Lesson video

Hello there, my name is Mr. Goldie.

Welcome to today's math lesson.

And here is our lesson outcome.

I can use column addition with regrouping to solve problems. And here are the keywords for today.

So I'm going to say each keyword.

Can you repeat it back? The first keyword is estimate.

And the next keyword is regroup.

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

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 is our lesson outline.

In the first part of the lesson, you're going to be using two addends to make a sum.

And in the second part of the lesson you're going to be finding two addends to make a sum.

Let's get started.

In this lesson, you will meet Jun and Laura, and they're going to be helping you with your maths, and asking you some questions as well.

What's that Jun, you want to say something? "The pandas are here!" There will be pandas in the first part of the lesson.

This table shows how far some pandas walked over two days.

Pandas have the tendency to be a little bit lazy, they don't tend to walk very far.

So here we've got five pandas, Pedro, Petra, Pia, Ping, and Polly.

And the table tells us how far they walked on Monday, and how far they walked on Tuesday.

Laura says, "Petra walked 278 metres on Monday." Jun says, "Ping walked 448 metres on Tuesday." Let's take a look at a question.

How far did Pedro walk over the two days? Here is the distance that Pedro walked on Monday, and here is the distance that Pedro walked on Tuesday.

Laura says, "We have to add together 359 metres, and 248 metres." "Let's start by estimating the answer," says Jun.

Jun and Laura start by estimating the sum of 359 metres, and 248 metres.

"359 is close to 350," says Jun, "248 is close to 250." So Jun has deliberately chosen those two numbers because they're easy to add together.

Laura says, "350 add 250 equals 600." We've got 300 and a 200, and a 50, and a 50 makes the extra 100.

A good estimate for the answer is 600 metres.

So Laura and Jun have estimated the answer.

They know that the answer's going to be close, quite close to 600 metres.

"Let's use column addition to add the numbers together," says Jun.

So Jun sets out the calculation as a column addition.

And when we're adding numbers using column addition, we always start with the numbers with the smallest place value first.

So let's start off with 9 add 8.

9 ones add 8 ones is equal to 17 ones.

10 ones are regrouped as a ten because there are more than 10 ones.

We've regrouped 10 of the ones as a 10.

So 7 is written in the ones column, and that extra 10 ones is regrouped as a 10, and written in the tens column.

Now we've got to add together the tens numbers.

5 tens add 4 tens, add the regrouped ten is equal to 10 tens.

10 tens are regrouped as a hundred, which means that Jun, and Laura have to write 0 in the tens column.

And those 10 tens are regrouped as a hundred, and written in the hundreds column.

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

3 hundreds add 2 hundreds, add the regrouped hundred is equal to 6 hundreds.

There's our answer, 607.

Pedro walked 607 metres altogether.

Not very much in two days, is it? Laura says, "That's great! The answer is very close to our estimate of 600 metres." Remember they estimated their answer at the beginning.

They've gotta look at their estimate at the end, otherwise there's no point doing it.

And they realise of course, that the answer they got, 607 metres, is very close to their estimate, which means it could be the right answer.

It's a good way of checking.

Let's take a look at another question.

Which panda walked 515 metres altogether over the two days? So here's our table again with the five pandas, and the distances they walked on it.

Laura says, "We're looking for two numbers with a sum of 515." "Could the panda be Petra? She walked 278 metres on Monday, and 226 metres on Tuesday." Jun says, "278 is close to 300.

226 is close to 200.

200 and 300 equals 500.

500 is close to 515." So Jun has estimated the sum of the two numbers, and he says it's going to be about 500.

It's gonna be close to 500 the actual answer.

515, it's pretty close to 500, so perhaps the panda is Petra.

Laura doesn't agree.

Laura says, "278 and 226 are both even.

An even number add an even number equals an even number." "515 is an odd number, so it cannot be Petra." So even though Jun's estimated it, and Jun's estimate was roughly 515, Laura says it can't be Petra because an even number add an even number equals an even number, and 515 is not even.

So they're still looking for two numbers with a sum of 515.

But Jun and Laura now know it's not Petra.

It's not Pedro either, because they've just worked that one out, haven't they? "Could the panda be Polly?," says Jun.

"336 is close to 300.

179 is close to 200.

200 add 300 equals 500.

500 is close to 515." So again, Jun has estimated the sum of the two numbers, and he says, "It's quite close to 515, perhaps the panda is Polly." Laura says, "336 is odd and 179 is even.

