Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson.

This lesson comes from the unit on addition and subtraction of two-digit numbers.

Is this new for you? Have you done anything like this before? I'm sure you've got lots of skills about numbers and addition and subtraction that you're going to be able to bring to this lesson.

So if you're ready, let's make a start.

So in this lesson we're going to be adding 2 two-digit numbers without crossing the tens boundary.

You might have been hearing about adding 2 two-digit numbers.

I expect you've done lots of adding two-digit and one digit numbers and adding lots of one digit numbers.

But today we're really gonna get into adding 2 two-digit numbers.

So are you ready to make a start? Let's go.

We've got one key word in our lesson today, and I'm sure it's a word you're familiar with, it's partition.

I'll take my turn to say it and then it'll be your turn.

So my turn, partition, and your turn.

Excellent.

As I say, this word's gonna be really useful to us.

We're going to be partitioning numbers to make them easier to add.

So let's make a start.

There are two parts to our lesson today.

We've partitioned it into two parts.

The first part, we're going to be using base 10 blocks to add 2 two-digit numbers.

And in the second part we're going to be using partitioning to add two-digit numbers.

So let's get going with some base 10 blocks.

I wonder if you've got some out that you can work with during the lesson as well.

And Andeep and Izzy are helping us in our lesson today.

I hope they've got their base 10 blocks ready as well.

Andeep wants to solve this equation, 34 plus 45 is equal to something.

He says, "I've never solved an equation like this before.

I don't know how to solve it." Oh, I wonder if we can help him.

Izzy says, "I have an idea.

Let's partition each number in the equation into tens and ones." Oh, that's a good idea, Izzy.

Let's have a go.

So 34 is equal to 30 and 4, 3 tens and 4 ones, and 45 is equal to 40 and 5, 4 tens and 5 ones.

Have you seen an equation like that before? You might have seen one quite recently like that.

"That looks much easier to solve," says Andeep.

Izzy wants to represent the equation with base 10.

So she writes it in a different way to show the tens and the ones that she will need.

So there we go, she's taken the partitioned parts of our two-digit numbers and written them out as an equation.

30 plus 4 plus 40 plus 5.

What's the same and what's different about the two equations? You might want to pause and have a think before Izzy and Andeep share their ideas.

Andeep says, "Both equations have the same number of tens and ones to have." We've got 30 and 40 in both equations are tens, and 4 and 5 in both equations are ones.

Izzy says, "You can clearly see the tens and ones in my equation, but you had to partition the tens and ones in your equation so they were easier to see." So yes, remember Andeep started with 34 plus 45 and we can clearly see those numbers in Izzy's equation, but we've partitioned them to make it easier to add.

30 plus 4, 34, and 40 plus 5 are 45.

And Andeep says, "When partitioned, we can see that they will have the same sum." So Izzy's used the base 10 blocks to represent the equation.

We've got 30 plus 4 and 40 plus 5.

"And now we've partitioned into tens and ones, they're easier to add," says Andeep.

30 plus 40 is equal to 70.

If three plus four is equal to seven, 3 tens plus 4 tens is equal to 7 tens, and that's 30 plus 40 is equal to 70.

So there's our total number of tens.

And 4 ones plus 5 ones is equal to 9 ones, nine.

And there's our nine.

So we've got 70 and 9.

So we've got 70 and 9.

70 plus 9 is equal to 79.

So our sum is 79.

Now Andeep added the tens first and then the ones, didn't he? Izzy wonders if she will reach the same total if she adds the ones first.

So she still got her partitioned base 10 blocks there to show 30 and 4 and 40 and 5, but this time she's going to add the ones first.

4 ones plus 5 ones is equal to 9 ones.

So there's our nine.

And then she's going to add the tens.

30 plus 40 is equal to 70, 3 tens plus 4 tens is equal to 7 tens.

And there's our 70.

So the only difference is that this time we've got our ones first, and we have to think carefully about that when we are recording our sum.

70 plus 9 is equal to 79, or 9 plus 70, but we are going to write it 79 with the seven digit first in the tens place.

And Izzy says, "We can combine the addends in any order.

The sum remains the same." And that's because addition is commutative.

So 34 plus 45 is equal to 79, whether we start with the tens or the ones.

Time to check your understanding.

Can you partition the tens and ones in the equation below? Then use base 10 blocks to solve it.

So we've got 23 plus 35 is equal to something.

Pause the video, have a go.

And when you're ready for the answers and some feedback, press play.

How did you get on? So 23 partitions into 20 and 3, 2 tens and 3 ones, and 35 partitions into 30 and 5, 3 tens and 5 ones.

