Lesson video

Hello everyone, I'm Mrs. Crane and welcome to today's lesson.

In today's lesson we're going to be adding by using the column method when more than one column requires regrouping.

In a moment, I'll go through all of the equipment we need so don't worry about getting that just yet.

Are you having a good day? I hope you are and I hope you're ready for some maths work.

If you can, please could you turn off any notifications that you have on your phone, tablet or whatever device you're using to access today's lesson in and then, if you can, try and find somewhere nice and quiet in your home so we're not going to be disturbed.

When you're ready, let's begin.

Okay then, let's have a look at today's lesson agenda.

So we're going to start off by regrouping in more than one column, what that looks like and how we did it.

Then it'll be your turn to have a go during our let's explore today.

Then we're going to look at what happens when regrouping in one column leads to regrouping in another column and I'll explain what that means a little bit later on.

Then it'll be time for your independent task and you'll be solving some additional equations.

So before we get started, if you haven't already, please could you go and get yourselves a pencil and some paper.

Pause the video now to get and those things if you haven't got them.

Welcome back, let's get started then.

So when would we use column addition? We've seen this table before, if you've done any of the other addition sessions.

So we're going to start off by thinking about how many people went to the Louvre.

Remember these are the different places in Paris, the different places you can go and sight see at.

So here's the Louvre and if we're looking at the 1st of June, we're looking here at this information and we're looking at the coach and we're looking at the boat.

So let's have a look that equation here if I wanted to add them together.

So my equation is 1,845 plus 1,956.

What do you notice about that equation? Well, I notice that the five and the six add together to make a number that's greater than 10.

Remember those number bonds, when they create a number that's greater than 10, we know we're going to need to regroup.

Also notice four and five, nope they don't make a number bond greater than 10, nine and eight, they definitely make a number bond greater than 10.

So I've noticed in my ones column and in my hundreds column the numbers in my additions are going to create bonds that are 10 or greater, which tells me I'm going to need to regroup.

In this equation, I'm going to need to regroup multiple times, more than once.

So let's see, how do I do that then? Before we get started, really important that we make our estimate.

Why is it important to make an estimate? have a think.

It tells us if we've gone horribly wrong in our answer.

So let's see, how are we going to estimate answer to this equation? Well, let's take our first number 2,719.

Think of where it is on the number line, it's near 2,700, which is going to help us because we're thinking round to the nearest thousand to be the most efficient, 3000.

Next number 5,847.

Let's have a look where that is.

It's quite close to 5,800, round to the nearest thousand it's going to give us 6,000.

So you can imagine 3000 plus 6,000 is equal to.

Fantastic, 9,000.

So I'm going to put that here with my almost equal to equation symbol here so that I know when I've calculated my answer if I've got horribly wrong or if I'm close to my approximate answer by my estimate.

So let's see what this looks like here.

So we have the first number here, 2719, one ten, nine ones, this is the ones column here, my face is just blocking the zero to tell you or the O to tell you sorry.

Again here it's made up in the same way, 2,719 just this time it's written as numbers, okay? Second number then, 5,847.

You can see that is made up here.

Now what I'm going to do is I'm going to show you how it's made with the place value counters and using our column method at the same time so you can see exactly what it looks like with place value counters as well.

So, which column do I need to start with? Tell your screen which column I need to start with.

Fantastic, we need to start with our ones just in case there's re-groupings.

So nine plus seven, nine plus seven.

What's nine plus seven going to give us? Oh, it's going to give us 16.

What do you notice about that there? Can I keep my 16 here? I can't, I have to do something.

What do I need to do? Fantastic, I need to do some regrouping.

So I'm going to regroup and exactly here, can't write 16 in here, can we? It doesn't look right.

So I'm going to regroup my 16 so that it becomes one 10 and six ones because 16, if I partition it into tens and ones is one 10 and six ones.

Now I can write that in here by saying six ones here and I'm going to regroup my one here into my tens column so that when I come to add my tens column, I know I need to add that regrouped one.

That one represents one ten which is why it's in that tens column.

If we look over here, we can see, oh, there it is, we cannot forget to regroup with that ten here because it's in our tens column.

So let's move on to our tens column next then.

So I've got one, two, three, four, five, six tens.

And here we have six tens.

I've included that one ten and here I'm going to put six tens in.

Next, have a look at my hundreds column, what have I noticed? I can see here I have got a lot of hundreds and I know if I'm looking here, seven add eight creates a bond that is 10 or greater so I'm going to need to regroup.

Let's add seven and eight and then work out how we regroup them.

So seven add eight is going to give me 15.

I need to regroup 15 into, this time, thousands and hundreds because the 15 actually represents, sorry, 15 hundreds so 1,500.

I can regroup 10 of my hundreds for 1000 and I'm left with five hundreds.

I show that here I can write it as one because I've regrouped one of, sorry, I've regrouped 10 of my hundreds for 1000, so I could represent that here and I still have five hundreds left, so I can write that in here.

Now, when I add my thousands, I cannot forget to add my extra regrouped thousand here, which is why I've left it here.