An even number add an odd number equals an odd number." 515 is an odd number, so it could be Polly.

So they've now worked out using estimation, and thinking about odd and even numbers, the panda could be Polly.

I wonder if they're right.

So Jun and Laura add together 336 metres and 179 metres.

Let's use column addition to add the numbers together.

So again, we always start with the numbers with the smallest place value first.

So we start off by adding together 6 and 9.

6 ones add 9 ones is equal to 15 ones.

10 ones are regrouped as a ten.

So 5 is written in the ones column, and those 10 ones are regrouped as a ten, and written in the tens column.

Next we've got to add together the tens.

So 3 tens, add 7 tens, add the regrouped ten is equal to 11 tens.

3 tens and 7 tens equals 10 tens.

Add that extra regrouped 10, that is equal to 11 tens.

10 tens are regrouped as a hundred.

So 1 ten is written in the tens column.

The other 10 tens are regrouped as a hundred, and written in the hundreds column.

And all Jun has to do is add together the hundreds.

300 add 100, add 100, and that is equal to 5 hundreds.

So the answer is 515.

Laura says, "It was Polly who walked 550 metres over the two days." So they managed to work out which panda it was.

Well done Jun and Laura.

And here's one to try on your own.

Which Panda walked 904 metres altogether over the two days? Laura says, "You're looking for two numbers with a sum of 904." Look carefully at the numbers.

Which panda do you think it was? So don't work out the actual calculation yet, but have a good look at the numbers, and see if you can work out which panda you think it could be.

Pause the video, which panda do you think it was? And welcome back.

Did you manage to work out which panda it was? Let's take a look, see if you were right.

So Jun says, "Could the panda be Ping?" So Ping walked 456 metres on Monday, and then Ping walked 448 metres on Tuesday.

Jun's going to estimate that answer, and he says, "456 is close to 450.

448 is close to 450, 450 add 450 equals 900.

900 is close to 904." So Jun is saying, "I think it's Ping that is the panda." You might have decided it was Pia.

If you look carefully at the distance that Pia walked on Monday, and Tuesday, and you estimate the sum of those two numbers, I think you get a sum that is too large.

Laura says, "Both those numbers are even.

An even number add an even number equals an even number." 904 is an even number, so it could be Ping.

And you're gonna continue answering this question on your own.

So add together 456 metres and 448 metres.

Jun suggests using column addition to add the numbers together.

So here's how you would set it out.

You might want to use pencil and paper, or whiteboard and whiteboard pen.

Jot down that calculation, have a go at calculating the sum of those two numbers and see what you get.

So pause the video, and see if you can work out the sum of 456 and 448.

And welcome back.

Did you manage to add the two numbers together? Did you get a sum of 904? Let's work out what the sum of the two numbers is.

Let's start off as always by adding together the ones numbers first.

So 6 ones add 8 ones is equal to 14 ones.

10 ones are regrouped as a ten.

So 4 is written in the ones column.

Those 10 ones are regrouped as a ten, and written in the tens column.

Next we've got to add together the tens.

5 tens, add 4 tens, add the regrouped 10 is equal to 10 tens.

10 tens are regrouped as a hundred.

So 0 is written in the tens column, and those 10 tens are regrouped as a hundred, and written in the hundreds column.

Now we've got to add together the hundreds.

4 hundreds add 4 hundreds add the regrouped hundred is equal to 9 hundreds.

So the sum of those two numbers is 904.

Laura says, "It was Ping who walked 904 metres over the two days." So very, very well done if you've got the answer 904, and very well done if you predicted it was Ping, who walked that distance over the two days.

Let's take a look at Task A.

So you're going to be using the table to help you answer each question.

Laura and Jun have a bit of helpful advice for you as well.

So Laura says, "Look carefully at whether the addends are odd or even numbers." Remember an even number add an even number equals an even number.

An odd number add an odd number equals an even number.

And an odd number add an even number equals an odd number.

That's the only way you can get an odd number answer when you're adding two numbers together is by adding together an odd number, and an even number.

Jun says, "Use estimation to help you work out the two addends needed." If you're trying to work out which pandas were involved, you might want to have a go at estimating to see if that'll give you a clue as to which two pandas it may have been.

So here are the questions.

Use column addition to help you work out the answers.