We are going to start by adding the tens.

So 2 tens plus 3 tens, 20 plus 30 is equal to 50, 5 tens.

And then what about the ones? 3 ones plus 5 ones is equal to 8 ones, three plus five is equal to eight.

So we've got 50 and 8, which is equal to 58.

So 23 plus 35 is equal to 58.

And you could have added the ones first.

The sum would've been the same.

Izzy thinks she will arrive at the same sum when she solves each of these equations.

Is she right? 52 plus 31 is equal to something and 25 plus 13 is equal to something.

Izzy says, "I know I am right.

The equations have the same digits but in a different order." Well, they have got a five a two a three and a one, haven't they? Hmm, they are in a different order.

I wonder if she's thinking about the order carefully.

Andeep says, "You must think about what each digit in the numbers represent." Ah, let's have a think.

He says, "I will partition each number then use base 10 blocks to explain it." So he's partitioned all the numbers in those additions.

52 is 50 and 2, 31 is 30 and 1.

25 is 20 and 5, 13 is 10 and 3.

Oh, was Izzy right? Is she going to get the same sum? Oh, she says, "Now I can see that the number of tens and ones in each equation is different." Yes, the numbers were the same, but they didn't represent the same values, did they? Now let's solve each equation.

So we've got 50 and 2 plus 30 and 1.

And we've got 20 and 5 plus 10 and 3.

Can you see that the digit five in the first equation is worth 5 tens, but the digit five in the second equation is only worth 5 ones.

So let's look at the tens in the first equation.

5 tens plus 3 tens, 50 plus 30 is equal to 80.

And then 2 ones plus 1 one is equal to 3 ones.

So we've got 80 and 3, and 80 plus 3 is equal to 83.

What about the second equation? This time we've got 2 tens and 1 tens, 20 plus 10, which is 30.

And then we've got 5 ones and 3 ones, which is equal to eight, and 30 plus 8 is equal to 38.

What do you notice about the sum in each equation? Ah, the tens and the ones digits were reversed in each equation.

So each sum has the same digits in a different order, but they are worth very different things, aren't they? So our five and our three in our first equation were worth tens.

The five and the three in the second equation were the ones digits.

In the first equation, our ones digits were two and one.

And in the second equations, our tens digits were the two and the one.

So our equations had very different answers, very different sums because the value of the digits was different in the different equations.

And it's time to check your understanding.

You're going to use base 10 blocks to solve each equation.

And what do you notice about each set of equations? So have a look at A, B, C, and D.

Solve them and then see what you notice.

Pause the video, have a go.

When you're ready for the answers and some feedback, press play.

How did you get on? So let's have a look at A.

We had 24 plus 32, so that's 20 plus 4 and 30 plus 2, and that gives us a sum of 56.

20 plus 30 is 50 and four plus two is equal to six.

What about 34 plus 32? That had a sum of 66.

And 44 plus 32 had a sum of 76.

So did you notice that in set A, the sum increased by 10 each time because the first addend was 10 more in each equation? The first addend went from 24 to 34 to 44.

So each time we were adding 10 more, and our sums went up by 10 as well.

56, 66 and 76.

And there you can see that first addend was 10 more in each equation.

So let's look at B.

15 plus 33 is our first equation.

So we've got 1 ten and 5 ones, plus 3 tens and 3 ones.

Well, one 10 plus 3 tens, well, that's equal to 4 tens, which is 40, and 5 ones plus 3 ones is 8 ones which is eight.

So we've got a sum of 48.

What do you notice about the next one? We've got 15 again, but this time we're adding 43.

It's 10 more.

So we've got a sum of 58.

And then 15 plus 53, another 10 more.

So we've got a sum of 68.

So in set B, the sum increased by 10 each time because the second addend was 10 more in each equation.

And there we are, we can see, 33 and then 43, and then 53.

What about C? Well did you notice in C that we have the sum first? So our sum was equal to 23 plus 33, which is 56.

Then we have 23 plus 34.

So our tens are the same, isn't it? 2 tens plus 3 tens, that's 5 tens, 50, but this time three plus four is equal to 7, 57.

And did you notice what's happened with the next one? We've got 23 again, but this time we're adding 35.

So it's one more again, 58.

So in set C, the sum increased by one each time because the second addend was one more in each equation, 33, then 34, then 35.

And finally in D, again, the sum was recorded first, 22 plus 24.

So we've got 20 plus 20 which is 40, and then two plus four, which is six.

So we've got 46.

