Lesson video

Hi everyone.

Thank you for joining me.

My name is Ms Jeremy and today's math lesson is focused on adding, using the column method.

So find yourself a nice quiet space for your learning and then once you're ready, press play to begin your lesson.

Let's start by looking at our lesson agenda for today.

So our warm up today is going to be recapping rounding in order to estimate.

We're then going to look at column addition using place value counters, before looking at column addition with estimation and we'll finish with three-step column addition before your independent task and quiz at the end of the lesson.

So for today's lesson, you will need a pencil and some paper and a nice quiet space.

Feel free to pause video now to find these resources and then restart when you're ready.

Let's begin with the warm up.

We're going to recap rounding in order to estimate.

And so let's just remind ourselves of why we use rounding in order to estimate.

So, whenever we've got a complex calculation, like the one you can see on the screen there 351,209 plus 267,883.

It's really useful to do some rounding to the nearest multiple of 100,000 or the nearest multiple of 10,000 prior to calculating, and that's just to give us a bit of a ballpark figure, a bit of an idea of what our answer might be, so that when we come to actually calculating the real answer, we've got a bit of an idea to help us out.

So the question asks, is it possible to use rounding in order to estimate the answer to this equation here? I'd like you to have a little think.

What might you round to, in order to estimate the answer to this calculation? And, what would your estimations be? So 10 seconds to decide what you're going to round each of those numbers to, and then work out what your answer would be.

Okay.

So let's have a little think.

So, you might have chosen to round both of those numbers to the nearest multiple of 100,000.

And so you would have got 400,000 plus 300,000 is equal to 700,000.

That is one way of estimating.

That is probably the least accurate way of estimating, just in terms of the fact that the answer you get is going to be further away from the actual answer, than it would be if you rounded to the nearest 10,000 or thousand, but, still a perfectly valid way of rounding to estimate.

And the best thing about that is that it often, when you're in rounding to the nearest hundred thousand, you are getting equations that are easier to calculate.

Some of you might have decided to round to the nearest 10,000, in which case your equation would have looked like this, 350,000 plus 270,000 and that was equal to 620,000.

And some of you might have decided to go for an even more accurate estimation around to the nearest 1000.

So this would have been your equation, 351,000 plus 268,000 is equal to 619,000.

And you can see, as you're moving down there with the different estimations, the numbers are getting closer, further and further away from each other.

So we start with 700,000, which is a very rough estimation.

Then we take it to 620,000, 619,000.

So either of those, any of those methods would have been absolutely fine in order to estimate the answer to this equation.

And today, in the column addition strategies that we're going to be using, we are also going to be estimating prior to calculation in order to ensure that our accuracy is really top notch.

So let's begin with a bit of work on column addition with place value counters.

Column addition involves adding together numbers that are challenging to add with the other strategies we might have spoken about before.

So, they're challenging to add with partitioning because there's lots of regrouping.

They might be challenging to add with round and adjust because they're not close to any kind of easy numbers for adding, and they might be challenging to add with any of the other strategies.

So we use column addition to help us out.

Now, there's a couple of ways we can use column addition.

One of the ways is to use what we call a pictorial method.

That's to draw a picture, to help us add together numbers.

And that's what I'm going to demonstrate to you first of all, now.

So I'm going to begin by representing my first number, using place value counters on my place value chart.

I need to represent 29,326.

So I want to start with my ten thousands.

I don't have any a hundred thousand, so I don't need to fill that column, but I've got two 10,000.

So I want to put two in there.

I can see I've got nine thousands.

So I'm going to use one, two, three, four, five, six, seven, eight, nine place value counters to represent that.

I've got three hundreds, one, two, three, I've got two tens, one, two, and I've got six ones.

So there we go.

I've represented 29,326.

I'm now going to change my pen colour because I now need to represent my next number, which is 34,275.

So I'm going to go in and add that in next to the blue.

