Lesson video

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

In today's lesson we're going to be adding, using the column method.

So, don't worry about getting any resources just yet.

In a moment, I'll run through everything that we need for today's lesson.

How's your day going? I hope it's going really well.

What I'd like you to do, please, is if you can try and turn off any notifications on your phone, tablet, or whatever device you're using to access today's lesson on.

Then if you can, try and find someone nice and quiet in your home so that today's lesson's not going to be disturbed.

When you're ready, let's begin.

Okay then, let's run through today's lesson agenda.

So, we're going to be looking at regrouping in the tens column and what happens when we need to regroup in the tens column.

Then we're going to be exploring and it'll be your turn.

Then we're going to be regrouping in the hundreds column and what that looks like.

It looks like my cat has decided to join us.

Hopefully she'll leave us alone.

Then we're going to be doing our independent task, which is solving addition equations.

So, for today's lesson, you'll need a pencil and some paper.

Please pause the video now to go and get these things if you haven't got them already.

Welcome back, let's get started then.

So, when would we use column addition? When do you think it might be appropriate for us to use column addition? Now, here I can see a picture of Paris and here we've got some information about different tourist attractions and how many people went to visit them on the 1st of June, the 1st of July, the 1st of August, and the 1st of September.

Here it also subdivides into coach trip.

So, how many people came by coach, and boats, so how many people arrived by boat to go and visit these different attractions.

Now, if I wanted to add up two of the amounts, what would be an appropriate method for me to use? Now, if I think back to different strategies we could use, we could use partitioning.

We could use counting on, we could use round and adjust, but a different method that we're going to look at today is going to be the column method.

Now, this method can be the most efficient method in lots and lots of different circumstances, but we've got to work out how we do it when there's regrouping.

So, that's what we're going to be focusing on today, looking at how do we regroup when we're using the column method to add four digit numbers together.

Tourists in Paris can choose to visit different attractions using the coach tour or the bus tour, the boat, the boat tour maybe even.

The table shows the number of tourists visiting each day on the first day, like we just discussed here.

So, we're going to take some numbers from that table.

We're going to use that table in a few different lessons so if you want to, after today's lesson there'll be another lesson, that we'll be building on how we do addition when it's multiple columns that need regrouping, okay.

But for today's lesson, we're just going to be focusing on if there's one or maybe two columns that need regrouping as a bit of a challenge.

Okay? So, this table will come in really handy when it comes to looking at some different additions.

So, when would we use addition? Let's have a look then at this equation, 3,683 plus 6,265.

Now, it's really important, especially when I'm adding with four digit numbers that we make a quick estimate.

Now, it shouldn't be something that takes us really long time at all.

It should be something that's really quick and easy to do.

Now, that is because when I'm adding with numbers like this, especially when there's regrouping, it can be quite straight, quite easy to make an error and to go wrong somewhere.

Now, if you've got an estimate, you can check against your estimate really quickly and think, Oh, gone wrong somewhere here Mrs. Crane.

Need to go back and check what I've done.

If you haven't made that estimate, you're not going to know if you've gone wrong anywhere.

So, it shouldn't take us too long to make our estimate at all.

We're just going to do a bit of rounding to get us to our estimate.

So here, I can imagine on my number line, that my first addend, 3,683, is quite close to the number 3,700.

Now, I'm going to round today to the nearest thousand to calculate my estimate just because it's most quickest, most quickest, oh dear, the most efficient strategy to use.

So, I'm going to use the number 4,000.

I'm going to put that in my head.

Then I'm going to think whereabouts does the number 6,265 go.

Well that's very close the number 6,300.

And I know if there's a three in the hundreds column and I'm rounding to the nearest thousand I round down.

So, I'm going to imagine that 6,000.

Now I've got 4,000 in my head, 6,000 in my head, 4,000 and 6,000 is, fantastic, it's 10,000.

So, here we've got this approximately equal to.

So, it's just an estimate just to show that our estimate is 10,000.

Did that take me forever to work out? No, it was nice and quick.

That's going to come in really handy when we come to answer this using the column method, because it's going to show us if our answer is anywhere near to our estimate or not.

Okay, so now you can see here I've represented my addition equation in two different ways.

I've represented it using a place value grid and using place value counters.

And I've also represented it using the column method with numbers.

So, what we're going to do today is I'm going to go through how you'd represent it and how you'd work it out with place value counters, and how you'd work out with just normal numbers.

If you want to, if you don't have anything at home that you could use as a counter, you can always draw them out.

That's what I would often do.

It's quite straightforward.

You literally just need to draw out the thousands, hundreds, tens, and ones, and in the column.

And then for each one just draw them out really quickly like this.

You can put zero, ones in it there, and you could put, you could put your tens in there, so you can see that your tens are there, and that is representing your tens.