So I know I need to do one, two, three, four, five, six, seven, eight thousands.

So I put in my eight here and I put in my eight here in my column method here.

So from that, the key things that it's really important to remember are, if we're regrouping, remember to show we're regrouping.

So remember to mark it, if you're using a place value grid, remember to draw it in, if you're using the column method written, remember to mark that in, and then once you've marked it in, remember to use it when you're adding your column, okay? How did we find out that a number needed regrouping? What was the way that we found that out? Well done.

If the two numbers in the same column create a bond that is 10 or greater, we need to regroup.

So let's have a look at our answer compared to our estimate.

8,566, is it close to 9,000? Absolutely.

So it shows us that we aren't too far off our estimate therefore we haven't gone horribly wrong.

Now, if you're feeling really confident today, I'd like you to have a go at this equation here on your own either using drawing out place value counters on a place value grid, that's the word I was looking for, or using the column method, it's up to you.

If you're not feeling so confident, that's absolutely fine.

Remember if you are going to pause the screen, make an estimate first so that you know if you've gone horribly wrong.

If you're not, don't worry, we're going to go through it together now.

So let's make our estimate first.

I know that 3,891 is close to 4,000 because there's an eight.

So I round up to the nearest thousand and I know that 4,700 is close to 5,000 because there's a seven in my hundreds column so I round up to 5,000.

4,000 add 5,000 is 9,000, so this is going to form my estimate.

So 9,000 is where we think we're going to get to roughly.

So let's have a look at calculating.

Again, we've made our numbers, 3891, 4783, and here you can see it written in our column method.

We've got our estimate here so we can use it to check at the end.

So which column do I start at again? Who can remember? Fantastic, I start in my ones column.

Remember there is a zero underneath this, underneath my face, you just can't see it.

So one add three, am I going to need to regroup that? I'm not because it doesn't make a bond that is 10 or greater.

So it gives me four.

I can put in four here.

Oh nine add eight.

Am I going to need to do some regrouping there? Does nine add eight give me a number bond that is greater than 10 or 10 itself? It does.

It gives me the number 17 because nine add eight is equal to 17.

Now I'm going to need to do some regrouping because I cannot leave 17 in my tens column, it doesn't work.

So I need to regroup 17 to 100 and seven tens because when I was saying 17, I was really meaning 17 tens which is the same as saying 170.

So I've got seven tens left and I've got 100 here.

Can I now put this into my written method? I can cause I can write one here in my hundreds column, not my thousands column, in my hundreds column because I know I need to regroup it and my seven tens still here in my tens column, that works.

Why do I have to leave that here and leave that here? Why is that important? It's important because if I don't leave my one that's been regrouped here or my hundred that's been regrouped here, then when it comes to adding in that column, it's not going to be the correct answer.

Now, if I look at this column without looking at my one that's been regrouped for a moment.

Seven add eight or eight add seven sorry, whichever way round, you would like to say it.

Does that create a bond that is 10 or greater? It does.

Now seven add eight add one definitely creates a bond that is greater so I know I'm going to have to do some regrouping here as well.

So I can imagine that one, this is how I would work it out, add one to that seven, that gives me eight add eight and I know that double eight is 16 so I know that my answer is going to be 16.

That's 16 represents 16 hundreds because it's in the hundreds column, which is the same as saying 1,600.

So I'm going to regroup it there's 1000 here and there's six hundreds here because it's the same number but then I can actually use it to add.

So over here, I need to put my one here to show that there's 1000, my six here to show the 600.

Now when I'm adding my thousands here, I need to remember to add that regrouped thousand.

So I can do three add four is seven add one is eight or mentally I could do three add one is four, four add four is eight.

Whichever strategy is easiest for you in your head, nice and quickly So here's my eight and here is my eight so let's put our answer in, 8,674.

Am I close to 9,000? Absolutely, I'm close to 9,000.

I'm not too far away from that at all.

So that tells me that I haven't gone horribly wrong and that I've regrouped correctly.

So, it's your turn, let's have a look then.

You're it, I'd like you to have a go please at estimating the answer to this following equation, 2,807 plus 5,678 then I'd like you to calculate the answer and finally, don't forget to check your calculation against your estimate.

Remember, you can use the speaking frame, regrouping will happen in the column and I know this because.

Pause the video now to have a go at today's let's explore.

Okay, welcome back.

Let's have a look then at how you did.

So my quick estimate was I rounded 2,807 to 3000 and I rounded 5,678 to 6,000, which 3,000 and 6000 gave me 9,000 so my estimate was 9,000 today.

Now I was going to enter my columns here and I'm not going to show you using the place value counters for this example.

Which columns did we need to regroup in? Is there a way of knowing this before we calculate it? So, how was it that I found out which columns we needed to regroup in? What was my strategy? Now I kept saying, if the numbers in the same column made a bond that was 10 or greater then I needed to regroup.

Seven and eight, do they make a bond greater or less than 10? Greater, 10 or greater.

Yep, absolutely, they do.

Zero and seven, they don't.

