Lesson video

Hello there.

My name is Mr. Goldie.

And welcome to today's maths lesson.

And here is our learning outcome.

I can use known facts and strategies to efficiently calculate and check column addition.

Sounds as quite a lot to do today, but it's not as tricky as it sounds.

Here are our keywords for today's session.

I'm going to say each keyword.

Can you repeat it back? So the first keyword is efficient.

The next keyword is estimate.

And the last keyword is regroup.

Let's take a look at what those words mean.

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

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

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

For example, 10 tens can be regrouped for 100.

100 can be regrouped for 10 tens.

And here's our lesson outline.

So the first part of the lesson is using efficient strategies.

The second part of the lesson is checking column addition.

Let's get started.

In this lesson, you will meet Jun and Laura.

And they're going to be helping you with your maths today.

What's that, Jun? You have something to say? "I really like column addition," says Jun.

Yes, he's a bit of a fan.

But I wonder, should you always use column addition when you've got to add together two numbers? Jun is enjoying using column addition.

"I really like column addition, but I sometimes find it a bit tricky," says Jun.

"There are lots of facts that can help you to calculate," says Laura.

Let's take a look at a problem.

What do you notice? Here are two numbers that Jun is going to add together.

296 add 96.

Is there anything you notice? Jun says, "There are doubles.

I know double six.

I know double nine." So we've got here six and six.

Six ones add six ones is equal to 12 ones.

10 ones are regrouped as a 10.

So Jun knows his doubles quite well, so he can work out the answers quite quickly.

Let's have a look at adding those 10s together.

So 9 tens add 9 tens add the regrouped 10 is equal to 19 tens.

9 add 9 is equal to 18.

Add one more is equal to 19.

10 tens are regrouped as 100.

So 9 is put into our 10s column and 10 tens are regrouped as 100 and written in the hundreds column.

And then all we've got to do is to add the hundreds together.

Two hundreds add the regrouped 100 is equal to three hundreds.

There's our answer.

Jun wonders what other facts he can use.

So we've got doubles, what else could you use to help him? "What else can help me?" "Let's take a look at another problem.

What do you notice?" We've got a different calculation this time.

562 add 348.

Aren't any doubles this time.

Is there something else you might spot? "I can see pairs of numbers that total 10," says Jun.

We've got here two add eight.

Jun knows pairs of numbers that total 10, so he can quickly work out two add eight.

2 ones add 8 ones is equal to 10 ones.

10 ones are regrouped as a 10.

A zero is put into that ones column.

Then we've got to add together those 10s numbers.

And again, there's a number pair that totals 10.

6 tens add 4 tens is equal to 10 tens.

And 6 tens add 4 tens add the regrouped 10 is equal to 11 tens.

And then 10 of those tens are regrouped as 100.

So we've got one 10 being put into the tens column and the 100 and the 10 tens being regrouped as 100 and moved into the hundreds column.

And then all we've got to do is to add together the hundreds numbers.

500 add 300 add the regrouped 100 is equal to nine hundreds.

Jun looks for known facts in these column additions.

You've got there three different column additions.

"I'm looking for number pairs that total 10 and doubles," says Jun.

I wonder, can you spot any in those column additions? So Jun looks at that first column addition and he spots 7 tens add 3 tens is equal to 10 tens.

We've got there a number pair that totals 10.

Look at that second one.

We've got double eight.

8 add 8 equals 16.

And that last one, we've got eight add nine.

There is a near double 8 tens add 9 tens is equal to 17 tens.

Because Jun knows that 8 add 8 equals 16 and 8 add 9 must be equal to 17.

Now, here's some for you to look at on your own.

Find known facts in each column addition.

So look for number pairs that total 10 and look for doubles as well.

So there are three column additions.

Have a good look at them.

See if you can spot any number pairs that total 10, any doubles, and anything else that might be helpful as well.

So pause the video and see what you can spot.

What did you see? What did you notice? Let's have a look at that first column addition.

Our first column addition, we have got seven add seven.

7 add 7 equals 14.

