Lesson video

Hi, everyone.

Thank you for joining me.

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

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

So looking at our lesson agenda first of all, we're going to begin with a warmup which is going to be a recap of column edition.

We are then going to look at column subtraction using place value counters and then we'll look at how to subtract using a column with estimation before.

And we'll finish with some bar modelling before your independent task and quiz at the end of the lesson.

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

So find these resources first, press pause now.

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

Let's begin with our warmup.

Our question asks, can you estimate and calculate the answer to 341,228 plus 543,821? So thinking back to how we estimate and why we estimate.

Well, first of all, the reason why an estimation is really handy with a question like this is that it offers us an opportunity to get an approximate answer to compare our actual answer to later on.

If our estimation and our actual answer are completely different, we know we've made an error somewhere and we need to go back and correct our mistake.

So when we estimate we could round our numbers to the nearest multiple of 100,000, 10,000, 1,000, 100, we decide.

In the past we've been rounding to the nearest multiple of 10,000.

So that's what we'll do today.

Let's look at these two numbers and round to the nearest multiple of 10,000.

So starting with the first one, I can see that the digit in the ten thousands is a four and I'm looking next door.

I can see that we're going to be rounding this number down to the smaller multiple of 10,000.

What is this number rounded to the nearest 10,000? It is 340,000.

Let's look at the next number.

Again looking at the digit in the 10,000 column I can see I'm also going to be rounding this number down.

What is this number rounded to the nearest multiple of 10,000? It is 540,000.

So here I go with my estimation equation.

I've got 340,000 plus 540,000.

Let me use my partitioning to work out what this would be.

Let me add my hundred thousands first.

So I've got 300,000 plus 500,000, which is equal to 800,000 and I've got 40,000 plus 40,000, which is equal to 80,000.

So I might, I know my answer when I actually come to calculate it should be around 880,000.

Let's move on to our calculation now and see what we get for our answer.

So I'm going to lay out my calculation and using my column method.

I've got 341,228 lining up my digits, 543,821.

We're putting the addition sign there so we know what we're doing.

And we're putting our equal sign at the bottom.

I'm going to change the colour of my pen so we can see what we're doing as we create our final column addition here.

So let's start with a ones column.

Eight ones plus one one is equal to nine ones.

So nine just goes here.

Now I've got my tens column.

Two tens plus two tens is equal to four tens or we could say 40.

if we want to.

Then we're looking at hundreds.

I've got 200 plus 800, which is equal to 1000.

I'm going to need to regroup because this is the same thing 10 hundreds.

So I'm going to regroup those 10 hundreds for one, 1000.

So now I've got 1000 plus 1000 plus 3000, which is equal to 5,000.

Then looking at my ten thousands column here, 40,000 plus 40,000 is equal to 80,000.

And then looking at hundred thousands column, 500,000 plus 300,000 is equal to 800,000.

And you can see that the similarity between our estimation, which was 880,000 and our calculation which was 885,049.

So let's move on to column subtraction with place value counters.

So we've practised our thing.

We've practised using the column method in order to add.

Let's look at how we would use the column method with place value counters in order to subtract.

The first thing I'm going to be doing is representing my equation or the first number in my equation using place value counters.

Let's read the equation together first of all.

The numbers in the equation are 45,325 minus 4,317.

The first thing I'm going to do is have a go at representing this number here using place value counters on my place value charts.

So I can see straightaway I don't have any hundred thousands.

I'm going to move straight onto my ten thousands.

I've got four, ten thousands.

So I'm going to put those in that one, two, three, four.

How many thousands do I have? I have five.

So I'm going to put five in here.

One, two, three, four, five.

How many hundreds do I have? I have three.

So I'm putting 300 in that.

How many tens do I have? I have two and I've got five ones.

One, two, three, four, five.

Now, if I want to add my 4,317, I'd be putting some extra place value counters in here to add them but I'm actually going to be subtracting.

So what I'm going to do is change my pen colour so you can see how I might subtract 4,317 from my 45,325.

The first thing I need to do is start with my ones.

Let's have a look.

I'm going to try and subtract seven ones.

I'm going to get my ones column.

I've got a problem.

Can you see what my problem is? There were only five ones currently.

I need to subtract seven ones.

So what I'm going to need to do is to take one of the tens and to regroup it for 10 ones.

One, two, three, four, five, six, seven, eight, nine, 10, because I need to subtract seven.

So I didn't have enough so I needed to recreate one of those tens.

Now I can cross out seven of my ones, count with me.

One, two, three, four, five, six, seven.

I've subtracted seven ones there.

How many ones do I have left? I have eight ones.