So Question A says, how far did Petra walk over the two days? B says, how far did Pia walk over the two days? Question C is, which two pandas walked 695 metres between them on Monday? Question D is, which two pandas walked 625 metres between them on Tuesday? So you've got four calculations to have a go at.

Don't forget to use column addition.

Don't forget to use estimation and thinking about odd, and even numbers to help you work out which numbers are being used.

Pause the video and see if you can answer those four questions.

And welcome back.

Let's take a look at those answers, and see how you got on.

So here are the answers for A, so how far did Petra walk over the two days? You had to add together 278 and 226, and the answer was 504.

So Petra walked 504 metres.

How far did Pia walk over the two days? So you had to add together there, 587 and 377.

And the sum of those two numbers is 964.

Now Jun's actually done the estimation after working out the calculation.

There's no reason you can't do that.

So Jun says, "587 is close to 600.

377 is close 380.

600 add 380 equals 980.

980 is close to 964." So Jun's used estimation to help him check the answer.

It looks like that could be the right answer.

So Pia walked 964 metres.

Let's take a look at the next two questions.

So which two pandas walked 695 metres between them on Monday, and which two pandas walked 625 metres between them on Tuesday? Laura says, "Both sums are odd." "So one addend must be odd, and one must be even," says Jun.

When you were choosing your two numbers, one of them needs to be odd, one of them needs to be even.

So the two numbers you should have chosen to have a sum of 695 were 359 and 336.

The two pandas were Pedro and Polly.

To get a sum of 625, you should have added together 248, and 377.

And the two pandas were Pedro again and Pia.

So very well done for having a go at completing Task A.

And let's move on to the second part of the lesson.

So the second part of the lesson is finding two addends to make a sum.

Jun uses some of the number cards to make two 3-digit numbers.

He uses column addition to add them together.

And he says, "The sum of the two addends is 915." Laura says, "I'm going to work out which six cards Jun used, and how he arranged the numbers." So he's used six of those cards.

There's eight cards altogether.

So Jun hasn't used all of the cards.

He's only used six of them.

So Laura starts by using two cards with a sum of 5.

"The only two numbers that have a sum of 5 are 3, and 2," says Laura.

So Laura uses 3 and 2 to make 5.

3 add 2 equals 5.

Next is the tens column.

The two tens digits have a sum of 1 ten.

There aren't two numbers that have a sum of 1, so the tens digits must add to make 11.

They can't make 1 ten, they've got to make 11 tens.

6 tens add 5 tens is equal to 11 tens.

I have to regroup 10 tens into the hundreds column.

Laura uses the 6 and the 5, she adds them together, and that equals 11 tens.

6 tens add 5 tens equals 11 tens, and 10 of those tens she regroups, and puts into the hundreds column.

"Oh no!", says Laura, "There aren't two numbers that add to the regrouped hundred to make 9 hundreds." There's a 100 regrouped from the tens, but there aren't two numbers that add together to equal 8 hundreds.

"Sorry Laura, I think it's a tricky problem," says Jun.

So Laura tries again, she's not gonna give up, Laura, she's gonna have another go.

"Maybe the ones numbers add to make 15.

I'm going to use 9 and 6." Of course they could add up to equal 5, but Laura says, "Perhaps they equal 15." So Laura uses 9 and 6, adds those two together to get the sum of 15.

And of course 10 ones are regrouped in the tens column.

7 tens add 3 tens, add the regrouped ten is equal to 11 tens.

So Laura is going to use the cards 7 and 3 in the tens column.

They add together to the regrouped ten, to equal 11 tens altogether, and then 10 of those tens are regrouped into the hundreds.

"Oh no!", says Laura.

"There aren't two numbers that add to the regrouped hundred to make 9 hundreds." "Third time lucky Laura!," says Jun.

So Laura is determined to solve the problem.

She knows it can be done 'cause Jun has done it.

"So I'm going to start with 9 and 6 again," says Laura.

So she thinks 9 and 6 could be the starting numbers, but perhaps she used the wrong numbers in the tens.

So again, she starts with 9 and 6.

9 add 6 equals 15.

10 of those ones are regrouped as a ten.

8 tens add 2 tens, add the regrouped ten is equal to 11 tens.

So this time in the tens column, Laura uses the digit cards 8 and 2.

8 tens add 2 tens, add the regrouped ten, is equal to 11 tens altogether.

5 hundreds add 3 hundreds, add the regrouped hundred is equal to 9 hundreds.