Double 7 is equal to 14.

For our second one, what have you noticed? We've got there 3 tens and 7 tens.

3 tens add 7 tens is equal to 10 tens.

And that last column addition, we have got six add five.

Six add five.

That's not a number pair to 10, is it? It's not a double.

It's a near double.

So if 5 add 5 equals 10.

6 add 5 is equal to 11.

There's also a number pair that totals 10.

1 ten add 9 tens is equal to 10 tens.

Very well done if you spotted all of those including that near double.

Jun thinks column addition is brilliant.

"I'm going to use column addition whenever I have to add numbers together," he says.

He did tell us earlier on how much he liked it, didn't he? Now, Laura isn't quite so sure.

Laura says, "Sometimes there might be other methods that are more efficient." Remember, an efficient method is something that gives you the answer quickly and it gives you the right answer as well.

"I don't think so," says Jun.

"Let me try a tricky problem." So Jun says, "Let's try this problem here." 544 add 199.

How would you add that together? Well, Jun starts off with the ones.

Always start with the numbers with the smallest place value first.

So four add nine.

4 ones add 9 ones is equal to 13 ones.

10 ones are regrouped as a 10.

So 3 ones are put into the ones column and then 10 ones are regrouped as a 10 and put into the tens column.

Then we go to add together the tens.

4 tens add 9 tens add the regrouped 10 is equal to 14 tens.

Then 10 tens are regrouped as 100.

So 4 tens are put into the tens column and 10 tens are regrouped as 100 and put into the hundreds column.

And lastly, five hundreds add 100 add 100 and that is equal to seven hundreds.

There's our answer.

743.

"See?" says Jun.

"Column addition is the best strategy." Laura thinks the column addition is useful, but so are other strategies.

"How would you calculate this, Laura?" asked Jun.

So it's the same calculation.

544 add 199.

"Now, the strategy you use depends on the numbers in the calculations," says Laura.

So sometimes column addition's brilliant, sometimes it might not be the best strategy.

So Laura says for this particular calculation, she knows that 199 is equal to 200 subtract 1.

So Laura says, "I would add 200 to 544 and then I would subtract 1." Adding on 200 and then subtracting 1 is the same as adding 199.

So Laura works out the answer to 544 add 200.

That is equal to 744.

And then she calculates 744 subtract 1.

And that is equal to 743.

And that gives her the answer.

So 544 add 199 equals 743.

"That was easier than using column addition," says Jun.

So it does depend on the numbers.

Jun is right, sometimes column addition is the best method to use, but sometimes there might be a quicker method that you might be able to use.

And it all depends on the numbers involved.

Jun thinks that Laura has made a very sensible point.

"How should I calculate this, Laura?" So 275 add 125.

How would you calculate that? Would you use column addition? Would you use a different method? Laura says, "Look carefully at the numbers.

What do you notice?" So Jun has a really good look and he says, "I know that 75 add 25 equals 100.

So 275 add 25 equals 300.

And then I add the 100 to get the answer 400." That was fairly straightforward, wasn't it? "And that was more efficient than using column addition," says Laura.

Column addition will give you the right answer, but it's not as quick.

Jun looks at another calculation.

This time, the calculation is 259 add 173.

Jun says, "This looks quite tricky.

Should I use column addition?" Laura says, "I think column addition would be the most efficient way to find the answer." There are other ways of doing it as well, but probably column addition is the quickest way that will give you the right answer.

So Jun sets it out by column addition.

He starts off by adding the ones together first.

Nine add three.

9 ones add 3 ones is equal to 12 ones.

And 10 ones are regrouped as a 10.

Then he has to go to the tens.

5 tens add 7 tens add the regrouped 10 is equal to 13 tens.

And 10 tens are regrouped as 100.

You got three tens and the 10 tens are regrouped as 100.

Then he's got to add together the hundreds.

Two hundreds add 100 add the regrouped 100 is equal to four hundreds.

That gives them the answer, 432.

Sometimes column addition is the most efficient way of finding the answer.

