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

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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

Start with the ones column so that regrouping can be represented
If the sum of the ones digits is ten or greater, regrouping is needed
Any complete tens are regrouped into the tens column

Common misconception

Pupils may regroup incorrectly, forget to write the regrouped ten or forget to add any regrouped tens when calculating the total for the tens column.

Emphasise that the regrouped number is a ten and that it needs to be added to the tens total. If necessary, revisit the use of base ten blocks.

Keywords

Column addition - Column addition is a way of adding numbers by writing a number below another.
Regroup - Regroup means moving an amount to make a calculation easier.

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Hello there, my name is Mr. Goldie and welcome to today's math lesson.

And here is our lesson outcome.

I can use column addition to add numbers by regrouping ones and it would be helpful today to have some paper and a pencil or a whiteboard and a pen and you might also want to have some base 10 blocks ready as well.

And here are our keywords for today's lesson.

I'm going to say each of the keywords, can you repeat them back? The first keywords are column addition.

And the other 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 ones can be regrouped one 10 and one 10 can be regrouped for 10 ones.

And here is our lesson outline.

So the first part of the lesson is regrouping with two-digit numbers and the second part of the lesson is regrouping with three-digit numbers.

Let's get started.

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

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

\"What happens when the sum of the ones numbers is 10 or greater?\" says Jun.

Here we've got an example of a calculation where the sum of the ones numbers is greater than 10.

Six add five gives a sum greater than 10.

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 26 and 35 using base 10 blocks.

So here we've got 26 and here we've got 35.

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

Six add five equals 11.

So Laura adds together the six and the five to get 11.

11 is regrouped into one 10 and one one.

The 10 is moved into the tens column.

So Laura's got a sum there of 11 ones and she said, \"You can regroup the 11 into a 10 and a one.\" Let's regroup them.

So 11 can also be represented like this.

But now we've got a 10 in the ones column, so that 10 we're going to move across into the tens column.

So the 10 is regroup into the tens column, but it's moved underneath that bottom line.

Laura says, \"Two tens add three tens, add the regrouped 10 equals six tens.\" So altogether there are six tens, two tens and three tens, add the regrouped 10 that we got from the ones and that is equal to six tens.

So 26 add 35 equals 61.

We've got six tens and one on, that is equal to 61.

Laura represents another problem using base 10 blocks.

First I'm going to represent 34 and 38 using base 10 blocks.

Here we've got 34, three tens and four ones.

And here we've got 38.

So Laura's going to add those two numbers together.

We always add the numbers with the smallest place value first, and the reason we do that is because of regrouping.

So four add eight equals 12.

So Laura adds together the four and the eight and gets a sum of 12.

Four add eight is equal to 12.

Now, 12 is regrouped into one 10 and two ones and the 10 is moved into the tens column.

So let's regroup them first of all into a 10 and two ones.

Let's move that 10 into the tens column.

And then three tens, add three tens, add the regrouped 10 equals seven tens.

So remember to add that regrouped 10 as well.

So the answer is seven tens.

Three tens add three tens, add one 10 is equal to seven tens.

Jun says, \"34 add 38 equals 72.\" Laura shows Jun how to add two-digit numbers using column addition.

So this time, Laura is not going to use the base 10 blocks to help her.

\"I'm going to add together 37 and 46,\" says Laura.

So Laura represents column addition like this.

She's got one number written below another.

And of course, we always start with the numbers with the smallest place value first.

So Laura adds together seven and six first of all.

Seven add six is equal to 13.

13 is regrouped into one 10 and three ones and the 10 is moved into the tens column.

So Laura writes the three ones in the ones column, the 10 ones is regrouped as a 10 and moved into the tens column.

And then three tens add four tens, add the regrouped 10 equals eight tens.

So Laura has to remember to add that regrouped 10 as well.

So the answer is eight tens.

Three tens add four tens, add one 10 equals eight tens.

So Jun says, \"37 add 46 equals 83.\" Laura shows Jun how to add another pair of two-digit numbers using column addition.

So this time Laura's going to add together 58 and 27.

So she sets it out as column addition with one number written below another.

So first of all, Laura has to add together the ones numbers.

So eight add seven equals 15.

15 is regrouped into one 10 and five ones and the 10 is moved into the tens column.

So the five ones is written in the ones column, the 10 ones is regrouped as a 10 and written in the tens column.

So you got there one lot of 10.

And then Laura has time to get to the tens.

Five tens add two tens, add the regrouped 10 equals eight tens.

Five tens add two tens, add one 10 equals eight tens.

So 58 add 27 equals 85.

Use column addition to add together these two-digit numbers.

So add together 28 and 23.

This is where you might want to use paper and pencil or a whiteboard and whiteboard pen.