So I'm going to put an eight just down there to show that's something I've got left.

So now it's like how many tens I need to subtract.

Well it says I've got to subtract one ten.

That's great, I only have one ten in there anyway.

So I'm going to subtract that one ten and you can see I'm left with no tens.

Looking at my hundreds now.

How many hundreds do I need to subtract? Ah, I've got 300 to subtract.

Well, that's great as well.

I only have three hundreds in there, so I'm going to subtract those one, two, three, and I have no hundreds left over.

How many thousands do I need to subtract? I need to subtract four.

Let's count them.

One, two, three, four.

I'm left with 1000 and 40,000 because I've got four in my ten thousands.

So my final answer is 41,008.

So you can see that we've picked too really.

That means with a picture represented this equation using place value counters, we needed to regroup ones for our ones column.

And we did that by taking one of the tens and breaking it up into 10 ones so that we could subtract our seven.

So now it's your turn.

I'd like you to have a go at this very same activity.

You've got the equation 399,622 subtract 158,351.

Can you use a place value table that you draw on your piece of paper? Can you draw in the place value counters for your first number and subtract 158,351 regrouping if necessary? Here's a hint.

You are going to have to regroup in at least one of the columns.

You are going to have to regroup at least one.

Okay, have a go, pause the video and then resume it once you're ready to see the answer.

Okay, how did you get on? You should have gotten answer 241,271.

If you are not quite clear on that or if that wasn't really what you got, go back and have another calculation check that you have regrouped where necessary to help you with this equation.

So let's look at column subtraction with estimation now.

Let's look at this equation on the screen, let's say it together, 872,119 minus 43,257.

We're going to have a go at answering this question using our column method.

We're not going to use the pictorial method anymore.

We're going to use the abstract method where we just use numbers.

But before that we're going to need to create an estimation, reminding ourselves that an estimation is a great way for us to create a comparison between our actual answer and our estimate to make sure that we are accurate with our calculations.

Let's begin by rounding this first number to the nearest multiple of 10,000 just like we did before.

So I'm looking at the digit in the 10 thousands column and I'm going to take a peek next door to see whether I'm rounding up or down.

I can see in this case I'm going to be rounding down.

So I'm rounding to 870,000.

Now looking at the next number.

And I also can see I'm going to be rounding down here to 40,000.

So now that I've got my equation for my estimation, I can calculate what the answer would be.

What I can see here that actually my 800,000 is going to stay the same because I'm not subtracting any hundred thousands but I'm subtracting 70,000, sorry, 40,000 from 70,000.

So I know the seven minus four is equal to three.

So 70,000 minus 40,000 must be equal to 30,000.

So my full estimation is 830,000.

Now that I've created my estimation, I'm ready for my calculation.

So this time I'm going to lay out the exact numbers, 872,119.

I'm going to use my subtraction symbol 43,257.

And be really clear on how you're aligning your digits.

So you can see that I've made sure I didn't put digits for the second number in the hundred thousands column, because there are no hundred thousands.

If you put a number in there, if you put digit in there, your calculation will be incorrect.

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

And looking at this calculation, I can already see that I'm going to need to be doing some regrouping in order to calculate the answer.

Can you have a look at that equation in the column using the column method.

Can you see which columns are going to require some regrouping? I'm going to give you five seconds to see if you can have a guess.

So you might've seen that we're probably going to need to regroup in the tens column because you can see the second digit is much greater than first.

We're also going to need to regroup in the hundreds column again because of the second digit is greater than the first and also in the thousands column there, the ten thousands, the hundred thousands, and the ones look okay to me.

But we'll have to see as we go along.

So let's start with ones.

We've got nine ones minus seven ones, which is equal to two ones.

So I'm going to put two just in there.

Then looking at my tens column, I've got one ten minus five tens.

I cannot do this without regrouping because one ten is much less than five tens.

So I'm going to need to take one of my hundreds just here and regroup it for 10 tens.

So now I've got 11 tens, and then I've got 11 tens minus five tens, which is equal to six tens.

Now looking at my hundreds, I've got zero hundreds subtract two hundreds.

Can I do that? I can't.

I'm going to need to regroup again.

I'm going to take one of my thousands here.

So now I only have one thousand and regroup it for my 10 hundreds here.

So I've got my 10 hundreds minus my two hundreds, which is equal to eight hundreds.

Then I've got 1000 minus 3000.

Again, I can't do this, I'm going to need to take one of these ten thousands.

So now it's sort of one of these ten thousands.

So now I only have 60,000 in there.

I'm going to take one over here.

So I've got 11,000 minus 3,000, which is equal to 8,000.

