# Lesson video

In progress...

Hi, everyone.

Thank you for joining me.

My name is Miss Jeremy.

Today's Math lesson is focused on, problem solving using the column method.

And once you're ready, press play to begin the lesson.

Let's begin by looking at the lesson agenda for today.

before looking at large integer addition and subtraction, using the column method.

We're then going to look at correcting errors and completing incomplete column method calculations.

We'll finish with your independent task and quiz at the end of the lesson.

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

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

Have a look at this question here.

It says can you represent this math story using a bar model? So, remember a bar model is a really good way of us representing either an equation or word problems, give us a bit more information about the problem that we're trying to solve.

The problem that we have in this case reads this, Two hundred and forty seven thousand, six hundred and twelve people, attended a sporting event over the weekend.

One hundred and forty three thousand, and ninety one attended on Saturday.

How many attended on Sunday? So we've got a overall total amount.

That's our whole.

And that's the number of people who attended on Saturday and Sunday.

And we've got part of that whole.

And they've told us the number of people who attended on the Saturday.

That's the one part.

We want to work out the other parts.

There are a number of ways we can represent this, using a bar model.

What I'd like you to do is, think about the way you would like to represent this, using a bar model.

Pause the video now, create a little drawing of your bar model to represent the problem that we can see on the board.

And then resume it to see what we can come up with together.

So now you've had a chance to have a go at this.

Let's have a look at it together.

What I'd like to do is, to represent this using a bar model, that shows me that I've got one whole, which is the equivalent of a Saturday and Sunday, put together.

I know one of the parts, which is Saturday.

And I'm trying to work out Sunday, which is the last part.

And I want to show you that on one bar.

So I'm going to draw one long bar to begin with.

And apologies.

My line is a little bit wobbly.

It's a little bit harder to draw on the screen, than it is on paper.

And that whole bar there, is my whole, that is equivalent to two hundred and forty seven thousand, six hundred and twelve.

And about, approximately, just over half of that bar is one of my parts.

One of my parts is one hundred and forty three thousand, and ninety one.

And this is the part of the whole, that I don't know yet.

I'm trying to work out.

And you can see here very easily, that because I've drawn a bar model, it helps us identify this as a subtraction question.

Because we're finding the difference.

We're finding the difference between our whole attendance, and our Saturday attendance.

And that will tell us how many attended on Sunday.

So this is a good way of representing using bar modelling, to show us what our calculation needs to be.

So let's look further at some addition and subtraction calculations.

At the moment, what I'd like us to focus on, is representing our calculations in three ways.

I'd like to us to first of all, bar model our calculation.

So we know our proportions roughly, and we can identify exactly what we're doing with our calculations.

I'd then like us to create an estimation.

And then I'd like us to actually calculate the actual answer.

The reason that estimation helps us, is because it offers us a close approximate answer, to what we're trying to calculate.

And that helps us because if our actual answer is wildly off the market, it doesn't matter our estimation.

We know we need to go back because we've made an error.

So I'm going to model the first one to ask for us.

The question is as you can see in the right hand side of your screen, forty thousand , one hundred and twenty three plus, twenty three thousand nine hundred and eight.

So I'm going to represent that with a, an additive bar model, first of all.

So I want a bar here, that is going to be longer than my second bar.

In fact, it's going to be about twice as long.

And that's going to be one of my parts, which is forty thousand , one hundred and twenty three.

And then I'm going to have a shorter bar, which is about half of the first bar.

Which is one of my other parts.

That's twenty three thousand nine hundred and eight.

And it's the whole, that I'm trying to calculate.

So that I'm going to put question mark on that, because we need to find out what that is.

And because you can see this is an additive bar model, we're adding together two parts to make the whole.

And that shows that our calculation, is an addition calculation.

So now, it's time for our estimation.

So as we've been doing in the past, we've been estimating by rounding to the nearest multiple of ten thousand.

I will continue with that today because it works quite well.

So I'd like us to start by identifying, what forty thousand one hundred and twenty three is, when rounded to the nearest multiple of ten thousand.

I'm going to give you three seconds.

Okay, so you should see that it rounds down, to forty thousand.

So we're going to have that as our first estimated part.

Then for the second number, twenty three thousand nine hundred and eight.

Can you work out what that is, rounded to the nearest multiple of ten thousand.