Have a go at trying to work the answer to that calculation, setting it out like Laura has written it there.

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

And welcome back.

How did you get on? Let's have a look, see if you got the right answer.

So first of all, you should've started by adding together the eight and the three.

Eight add three equals 11 and 11 is regrouped into one 10 and one one, and the 10 is moved into the tens column.

There we have one one written in the ones column and the 10, the 10 ones are regrouped as a 10 and put into the tens column.

Two tens add two tens, add the regrouped 10 equals five tens.

There we have our answer.

So 28 add 23 equals 51.

Very well done if you managed to get the right answer and you remembered to regroup that 10 and you remembered to add it to the other tens as well.

Excellent work.

Jun wonders what happens when the ones numbers add to ten exactly.

\"Let's add together 38 and 52,\" says Laura.

Now, Laura's chosen those numbers, because the ones numbers add together to make 10 exactly.

Laura sets it up as a column addition, 38 add 52.

And again of course, she starts by adding the ones numbers first.

Eight add two equals 10.

The 10 is moved into the tens column and zero is written in the ones column.

So those 10 ones are regrouped as a 10 and moved into the tens column.

That leaves us with a zero in the ones column.

Three tens add five tens, add the regrouped 10 equals nine tens.

There we have our answer.

So 38 and 52 equals 90.

So where those one numbers add up to make 10 or a multiple of 10, you should end up with a zero in that ones column.

Jun adds together two two-digit numbers.

Watch his process.

\"I'm adding 47 and 33 together,\" says Jun.

So Jun sets it up as a column addition, 47 add 33.

First of all, he starts by adding the ones.

Seven add three equals 10.

The 10 is moved into the tens column and zero is written in the ones column.

Jun writes zero in the ones column and he regroups that 10, those 10 ones, into a 10 and writes it in the tens column.

Four tens add three tens equals seven tens.

So Jun gets the answer, 70.

Has Jun calculated the correct answer? What do you think? Pause the video and see if you can work out if Jun has done it right or whether he has made a mistake.

And welcome back, how did you get on? Did you manage to spot a mistake or do you think Jun has done it perfectly and got the right answer? Let's take a look.

Laura says, \"Sorry, Jun, you forgot to add the 10 regrouped from the ones.\" \"Oh,\" says Jun, \"Four tens add three tens, add one 10 equals eight tens, the sum is 80.\" So Jun should've added on that regrouped 10 as well.

So the answer should've been 80.

Very well done if you spotted Jun's mistake there and I hope you don't make the same mistake as Jun when you are calculating today.

So here is task A.

You're gonna calculate the sum of each pair of numbers.

So don't forget, if there are more than 10 ones, you've gotta regroup them as a 10.

Don't forget to add them when you are adding the tens later on.

Now, here's part two of task A.

So you may have spotted there, sometimes the ones numbers add together to make 10.

And here is part three of task A.

So you're gonna choose two of these numbers, how many ways can you make a sum of 72? So you're looking for two numbers that add together to make 72.

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

And welcome back and I hope you got on well with task A.

Let's take a look at those answers.

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

So 49 add 12 is equal to 61.

And hopefully you remembered to regroup 11 as one 10 and one one and you remembered to add that regrouped 10 when you were adding the tens together.

Very well done if you got the right answers there.

Here are the answers for part two of task A.

45 add 35 is equal to 80.

59 add 39, well, nine add nine is a double, isn't it? Nine add nine equals 18, so the answer there would've been 98.

So very well done if you got on to part two of the task A.

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

So you gotta choose two of the numbers and you were looking for different ways you could get a sum of 72.

And there are the three ways you could've ended up with a sum of 72.

So 34 add 38 equals 72.

47 add 25 equals 72 and 56 add 16 equals 72.

Very well done if you got the right answers there.

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

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

Laura uses column addition with three-digit numbers.

I'm going to add together 148 and 136.

So Laura writes the two numbers out with one number underneath the other.

So Laura needs to start with the numbers with the smallest place value first.

So eight add six equals 14.

The 10 is moved into the tens column and four is written in the ones column.

So eight add six equals 14.

So there's four in the ones column and those 10 ones are regrouped as a 10 and written underneath the tens column.

Four tens add three tens, add the regrouped 10 equals eight tens.

And four add three, add one equals eight.

Four tens add three tens, add one 10 equals eight tens.

\"One hundred add one hundred equals two hundreds,\" says Jun.

So 100 add 100 equals 200 and we have our answer.

148 add 136 equals 284.

Laura adds together two different three-digit numbers.

So this time, Laura is going to add together 328 and 119.

So 328 add 119.

And again, you've probably spotted that the ones numbers add together to make a sum greater than 10.