So Laura can use the digit card 5, and 3 in the hundreds column.

And 5 hundreds add 3 hundreds, add the regrouped hundred equals 9 hundreds.

So Laura has solved the problem.

That's brilliant Laura," says Jun.

He's pretty impressed.

"But I actually used different numbers." Laura has solved Jun's problem in a different way.

That's not wrong, she just used different numbers.

Laura wants Jun to show her how he created the problem.

"So I started with 8 and 7," says Jun.

So Jun used 8 and 7 in the ones to equal 15 ones.

6 tens, add 4 tens, add the regrouped ten is equal to 11 tens.

So Jun uses 6 and 4 in the tens column.

5 hundreds add 3 hundreds, add the regrouped hundred is equal to 9 hundreds.

So Jun uses the digit cards 5 and 3 in the hundreds, they add together to the regrouped hundred to equal 9 hundreds.

"That's awesome!", says Laura.

"There were two ways to make your sum." Now it's time for you to try, and answer the problem on your own.

So use the number cards to make two 3-digit numbers.

There are eight cards to choose from, you've gotta use six of them to make two 3-digit numbers.

Can you find two numbers that have a sum of 907? You need to set them out as two 3-digit numbers.

They add together to give a sum of 907.

Laura says, "Is there more than one answer using different cards each time?" See if you can answer the question one way, and then using six slightly different cards, can you answer it at different way? You can't just use the same six cards again.

Pause the video and have a go at answering that question.

And welcome back.

Did you manage to find a solution? Very well done if you did.

Did you manage to find two different solutions using slightly different cards? That is brilliant if you did.

Let's take a look at two possible answers.

So here are two possible solutions.

Your solutions may look slightly different to this.

649 and 258, have a sum of 907.

You may have come up with the answer 579 add 328.

Those two numbers also have a sum of 907, and slightly different cards have been used each time.

In that first solution, the digit cards, 6 and 4 have been used, and in our second solution, all the number cards are the same, all the digit cards are the same except that 5 and 3, have been used instead of using 6 and 4.

Very well done for solving that problem.

Let's move on to Task B.

So in the first part of Task B, use the number cards to make two 3-digit numbers.

Can you make each sum by adding two numbers together? So can you make the sum 603, 900 and 936? So three different problems there.

That's Part 1.

Part 2, use the same number cards.

Can you find two different ways to make the sum 843? And Laura is just reminding you, "You must not use exactly the same cards each time." Some of the cards will be the same, but you've gotta use some cards that are different.

And then Part 3 of Task B, can you make a sum of 924 in two different ways? And again, you must not use exactly the same cards each time.

Think about all those things you've learned in the lesson.

Think about using odd and even numbers.

If you're aiming for 924, you've got to add together two even numbers or two odd numbers.

An odd and an even number will not give you a sum of 924.

Think about using estimation as well.

If you've got 924, how many hundreds are you going to use in each of the numbers? Pause the video, and have a go at trying to solve Task B.

And welcome back, and let's take a look at those answers.

I wonder how you got on.

Here are the answers for Part 1 of Task B.

So to get a sum of 603, you may have used the numbers 246, and 357.

You may have moved those numbers around slightly.

For B, to get 900, you may have made the numbers 374, add 526.

Those numbers have a sum of 900.

And to make 936, you may have used the numbers 587, and 349.

Those two numbers have a sum of 936.

So well done if you completed Part 1.

Here are two possible solutions for Part 2 of Task B.

So 378 add 465 gives a sum of 843.

And the numbers used in each of those solutions are slightly different.

And here are two possible solutions for Part 3 of Task B.

So 328 add 596.

They have a sum of 924.

679 add 245 is also equal to 924.

And again, slightly different numbers have been used in each solution.

Very well done if you had a go at Parts 2 and 3 of Task B, and you managed to find some solutions as well.

And if you managed to find two different ways of making the sum, absolutely brilliant work.

Very well done in today's lesson.

And I hope you've enjoyed some of that problem solving, and you've thought carefully about estimation, and using odd and even numbers and when you get an even number, when you get an odd number.

And about when you should use column addition to work out an answer.

So excellent work today.

Very well done.

Let's move on to our lesson summary.

So use strategies to help you check your calculations.

Look carefully at the addends.

Are the numbers odd or even? Look carefully at the sum.

Is it odd or even? And remember, estimation gives you a value close to the correct answer.