Okay, so you should have seen it rounds to twenty thousand.

And so our estimation is fairly simple for us, to calculate using unknown facts.

We know that four plus two is equal to six.

So forty thousand plus twenty thousand, is equal to sixty thousand.

So our estimation should be close to sixty thousand.

Now it's time for our actual calculation.

Let's see.

We've got our ones first of all, the three ones plus eight ones, which is equal to eleven ones.

And so what I'm going to do is regroup them.

What I've done is, I've kept one of the ones in the ones column, and then I've taken a ten over to the tens column.

I've regrouped.

Now I've got two tens plus one ten, plus no tens.

Which is equal to three tens.

Or we can say thirty.

Now looking at my hundreds, I've got one hundred plus nine hundred, which is equal to one thousand.

So I'm going to have no hundreds left over here.

Because I'm going to have to regroup my one thousand, into my thousands column there.

Now I've got one thousand plus zero plus three thousand.

Which is equal to four thousand.

And looking at my ten thousands column, I've got forty thousand plus twenty thousand, which is equal to sixty thousand.

So my answer is sixty four thousand and thirty one.

And looking at the similarity between our estimation, it does look like it's a fairly close estimate that we've got there, and it does look like our answer is potentially correct.

So now we know that the whole is equal to sixty four thousand and thirty one.

So now it's your turn to have a go.

Have a look at this calculation here.

Can you create a bar model to represent this? And then estimate the answer, before calculating the final answer? Pause the video to complete the task, and resume it once you're finished.

Okay, how did you get on with your bar model estimating calculation.

Let's have a look.

So first of all, I'm going to create my bar model.

So I can see I'm adding together, seventy thousand four hundred and twenty six, and thirteen thousand nine hundred and two.

So my first part is a lot bigger than my second part.

So that needs to be reflected in the size of my bars.

So I'm going to have quite a long bar there.

That is representative of my first part, which is seventy thousand four hundred and twenty six.

And then a much shorter bar, which is reflective of my second part, thirteen thousand nine hundred and two.

And then I'm trying to find out my total amount.

So that is a question mark currently.

Because that is the whole that I'm trying to calculate.

So estimating here, we should have rounded to the nearest multiple of ten thousand.

So you should have got eighty thousand.

for the first part, rounded number.

Plus ten thousand, for the second one.

Which is equal to ninety thousand.

So we know our answer should be roughly around, the value of ninety thousand.

So let's look at our calculation now.

You should have got, as your final answer ninety two thousand, three hundred and twenty eight.

And if you'd looked and matched up with your estimation, you should have seen that, they were actually fairly similar there.

So hopefully, that was fairly straightforward, in terms of your calculation.

And hopefully, you've seen how estimating can really help to make sure we're not so in the dark with what our answer should be.

We know a rough approximate answer before we have.

So now that we've looked at some large integer addition, let's have a look at how we might do the same thing, but with subtraction.

So we've got this question here it says, three hundred and two thousand, three hundred and twenty one, minus one hundred and fifty four thousand, two hundred and ten.

So it's a subtraction question.

We want to bar model this first.

I'd like to demonstrate a comparative bar model now.

I'd like to show you how you might demonstrate a comparative bar model where you're finding the difference between two values.

Which is effectively what we're doing here.

When we find the difference we're subtracting.

So the way I like to do this, is to start with a larger bar at the bottom of my, bar model.

So this is going to be reflective.

This bar model here, this bar, here is going to be reflective of, three hundred and two thousand, three hundred and twenty one.

And then I want to demonstrate a smaller bar, at the top of that, which is actually this first the solo numbers, of roughly halfway between the two.

So I'm going to put that down as one hundred and fifty four thousand, two hundred and ten.

And what we're doing, is we're finding the difference between, both of those values to work out what the missing part is.

So let's move on to our estimation.

In order to estimate we're going to again, round to the nearest multiple of ten thousand, for both of these numbers.

What is the nearest multiple of ten thousand? For the first and second number, I'm going to give you five seconds to calculate or work it out.

So you might have seen that, we're rounding the first number, to three hundred thousand, when it's rounded to the nearest multiple of ten thousand.

And remember, we're subtracting, and we are rounding the second number to one hundred and fifty thousand.

So our estimation is going to be three hundred thousand, minus one hundred and forty thousand.