Look at these three calculations.

You've got there three calculations.

Should you answer them using mental strategies or column addition? You don't have to find the answer.

You're just thinking carefully about whether you should use column addition to work out the answer or whether you think you could calculate the answer quickly, efficiently in your head.

What do you think? Pause the video and see if you can work out how you would answer those three calculations.

And welcome back.

Let's take a look.

See if you agree.

So for our first calculation, column addition is a good choice here.

The numbers are difficult to add together mentally.

Look at that second one.

A mental method would be most efficient for this calculation.

We don't have to cross any hundreds.

That would be quite efficient probably to do in your head.

And that last one, column addition would be a good choice here.

So if you decided to use column addition for that one, that's absolutely fine.

However, you might have spotted that 51 add 49 is equal to 100.

So you could calculate that one mentally.

It all depends on what you know.

Remember what Laura said earlier.

She said it all depends on the numbers involved.

You've gotta look carefully at those numbers to decide which method would be easiest to use.

Let's move on to task A.

So the first part of task A is use column addition to calculate each sum, but look carefully for number pairs that total 10, doubles, and near doubles.

So if you look at A, for example, 579 add 71, you might spot that 9 add 1 adds together to make 10.

And 70 and 70, that is a double.

So use those strategies to help you work out the answers.

And then part two of task A.

Work out the answer to each calculation.

Think carefully about whether to use column addition or a different strategy.

So you will need to work out the answers to these, but think about the method that you could use to work out the answer.

And it could be mostly done in your head.

It might be done with some jottings.

You might need to write something down.

Or you might need to use a column addition.

But you shouldn't be using column addition for all of them.

And for some of them, you should be using a column addition.

So think very, very careful about how you'd work those out.

So pause the video and have a go at task A.

And welcome back.

Let's take a look at those answers.

So here are the answers for part one of task A.

So 579 add 71.

The answer was 650.

The sum of those two numbers is 650.

268 add 662.

We've got there a number pair the totals 10.

8 add 2 equals 10.

And 60 add 60 is a double, isn't it? Very well done if you got the right answers, but incredibly well done if you were using strategies like doubles and number pairs that total 10 to help you work out the answers.

Now let's take a look at part two of task A.

This is where you had to think carefully about whether you'd use a column addition to work out the answers or whether you'd use a different strategy instead.

So for that first calculation, you probably have decided to use column addition as the most efficient way of working out the answer.

It's quick and it probably will give you the right answer as well.

For B, that could be calculated efficiently using a mental method.

So 402 add 57, you might be able to do that completely in your head or you might need to do some jottings.

And then C, 270 add 130, where you may have spotted that 70 add 30 equals 100.

And this could also be a quick mental calculation.

So 270 add 130 could be done as a mental calculation.

For D, you should have used column addition.

But again, you've got there 7 add 3 equals 10.

So we have got some number pairs that total 10 in there as well.

A could use column addition, but it's probably not the quickest method.

So if you're adding 299, that is the same as adding 300 and then subtracting 1.

That is probably the most efficient way to calculate the answer.

And then the last one, 348 add 268.

Hopefully, you decided to use a column addition to work out the answer there.

But again, we've got there doubles.

Double eight.

And we've also got number pairs that total 10 as well.

Okay, so hopefully you're using some of those methods from earlier too.

So, very well done for completing task A.

So the second part of the lesson is checking column addition.

So Jun practises using column addition.

So he's already wrote out the answer to this one.

So 677 add 215, he says is equal to 892.

"I've added together two numbers, but how do I know whether I have the correct answer or not?" How does he check his work? "There are a few strategies you could use to help you check," says Laura.

So Laura starts by helping Jun look at odd and even numbers.

And she says, first of all, that the sum of two odd numbers is always an even number.

Can you spot in Jun's calculation where he's added together two odd numbers? Well, he's added together seven and five.

Seven add five.

Seven and five are both odd numbers.

They should add together to equal an even number.

Doesn't mean it's the right even number, but it's an even number.