So eight add nine equals 17.

So the 10 is moved into the tens column and seven is written in the ones column.

So eight add nine equals 17, and there's the seven in the ones column and those 10 ones are regrouped as a 10 and written in the tens column.

Two tens add one ten, add the regrouped 10 equals four tens.

And then three hundreds add one hundred equals four hundreds.

So 328 add 119 equals 447.

Use column addition to add three-digit numbers together.

So add together 235 and 125.

So pause the video and have a go at adding those two numbers together and see if you can get the right answer.

How did you get on? Did you get the right answer? Let's take a look to see whether you were right.

So first of all, we start with the numbers with the smallest place value first.

So five add five equals 10 and the 10 is moved into the tens column and zero is written in the ones column.

So five add five equals 10 and then the zero is put in the ones column, those 10 ones are regrouped as a 10 and written in the tens column.

Three tens add two tens, add the regrouped 10 equals six tens.

And then two hundreds add one hundred equals three hundreds.

235 add 125 equals 360.

Very well done if you got the right answer.

Laura challenges Jun to find the missing number.

\"What's the missing ones number?\" she says.

Jun says, \"There's a 10 regrouped in the tens column.

So the ones numbers have a sum of 13.\" And we've got there five add another number equals, well, it can't equal three, can it? So it must equal 13.

So what number adds to five to equal 13? And there's our regrouped 10.

So what number added to five equals 13? \"To find a missing part,\" says Jun, \"Subtract the other part from the whole.\" So 13 subtract five equals eight.

So the missing number must be eight.

135 add 128 is equal to 263.

Laura challenges Jun to find the missing numbers.

This time there are two missing numbers.

There's a missing tens number, there's also a missing ones number.

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

Jun looks carefully again and he spots there's a 10 regrouped into the tens column.

The ones numbers have a sum of 10.

There's a zero written in the ones column, but there's a 10 regrouped into that tens column.

So two ones numbers must have a sum of 10.

So four add what number equals 10? \"Ah, something add four equals 10,\" says Jun.

\"I can use number pairs that total 10 to work that out.\" So six, four add six is equal to 10.

So the missing ones number must be six.

And then Jun needs to work out the missing tens number.

There are eight tens altogether.

There's one 10 in 116, there's a regrouped 10 and there's also our missing number.

So one add one, add what number equals eight? Well, the missing tens digit must be six.

Eight subtract one, subtract one equals six.

264 add 116 equals 380.

Calculate the missing numbers.

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

What's the missing tens number? What's the missing ones number? And again, you might want to write the calculation out to help you try and find the answer.

Look really carefully.

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

And welcome back, did you manage to work out what the answers are? Again, let's take a look and see whether you were right.

So Jun says, \"There's a 10 regrouped into the tens column.

So the ones numbers have a sum of 12.\" We got two ones and the regrouped 10, there are 12 ones altogether.

So six add what other number is equal to 12? Must be six.

Something add six equals 12.

The missing ones digit is six.

So six add six is equal to 12.

So Jun's worked out the missing ones number.

Hopefully you got the same ones number.

And he's got to look at the missing tens number.

There are nine tens altogether.

The missing tens digit is four.

Four add four, add the regrouped 10 remember, is equal to nine tens.

So the missing tens digit is four.

So 146 add 246 is equal to 392.

Very well done if you managed to work out both missing numbers.

And here is task B.

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

So add those numbers carefully together and see if you can work out what the missing sum is.

There will be some regrouping in those ones.

Part two, calculate the missing numbers.

So can you work out what numbers are missing from those calculations? Look really carefully to see if there's a regrouped 10 anywhere.

And lastly, part three of task B.

So choose two of these numbers.

How many ways can you make a sum of 453? So there are three different ways you're looking for, two of those numbers add together to make 453 and there are three possible answers.

Can you find all three of them? And there will be some regrouping going on as well.

Be really careful about the numbers that you choose.

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

And welcome back and let's take a look at those answers to see how you got on.

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

So 127 add 117 has a sum of, is equal to 244.

In all of those column additions you've had to regroup the ones to make a 10.

On that last one, see, we've got seven add three equal 10.

So of course, we end up with a zero in that ones column.

So very well done if you did part one of task B.

Here are the answers for part two of task B.

So these are our missing numbers.

So for that first one, for A, the missing digit was eight ones.

Eight and four is equal to 12 ones.

For C, there was a missing ones, tens and a missing hundreds number.

So seven was the missing ones number.

Seven add nine is equal to 16 ones.

The missing tens number was four.

Four tens add three tens, add one 10 is equal to eight tens.

And then the missing hundreds number, the missing hundreds digit was two.