Using unknown number facts here, we can help ourselves out.

We know that 30 minus 15 is equal to 15.

So three hundred thousand, minus one hundred and fifty thousand, is equal to one hundred and fifty thousand.

So our answer, should be around one hundred and fifty thousand.

And we did get that actually when we look at our bar model, we can see our missing part is about halfway between the two.

So we do know that it's going to be roughly, one hundred and fifty thousand.

Let's now calculate it.

We've got one minus zero, which is equal to one.

Then we've got two tens minus one ten, which is equal to one ten.

No regrouping so far.

Then we've got three hundred minus two hundred, which is equal to one hundred.

Now looking at our thousands column, we want two thousand minus four thousand.

Unfortunately, we can't do this.

We're going to have to re group.

So I'm going to have a look next door.

Oh, dear.

I've got nothing in my ten thousands columns.

What do I do now? Have a think.

What do you think my next step would be? Because normally I'd take one of the ten thousands, and regroup for ten one thousands.

But I can't do that.

So what should I do next? So some of you might already know, that I'm going to actually regroup from my hundred thousand.

I'm going to take one of the hundred thousands.

So now there's just two hundred thousand, and regroup it for my ten ten thousands.

Then I've got to take one of my ten thousands.

So now I've got ninety thousand there, and regroup it for my ten one thousands.

So now, I can, Now I can carry on.

I've got here my twelve thousands minus my four thousand.

Or saying this in another way, and my twelve thousand minus my four thousand.

So twelve thousand minus four thousand, is equal to eight thousand.

Now I've got ninety thousand minus fifty thousand, which is equal to forty thousand.

And two hundred thousand minus one hundred thousand, which is equal to one hundred thousand.

So as you can see there, we had to regroup a little bit.

And what I, What's really important to remember, is that if you, if you can't regroup from the column that is next door to your number, you need to go to the next column.

But you need to regroup in sequence.

You can't do a big jump.

I couldn't have regrouped from a hundred thousand, all the way to my thousands.

I needed to by pass, I needed to work through my ten thousands.

And then my estimation and my actual answer are very similar.

So I know I'm probably correct.

My missing part, has a value of one hundred and forty eight thousand, one hundred and eleven.

It's your time to have a go.

I'd like you to have a look at the calculation on the right hand side of your screen.

I'd like you to represent this using a bar model, then create an estimation before your final calculation.

Spend a bit of time doing this, pause your video to complete the task and then resume it once you're finished.

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

So creating our comparative bar model.

First of all, I'm going to start with my larger bar at the bottom.

And this is going to have a value of seven hundred and sixteen thousand, five hundred and ninety eight.

My smaller bar, once again, is around halfway between, my large bar, or about halfway up, to halfway of my large bar there.

And that has a value of, three hundred and fifty four thousand, seven hundred and ten.

And that's for that part there.

And then I've got a missing part here, which I've got a question mark for.

Your estimation should have looked a little bit like this, if you're rounding to the nearest multiple of ten thousand.

Seven hundred and twenty thousand, minus three hundred and fifty thousand.

So that was if you were rounding to your nearest multiple of ten thousand.

And you should have got, as an answer, three hundred and seventy thousand.

Let's have a look at what your final calculation should have been.

Three hundred and sixty one thousand, eight and eighty eight.

So a nice match up between your estimation and your calculation there.

Let's move on to some different types of problems. Sometimes using the column method, we make a mistake.

We might regroup incorrectly.

We might not align our columns correctly.

There are a whole host of things we can do wrong.

And what's really important is that, we're able to spot what these errors are.

So let's look at an example of this.

Is it possible to describe error that has occurred in the calculation below? So let's have a look at the calculation.

We've got fifty thousand, three hundred and forty five, minus thirty four thousand, five hundred and twenty one.

And the answer was eighty four thousand, eight hundred and sixty six.

What error has been made here, and how do you know? I'm going to give you 10 seconds to see if you can spot it.

Whenever I come to looking at errors, one of the first things I do is, to look at the symbol.

And I can see this is a subtraction.

So that means that my last part, should be smaller than my whole.

Because both parts should be smaller, or should be less than my whole.

And I can see here, that's not the case.

This part at the bottom here is a lot larger than my whole.

So I know that what I've done here, is instead of subtracting I have, added.