"So that's good," says Jun.

"12 is an even number." Laura says, "The sum of two even numbers is always an even number." So can you see where Jun's added together two even numbers? So he's added together six and two.

Six hundreds add two hundreds.

Jun says, "Phew! Six and two are both even.

Six hundreds add two hundreds is equal to eight hundreds." So even number add an even number equals an even number.

Eight is also an even number.

"Of course, it doesn't mean it's the right answer," says Laura.

"It's just a way of helping to spot mistakes." So it might not find a mistake you've made, but it is quite a useful strategy to use.

So looking at odd and even numbers is quite helpful.

Jun wonders whether there's anything else he can do to check.

"What else can I do?" "You can use estimation to help you find the answer," says Laura.

"I know what that is," says Jun.

"If I estimate, it means I find a number close enough to the actual answer." So Laura says, "677 isn't that far from 700." It's not that far from 700.

"And 215 isn't much larger than 200." So Laura's deliberately chosen two numbers that she can add easily together.

"So 700 add 200 equals 900," says Jun.

"900 is a good estimate.

My answer was 892, and that is very close to 900." So an estimate just gives you a rough idea of what the answer should be.

It's not gonna give you an exact answer.

And it doesn't mean the answer's definitely right, but it does help you check.

Laura says, "892 could be the correct answer." It's not a guarantee, but it could be.

Estimate the sum for each calculation.

So you've gotta think carefully about which numbers are close to the two numbers and look for two numbers that are easy to add together.

So pause the video.

See if you can have a go at estimating the sum for each calculation.

And welcome back.

Let's take a look and see if you agree with how Jun and Laura have estimated each answer.

So Jun starts off by saying, "548 is very nearly 550." It's only two away from 550.

"And 49 is very nearly 50." Laura says, "550 add 50 equals 600.

So 600 is a good estimate for the sum of 548 and 49." It's gonna be quite close to that actual answer.

Let's take a look at the second one.

So Jun says, "333 is only a bit bigger than 330.

198 is very nearly 200." Laura says, "330 add 200 is equal to 530.

530 is a good estimate for the sum of 333 and 198." So it's not going to be exact, but it's close enough.

So hopefully, your estimations were similar to Jun and Laura's.

They probably weren't exactly the same, and that doesn't matter.

You're just supposed to be finding two numbers you can add easily together to give you a number close enough to the real answer.

Jun cannot be sure he has the right sum.

"What can I do to be certain I have the correct answer?" "I could work it out to see if I get the same answer," says Laura.

So another strategy you can use is to work out the answer again or get a friend to work it out for you, see if they get the same answer.

So Laura's going to add together 677 and 215.

See if she gets the same answer.

So Laura starts off by adding together seven add five.

7 ones add 5 ones is equal to 12 ones.

10 ones are regrouped as a 10.

Next, Laura has to add together the tens.

7 tens add 1 ten add the regrouped 10 is equal to 9 tens.

Put a nine.

9 tens in the tens column.

And then Laura has to add together the hundreds.

600 add 200.

Six hundreds add 200 is equal to eight hundreds.

"You got the same answer that I did," says Jun.

"Now I'm sure that I worked it out correctly." Would you agree with Jun? What do you think? Laura says, "Yes, you were correct.

Unless we both got the same wrong answer." So Laura's still not completely convinced it's right because she said they could have both made the same mistake.

But it's unlikely.

Jun adds together two numbers.

He adds together 468 and 465 and gets the answer 934.

"Have I definitely got the right answer?" says Jun.

So think careful about how you could check Jun's answer.

You could use odd and even numbers.

You could use estimation.

You could even work out the answer again.

Do you get the same answer? Has Jun got it right? And if he hasn't got it right, can you spot the mistake he has made? Pause the video and see if you can check Jun's work.

And welcome back.

Did you spot Jun's mistake? Did he make a mistake? Let's take a look.

So Laura says, "I'm going to use estimation.

Both numbers are a bit bigger than 450." They're not very far away from 450, them.

