Lesson video

Hello, my name's Mrs. Hopper, and I'm really happy that we're going to be working together in our maths lesson today.

We're gonna work hard.

We're going to do lots of thinking about our maths, but I'm really looking forward to sharing this learning with you, so let's see what's in today's lesson.

So, today's lesson is all about using column addition to solve problems, and it's part of our unit on column addition.

So, let's see what problems we're going to solve today.

We've got some keywords: addend, sum, and column addition.

You may well have come across these before, but let's just practise them.

They're important words that we're going to use in our lesson today.

So I'll say it.

And then it'll be your turn.

So, my turn: addend.

Your turn.

My turn: sum.

Your turn.

My turn: column addition.

Your turn.

Fantastic, let's remind ourselves what these words mean and how we're going to use them in our lesson today.

So, an addend is a number added to another.

Lots of addends around when we are thinking about column addition, and we've been thinking about where we record them and how we use them.

The sum is the total when numbers are added together so the answer, perhaps, to our column addition.

There'll be lots of those floating around the lesson today as well, and column addition is a way of adding numbers by writing a number below another.

It allows us to organise our numbers.

It allows us to handle bigger numbers and keep a track of how we are adding them together, and it links a lot to our partitioning, thinking about hundreds, tens, and ones, so let's get into today's lesson, see what it's all about.

So, in the first part, we're going to be solving problems with two-digit numbers; and in the second part, three-digit numbers.

And we've got Jun and Laura helping us out today.

I think Jun's got a message.

He says, "Are you ready for my challenges?" (sucks) Ooh, that sounds exciting.

Let's get into the lesson and see what challenges Jun is setting.

Jun's got some number cards.

He's got six cards: 0, 1, 2, 3, 4, and 5.

He chooses four and arranges them using column addition, so there we go.

We don't know what the numbers are that he's chosen, hmm.

Jun says, "The sum of the two addends is 85.

What two addends did I make?" so all he's told us is that the sum is 85, and there it is.

Laura says, "I'm going to work out how Jun arranged the cards." (sucks) Ooh, let's see how she's going to go about this.

So, Laura starts by using two cards with a sum of 5, so she's remembered that, when we're doing column addition, it's good to start with the digits that have the lowest place value, so she's starting with her ones.

What two cards could she pick that have a sum of 5? Oh, Laura's decided to go for 5 and 0, so she's used the 5, and she's used the 0.

5 ones + 0 ones = 5 ones.

What two number cards can Laura use next? Jun says, "There aren't two cards that add up to equal 8 tens." Laura says, "That's okay.

I now know that I can't use 5 and 0 to make 5 ones," So she's learnt from it.

That's okay.

She'll have another go.

So Laura tries two different cards with a sum of 5.

What else could you choose that has a sum of 5? Laura's gone for 3 + 2 = 5, so she's used 3 and the 2: "3 ones + 2 ones = 5 ones." Yep, that sounds all right as well.

What two number cards can Laura use next? Are there two more cards that she can use in the tens so that she can have a tens total of 8 tens? Jun says, "Sorry, Laura, there aren't two cards that add up to equal 8 tens." Laura says, "That's good.

I now know that 3 and 2 cannot be used to make 5 ones." So she realised that she couldn't use 5 and 0.

And she couldn't use 3 and 2.

What can she use? She's gonna try again with two different cards.

"4 + 1 = 5," she says, so she's used the 4 and the 1 in her ones.

4 ones + 1 one = 5 ones.

What two number cards can Laura use next? (gasps) She says, "I can use 5 tens and 3 tens to equal 8 tens." So she's going to use those two cards: 5 tens + 3 tens = 8 tens.

54 + 31 = 85.

"The two addends were 54 and 31," she says.

"Well done, Laura," says Jun: "They were the two addends that I made." Fantastic, so she solved his problem.

She didn't solve it first time though.

She had to do some thinking.

She made a couple of false starts, but she learned from those, and she solved the problem.

Jun uses cards to create another challenge.

He chooses four and arranges them using column addition again.