Then we've got 23 plus 24.

That's one more, isn't it? 47.

And then 24 plus 24.

Oh, which is a double, isn't it? Double 20 is 40, double four is eight, 48.

One more again.

So indeed the sum increased by one each time because the first addend was one more in each equation.

There we are, 22, 23, and 24.

Well done if you were correct with all of those and spotted those patterns.

And on into the second part of our lesson.

We're going to be partitioning to add two-digit numbers.

Andeep thinks he can solve this equation without base 10 blocks.

Hmm, I wonder what he's going to do.

He's got 52 plus 36.

He says, "I can easily see the tens and ones if I partition the numbers.

So he's partitioned his 52 into 50 and 2, and 36 into 30 and 6.

Then he says, "I will draw the tens and ones to help me to solve the equation." So he's drawn a line for each of the tens and a sort of dot for each of the ones.

He says, "I can add the tens first or the ones first.

I think I'll add the tens," he says.

So we've got 50 plus 30, 5 tens plus 3 tens, which is 8 tens, which is 80.

And then he's got 2 ones plus 6 ones, which is equal to 8 ones.

So he's got 80 and 8.

And 80 plus 8 is equal to 88, 8 tens and 8 ones.

Time to check your understanding.

Can you partition the numbers and then draw the base 10 blocks to help you solve this equation.

21 plus 46.

Think about what Andeep did and see if you can do that too.

Pause the video, have a go.

When you're ready for the answers and some feedback, press play.

How did you get on? Did you partition 21 into 20 and 1, and 46 into 40 and 6, and then you could draw lines and dots to draw your own base 10 blocks.

So there we go, 20 and 1 and 40 and 6.

I wonder where you started.

Did you start with the tens or the ones? We started with the tens.

So we've got 20 plus 40, 2 tens plus 4 tens is 6 tens, 60.

And then the ones.

1 one plus 6 ones, one plus six.

One more than six is equal to seven, so 7 ones.

So we've got 60 plus 7, which is equal to 67.

Well done.

I hope your drawings maybe helped you without using the base 10 blocks this time.

Izzy wants to solve this equation.

She's got 23 plus 44 is equal to something.

She says, "I know how to add tens and ones.

I think I can solve the equation without drawing the tens and ones." Go on then Izzy, show us how you're going to do it.

First she says, "I will partition the tens and ones." So 23 is equal to 20 and 3, and 44 is equal to 40 and 4.

"Now I can add the tens and then the ones," she says.

She says 20 plus 40 is equal to 60, 2 tens plus 4 tens is equal to 6 tens, which is 60.

And three plus four is equal to seven.

She might've done that with the near double or she might have known that three plus four is equal to seven.

So she's got 60 and 7.

And she says, "Finally, I will recombine," 67.

So let's look at those three stages she went through, she said, "First I will partition the tens and the ones.

Now I can add the tens and the ones.

And finally, I can recombine." So she partitioned, she added her tens and then added her ones, and now she's recombined her tens and her ones together to get her sum of 67.

Great thinking, Izzy.

I wonder if we can use that to help us as we go on through this lesson.

Well, here's your chance to practise.

Time to check your understanding.

Can you use Izzy's stages and solve this equation by partitioning the tens and the ones? Think about her stages.

First, she partitioned, then she added the tens and the ones, and finally she recombined.

Pause the video, have a go.

When you're ready for the answers and some feedback, press play.

How did you get on? So first, I will partition the tens and the ones, that was Izzy's strategy, wasn't it? So 31 partitions into 30 and 1, and 26 into 20 and 6.

Now I will add the tens and then the ones.

So she's added her tens, 20 plus 30 is equal to 50, and then the ones, one plus six is equal to seven.

Finally, I will recombine.

So she's going to put her tens and ones back together.

50 plus 7 is equal to 57.

So 31 plus 26 is equal to 57.

Well done, Izzy, great steps.

And I hope you were able to use Izzy's steps as well.

Izzy thinks these two equations will have the same sum.

How can she prove it? Do you think she's learned from the ones that she thought were the same in part one of our lesson? What do you think this time, and how can she prove it? Izzy says, "I will partition the numbers into tens and ones to prove that there are the same number of tens and ones." Ah, let's have a look.

So she got 46 add 32, and that partitions into 40 and 6 and 30 and 2.

And then in the other equation, she's got 42 plus 36, and that partitions into 40 and 2 and 30 and 6.

So can you see, she's got 40 and 30 as her tens in both equations, and six and two as her ones in both equations.

And there we are.