And it can just be really quick jotting, that you can use that would be really helpful if that's helpful for you today.

If you find when I'm doing it with these pictures, and that's helpful, you're more than welcome to use those jottings on your piece of paper as well.

Okay, so don't forget that.

So, when I'm adding, we always start in the ones column.

So, we're going to start here, but oh, before we do that, let's just check how we've represented our numbers, sorry.

So, here we can see, this is the number 3,683, 3,000, the six hundreds, eight tens, plus three ones.

And over here you can see the other number, 6,000 in the six thousands, 200, and 65, okay.

Now, as I said, we're going to start with our ones.

So, I need to do five ones, add three ones.

I've done five ones add three ones because I find it easier to put the largest number first in my head and add three.

Five add three is, fantastic, it's eight.

So, I can put my eight in my answer box here.

And over here, my equation, I'm going to write eight in.

I'm going to show you one, so I'm going to show you both at the same time.

So, I'm going to work out firstly on this place value grid.

And then I'm going to show you what it looks like when it's written.

Okay then, add tens.

Now, I've got eight tens here and I want to add six tens to that.

Now eight add six, let's work it out in our heads, going to use my number rules to ten, to get me to ten, and then four, perfect, so my answer would be 14.

Really important that when I show that, that my four here, so I've got four tens, but I've also got 100 here.

Now what I did it in my head, I did eight add six, now actually, because it's in the tens column, that's 80 add 60, not eight add six.

So, 80 add 60 is going to give me 140.

So, I have to regroup and I have to put my 100 here, my four tens here.

I can't write it like this.

Why can't I write it like that? I can't have 14 in my tens column, can I? So, I have to show it in a different way.

I have to show it, my one here, because that one represents that 100 here, and my four tens here to show that there are four tens in that column there, okay.

Now, I can't just do six hundreds add two hundreds because I've got that one here, again here.

If you look at this column, six add two and that one.

When I'm saying six add two, I know that that six and that two represent hundreds because they're in that column.

So, I need to do six hundreds.

I'm just going to say six for the moment.

Six add two is eight, fantastic.

Add one is nine, that nine represents nine hundreds, going to put those in here.

And then over here, I can put my nine in.

Fantastic.

Now, I've got three thousands here and I've got six thousands here.

Three add six is, fantastic, nine.

I know that nine presents 9,000, and I put my nine in here.

Let's have a look then before I put my answer in the box, what was our estimate? Tell me what that estimate was.

Fantastic, our estimate was 10,000.

What was our answer? 9,948, is that quite close to our estimate? Yeah, fantastic.

That shows us that we haven't gone awfully wrong somewhere.

If there was a 2,000 here, I'd be a bit worried.

If there was a 20,000 here, I'd be a bit worried.

We know we're not too far off our estimate.

So, our answer is 9,948.

Now we're going to try another example.

If you're feeling really confident and you want to have a go at jotting it down, working without me, that's absolutely fine.

If you're not, don't worry.

We're going to go through it together now.

So, my next example, 4,376 plus 2,582.

How are we going to estimate the answer? So, we talked about estimating our answers.

And we talked about rounding to the nearest thousand as being the most efficient method.

So, I know that 4,360, that's not 60, and 76, rounded to the nearest thousand is going to give me 4,000.

There's a three in the hundreds column.

I know if there's a three in the hundreds column, I round down.

2,582, then rounded to the nearest thousand, it's going to round up to 3,000 because there's a five in the hundreds column.

S, then I can do five, that's not five.

I was talking about the five in the hundreds column, got myself distracted.

I can do 4,000 add 3,000 is 7,000.

I can use my facts, my number facts are four add three to give me seven and then my place value to help me work that out nice and quickly.

So, it didn't take us long at all.

So my estimate is 7,000.

I'm going to show it here with the approximately equal to sign.

So, you can see there I'm just going to move myself a tiny bit so you can see that's the ones column.

As I said, if you want to pause the video to have a go at working it out before I do, that's absolutely fine.

If you want to work it out and pause that as we go, that's also absolutely fine.

If you want to draw it out, that's fine, okay.

Or if you just want to sit and watch what I'm doing, also absolutely okay.

So, we've got our estimate in our box here to remind us that we're looking for a number around 7,000.

Let's check, we've represented our numbers using place value counters 4,376, 2,582, absolutely.

Which column do we start with? Well done, we start with our ones column.

So, I'm going to do six ones, add two ones.

Six add two is, absolutely, it's going to give us eight, and I'm going to put that into my column here.

Now, as soon as I look at this, I can see I'm going to need to do something.

If I look at my seven and my eight here, how do I know that I need to regroup? What tells me that I need to regroup? Well, if my numbers in the same column, make a bond that's more than 10, then I'm going to need to regroup.

I know that the number seven and the number eight create a number that's greater than 10.