"The sum of the two addends is 93.

What two addends did I make?" he says.

So there's our sum, which is 93.

We don't know what the addends were.

All we know is he chose four cards from 0, 1, 2, 3, 4, and 5.

"Can you work out what the numbers are," says Laura? Ooh, she's setting a challenge.

She is setting you a challenge.

Can you work out what Jun's two two-digit addends are using four of those cards? Pause the video now.

And then we'll come back and have a think about it together.

How did you get on? Laura says she started with 3 + 0 = 3, so she's used the 3 and the 0.

What two number cards could you use next? Ooh, tens column is quite easy.

She says, "The only way to make 9 is to use 5 and 4." So, 5 tens + 4 tens = 9 tens.

So, 53 + 40 = 93.

The two addends were 53 and 40.

Jun says, "That works.

I actually used the addends 52 and 41, hmm." So Laura pointed out that 5 and 4 was the only way to get a total of 9 so those had to be the numbers in the tens.

But there was another way to get a total of 3, wasn't there? We could've used 2 and 1, and Jun said he actually did 52 at 41, and Laura says, "There was more than one way of solving your problem, Jun." Interesting to watch out for that: is there only one way, or are there more ways than one to solve a problem? Time for you to have some practise.

Can you use those same six number cards and use column addition to arrange four of the cards each time into two two-digit numbers that give the sums that are written down? So A, we're looking for two two-digit numbers that have a total of 46; B, two two-digit numbers that sum to 81; and C, two two-digit numbers that sum to 77.

And then you can record your final calculation as an equation underneath, and when you've looked at that, part two, can you find two ways to make each of these sums using different cards for each solution? And Jun's saying, "You cannot use the same four cards each time." So, here are two possibilities, so making a sum of 57 and a sum of 64, you can use the cards in different ways.

So pause the video, and have a go at solving those problems, adding two two-digit numbers.

How did you get on? Did you manage to make the sums using four of the cards to make two two-digit numbers? So, for A, you could've had 12 + 34 = 46: 2 + 4 = 6 and 1 + 3 = 4.

You might've had 14 + 32, perhaps, if you'd had your numbers the other way round, but you had a sum of 46.

So, for B, we were looking for a sum of 81, and we've got 50 + 31, or you might've had 51 + 30.

And for C, the sum was 77, so we've got 53 + 24, or you might've had 54 + 23.

For part two, you had to find two ways to make each sum correct using different cards for each solution, so for 57 you could've chosen 12 and 45 so the cards 1 and 4 for your tens and 2 and 5 for your ones, or you could've had just a 5 in your tens and a 3 and a 4 in your ones.

And for 64, you could've had 50 and 14, so you could've had 5 tens and 1 tens and 4 ones and 0 ones, or you could've had 3 ones and 4 ones and 4 tens and 2 tens to equal 64.

So two different ways of solving each of those problems. How did you get on? Did you enjoy playing with the number cards and trying different solutions? Let's move on and see what's gonna happen in the second part of our lesson.

So, in the second part, we're going to be solving problems with three-digit numbers, so let's get in, see what problems we're going to be set this time.

Jun uses these number cards to make two three-digit numbers, so he's going to use all the digit cards this time.

He uses column addition to add them together, so there we go: six cards arranged into two three-digit numbers.

He says, "The sum of the two addends is 582.

What two addends did I make?" Hmm, I wonder if we can use any of those strategies Laura had to help us.

So, there's our sum of 582.

Laura says, "I'm going to work out how Jun arranged the cards." So where's she going to start? We like to start with the lowest value so starting with the ones.

So, she says, "The only two numbers that have a sum of 2 are 0 and 2, so they have to be the two numbers in our ones column, so 2 and 0." Now what are we left with? She says, "The only two numbers that have a sum of 8 are 5 and 3, so 5 and 3 have to be our tens numbers, and 4 + 1 = 5, so they must be our hundreds numbers." So Laura has solved Jun's problem.

She says, "452 + 130 = 582." Jun says, "You solved that very quickly, Laura.