So I've got three 10 thousands to add in one, two, three, I've got four thousands, one, two, three, four, I've got two hundreds, one, two, I've got seven tens, one, two, three, four, five, six, seven, and I've got five ones, one, two, three, four, five.

Great stuff.

So you can see that in the blue, I've got my first number, in the pink, I've got my second number and I've added those together in their separate columns.

I'm going to change my pen colour again, because now in a kind of bright red, I'm going to see what I can work out, what is in each column, and what our final answer is.

I may need to do some regrouping.

Remember, if we find that we've got more than nine place value counters in one column, we're going to need to do some regrouping because we can't fit a double digit into one column.

So I want to start with my ones here.

I can see in my ones, I've got four, eight, nine, 10, 11, place value counters.

That is too many.

So I'm going to have to regroup 10 of them.

I'm going to put a circle around 10 of them, leave one in there, and I'm going to regroup them for one 10 instead.

And I'm left with my, just, just my one, one in this.

I'll just write one below so I know what that is.

Let's look at how many tens I have.

Counting my fours first, four, eight, nine, 10.

I've got 10 again.

I'm going to have to regroup all of these now, for one, 100 instead.

So I'm going to put a circle around them, cross them out and regroup for one 100.

So now I don't have any tens.

I'm going to put a placeholder in there zero to show I don't have any tens.

How many hundreds do I have? I've got 600.

So I want to put six there.

I don't need to do any regrouping.

Looks like my thousands will need some regrouping.

Let's have a look at how many I've got.

I've got four, eight, 12, 13 thousands.

So I'm going to need to regroup 10 of these into one 10,000.

So I'm going to take these 10 here, I'm going to cross them out and I'm going to regroup them for one 10,000.

So now I only have three thousands in there and I've got six, 10 thousands.

So you can see my answer is 63,601.

And we've represented that pictorially and that means with a picture.

We've drawn our place value counters, we've added our second set place value counters, we've completed our regrouping, we've identified what's in each column.

So, I'd like you to have a practise of that.

You've got your own equation here on the board.

It says 63,198 plus 25,764.

I'd like you to use your place value counters in a place by the grid.

Just like we've created on the, on the screen here.

Draw that out.

It doesn't need to be particularly neat, just that you've got enough space in each column to draw out your place value counters, and just like I did for the previous example, I would like you to represent that addition equation, using place value counters, regrouping where necessary.

You will have a fair bit of regrouping to do for this question.

So be warned, be, keep your eyes peeled for where you'll need to regroup.

Pause the video now to complete your task and resume it once you're finished.

Okay, how did you get on? So hopefully you found that using your place value counters, your answer was 88,962, and you should be now to use your place value counters to represent both those numbers and complete your addition.

So moving on, what we did that was used column addition with pictorial representations of the numbers.

But let's talk a bit about how we can use column addition with estimation now.

Let's look at the equation that we have on the screen.

It says 372,158 plus 129,832.

And what I'd like to do is first of all, create an estimation of what our answer is going to be before we calculate it using the column method.

So, I'm going to decide that I think we're probably going to estimate to the nearest multiple of 10,000.

I think that gives a happy medium.

If it were estimated to, by rounding to the nearest multiple of 100,000, that would be fine.

And to the nearest multiple of 1000, that'd be fine as well.

But 10,000 is in the middle.

It gives us a nice, happy medium of accuracy, but ease of calculation as well.

So let's round the first number to the nearest multiple of 10,000.

I'm looking at the digit in the 10 thousands.

I'm taking a peak next door.

I can see this is rounding down to the smaller multiple of 10,000.

So it's rounding to 370,000.

And I am looking at the next number and amount of the nearest multiple of 10,000.

This one is going to be rounding up to the larger multiple of 10,000.

So it's rounding to 130,000.

Now looking at our known facts, thinking about our own facts, if I were to try and add 370,000 plus 130,000, well, first of all, can I do 37 plus 13? Well, I know 37 plus 10 is equal to 47.

And then I'm going to add the extra three, that's equal to 50.