So, I know I'm going to need to regroup here.

So, let's see what happens when we move it into here.

Sorry, my cat obviously wants to come and join us for some addition today.

And she's making an appearance behind me right now.

Let's focus on what we're doing here.

So, seven and add eight.

So, I can see seven add eight is giving me 15.

Now, when I'm saying seven add eight, I'm actually saying 70 add 80 is equal to 150.

Those counters represent 10.

I know that, they're in the tens column.

How am I going to write that? What do I need to do? Fantastic, I needed to do some regrouping.

We discussed that a moment ago because we knew that our bond was greater than 10.

So, I can't write it in here like that because I can't have a two digit number in one column.

It has to be a one digit number.

So, the greatest number that can ever be in one column would have to be a nine.

So, I'm going to regroup here for 100 and five tens because I know that 15 was representing 150.

This still represents 150.

You see here, those 100, she really does want to know what's going on today.

I think she's going to have to go outside for a little run around in a moment.

I'll be testing her on the quiz at the end of the lesson.

Then we've got our five tens here, okay.

So, I'm going to take this out of this equation here and I'm going to write it correctly.

So, I'm going to write my one here and my five here.

That one that presents 100, that five represents five tens.

Then what I'm going to do is I'm going to do my 300 here.

I have my 500 here, gives me eight.

Can I put eight into this box here? Stop Mrs. Crane, no you can't.

Why can't I, what have I forgotten to do? I must include this 100 in my calculation.

So, I must do three, add five is equal to, add one is equal to nine, fantastic.

So, in this box here, I can put nine, and in this box here I can put nine.

I have to remember that I've regrouped one and a half of that here.

Now when I'm saying nine I'm meaning nine hundreds.

Last column then, I have four plus two is equal to six.

Fantastic, I know that six really represents six thousands.

So, let's have a look at my answer, 6,958.

Is that close to my estimate? Absolutely, not far away from that at all.

So, I know that I haven't gone drastically wrong somewhere.

So, I'm going to put in my answer next.

Okay then.

I think it's going to be time for your turn.

So, you're it, I would like you to have a go at answering this equation here 3,405 plus 5,873.

One, I'd like you to make an estimate before you answer it.

That's really important.

Don't take too long doing it, but it will mean that when you've answered it, you can check against it.

So, that brings me nicely on to two, calculate the answer.

Three, check it against that estimate.

So, make sure you go back and check it.

Remember you can use the speaking frame, which says regrouping will happened in the column.

I know this because.

Why did we know that regrouping would happen? How did we know that regrouping would happen in a different column? We knew that when the two numbers in the same column created a number bond that was greater than 10, we were going to have to regroup.

So, what I'd like you to do is pause the video now to have a go at today's let's explore.

Okay.

Let's have a look at how we answered it.

So to answer it, I did a quick estimate.

I rounded 3,405 down to 3,000 because there's a four in the hundreds column, and I rounded 5,873 up to 6,000 because there was an eight in the hundreds column, which gave me the number 9,000.

Now, I'm not going to show you with the place value counters, just going to show you how I worked it out using the formal written method.

So, we've all lined up thousands, hundreds, tens, ones.

Which column do I start in? Fantastic.

Start with my ones, five add three is equal to eight.

This one's a bit more straightforward.

Zero add seven, seven.

Four add eight, oh, pause.

What have I spotted, four add eight.

I spotted a number that create two numbers, sorry, that create a bond greater than 10.

So, I know that when I'm doing four add eight, I'm going to need to regroup.

So, four add eight gives me 12.

So, I need to regroup that.

I know that that 12 really represents 1,200 because I'm actually saying 400 add 800.

So, I'm going to write it in by showing my one here that represents the 1000, my two here that represents the 200.

Can I carry on? Absolutely.

What must I not forget to add? My regrouped one.

So, five add three or three add five, whichever way round you find easiest, gives me eight.

Plus my one, fantastic, it gives me nine.

So, my answer is 9,278.

Let's check.

Is that close to my estimate? Absolutely, it's close to my estimate so I can put my answer in.

What was different in this equation to the equations that we looked at before? Have a think.

Think about the column that we needed to regroup in.

Absolutely, we had to regroup this time in our hundreds column, into our thousands column, before we were just looking at regrouping when we're looking at tens column.

Was that any different? Not really, as long as we remember what each column represents, even if we're regrouping in our ones column it doesn't make much difference to how we do it.

We've just got to remember what our numbers represent.

Which is why having those pace value counters drawn out is sometimes really helpful for you.

So, we're going to carry on and look at regrouping in the hundreds.

So, if you're feeling really confident after that example that we've just looked at, I'd like you to have a go at this and you can pause the video.

You can make your estimate, answer, and then check against your estimate and then resume your video so you can see how we got on together.