Why was that one so much quicker?" Laura had spotted some things, hadn't she? She'd spotted that there was only one way to make a sum of 2, so she knew what the ones digits could be.

And then there was only one way to make a sum of 8 from the remaining cards, and the final two cards had to have a sum of 5, so she was able to solve that one quite quickly.

There was only one solution.

Jun makes two different three-digit numbers.

He uses column addition to add them together again.

"The sum of the two addends is 834.

What two addends did I make?" he says.

So, there's 834, which is our sum.

Laura says, "I'm going to work out how Jun arranged the cards." Think it's going to be as straightforward this time.

How many ways are there to get a sum of 4? So, Laura starts by using two cards with a sum of 4.

3 and 1 have a sum of 4, so she's going to use the 3 and a 1 in her ones column.

Next is the tens, and the two numbers have a sum of 3, hmm.

The only way to get a sum of 3 is by adding 3 and 0 or adding 2 and 1, and Jun says, "But you've already used the 3 and the 1, and they were important for each of those possibilities." So Laura now knows that she cannot use 3 + 1 to equal 4, so she's got to find 4 in a different way.

How else could she make 4 using those cards? She's gonna hand it over to you.

So, we couldn't use 3 and 1 to equal 4.

Is there another way we can equal 4 in the ones? Can you finish off solving the problem for Laura? Pause the video.

Have a go.

And then we'll discuss it together.

How did you get on? Did you work out where Jun used each of the number cards? Laura says, "Let's look at the answer." Well, if we couldn't use 3 and 1, we had to use 4 and 0 to equal 4, didn't we? So we knew that had to be 4 and 0, and now there's only one way we can make 3, isn't there? We have to use 1 and 2 to equal 3.

And then we know that we are left with 5 and 3 to equal 8, so 514 + 320 = 834, and Jun says, "It doesn't matter if the addends are different.

Your answer might be 314 + 520." We could've changed things around, moved things around, but as long as we have a 4 and a 0 in our ones, a 1 and a 2 in our tens, and a 5 and a 3 in our hundreds, we know we are going to have a sum of 834.

Ooh, Laura's gonna set Jun a challenge this time.

We got the same digit cards, and we're adding together two three-digit numbers in column addition.

Laura says, "How many different even numbers between 400 and 500 can you make?" (gasps) Gosh, there's a lot of information there: "How many different even numbers?" so we are looking for a sum that is an even number, and it's got to be between 400 and 500.

How many different ones can Jun make? Jun says, "To get an even number, I have to add two even numbers or two odd numbers together." Can't be one even and one odd number, so he's got a bit of a clue there.

He's either got to add two even numbers or two odd numbers together.

Jun starts by thinking about the numbers.

He says, "I'm going to keep the 3 and the 1 for the hundreds digits," because he's got to make a number between 400 and 500.

So he is definitely going to keep the 3 and the 1 for the hundreds digit, so he is going to start with a 4 and a 0 in the ones.

So, 4 ones + 0 ones = 4 ones.

He knows he wants to keep the 3 and the 1, so he's going to use the 5 and the 2 in the tens column.

And then he's got his 3 and his 1 in his hundreds, so now he can add his number up: 4 ones + 0 ones = 4, 5 tens + 2 tens = 7 tens, and 3 hundreds + 1 hundred = 4 hundreds.

So has he solved the problem? Has he found one of those numbers? It's a number between 400 and 500.

It's 474, and it's even.

We know it's even because it's got a 4 in the ones.

So, Jun has found one possible way of using all six cards to create an even number between 400 and 500, and Laura says, "Can you make any different numbers?" I wonder.

"Can you?" Laura's challenging you to make some, so can you make a different even number between 400 and 500 by using all six cards? She says, "Jun has already made 474, so can you arrange the cards in a different way to make a different even number between 400 and 500?" Pause the video and have a go.

How did you get on? Did you remember Jun's useful thinking about the 3 and the 1? I wonder.

So, Jun says, "Here are two more possible answers." You could've had.

Ooh, now he hasn't this time.