She says, "In each equation we must add 4 tens and 3 tens, and 6 ones and 2 ones.

40 plus 30 is equal to 70, 40 plus 30 is equal to 70.

Six plus two is equal to eight.

Two plus six is equal to eight.

So now we recombine.

70 plus 8 is equal to 78.

So the sum for both equations was 78.

Well done, Izzy, you got it right this time.

You checked the value of the digits as well as just the numbers that were there in the equation.

"I was right," she says.

You absolutely were, Izzy.

And great progress from the first part of the lesson.

Time to check your understanding.

Which equation A, B, or C will have the same sum as the one shown? So we've got 72 plus 23.

So will that be the as A, 27 plus 32, B, 73 plus 22, or C, 22 plus 37? Pause the video, have a think.

And when you're ready for the answers and some feedback, press play.

What did you reckon? Did you look carefully at the value of the digits and not just to see that there were sevens and twos and threes in there? It's B, isn't it? We've got in our equation 70 and 2, and 20 and 3.

And in B, we've also got 70 and 20 and a 3 and a 2, but this time, our 3 ones are with our 7 tens, and our 2 ones are with our 2 tens.

So B will give the same sum as the one shown.

72 plus 23 is equal to 73 plus 22.

Well done if you got that right.

And there we've got the partitioning to show us.

And both of them will have a sum of 95.

Andeep thinks this equation will have a sum, which is in the 60s.

Is he right? What do you think.

Izzy says, "Well, I'll look at the tens digits." She's going to check for him.

"The tens digits are two and four, so they represent 20 and 40.

20 plus 40 is equal to 60 and the ones do not cross the tens boundaries.

So yes, the sum will be in the 60s.

You were right," she says.

Can you see that? We can see that we've got 20 and 40, which is equal to 60.

And then we've got 3 ones and 2 ones.

So we're not going to go above another 10, are we? So our answer will be in the 60s, this equation will have a sum in the 60s.

Well done, Andeep.

And in fact if we work it out, the sum is 65.

Time to check your understanding.

Which of the following equations will have a sum of about 70? Is it A, B, or C? Pause the video, have a think.

And when you're ready for the answer and some feedback, press play.

What do you reckon? Which ones will have a sum of about 70? Well, in A, we've got 32 plus 25, so we've got 3 tens and 2 tens, 30 plus 20.

Well, that's 50, isn't it? And we haven't got lots of ones.

They're not going to go over our tens boundary.

In B, we've got 70.

Oh, we've got 70 there.

We wanted a sum of about 70, but we're adding on 22, so we're adding on twenty something.

So that's going to be well over 70.

That's going to be in the 90s.

What about C then? We've got 23 plus 52, so we've got 2 tens and 5 tens, which is 7 tens, which is 70.

So I think it's gonna be C.

Well done.

In C, 5 tens must be added to 2 tens.

And then there are some ones to add.

The ones do not cross the tens boundary, so the sum will be about 70.

It'll be just over 70, won't it? Izzy's looking at two equations here and she's wondering which will have the largest sum.

She's done the partitioning for us, that first step.

So she's got 34 plus 45, 30 and 4 plus 40 and 5.

And then she's got 43 plus 54.

40 and 3 plus 50 and 4.

Can you see we've got 3, 4, 4 and 5 digits in both of those equations, but which will have the larger sum? Izzy says, "43 plus 54 will have the larger sum because it has more tens." Can you see it's got 4 tens and 5 tens? And our other equation's got 3 tens and 4 tens.

So it must have the larger sum.

We don't have to work out the sum, we know it will be larger, we can reason.

But she says, "I will draw the tens and ones to prove it." So we've got 34 and 45.

And on this side we've got 43 and 54.

So we've got 70 in our first lot of tens, and 9, 79.

And we've got 90 and 7, which is equal to 97 in our second equation.

So Izzy was right, the second one, the one on the right definitely had a larger sum.

And it's time for you to do some practise.

In question one you're going to partition each number to solve each equation, and you're going to estimate the sum first.

Have a look at those tens digits.

Think about what you think the answer might be before you solve it.

In question two, you're going to circle the equation, which will have the larger sum and explain how you know.

You might want to think about your partitioning again to help you to make those decisions.

This time, you might want to decide on the larger sum and not just calculate and then circle the largest sum.

Have a think about the numbers involved first.

And in question three, you're going to partition each number to solve each equation.

But can you use the first equation to predict the sum of the second one? So can you use the top equation in A to predict the sum of the bottom equation in A, and the same for B? Pause the video, have a go at those three questions.

