Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you on this lesson from our unit on reviewing column addition and subtraction.

Are you ready to work hard? Are you ready to remember, perhaps some things that you've learned before? Well, if so, let's make a start.

In this lesson we're going to be looking at the known facts and strategies we can use to calculate efficiently and to check our column additions.

Lots of things hopefully, that you've learned about before.

Known number facts, doubles, near doubles, maybe using numbers that are close to 10, close to 100.

Lots of strategies that hopefully you'll have seen before, but we're going to look at how we can use them to help us to be accurate with our column additions.

And also to check that we've got our column additions correct.

Let's look and see what's going to be in our lesson today.

We've got three keywords today: efficient, estimate, and regrouping.

I'm going to say them, and then you're going to repeat them back.

My turn, efficient.

Your turn.

My turn, estimate.

Your turn.

My turn, regrouping.

Your turn.

Well done.

Let's look at what those words mean.

You may have come across them before, but it's always useful to go back and have a think.

Being efficient means finding a way to solve a problem quickly whilst also maintaining accuracy.

We want to be quick, but we want to be sure we're getting it right, and being efficient is doing both of those things.

Estimation means to find a value that's close enough to the right answer, usually with some thought or calculation involved.

We're going to give that, well, it's about that sort of answer, and that will help us to check when we've calculated to make sure that we're in the right area with our answer.

And the process of unitizing and exchanging between place values is known as regrouping.

For example, 10 tens can be regrouped for 100, and 100 can be regrouped for 10 tens, and you might have come across regrouping when you've been doing your column additions so far.

Let's get on with the lesson.

In the first part we're going to be making use of facts and strategies, and in the second part of the lesson we're going to be checking column addition, using those facts and some strategies as well.

And we've got Alex and Lucas helping us in our lesson today.

Alex is finding column addition a bit tricky.

Oh dear, Alex, let's see if we can help you out.

He says, "There's so much to remember." Well that doesn't sound right, Alex.

Column addition should make sense to us, we should know what's going on.

So let's have a look, see if we can help Alex.

Lucas says, "You need to use what you know, let's take a look at column addition," he says.

Here's a column addition to work out, 273 add 477.

Lucas says, "Look really carefully at the digits.

"What do you notice?" What do you notice? What could you help Alex with? Well, Alex says, "I can see a number pair that is equal to 10." Can you see it too? Three ones add seven ones, is equal to 10 ones, and 10 ones are regrouped as one 10.

We'll have a one regrouped into our tens and zero in our ones, because all our 10 ones have been regrouped into a 10.

We've got no extra ones to record.

Alex says, "There's a double too, I know that double seven is equal to 14." Oh, that's interesting isn't it? Did you spot the double as well? So, seven add seven is equal to 14.

But what else have we got to remember? Ah, seven tens add seven tens, add the regrouped 10 is equal to 15 tens.

And 10 of those tens are regrouped as 100.

So, we're going to have 10 of the tens regrouped as 100 and the five tens in our tens column.

What else do you notice then? Well now it's quite straightforward, isn't it? We haven't got any regrouping to do, because it's two hundreds plus four hundreds, plus the regrouped 100 is equal to seven hundreds.

So, our answer is 750.

Alex says, "That made it much easier." Looking really carefully at the digits and thinking what you know about the numbers can really help you when you're using column addition.

Alex looks carefully at each column addition.

I wonder what he's going to spot.

So, here are three column additions.

What would you be hoping that Alex would spot about these? You might want to have a little look yourself, before Alex has a look.

What's he going to find? He says, "I'm looking for number pairs that total 10, and doubles." Can you see any number pairs at total 10, I wonder? Can you see any doubles? Five tens add five tens, is equal to 10 tens.

We've got a double there, five and five is equal to 10.

We've got another double here.

Seven add seven is equal to 14, seven ones add seven ones.

Oh and there's a pair, that makes ten two tens add eight tens, is equal to 10 tens, which would be regrouped as 100 in our column addition.

And there's a near double.