Eight add six, yep.

They definitely make a bond that is 10 or greater.

Two and five, nope they don't make a bond that is greater.

So I know there's two columns that I definitely need to regroup in so let's have a look.

Seven add eight, in your heads, what's seven add eight? Fantastic, it's 15.

Now I need to remember that it's not zero add seven because it's zero add seven add one, 10, remembering it's in the tens column.

So seven add eight, add one maybe even is eight, I wanted to tell you the answer, then now I'm going to do eight add six.

Do I need to add any regrouped number? I don't because there wasn't any regrouping.

Eight add six is equal to 14, that represents 14 hundreds, not just 14 on its own because of the columns that it's in.

Two add five is seven, can I put seven here? Mrs. Crane you can't put seven because you've regrouped one, you have to add it in, so your answer is eight.

So your answer is 8,485.

Let's check it against our estimate.

Not too far from our estimate so we know we haven't gone horribly wrong.

Fantastic.

Okay then, now we're going to look at what happens when regrouping in one column leads to regrouping in another column.

So let's look at this equation here and let's think about this question here.

Which columns do we need to regroup in and is there a way of us knowing this before we calculate? Then we'll make our estimate, then we'll calculate our answer.

So, remember what we said.

We know that a seven and an eight together make a bond that is 10 or greater so we'll have to regroup.

Eight and one don't so we don't think we'll have to regroup, four and three don't so we don't think we'll have to regroup and two and one don't we don't think we'll have to regroup.

Let's have a look then at how we estimate that answer.

2,400 rounds down to 2000, 1,300 rounds down to 1000, 2,000 add 1,000 is equal to 3000.

So this is going to give us our estimate for our answer today.

So put it here.

We've made our numbers and our place value grid here.

We're going to use that at the same time as using our column method here.

So the number 2,487 and the number 1,318, which column do we need to start in? Absolutely, we start in our ones column.

Seven add eight is 15.

Here's my 15.

I know that I can't leave it there.

I have to regroup 15 for one ten and five ones.

Here's my one ten, here are my five ones.

Can I write that in here now? Absolutely, my one ten and my five ones.

Next column then, I have got, oh, let's see, I've got eight tens here, nine tens, 10 tens.

Oh, I've made a bond that is 10 or greater.

Originally, we've said eight add one, we didn't need to regroup that didn't we? Now, because we've had to regroup in our ones column adding an extra 10, I regrouped 10 into our tens column, we now have got an answer that also needs regrouping.

So I can put my 10 tens here but I cannot write 10 tens into here because it won't work and I can't leave them there like that.

So I'm going to regroup 10 tens for 100 'cause I know that 10 tens is the same as saying 100.

This time I'm not left with any in that column so I have to put a zero in here and a one in here to show that I've regrouped and I now have 100.

Now can I add them? I've got four add three add one.

Four add three is seven, add one is eight.

So yes I can.

I can put them in here and I can write them into my column here, fantastic.

Then I'm going to do my thousands column last.

Okay, so let's have a look lastly at our thousands column, we've got 2000 add 1000.

Do I need to add anything that's been regrouped? Nope, 'cause nothing's been regrouped so it's going to give me 3000.

So my answer is 3,805, put that in here.

Is it quite close to my estimate? It's quite close, not really that close, but remember we rounded down to 2000 from 2,400 and we also rounded down from 1,300.

Four and three actually gives seven so I know that it's going to be closer to 3,700 than it was to 3000 so again, not too far off, we know we haven't gone horribly wrong.

Now it's time today for your independent task.

You are going to be solving some addition equations.

I'd like you to have a look at the following equations here and I'd like you to calculate the answers using the column method.

Remember make those estimates before you calculate.

My challenge to you today is can you work out which columns require regrouping in? Please pause your video now to complete your task.

Remember, don't forget to resume it once you're finished so we can go through the answers together.

Okay, welcome back.

Right then we're going to go through the first three questions together first.

So let's have a look.

Our answer is, sorry, I'll go through the question first, 5,481 plus 2,709 is 8,190.

There was regrouping in the ones column and in the hundreds column.

Next question then, 3,753 plus 5,762 gave me 9,515.

This time there's regrouping in the tens column and the hundreds column.

Last equation, 2,553 plus 6,366 is equal to 8,919 and there was just regrouping in the tens column this time.

Now, the next three questions.

So 6,428 plus 2,481 is equal to 8,909.

Again, there's regrouping in the tens column.

3,672 plus 4,354 is 8,026.

There's regrouping in the tens and the hundreds this time.

And the last equation was 4,807 plus 2,736 is equal to 7,543.

There would be regrouping in the ones and the hundreds this time.

Remember, if you'd like to please ask your parent or carer to share your work from today on Twitter, by tagging @OakNational and using the hashtag, LearnWithOak.

Great work today using all of those columns and thinking about how we regroup.

It can be quite complicated so you have to take one column at a time.

Don't forget to complete your quiz to show off all of your fantastic knowledge and hopefully I'll see you again soon for some more maths work.

Thank you, have a nice day and goodbye.