So the answer to this, if 37 plus 13 is equal to 50, 370,000 plus 13,000, must be equal to 500,000.

So we should find that our answer is close to 500,000 when we actually calculate it.

If we are wildly off mark, and if the answer is very different to that, we need to go back, check our estimation, check our calculation.

So looking at our calculation now, let's see, I'm going to lay this out, set this out in a way, that allows me to make sure I've got all my columns aligned.

So I've got 372,158.

And I'm adding, remember that sign is very important.

129,832.

The very first thing you need to make sure you're doing when you are calculating column, addition or subtraction is to line up your values really carefully to make sure they're all in line.

If you were to get the alignment wrong, your answer would immediately be incorrect.

I'm going to change my pen colour again, so we can see what we're doing as we add.

So exactly the same as we did with the place value counters, but this time using just digits, we're using an abstract method this time, let's start with ones column and let's go through with our addition.

So we've got eight ones plus two ones, which is equal to 10 ones.

And I can't fit a 10 in that column, so I'm going to need to regroup.

I'm going to put a zero here and regroup my 10 ones for one 10, which is just going to go at the top there.

So now I've got one 10 plus five tens plus three tens.

What is that equal to? That's equal to nine tens or 90.

So I'm going to put nine in the 10th column, just like that.

Now moving to a hundreds, 100 plus 800 is equal to 900.

Looking at thousands, I've got 2000 plus 9,000, which is equal to 11,000.

I need to regroup here because I can't put an 11 in there.

So I'm going to keep my 1000 here and regroup my 10 1000 up here for a 10,000.

So I've swapped it for 10,000.

Okay, so now I've got one 10,000, 70,000 and 20,000 there as well.

So 10,000 plus 70,000 plus 20,000 is equal to 100,000.

So I'm going to put zero there and regroup my one up here and I've got 500,000 to finish off.

So my final answer is 501,990.

And you can see it's very close to my actual estimation.

So that estimation has helped us identify what the answer could be and helped us to see that our calculation is correct.

So let's have a look at another example.

Let's look at the equation on the screen.

Let's say that equation together.

It is 842,663 plus 78,256.

And just like last time, we're going to start with an estimation.

Estimations are helpful to us because they allow us to compare our final answer to the estimation and to work out whether our answer is likely to be accurate or not.

So again, let's round to the nearest 10,000 for both of these digits.

Let's start with the first one.

What is 842,663 rounded to the nearest 10,000? Going to give you three seconds.

Have you got it? Let's look at the digit in the 10 thousands column, which is a four.

And let's have a look at the digit next door to it, which is a two.

This is going to be rounding down.

So it rounds to 840,000.

Now let's look at the next number.

Well, this is the digit in the 10 thousands column.

Are we rounding up or down in this case? We're going to be rounding up because eight is over a four.

So we're going to round up to 80,000 here.

So, our estimation equation is 840,000 plus 80,000.

Well, let's use some known facts to help us here.

Why don't we try and add 84 plus eight.

Let's use, I'm making 10 strategy.

I know that 84 plus six is 90.

I've got to add two more onto that.

So it becomes 92.

So my answer is 920,000.

So I know when I actually come to calculate this, if I get an answer that is wildly different to this, I've gone wrong somewhere, either in my estimation or my actual calculation.

So, another measure to help us make sure we're accurate.

Let's move to our actual calculation.

So first of all, I'm going to line up my values.

Now this is going to be tricky for this one.

Can you see why this equation is a bit harder with alignment in terms of alignment than my previous one? You might have noticed that the first number has six digits, whereas the second number only has five.

I need to make sure these are nicely aligned.

So I'm starting with 842,663 and I'm adding, and here I go, 78,256.

An error that a lot of people make, is to put, if I were to put our seven underneath the eight.

That's seven is 70,000, it's in the 10 thousands column.

It does not belong in the hundred thousands columns so make sure you've lined up your values correctly.