And then I've got 60,000 minus 40,000, which is equal to 20,000.

800,000 minus nothing which is equal to 800,000.

Again, making comparison between my estimation and my actual answer, it looks like we're about spot on with that.

We could double check using different methods using the inverse, for example, but for the moment it looks like we're okay.

And our guess as well that we had to regroup in our tens, in our hundreds and in our thousands was correct.

We also can see that we had to take some from our ten thousands.

We had to take one from our ten thousands so that was regrouped there.

So moving on, let's have a look at another example.

This time, let's say the equation together.

It says 598,104 minus 358,221.

What are we going to do first? We're going to estimate, and we're going to estimate by rounding to the nearest multiple of 10,000.

So let's get started with having a go at this.

So let's look at the digit in the ten thousands here.

Now I can see I'm going to have to round this up.

And because I've got 90,000, the next 10,000 up I'm going to need to regroup.

So this rounds to 600,000, then looking at my next number I'm subtracting.

And I'm also rounding up for this one I'm subtracting 360,000.

And in order to calculate this, I'd like to use regrouping.

So I'm going to create, or I'm going to partition.

I beg your pardon, I'm going to use partitioning here.

I'm going to partition this out into 300,000 first and then 60,000.

And I'd like to subtract my 300,000 first and then subtract my 60,000.

So I've got 600,000 first and minus 300,000, which is equal to 300,000.

And then let me subtract my 60,000.

Well, if I'm doing 300,000, subtract 60,000, have a think, have a go.

First of all, think about maybe your number bonds there.

30 minus six might help you with this one.

What is the answer to 300,000 minus 60,000 is 240,000.

So my answer should be similar to 240,000.

Well, have a look once we calculate it.

So writing out my digits again, 598,104 minus 358,221 drawing my equal sign.

This is a six digit minus a six digit equation.

Which columns will require regrouping for this particular equation can you see? You can see that the ones look okay, the tens will need to regroup for, hundreds will need to regroup for.

We will inevitably then need to regroup the thousands I imagine.

And the ten thousands and hundred thousands at the moment look okay.

So we'll have to see how our regrouping looks, but again a lot of regrouping required to subtract this number 358,221 from 598,104.

Let's start with our ones again.

Four ones minus one one is equal to three ones.

So I'll put three just in there.

Then I've got my tens, zero tens minus two tens.

I can't do this, I'm going to need to regroup.

So I'm going to take one of my hundreds and regroup it for 10 tens.

So now I've got 10 tens minus two tens, which is equal to eight tens.

Look at my hundreds there, I now have no hundreds minus two hundreds I can't do that.

I'm going to need to regroup again.

So now I've got 10 hundreds minus two hundreds, which is equal to eight hundreds.

Looking my thousands, I've got 7,000 minus 8,000.

Can't do this, I'm going to need to regroup again.

So here I go, regrouping for my ten thousands.

So that's my 17th and I've got 17,000 minus my 8,000, which is equal to calculate it really quickly, 9,000.

And then I've got 8,000 minus five, sorry, 80,000 minus 50,000, which is equal to 30,000, 500,000 minus 300,000, which is equal to 200,000.

So lots and lots of regrouping there you can see.

But when we compare this to our estimation, it looks about accurate to me.

That's why the estimation is so important to do initially.

So now we've had a go at that, it's your turn.

There are two equations on the screen there, which I'd like you to first of all create an estimate for by rounding to the nearest 10,000.

You can round to the nearest 100,000 if you'd prefer, but remember your estimation might be a little bit further away from the actual answer than it would be if you round to the nearest 10,000.

Once you've created your estimation, calculate the answer using the column method.

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

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

So for the first calculation, you should have got 600,749.

After the second, you should have got 538,428.

Hopefully did okay with that and you created your estimations as well.

Okay, the final thing that we're going to look at today is something called bar modelling, which you might have heard of before, but it's a way of us representing equations or word problems and matching these to actual calculations.

So you can see on the screen there, I've got a bar model.

I've got a long bar at the bottom there, which says it's equal to 324,631.

And then I've got a shorter bar just above it, which says that's equal to 162,310.

The first question says, what equation is being represented by this bar model? So I can see that the longer bar and the shorter bar, our values have been given for those, but we want to know the difference between them.

That's why there's a question mark above the difference between the two bars.

In order to find the difference we are subtracting.

So my equation would be 324,631 minus 162,310.

And that is what that bar model is representing there.

Let's go straight onto our estimation.

We are estimating by rounding to the nearest multiple of 10,000.

Can you really quickly work out what the equation will be for our estimation, five seconds.