If you're not feeling so confident, that's fine because we're going to go through it together right now.

So, my new equation, 6,265 plus 2,933.

Now, first thing I need to do is I need to do some rounding.

6,265, I'm going to round to 6,000.

2,933, I'm going to round to 3000.

I'm looking at that hundreds column the whole time.

And then I'm going to do 6,000 add 3000 is 9,000 using my number facts, six add three is nine.

That did not take me long at all.

So, it shouldn't take you long at all.

It's just a really quick mental arithmetic calculation to check your answer against.

Okay, then we're going to use that estimate here to help us when it comes to working out our answer.

So you can see here, we've got our 6,265 here.

We've got our 2,933 here.

So, we're going to start off with our thousands column.

Mrs. Crane, what are you doing? We always start with our ones columns.

So, five add three is equal to eight, fantastic.

Now we're going to move on to our hundreds, no we're not, we're going to move on to our tens column.

We go from each column, we work our way through systematically.

So, our tens column, we've got six, add three is equal to absolutely, oh, I've got myself carried away here.

I have to write that eight in here, of course.

Six add three is equal to nine.

I know that that nine represents nine tens.

I'm going to put in my nine here.

200 add 900, oh, what have I spotted as soon as I've seen that? I spotted two numbers that make a bond that is 10 or greater.

So, I know I'm going to need to do some regrouping.

As you can see here, I cannot put 11 hundreds into this column here.

If I write it here, it doesn't fit.

I have to have a one digit number.

So, I'm going to regroup my 11 hundreds because 11 hundred is the same as saying 1,100, into 1000 here and 100 here.

So, then I can write it in correctly here 1,100.

If you imagine that those were zeros there, just to show you where that 1,100 was.

It looks like 11 because it represents 11 hundreds.

Next then I can do my six, add my two.

What do I have to remember? My one, so six add two add one is equal to nine.

Absolutely.

Now, I know that nine there really represents 9,000.

So, my answer that I've got is 9,198.

Is that close to my estimate? Absolutely, it's not far off my estimate at all.

So, your independent task today, you are going to be solving addition equations.

Also seems like my dog wants to come and join in with some addition today too, but he's not going to just yet.

I'll teach him how to do the addition afterwards.

So, you're independent task today.

Today, I would like you to calculate the following equations using the column method.

Remember to make that estimate before you calculate.

Really important, because it means you can check quickly once you've calculated.

Can you find the only equation where you need to regroup in the hundreds column? That's my little challenge to you today.

You've got four equations here.

Remember if you find it helpful to, you can use the place value grid here to help you.

I'd like you now to pause the video and do you independent task for today.

Don't forget to resume it when you're finished, we'll go through the answers together.

So, we're going to look at the two questions at a time, just so that you can see really clearly how we answered them.

So, my first one I'm going to do, make an estimate.

My estimate was 9,000.

I do two add four is six, zero add three is three, eight add nine is 17.

And I show it, I put my one here remembering I know that represents my hundreds.

I'm just saying it how I work out.

Five add two is seven plus the one is eight.

Question two then, make my quick, oh, let's just check quickly, yeah, it's not far off my estimate.

Make my quick estimate.

My estimate was 9,000.

Four add eight is, oh, I spotted something.

I need to regroup.

It's 12, two add one add one is four, six add nothing is six, one add seven is eight.

Is it close to my estimate? Absolutely.

Next two questions then, nine add seven.

Oh, I've spotted something again, I know I'm going to need to regroup.

That makes a bond that is greater than 10, or 10 or greater, sorry, it makes them, oh sorry, I've got carried away.

The first thing I have to do is put that estimate in.

Really important because when it comes to checking my answer, I can see if it's close to it or not.

Made it by rounding and I've made the number 8,000.

So, now I can put in 16 here.

Two add nothing add one, don't forget that one, it gives me three.

Three add four gives me seven, two add six gives me eight.

Is it close to my estimate? Not far off my estimate, if you look though, I had to round down from 6,400 to 6,000 to make that estimate.

So, that's 400 above it.

And I had to round down from 300, 2,300, sorry.

So it was 300 above it, three and four is seven.

So, I'm expecting it to be higher than my 8,000.

That's a quick way of just checking against that estimate.

And my next question then, eight add eight.

Oh, I've got carried away again.

I've forgotten to make that estimate.

Again it's really important, my estimate was 9,000.

Eight add eight is 16, one add one add one is three, two add five is seven, three add five is eight.

Is it close to my estimate? Absolutely.

If you would like to, please ask your parent or carer to share your work today on Twitter, by tagging @OakNational and using the hashtag #LearnwithOak.

Great work today.

Don't forget to complete your quiz to show off all of your fantastic knowledge on using that column method.

Hopefully I'll see you again soon for some more maths.

Thank you, and goodbye.