I'm going to draw an equal sign below, and then I will switch our pen colour so we can see, what we are doing.

So let's make it a nice red there.

Let's start with our ones like we did last time.

This time I've got three ones plus six ones, which is equal to nine ones.

So I put nine in there, no regrouping required.

We're ready to move on to our tens.

This time I've got six tens plus five tens.

So this one does require regrouping because that is equal to 11 tens.

I'm going to keep my one 10 in here and regroup 10 tens for 100 up here.

Now I've got 100 plus 600 plus 200, which is equal to 900.

I've then got my thousands, which is 2000 plus 8,000, which is equal to 10,000.

So again, I'm going to regroup.

I'm going to have a zero here, no thousands anymore, but one 10 thousands up in the 10,000 place there.

And then I've got a 10,000, so one 10,000 plus a 40,000 plus 70,000.

So what is 70,000 plus 40,000? Maybe let's start with that first.

And then plus your 10,000, so I've got to have 120,000.

120,000.

So I'm going to keep my two in here for my 10,000 and my 100,000 goes up there that represents 120,000.

And then I've got 10,000 plus eight, sorry, 100,000 plus 800,000, which is equal to 900,000, just there.

Have a look at that and look at our similarities between our estimation and our actual answer.

It looks like we were correct with our estimation and our actual answer.

Great to go.

We can move on to the next question.

So now it's your turn.

You've got calculations on the board.

The first one is a six digit plus a six digit number.

The second one is a six digit plus a five digit number.

So be aware of that alignment.

I'd like you to estimate the answer to the calculation first using rounding to the nearest 100,000 or round to the nearest 10,000, if you want, and then calculate the answer using the column method.

Pause the video to complete your task and then resume at once you're finished.

Okay, how did you get on? Let's have a look.

So the final answers you should have got to were 595,801 and 678,792.

How did you get on with those? All Okay? Did you find that your estimations matched up with your actual answers? Do you think that's going to be a useful strategy going forward? Power think about how you might use it for calculations you do in the future.

So let's move on to our final bit of activity before your independent tasks today.

we're going to be looking at three-step column addition.

So as we've been doing so far, we've added two numbers together.

But you can do exactly the same strategy or in exactly the same kind of method using three-step addition, where you've got three numbers to add instead of two.

We've got an example on the screen here, let's read this equation together.

It says 6,327 plus 4,836 plus 2018.

So let's begin by looking at how we can estimate the answer to this by rounding to the nearest thousand.

So look at the first number here, can you tell me what that would be rounded to the nearest multiple of 1000? The answer is 6,000.

So we're going to round that to 6,000 there.

The next number I'm looking around into the nearest thousand, I can see that I will be rounding up in this case.

So I'm rounding to 5,000 and the last number rounded to the nearest thousand, having a peak, I'm going to be rounding to 2000.

So, I know that my estimation is going to involve the equation 6,000 plus 5,000 plus 2000.

Well, I don't know what that is off the top of my head, but I'm going to use my known facts.

I'm going to do six plus five first of all, in my head, which is equal to 11 plus two, which is equal to 13.

And because we're dealing with thousands, digits that numbers are in the thousands here, my estimation is 13,000.

Using my known facts to create my estimation.

So now that I've created my estimation, let's complete our calculation.

You can see that this has already been laid out for us.

We've got a really nice column of numbers that are all aligned with the ones, the tens, the hundreds and the thousands all in line.

We've got our equal sign at the bottom, and we're going to start by adding our ones together.

So I've got seven ones plus six ones, plus eight ones.

Well, I'm going to try and use the commutative law here, to mix up these numbers a little bit to help me out because, I'd like to add seven plus eight first of all.

Because I know that double seven is 14, seven plus eight, it's just one more than that.

So that must be equal to 15 ones.

And then I've got to add my six while using my make 10 strategy, if I add five to 15 I get to 20, and then six is one more than that, so that's 21.

So 21 ones.

Ooh, I'm going to need to regroup here.