He's used a number.

He's used 421, but he's used 0 in the tens, so we've actually got a three-digit plus a two-digit number here.

So, he's used 421 + 35, which gives us 456, which is an even number between 400 and 500.

I wonder what else he found.

Ah, he's gone back to his 3 and 1 for his hundreds there, hasn't he? But he's made sure that he's got an even number in the ones.

He's done 0 + 2, which equals 2.

5 + 4 is 9.

3 + 1 is 4, so he's got 492, just squeaking in right at the top end there, nearly at 500.

So, 350 + 142 = 492.

I wonder if you found those ways or whether you found any other ways.

Did you use the 0 in the hundreds column so that you could use your 4 as your other hundred? I wonder.

Time for you to do some practise, so we're still using those same six number cards.

So, you're going to use column addition.

You're going to arrange the cards into two three-digit numbers to make the sums that you can see there, so in A, we're trying to make a sum of 735.

In B, we're making a sum of 555.

That's an interesting one, and in C, we're making a sum of 186.

So can you use all six cards to make two three-digit numbers and to get those sums? And for part two, you're going to arrange the cards into two three-digit numbers, and you're going to try and make three different odd-number sums between 600 and 700 so three different odd-numbered sums between 600 and 700, so think about how you might create an odd number.

Jun talked about how we made an even number before.

How would you create an odd-number sum? And then your final part of your challenge, you've got some tighter targets to hit here.

So, for A, you're going to arrange those same six cards again to make a sum between 700 and 720; in B, to make a sum between 380 and 400; and in C, to make a sum between 250 and 270.

So good luck.

Have fun rearranging your cards.

And when you've paused the video and had a go at your practise, we'll go through the answers together.

How did you get on? There were some different possibilities for these ones, but for A, we had to make a sum of 735, so the calculation we've got is 325 + 410.

You may've had the numbers arranged slightly differently, but 325 + 410 gives a sum of 735.

For B, we've got 403 + 152 = 555.

Again, you might've had the numbers in a slightly different arrangement within your three-digit numbers, but that was an interesting one, the three different combinations that gave us a sum of 5: 5 ones, 5 tens, and 5 hundreds.

And for C we've got 134 + 52.

We only had a very low total that time, so we had to have a 1 and a 0 in our hundreds there.

I wonder if you did that thinking before you started, as well.

And then for question two, we've got 542 + 103 = 645.

These are just some of the possible answers that you might've had for odd numbers between 600 and 700.

Did you spot, this time, that, in the ones, we needed one odd and one even number in order to get our total or an odd number plus 0 to get our odd number in the ones column, which would give us an odd number overall? I wonder how many different ways you found of getting odd-numbered answers between 600 and 700.

And the final part, you had to hit quite a small target.

So for A, you had to make a number between 700 and 720, so by using 514 and 203, we made a total of 717.

Between 380 and 400, you could have 140 + 253 = 393.

And then for a number between 250 and 270, we've got 253 + 14, so the 0 is a hundred value there, giving an answer of 267.

Again, you might've swapped the digits around between your numbers.

Might've found another way, but I hope you've had fun playing with those digit cards and creating different numbers to solve our problems. And we've reached the end of our lesson.

So, we've been learning all about using column addition to solve problems and solving problems with column additions.

So what have we learned about today? Well, we've reminded ourselves that, when we are using column addition, we start by adding the numbers with the smallest place value first, and as I say, that will become more important as we go on to learn more about column addition.

We can use a 0 to show that there are no tens or ones in a three-digit number, and I know we used it a bit with our hundreds.

We don't have to.

But it showed us that we'd use the card, didn't it? And when you're solving problems, it's very important to learn from your mistakes when you're trying to solve a problem.

Laura was really quite cheerful when she made a mistake, because it gave her useful information that would help her to go on and solve the problem, so learning from your mistakes, making improvements based on what you've tried already, is really useful and really important when you're solving problems. Thank you for your hard work today.

I've really enjoyed working with you, and I hope we'll get to work together again soon, bye-bye.