Okay, so you might have seen, our estimation is going to be 320,000 minus 160,000.

Now let's work out what this would be.

I'm going to use my known facts to help me here.

I want to look at the fact that 32 minus 16 is equal to 16.

I know that because if I double 16, it gives me 32.

So effectively I'm halving it here.

So 320,000 minus 160,000 is equal to 160,000.

That is my estimation done and dusted.

Let's move on to our actual calculation.

So first of all, I'm going to lay this out 324,631 minus 162,310, creating my equal sign.

And then I'm going to swap pen colour so we can see where we're regrouping.

And I can see that not as much regrouping will be required in this one, but we might need to do some regrouping.

Let's start with our ones column, one minus nothing is equal to one.

Looking at our tens, three tens minus one ten is equal to two tens.

Looking at our hundreds, 600 minus 300 is equal to 300.

Thousands, we haven't had to regroup so far yet.

Let's see 4,000 minus 2000 is equal to 2000.

Right, our ten thousands here, 20,000 minus 60,000.

We can't do this, we're going to have to regroup.

We're going to have to take one of these hundred thousands.

So now I've got 12 in my ten thousands minus six in my ten thousands, which is equal to 60,000.

And in 200,000 minus 100,000 is equal to 100,000.

So my answer is 162,321.

Looking at that comparison between my estimation and my actual answer looks about similar.

I can also see it's very, very similar to my original number inside my equation.

So we can see this is almost exactly half way between our whole and the first of our parts, which is really interesting, which is why a bar model took up about half of the original bar.

So now it's our turn.

Let's start by representing this equation using a bar model.

It says 653,119 minus 120,401.

If you'd like to pause the video now, have a go at creating your own representation of this equation using a bar model.

Resume it once you're ready to have a look at how we might do it together.

Okay, let's see how we might do this.

So we're going to do it the same way that the previous bar model was demonstrated.

So I'm going to start with my larger bar below.

This is going to be equal to 653,119.

My smaller bar is going to be at the top and it's going to be a fair bit smaller.

It's going to be about a sixth of the size, in fact that's probably even potentially slightly too large.

So I'm going to just make it a little bit smaller.

And that is equal to 120,401.

And this is the part that we don't know.

So you can see already here, there are part that we don't know, the part that we are calculating.

It's going to be larger than 120,401.

And it's going to be less than 653,119.

That's why bar modelling is quite useful.

It helps us give us a bit of an approximation, a bit of an understanding of what numbers we're dealing with.

So now it's time for our estimation.

Can you round those two values to the nearest multiple of 10,000 in order to estimate or create our estimation equation? I'm going to give you five seconds.

So you should have seen that our calculation is 650,000 minus 120,000.

And again, I'm going to see whether I can use my partitioning.

So I'm going to start by doing 650,000 minus 100,000 that's 550,000.

Then minus my 20,000, which is equal to 530,000.

And now we're ready for our calculation.

So we're going to put our original numbers back in.

So 653,119, we're subtracting 120,401.

Whilst I go and change the pink colour, have a look and see if you can work out where any regrouping is going to be required.

What do you think? Any regrouping here? I have a feeling we're going to need to regroup at least once in this, let's see what actually happens.

Starting with our ones we've got nine ones minus one one, which is equal to eight ones.

Great, then we've got one ten minus nothing, which is equal to one ten.

We've got 100 minus 400.

Now this is where regrouping is going to be required because we can't do that.

Let's go and take one of the thousands and regroup it.

So now we've got 11 hundreds minus 400, which is equal to 700.

And then we've got 2000 minus nothing which is equal to 2,000.

50,000 minus 20,000, which is equal to 30,000 and 600,000 minus 100,000, which is equal to 500,000.

And looking again at our estimation, that seems fairly accurate to me.

It also seems fairly accurate that this would take up this much space on our bar model, this number here, because it's a lot greater than 120,401.

So now it's time for your independent task.

You've got a series of three equations, which you will be required to create a suitable estimate for before calculating using the column method.

And then for question two, can you create a bar model first to represent and then calculate the answer to the equation you'd been provided with? Pause the video to complete your task and resume it once you're finished.

Okay, how did you get on with those? So as you can see the answers to A, B and C and question two are on the board there.

And hopefully that estimation process that you completed was helpful in helping provide you with a rough approximate answer prior to calculation.

If you'd like to please ask a parent or carer to share your work on Twitter today, tagging @OakNational and hashtag learn with Oak.

Now it's time to complete your quiz.

Thank you so much for joining me for today's lesson.

It's been great to have you do join me again soon.

Bye bye.