Are they? And Laura's deliberately chosen 450 because they're quite easy to add together.

450 add 450 is equal to 900.

Jun's got an answer of 934.

It's not very far away from 900.

"So Jun's answer could be correct," says Laura.

"Hang on a moment," says Laura.

She spotted something.

We've got eight, an even number, add five, an odd number, and we get the answer 14.

And Laura says, "An even number add an odd number is equal to an odd number." 8 add 5 does not equal 14.

Laura doesn't even need to work out the answer to 8 add 5.

She knows it can't be 14.

So Jun has not got the right answer.

He's made a mistake with his ones.

"Sorry, Jun, you do not have the correct sum." Oh dear, it's wrong.

But Jun says, "Thank you very much for helping me check." What a polite boy he is.

Let's move on to task B.

So the first part of task B is to estimate the answers to these calculations.

So you don't need to work out the answer, you're just estimating them.

Of course, if you get time later on, you want to go back and actually answer the questions, that is absolutely fine.

Here's part two of task B.

So Jun has used column addition to calculate these sums. So check his work.

Can you find any mistakes? So has he got the right sum each time? Has he added the two numbers together and got the right total? So have a good look.

So don't forget to use estimation to help you work out the answers.

Don't forget to look at odd and even numbers.

And you might even want to work out the answer again to double check that it is right.

And here's part three of task B.

So work out the sum for each column addition.

Check your answers carefully, thinking about odd and even numbers, estimation, and maybe even working out the answer again to see if you get the same answer again.

So have a go at each of those calculations, work out the answer, and then check them really carefully using some different strategies.

So pause the video and have a go at task B.

And welcome back.

Let's take a look at those answers.

Here are some estimations for part one of task B.

Your estimations, of course, might be different, but these ones were quite quick estimations.

Quite quick, efficient estimations that you could do to work out the answer.

So A, 150 add 120, that's easy to calculate.

It gives the answer 270.

And the actual answer to 152 add 119 would be about, would be close enough to 270.

Let's look at B.

So 307, we could say it's very close to 300.

197, that's very close to 200.

300 add 200 equals 500.

So the answer to B will be very, very close to 500.

So hopefully, your estimates look similar to some of those.

Let's have a look at part two of task B.

So did you find Jun's mistakes? Well, in that first one, A, an odd number add an odd number is equal to an even number.

And 3 add 9 cannot be equal to 13.

3 tens add 9 tens cannot equal 13 tens.

B is not right either.

Now, you may have spotted it by adding together the hundreds, double checking the hundreds, and working out that there are not nine hundreds there.

Or you might have estimated the answers.

So you might have said 485, that's quite close to 500.

287, that's quite close to 300.

500 add 300 equals 800.

Now, the estimate is very different to the actual answer.

And in fact, if you add together 400 add two hundreds add 100, you only get seven hundreds.

So that's not the right answer.

C though is correct.

C, Jun got everything correct.

So, well done, Jun.

And then here are the answers for part three.

So hopefully, you got each of these correct, particularly if you were going back and checking them.

And don't worry if you made a mistake.

Because if you made a mistake and you went back and found that mistake, that is brilliant mathematics.

That is really, really good.

'Cause that shows that you're being really, really careful.

And all mathematicians make mistakes.

We all make them occasionally.

But if you spotted the mistake you've made, that shows that you are being really, really careful.

So, very, very well done indeed.

And in fact, underneath each of those, there are some estimates for each of the answers as well.

So you might have used estimation to help you check the answers too.

Remember, estimation will only give you a rough answer, a close enough answer.

It won't tell you if the actual answer is exactly correct.

But well done on today's work.

Quite a lot of thinking involved in today's lesson.

But hopefully you're feeling much more confident about checking answers and thinking about efficient ways to calculate the answers to column addition.

Excellent work today.

Very well done.

And finally, let's move on to look at our summary.

So look carefully at the numbers in a calculation.

Is column addition the most efficient method to use to find the sum? Use strategies to help you check your calculations.

And estimation gives you a value close to the correct answer.