Eight tens add seven tens, is equal to 15 tens.

You might've worked it out from the seven, add seven equals 14, and added one more, or you might've known eight add eight equals 16, and taken one away.

But eight add seven is a near double and it's equal to 15.

15 tens in this case.

Did you spot all of those? Time for you to have a look.

You're going to look at some column additions and you're going to look for pairs that total 10, and doubles, and maybe some near doubles as well.

Are you ready? Here are your column additions.

Pause the video and just look for those known facts.

We don't want the answers this time.

Then pause the video, we'll come back for some feedback.

How did you get on? Did you spot a pair that makes ten? Nine ones add one ones, is equal to 10 ones.

And what would happen to the 10 ones? That's right, they'd be regrouped into the tens.

There's a number pair that's equal to 10.

What else did you spot? Aha, did you spot the double eight? There's a double, eight tens out eight tens is equal to 16 tens.

Anything else in here? Ha, there's a near double.

Five add four is equal to nine.

And one more, do you think? That's right, yes.

Another pair that makes ten.

Three tens ad seven tens, is equal to 10 tens.

And you could then think about what would happen to those 10 tens.

They'd be regrouped into 100 and added in with the hundreds.

Well done if you spotted all of those known facts.

It's really useful to look out for those when you're doing your column additions.

Alex is looking at this column addition, he's got 632 add 199.

He says, "This looks tricky, I need to regroup in the tens, and in the ones." He's spotted that.

Well spotted Alex.

Yes, we've got to regroup in the ones and the tens.

He says, "I can't see any number pairs that are equal to 10, or any doubles." It's not looking good, is it, Alex? Lucas says, "Sometimes column addition isn't the most efficient method." Remember efficient was something that was quick but reliable in getting us the right answer.

Lucas says, "It might be more efficient to use a mental strategy or to jot down your thinking." What do you notice about those numbers? Lucas says, "199 is equal to 200 minus one.

It's only one away from 200.

Adding 199 is the same as adding 200 and then subtracting one." Perhaps we could do this as a mental strategy.

632 add 200, subtract one.

What's 632 add 200, can you work that out? We're only changing the hundreds aren't we? 632 add 200 would be 832.

But then we've got to subtract the one and 832 subtract one, is one less is 831.

So our answer was 831 and I think that might be more efficient than doing all those regrouping in the ones and the tens.

And Alex says yes, "That looks much easier than using column addition." It's always good to look at the numbers carefully.

Is there an easier or more efficient way you can work? Alex looks at some other calculations.

He says, "How do I know whether to use addition or not?" Is there a better strategy? Have you had a look at those? Can you think of where you'd use column addition and where you might use a better strategy, or a more efficient strategy? Lucas says, "Look carefully at the numbers.

Is there a more efficient way to add them?" What do you think? Well, a mental method would be efficient for this calculation.

Alex could add 300, and then subtract two to find the answer.

'Cause 298 is 300 subtract two.

What about the middle one, what do you think? Column addition is a good choice here.

The ones digits have a total of 10, so there's a six plus four in the tens, but then the tens digits are more difficult and we've got some regrouping to do there.

And there aren't any numbers that are close to a hundred, or a multiple of a hundred.

I think column addition is a good idea here.

What about the last one? Well, column addition could be used.

But did you spot that we've got 51 add 49, or 49 add 51, and they are equivalent to a hundred, 'cause they're almost like doing 50 add 50.

If we take the one from the 51 and give it to the 49, we've got 50 add 50.

So we could calculate this mentally if we'd spotted that pair of numbers that equal a hundred.

Time for you to have a go.

Look at these three calculations, and what do you notice? Look carefully at the whole numbers.

What's the most efficient way to add them? So look carefully, maybe have a chat to someone about them and decide which is the most efficient way to add these pairs of three digit numbers.

Pause the video, have a think, and we'll talk about them together.

What did you reckon? Or for this first pair, 555 add 459 column addition is a good choice here.

The tens digits have a total of 10, five tens add five tens.