So I can say I can see that the error made here is that, I have added instead of subtracted.

I know this because my parts, that I've calculated is larger than my whole.

And therefore I've used the incorrect symbol.

Or I've used the incorrect operation to solve this equation.

So that one is a fairly straightforward error that we can correct very easily.

I'd like you to have a look at these two now.

The first one on the left and the second one is on the right.

I would like you to see whether you can work out, what the error is, that has been made.

And how you know.

If you're finding it challenging, one thing I would suggest is to actually work it out yourself.

If you were to work out the calculations yourself, you can probably work out where, this person has gone wrong.

So pause the video now to complete your task, and resume it once you've found the errors.

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

So on the left hand side here, the error that has been made is if you look at the very first column, two minus four, this person should have regrouped, when calculating the answer to this.

Instead of regrouping, what they did was they swapped around the four and the two.

And they did four minus two.

And then they continued with the rest of the equation.

They also did exactly the same thing here.

They swapped the seven and the three.

Now, subtraction is not commutative, in the same way that addition is.

So you cannot swap around the numbers, and your answer will not be accurate if you do that.

So in order to do this, regrouping would have been required.

So therefore this answer is incorrect.

On the right hand side here, there's a slightly different error that has been made.

As you can see here, the first thing they've done is they've tried to do one minus three, which they couldn't do.

So they regrouped from the two tens here, and they did eleven ones minus three.

Which they were correct and saying was equal to eight.

However, what they didn't do was cross out their one here.

Also their digit in the tens column, the two in the tens column, and make it into one ten.

Because actually, what they would have seen is that this digit here should have been one instead.

Similar errors have been made, later on in the equation as well.

So you can see often, we need to calculate the answer to the problem, in order to work out what the error has, what the error is.

And it's really important we look for these errors in our own calculations.

Because they're quite easy to make.

Final thing we're going to look at is completing incomplete column methods.

So as you can see on the screen here, we've got an example of this.

We've got a column method equation that has been written out, but we have got it is currently incomplete.

And we need to work out what the digits in the boxes should be.

So let's have a look at it together.

I'm going to start with my ones column, just like I always do.

So I'm looking just down on my ones column here, and I've got eight ones, plus one one.

Which is equal to nine ones.

Nice and easy.

So that first part here I've completed.

Now it's slightly more challenging, because I've got to complete one of my parts.

I've got nine tens here.

And five tens add something, is equal to nine tens.

What do I add to five tens to give me nine tens? I add four tens.

So this should say four up here.

Okay, looking at my hundreds now.

I've got three hundred plus zero, which is equal to three hundred.

That is correct.

Now I'm looking at my thousands.

Now this is where it gets a bit more challenging, because I can see that it says, six thousand plus something is equal to five thousand.

How can that be possible? How can I have a smaller number in my thousands answer, than I do in my first part, in one of my parts? Well, actually, I wonder whether regrouping has happened here.

Let's imagine that instead of five thousand, this was equal to, fifteen thousand.

Let's imagine I regrouped a ten thousand up here.

So in order for me to, have achieved fifteen thousand, what do I add to six thousand to give me fifteen thousand? Well, I add nine thousand.

So now that will be correct.

And then I've got ten thousand.

So then thousand plus fifty thousand, plus twenty thousand, which is equal to eighty thousand.

Just there.

So you can see how you might need to work with some regrouping.

The best thing I can now do, if I wanted to double check this, is to write out my equation, again, recalculate it, check.

Does it make sense? Is it correct? Let's move on to your independent task for today.

Today, you've got lots of different problems, to complete today.

For the first couple, you're going to be adding and subtracting, using the column method.

And I'd like you to estimate and then calculate.

You're then going to see whether you can find the error that has been made, in this particular equation here, for question three.

And then I'd like you to create your own word problem, and your own bar model to match it, for question number four.

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

Okay, so how did you get on? Let's have a look at the first couple of answers.

So you can see here the answers to the questions are written there.

Your estimations aren't put on there, because you might have rounded to the nearest hundred thousand, ten thousand, thousand.

So I put on your final answers, which should have been the calculations that you, The answers you got to go calculations when you did the column method.

And the error that you should have spotted, is the digits were not aligned correctly.

You can see the digits for the second number here, should have been moved along one digit.

Because they were not in the correct columns.

And therefore the answer was incorrect.