And when you're ready for the answers and some feedback, press play.

How did you get on? Let's look at question one.

You were thinking about giving an estimate before you did the calculations, before you used your partitioning.

So did you think about this? In each equation in set A, there are 3 tens and 2 tens to add, and the ones do not cross the tens boundary.

So the sum will be about 50 in each case.

It'll be in the 50s.

So 35 plus 22.

3 tens plus 2 tens is equal to 5 tens, that's 50, and 5 ones and 2 ones is equal to seven.

So the sum is 57.

In the second one, we've got 35 plus 23.

We've got one more this time, we've got 8 ones, so 58.

And 35 plus 24.

Can you see we've got another one again? This time we've got 5 ones and 4 ones, so 59.

And as we spotted while we were working through them, in each example in A, the second addend increases by one.

So the sum will also increase by one each time.

Let's have a look at B.

Let's think about that estimate.

So in the first equation, there are 3 tens and 4 ones to add.

And the ones do not cross the tens boundary.

So the sum will be about 70.

Is that true for all the others though? It isn't, is it? Those tens are increasing in our first addend.

Let's look at the first one first.

So we've got 36 and 41.

So we've got 30 plus 40, which is 70, and six plus one, which is seven.

So our sum is 77.

What happens next though? In the next one we've got 46 plus 41.

So we've got 4 tens to add to 4 tens.

The ones don't cross the tens boundary, so the sum will be somewhere around 80, won't it? 40 plus 40 is equal to 80, and six plus one is equal to seven again.

So we've got 87.

Ooh, can you see what's happening here? And what about the final one? We've got 56 plus 41.

We've got 10 more again, haven't we? So we've got 5 tens and 4 tens.

So we're going to be in the 90s for this answer.

Again, our ones don't cross the tens boundary, so it's ninety something.

Can we see a pattern though here? We've still got 6 ones and 1 one to add.

So our sum this time will be 97.

And as we noticed, the first addend increased by 10 each time.

So the sum also increase by 10.

In question two, you were deciding which was going to have the greater sum.

So let's have a look.

In A, it was the bottom one.

63 plus 24 will have a greater sum than 36 plus 42.

And we know this because we've got more tens.

6 tens plus 2 tens is going to be greater than 3 tens plus 4 tens.

We're going to have 8 tens in our lower equation.

Our ones don't bridge through 10, so we can just focus on the tens.

There are more tens in that bottom equation.

And if we calculate the answers, we'll find that our top equation has a sum of 78 and our bottom one has a sum of 87.

So the other thing you can spot in A is that we had 36 plus 42, and in the other one, we reversed the digits, 63 plus 24.

So we had 78 as the answer to our first and 87 as the sum for our second.

Let's have a look at B, 21 plus 54 and then 12 plus 45.

Can you see those digits have changed places again? What's that done to the sum? Which is going to have the greater sum this time? It's the top one this time.

We've got 2 tens and 5 tens, and that's going to be greater than 1 ten and 4 tens.

And if we work out the sums, 21 plus 54 is equal to 75, and 12 plus 45 is equal to 57.

And in C, we were seeing if we could predict the answer to the second equation from the answer of the first equation in each case.

So let's have a look at A.

We've got 36 plus 42.

But can we use that to predict the second one? What did you notice? Well, I noticed that there are the same number of tens and ones to add in each equation.

So I knew that the sum would be the same for the equations in A and the equations in B.

Let's have a look closely.

We've got 36 plus 42.

And then we've got 32 plus 46.

So our tens are three and four in each, and our ones are two and six in each.

So yes, the sum will be the same.

And when we partition it, we can clearly see that 30 and 6 and 40 and 2.

And in the bottom one we've got 30 and 2 and 40 and 6.

The same number of tens and the same number of ones, and the sum will be 78 for both.

And can we see that in B as well? We've got 20 and 1 and 50 and 4, 20 and 4 and 50 and 1.

The same number of tens and ones.

And the answer will be 75 for both.

Well done if you spotted that.

It's really good to look at calculations and equations before we solve them just in case we can see anything that helps us.

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

We've been adding two-digit numbers without crossing the tens boundary.

What have we learned about? Well, we've learned that we can add two-digit numbers using base 10 equipment to add the tens and the ones.

Partitioning two-digit numbers can help us to add them.

We know that we can either add the tens first or the ones first and the sum will remain the same.

And considering the number of tens when adding two-digit numbers can help us to estimate the sum.

Thank you for all your hard work and your mathematical thinking in this lesson, and I hope I get to work with you again soon.

Bye-bye.