But, the numbers are difficult to add mentally.

And we've got some regrouping to do from the ones into the tens, and then from the tens into the hundreds as well, haven't we? So there might be a lot to keep hold of in our heads, but no real friendly numbers to make us think it would be easy to do in a mental calculation.

What about the middle one, 570 add 230? Anything you spotted there? Yes, well a mental method would be quite efficient for this.

Did you spot the 70 add 30? 70 add 30 is equal to 100, 7 tens add three tens.

We've actually got 500 plus 200 plus another hundred.

Our answer would be 800.

And what about the last one? Did you spot something there? Yeah, column addition might be good, but there is a mental method we could use isn't there? Lucas says, "I could add 202 and 700 mentally, and then subtract one from my answer." He spotted that 699 is only one away from 700.

Some different ways of thinking about those calculations.

You don't always have to use column addition.

Sometimes there is a more efficient strategy that we can use mentally.

Useful to look out for that as you work.

Time for you to do some practise now.

You are going to use column addition to calculate each sum, but you're going to look carefully for pairs at total 10, doubles and near doubles as you work.

Think about Alex trying to make things simple for himself as he used his column addition strategy.

Look for those pairs that make 10, doubles and the near doubles.

And then for part two, you're going to have a look carefully at each calculation and think about whether to use column addition, or a different strategy.

Pause the video, have a go, and then we'll come back and look at them together.

How did you get on? Well here are the answers to our calculations, to our column additions.

But what I wanted you to do was to look for those pairs that make 10 and those doubles.

Did you find any? Was a double in the first one isn't there? Seven add seven, is equal to 14.

What else did you spot? There's a pair that makes ten.

Six ones add four ones, is equal to 10 ones.

So we'd record a zero in our ones column and we'd regroup the 10 into the tens column.

Anything else? Oh, that's an interesting one.

Once we've regrouped that 10, we've got eight, add one, add one, eight, add two, which is another pair that equals 10.

So we had another regrouping to do and a zero in the tens.

Our sum for B was 900, that's interesting, isn't it? You might have spotted that 86 and 14 is equal to a hundred.

I wonder if you spotted that.

And in C we had another double.

Five add five is equal to 10, giving us another zero in the ones because our 10 ones were regrouped as a 10.

And can you see something else in that calculation? That's right, nine add eight is a near double, but with our regrouped 10 we've also got nine add nine.

We've actually got the full double there, haven't we? Nine add eight, add one, it's the same as nine add nine, and it's nine tens add nine tens, which is 18 tens.

We've regrouped another 10 tens into a hundred.

I hope you spotted all those known facts that would help you with those calculations.

And what about part two where you were looking for the different ways of working? We've got the answers here, but I wonder how you calculated them.

99 out 57 could be calculated efficiently using a mental strategy.

57, add 99, t's like adding a hundred and subtracting one.

57 outta a hundred would be 157.

Subtract one would be 156.

An efficient mental strategy was a good way of solving A.

What about B? I think B was the one to do with the column addition.

There weren't any really friendly facts there, and there was a bit of regrouping to do.

So it made it a bit trickier, but nothing friendly to make us think that we could do it as a mental calculation.

And what about C, anything you spotted about C? Look at the tens.

Ah, there's a pair that make 10 there, but that also means that we've got a pair that total a hundred.

60 plus 40 is equal to a hundred.

560 plus 240 we can think of as 500 plus 200, plus another hundred, which would equal 800.

That would be a quick mental calculation.

No need to do a column addition there.

What about D, did you spot the 298? Yes, that's close to 300, isn't it? We could add 300 and subtract two.

What about E? The 555 makes it look quite friendly, doesn't it? But we are not adding on numbers that are that friendly.

There is a pair to make 10 in the tens, but we had to regroup in the ones as well, haven't we? I think a column addition is probably a good way of working for E.

And what about F? Well you could have used your column addition strategy, or you could have thought about adding 300 onto 278 and then adding on the three.

Perhaps adding two to make 580, and then another one to make 581.