I'm going to keep my one one here, but I'm going to regroup my 20 or my two tens up here to the top of the tens.

So now I've got two tens plus two tens, which is equal to four tens plus three tens, which is equal to seven tens plus one 10, which is equal to eight tens.

So eight tens goes just down here.

Now let's look at our hundred column.

Well, I've got 800 plus 300, which is equal to 11 hundreds or another way of saying that is 1,100.

So I'm going to keep 100 here.

But I'm going to have to regroup the ten one hundreds, for a thousand up there.

And now I've got 1000 plus 6,000 plus 4,000 plus 2000.

Using my commutative law again, I can see number bonds to tend to help me out here.

I've got a six plus a 4000 there, and I know that's equal to 10,000.

Then I'm going to add a 1000 that's 11,000, plus 2,000 what 13,000.

So I can't put 13,000 in here, but I can fit 3000 in here.

And my spare 10,000, isn't going to be regrouped because I've got no more numbers to add, but I'm going to place it in my 10 thousands column, just like that.

So my answer is 13,181.

And referring back to my estimation, you can see how similar those numbers are.

I must be spot on.

Fantastic.

Ready to move on.

So now it's your turn.

You've got an equation here on the screen that I'd like you to calculate the answer to.

Start off by using estimating by rounding to the nearest multiple of 1000, and then use the column method, with your numbers aligned to calculate the actual answer.

Pause the video, to complete your task and resume it once you're finished.

Okay, how did you get on? Let's have a look at how you might tackle this problem.

So first of all, we're going to create our estimation.

And you should have thought to round your, all of their values in your equation to the nearest multiple of 1000.

So the first number of rounds to 9,000, it rounds up.

The next number rounds to 4,000, it also rounds up.

And the next number rounds to 2000, that one is rounding down.

And using my known number facts, I'm going to add a nine plus four plus two.

So I know that nine plus four is equal to 13.

Plus two is equal to 15.

So my answer should be around 15,000 when I comes to calculate it.

So let's look at the calculation.

I can see here, I've got to add my ones first of all.

So I've got one, one plus two ones plus seven ones, which is equal to 10 ones.

So I'm going to put zero here, in the ones column and regroup my 10 ones for one 10.

Now I'm adding together my six tens plus five tens plus one 10, which equals 12 tens or 120.

So I'm keeping my two tens here and regrouping my 100 up here.

Looking at my hundreds column now, well I'm going to use my number bonds to tend to help me.

So I'm going to add my 900 here with my 100 and that's equal to 1000.

And then I've got my 500 plus my 400 that's 1,900 when I add all of those together.

So keeping the nine here and regrouping my 1000 up here.

And now adding together my thousands.

But I can see that 8,000 plus 1000 is equal to 9,000.

Plus my 3,000 here is equal to 12,000.

Plus my two here is equal to 14,000.

So keeping the four here and regrouping my one 10,000 into the next column, my answer is 14,920.

Which you can see is very close to my estimation, which suggests that our calculation is accurate.

So moving on to your independent task.

You've got a set of questions here.

For each of the equations below, I'd like you to provide a suitable estimate before calculating using the column method.

Be warned, some of these questions have a mixture of six digit and five digit numbers.

And some of them use three numbers in a row.

So, using the skills you've learned in this lesson, have a go at answering those, using your estimations first.

Pause the video to complete your task and then resume it to check your answers once you're finished.

Okay, how did you get on with those? Let's have a look at the answers.

You can see all the answers are there in pink.

If you'd like to, pause the video now to mark your answers and check how you got along.

Today you've done a really good job of participating in the lesson.

We've had lots to think about estimation, rounding and column method to calculate answers.

If you'd like to, please share your, please ask your parent or carer, to share your work on Twitter, tagging @OakNational and #LearnwithOak.

We'd love to see what you've been up to.

Now complete the quiz.

Thank you for joining me for another math lesson today.

It's been great to have you.

Do join us again soon.

Bye bye.