.

And excellent work if you completed part three.

And hopefully, from today's lesson, you're feeling much more confident with using column addition to regroup tens with two-digit numbers and three-digit numbers.

Very well done today for working so hard.

Excellent work.

And finally, let's take a look at the lesson summary.

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

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

And any complete hundreds are regrouped into the hundreds column.

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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491238%2Foprxzm6h29zfm6pofvmf.png&w=640&q=75", "imageKey": "801476a5-acba-d5ab-6fbf-d348db7e8cc7/question/bd5c7a7b083e7fd27064892dd7e08d27.png" }, "questionType": "Short answer", "correct": [ { "text": "755" }, { "text": "seven hundred and fifty-five" } ], "id": "7ce731b0-966e-e1c0-8d29-efab32c6b736", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "What is the value of the digit 7 in this column addition?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491240%2Fyswe6agl1vw2fyprstjo.png&w=640&q=75", "imageKey": "801476a5-acba-d5ab-6fbf-d348db7e8cc7/question/0387515ff95acd9cd343ccd1083bf91c.png" }, "questionType": "Short answer", "correct": [ { "text": "70" }, { "text": "seventy" } ], "id": "a72af083-3f94-1842-2fe7-423a24752e31", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "What number is missing from this column addition? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491240%2Fuxky7ynjfi4ger6sfuk5.png&w=640&q=75", "imageKey": "801476a5-acba-d5ab-6fbf-d348db7e8cc7/question/ae19386c617aa45c3815e2e0f2441c88.png" }, "questionType": "Short answer", "correct": [ { "text": "6" }, { "text": "six" } ], "id": "e1fa533a-d2b5-dad0-501b-cf44bf36524f", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" } ], "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Column addition", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Use column addition to add numbers by regrouping tens" } }, { "id": "d731d647-50ed-9499-7761-d0fa740360e9", "type": "Resource", "resourceType": "Quiz", "title": "Use column addition to add numbers by regrouping tens", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "150 can be regrouped into…" }, "questionType": "Multiple choice", "correct": [ { "text": "1 hundred and 5 tens" } ], "choices": [ { "text": "1 ten and 5 hundreds" }, { "text": "1 ten and 50 ones" }, { "text": "1 hundred and 5 ones" }, { "text": "1 hundred and 5 tens" } ], "id": "b2a9872d-bfb9-9560-521e-94a0ad0792fb", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "Match each tens numbers to the correct regrouping. " }, "questionType": "Matching", "pairs": [ { "left": { "text": "240" }, "right": { "text": "2 hundreds and 4 tens" } }, { "left": { "text": "420" }, "right": { "text": "4 hundreds and 2 tens" } }, { "left": { "text": "440" }, "right": { "text": "4 hundreds and 4 tens" } } ], "id": "01d19826-4671-2515-8f28-a4d2de666019", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "Calculate the missing sum.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491237%2Fjuggkyvsrwxmcuhx4zxw.png&w=640&q=75", "imageKey": "d731d647-50ed-9499-7761-d0fa740360e9/question/d885736af05be253aff9275f4018bf4a.png" }, "questionType": "Multiple choice", "correct": [ { "text": "127" } ], "choices": [ { "text": "217" }, { "text": "127" }, { "text": "107" }, { "text": "67" } ], "id": "59d6986b-c834-0f75-b597-ecf04d26cc8c", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "What tens digit is missing from this column addition? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491237%2Fubdkulg1xkc53ukhr9ej.png&w=640&q=75", "imageKey": "d731d647-50ed-9499-7761-d0fa740360e9/question/0ce4e03c88c7ccb1539a2c2f8daf54aa.png" }, "questionType": "Short answer", "correct": [ { "text": "2" }, { "text": "two" } ], "id": "7738e87a-f889-3dbd-26ba-2e19c44e1e15", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "What is the missing tens digit? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491237%2Fickm3w1eialxkzabzbma.png&w=640&q=75", "imageKey": "d731d647-50ed-9499-7761-d0fa740360e9/question/17525131b9d236cc6f38179a568204f1.png" }, "questionType": "Short answer", "correct": [ { "text": "0" }, { "text": "zero" } ], "id": "ce560961-31f9-8a50-a7a6-428c2c539df5", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" }, { "type": "Question", "question": { "text": "What is the missing tens digit? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707491238%2Ffdsmpdjyohcu9w1yqunc.png&w=640&q=75", "imageKey": "d731d647-50ed-9499-7761-d0fa740360e9/question/6fba1771eae6c51a58ce1a2feb928c99.png" }, "questionType": "Short answer", "correct": [ { "text": "7" }, { "text": "seven" } ], "id": "dc8ba0a7-ad4d-7035-442c-14c6546d5292", "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe" } ], "lessonId": "1cafed3c-5f84-bd14-c4c4-5bcf0db6a3fe", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 3", "topic": null, "unit": "Column addition", "lessonCount": "10", "age": [ 7, 8 ], "gradeId": "age_7_8", "gradeStage": "Key Stage 2", "lesson": "Use column addition to add numbers by regrouping tens" } } ] }