You might've spotted that as a mental strategy, or you might've done a column addition, but I hope you were successful, and I hope you had a good think about which was the most efficient strategy to use.

Okay, onto the second part of our lesson where we're going to be checking column addition.

Alex is wondering how he could check this answer.

He says, "I've added two numbers together, how do I know whether I've got the correct answer or not?" This a very good question, Alex.

Lucas says, "There are a few strategies, but let's start by thinking about odd and even numbers." Hmm, that's an interesting thing to think about.

Alex says, "I know that two odd numbers add together to equal an even number." I wonder if we could think about that with the ones digits.

Seven and five are both odd, so they add together to equal 12, which is even, so can we see that in Alex's calculation? Yes, we can.

Seven add five, equals 12.

12 ones, we've had to regroup 10 of them into the tens column, but we can still see that answer of 12.

So that looks good.

Alex says, "I know that an even and an odd number add together to equal an odd number." Hmm, but what do you notice about the tens? Eight is even and five is odd, and they add together to equal 13 tens.

But the regroup 10 is then added in to equal 14 tens.

So we do have an even number.

Eight tens outta five tens is 13 tens, plus another one is 14 tens.

10 of those are regrouped into the hundreds and four are left in the tens column.

Alex checks a different column addition.

He says, "I've added together two numbers and I'm checking the answer by thinking about odd and even numbers.

An even number add an even number is equal to an even number six, eight, and 14 are all even numbers." And six add eight, is equal to 14.

An even number add an odd number is equal to an odd number.

Three add four, is equal to seven.

Hmm, can you see what's happened here? Wait, says Alex, "I've forgotten to add the regrouped 10.

The answer should be an eight in the tens, not seven tens." That's not correct, is it Alex? But good checking to spot that answer.

Four plus three is equal to seven, but he forgot to add in the regrouped 10 to give him eight tens.

Can you check Alex's column addition here? Alex says, "Use odd and even numbers to help you work out if I might have the correct answer or not." Pause the video, have a look, and then we'll have a talk about it together.

How did you get on? Alex says, "An even number add an odd number, is equal to an odd number.

Nine add six cannot be 14, because 14 is even and not odd." Ah, well spotted Alex, that's not correct, is it? His answer isn't correct, he's made a mistake adding his ones.

What do you think the correct answer should be? Alex is wondering how else he could check this answer.

He says, "I'm still not sure it's definitely right." He's used his odds and even knowledge to think about it, but has he got the answer right? How else could he check it? Ah, Lucas says, "You could use estimation, use numbers that are really easy to add together to give you a rough idea of the actual answer." We're gonna find some easy numbers to add together that are close to the numbers that we've got in the addition that we're trying to work out.

Lucas says, "487 is close to 500, and 455 is very close to 450." So if we add 500 and 450, we'd have a good estimate of the answer And Alex says, Those numbers are easy to add together.

500 add 450 is equal to 950." "Brilliant work," says Lucas.

"Your estimate is 950, which is really close to the answer that you got." Alex tries estimating the answer to this calculation.

What would you give as an estimate do you think? He says, "I need to choose numbers that are easy to add together and close to the actual numbers.

319 is close to 300, and 278 is close to 300 as well.

300 add 300 equals 600.

600 is a good estimate for the sum of 319 add 278." What do you think would be the best estimate for this calculation? Is it A, B, or C? Alex says, "Which numbers are easy to add together and close to the actual numbers?" Pause the video, have a think, and we'll talk about the answer together.

What did you reckon? Well, A is an estimate that would be really close to the actual answer.

387 is close to 390, and 446 is close to 440, but the numbers aren't that easy to add together are they? So it would give an accurate estimate, but we'd have to do quite a lot of work to add the numbers together.

Perhaps not the best estimate.

Let's look at C.

The estimate would be really easy to calculate, but 446 has been changed into 400.

So the estimate would not really be all that accurate.

You have to have something that's close to the original number.

So maybe not C.

What about B then? This estimate is easy to calculate and would be close to the actual answer.