Six hundreds add two hundreds equals eight hundreds.

So well done if you did part two of task B.

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

So 228 and 225 have a sum of 453.

147 add 306 is also equal to 453.

And finally, 339 and 114 has a sum of 453.

So very well done if you managed to find all three different ways of making 453.

And excellent work in today's lesson and hopefully you're feeling much more confident at regrouping ones when you have to do column addition.

Excellent work today, very well done indeed.

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

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

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

Any complete tens are regrouped into the tens column.

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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707153482%2Fqno0d79aqbrhjiyx1ppw.png&w=640&q=75", "imageKey": "6ed7642d-de7d-e1e9-cf9d-6de1fd43796e/question/423a4075c656d79196a740010ac51d3a.png" }, "questionType": "Short answer", "correct": [ { "text": "50" }, { "text": "fifty" } ], "id": "98b5103b-d291-30d4-f8f5-3378bd3e7158", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "type": "Question", "question": { "text": "What is the missing addend in the column addition? 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", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707153483%2Fdar526cdi4xv5a57v3d6.png&w=640&q=75", "imageKey": "6ed7642d-de7d-e1e9-cf9d-6de1fd43796e/question/af507585f0361c37e03a0d18720796bc.png" }, "questionType": "Short answer", "correct": [ { "text": "234" }, { "text": "two hundred and thirty-four" } ], "id": "8a4a5668-6c11-a3bc-fb6d-cdb760802b5b", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" } ], "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41", "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 ones" } }, { "id": "39878ffb-abd5-88dd-4620-88a727f36c9e", "type": "Resource", "resourceType": "Quiz", "title": "Use column addition to add numbers by regrouping ones", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "13 can be regrouped into…" }, "questionType": "Multiple choice", "correct": [ { "text": " 1 ten and 3 ones" } ], "choices": [ { "text": "1 ten and 5 ones " }, { "text": "3 tens and 1 one" }, { "text": " 1 ten and 3 ones" } ], "id": "d63fb351-e852-ebfe-35c8-5e1c5ee7c568", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "type": "Question", "question": { "text": " Match each ones numbers to the correct regrouping. " }, "questionType": "Matching", "pairs": [ { "left": { "text": "11 " }, "right": { "text": "1 ten and 1 one" } }, { "left": { "text": "14" }, "right": { "text": "1 ten and 4 ones" } }, { "left": { "text": "41" }, "right": { "text": "4 tens and 1 one" } }, { "left": { "text": "44" }, "right": { "text": "4 tens and 4 ones" } } ], "id": "da9e8692-d760-d103-817e-d0d151cceff1", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "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%2Fv1707305548%2Fnlnd6fmpgdf5xuhj6rir.png&w=640&q=75", "imageKey": "39878ffb-abd5-88dd-4620-88a727f36c9e/question/1892de877af2e1706381e2480ad18108.png" }, "questionType": "Short answer", "correct": [ { "text": "42" }, { "text": "forty-two" } ], "id": "fc991671-bade-4ecd-5a0a-9cc045b7ecaf", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "type": "Question", "question": { "text": "Calculate the missing number in the column addition. ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707305548%2Fopndheqwismtiyibamu3.png&w=640&q=75", "imageKey": "39878ffb-abd5-88dd-4620-88a727f36c9e/question/781b4c2c64bb4f330b15b5c8b8d5ccfd.png" }, "questionType": "Short answer", "correct": [ { "text": "2" }, { "text": "two" } ], "id": "b88de838-cc1e-4f9b-f9fe-0dea58290b6c", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "type": "Question", "question": { "text": "What is the missing sum?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707305549%2Foldlnpwkhtwiqqlqtbhn.png&w=640&q=75", "imageKey": "39878ffb-abd5-88dd-4620-88a727f36c9e/question/88e733dfc125576ebca5b6896c20eced.png" }, "questionType": "Multiple choice", "correct": [ { "text": "270" } ], "choices": [ { "text": "260" }, { "text": "270" }, { "text": "273" }, { "text": "370" } ], "id": "86f640d7-c78c-12db-ae4e-e9d22075d7df", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" }, { "type": "Question", "question": { "text": "What is the missing number in the column addition? ", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1707305549%2Feihabkoouxsrustethpb.png&w=640&q=75", "imageKey": "39878ffb-abd5-88dd-4620-88a727f36c9e/question/aa749ced542d65e600b7267dd85e2731.png" }, "questionType": "Short answer", "correct": [ { "text": "9" }, { "text": "nine" } ], "id": "c6edfa96-a49f-8cfc-e40b-07ebc0680acb", "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41" } ], "lessonId": "23cde0ca-b912-f3eb-0469-dd645df9bd41", "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 ones" } } ] }