This would be the best estimate.

Well, 387 is close to 400, and 446 is close to 450.

Those numbers would be easy to add together and are close to the original numbers.

B would be the best estimate for this calculation.

Alex thinks his answer is definitely correct.

"We've looked at whether the answers should be odd or even, and we've estimated the answer.

"I'm sure this must be the correct answer," he says.

Lucas says, "We haven't found a mistake, but it doesn't mean it's the correct answer.

You might still have made a mistake.

It's a good idea to get a friend to work it out.

Then you can check you have the same answer.

And I've got a friend I can ask," he says.

Haha, that means you.

Time to check your understanding.

Can you check Alex's answer, use column addition to add the digits together.

Pause the video, have a go, and let's check and see if you did get the same answer as Alex.

How did you get on? Lucas says, "You should have worked out the answer to be 942." Let's see if you did.

Seven ones add five ones, is equal to 12 ones, that's 10 regrouped into a 10, and two in the ones column.

Eight tens add five tens is 13 tens, add another 10 is 14 tens.

That's 10 tens to regroup into the hundreds, and four tens in the tens.

And then four hundreds add four hundreds, add one more hundred is nine hundreds.

942, yes you were right, and so was Alex.

"If you get the same answer as a friend, it's probably right unless you both made the same mistake." And then it's always wise to do it again.

See if you can match one of the answers.

Time for you to do some practise.

Alex has used column addition to calculate these sums. Can you check his work? Can you find any mistakes? Lucas says, "Think carefully about odd and even numbers and use estimation to help you too." For part two, you're going to work out the sum for each column addition, and you're going to check your answers carefully, thinking about odd and even numbers, estimation, and working out the answer again.

And Alex says, "Remember to use number pairs at total 10, and doubles to help you too." Pause the video, have a go at your tasks, and then we'll get together for some feedback.

How did you get on? Did you check Alex's work? What did you spot in A? Well, we've got an odd number plus an odd number, and that must be equal to an even number.

Seven add nine can not equal 15, so A is not correct.

What about B? Hmm, 300 add 300, is equal to six hundred.

Nine hundred and sixty four is too far away from this estimate and cannot be correct.

Unfortunately B is incorrect as well.

What about C? Yep, this answer is correct.

Five ones add seven ones.

An odd number plus an odd number is going to give us an even number.

We had a five plus five to equal 10, plus our regrouped one to give us 11 in the tens and then five hundreds plus 100, plus the regrouped hundred, equals seven hundreds.

So C was correct.

And what about two? You were looking for ways to check your own calculation and looking for those pairs of numbers to help you.

What did you spot? Well, we made an estimation for A.

We said that 400 add 200, equals 600 is a good estimate.

The answer 621 is close to the estimate, isn't it? You might have thought about near doubles, or you might have thought about odds and evens as well.

What about B? Oh 700 add 250 is quite a good estimate, 950.

So 933 is close.

And then we could have checked by doing the calculation again or thinking about those odd and even answers as well.

What about C? Both of the numbers are quite close to 500, aren't they? Our answer's going to be a bit less than a thousand, which is right 954.

A thousand was quite a good estimate as long as we knew we were looking for a number less than a thousand.

And again, we could use odds and evens to help us to work out whether our digits were correct.

And we've come to the end of our lesson.

We've been thinking about using known facts and strategies to calculate efficiently and accurately and using those strategies to check column addition.

Sometimes we haven't always used a column addition, and we've known that there are other strategies which might be more efficient.

What else have we learned about? We've learned to look carefully at the numbers in a calculation.

Is column addition the most efficient method to use to find the sum is a good question to ask yourself.

Sometimes it might not be.

You can use strategies to help check your calculations, thinking about odds and even numbers.

And estimating the answer first can improve your accuracy so you can get a good idea of what the answer should be, so that you can check your answer carefully.

Thank you for all your hard work and all your thinking today.

I've enjoyed the lesson.

I hope you have too, and I hope to work with you again soon.

Bye-Bye.