Lesson video

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

It's from our unit "Adding and subtracting ones and tens to and from two-digit numbers." So we're going to be looking at two-digit numbers and we're going to be thinking about adding and subtracting and hopefully, using our known facts to help us.

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

So in this lesson, we're going to be using our number facts to add multiples of 10 to two-digit numbers.

So have you got your number facts warmed up nice and ready? Excellent.

Let's see what's in our lesson today? Well, we've got two keywords.

Well, well first one's a bit of a key phrase, isn't it? We've got multiples of 10 and recombine, so I'll take my turn and then it'll be your turn.

My turn.

Multiples of 10.

Your turn.

My turn.

Recombine.

Your turn.

Excellent.

I hope they're words that you are familiar with, but they're going to be really useful.

So listen out for them in our lesson today and hopefully, you'll be using them a lot in the way you talk about your maths as well.

So there are two parts to our lesson today.

In the first part, we're going to be adding multiples of 10 to two-digit numbers, and in the second part, we're going to be using known facts to add multiples of 10.

So let's make a start on part one.

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

Alex wonders how he can solve this equation.

24 plus 30.

I wonder how you would solve this equation.

Hmm.

He says, "I know 30 is 3 tens, so I can count on three more tens." So here's his number line.

He's got 24, he's gonna count on in tens.

24 plus one 10 is equal to 34, plus another 10 is equal to 44 and plus another 10 is equal to 54.

He said he knew it was three 10.

So he's counted on 3 tens.

And his answer is 54.

What do you notice about the tens digits and the ones digits in the equation? Well, Alex says, "The tens digits change, but the ones digits stayed the same." So we had 24 plus 30 is equal to 54, but we only had a four in the 24 and we've still got a four in our sum in our whole, which is 54.

Now, Alex wants to solve a different equation.

24 plus 70 is equal to something.

He says, "I'm adding a multiple of 10." That's 70, isn't it? "So the ones digit will not change." That's right, Alex.

So he knows that his sum will have a four in the ones.

70 is equal to 7 tens.

So I will count on 7 tens.

Are you ready? 24, add 10 is 34, add 10 is 44, add 10 is 54, add 10 is 64, add 10 is 74, add 10 is 84, add 10 is 94.

And we can count, he's counted on 7 tens and he's ended up with a sum of 94.

Sam says, "That took ages.

I think there must be a more efficient method." Efficient methods allow us to work more quickly perhaps and to use other things that we know to help us.

Let's go back to the first example.

24 plus 30.

Sam says, "We know the ones will not change." So we know that our answer will be something 4.

She says, "I think we can use what we already know about adding multiples of 10." Good thinking, Sam, always good to use what we know already.

She's drawn a part-part-whole model.

So we know that 2 plus 3 is equal to 5.

So 2 tens plus 3 tens is equal to 5 tens.

And can you see, we've got 2 tens in 24 and 3 tens in 30.

So she says, we know that 20 plus 30 is equal to 50, so our answer are some must be 54.

Let's explore this with base 10 blocks.

We've still got 24 plus 30 as our equation to solve.

First, the two-digit number is partitioned into tens and ones.

And Alex says 24.

That's the two-digit number we're working with is equal to 2 tens and 4 ones.

That means 24 plus 30 is the same as 20 plus 4 plus 30.

Ah! And there he's recorded it as an equation.

We've still got 24 plus 30, but we've partitioned the 24 into 20 and 4.

Now, we can think about our tens and we can add them using a known addition fact.

Alex says, "I know that 2 plus 3 is equal to 5, so 2 tens plus 3 tens is equal to 5 tens, and that's 20 plus 30 is equal to 50." So now, we've got all our tens combined.

Finally, the tens and ones are recombined to find the sum, we're going to put them back together again.

5 tens plus 4 ones is equal to 54.

50 plus 4 is equal to 54.

So our sum is 54.

What do you notice about the tens digit and the ones digit in the equation? Well, Alex says, "The tens digit changes, but the ones digit stays the same." So 24 plus 30 is equal to 54.

We've only ever got a four in the ones, so that stays the same.

Alex uses a part-part-whole model to solve the same equation.

Let's see what he did.

So he says, "First, 24 is partitioned into tens and ones." So we can see that 24 and he's partitioned it into 4 ones and 2 tens.

He's recorded it that way round 4 and 20.

So 24 is equal to 20 plus 4.

Now, we can add the tens and he says we can add the tens using a known addition fact.

So 20 plus 30 is equal to 50 because we know that 2 plus 3 is equal to 5.

So 2 tens plus 3 tens must be equal to 5 tens, and that's 50.

So now, we can say that 2 tens plus 4 ones, plus 3 tens is equal to 5 tens and 4 ones.

So we can recombine the tens and the ones, 50 and 4 is equal to 54 to find our sum.

So 24 plus 30 is equal to 54.

And there's our sum.

So let's have a look at those stages.

First, we partitioned the two-digit number with tens and ones, so that we could see the tens that we were adding.

Then we added the tens, so the 20 and the 30 were added and we used our known fact of 2 plus 3 is equal to 5 and applied it to our multiples of 10.

And then we recombined, we recombined our tens with the ones that we'd partitioned.

So there were three stages to the way we worked and we used a number fact in the middle to help us.

Sam thinks she can show what Alex did using a place value chart.

Let's have a look.

So first, the two-digit number is partitioned into tens and ones.

2 tens and 4 ones for 24.

And there it is recorded as an equation.

Then we're going to add the tens.

We know we've got to add in three more tens.

So then the tens are added using a known addition fact.

2 plus 3 is equal to 5.

So 2 tens plus 3 tens must be equal to 5 tens.

20 plus 30 is equal to 50.

So there's our adding the tens stage.

And then we need to recombine 2 tens and 4 ones, plus 3 tens is equal to 5 tens and 4 ones.

And we can see that in the place value chart.

So now, we need to recombine our tens and ones to find the sum.

50 plus 4 is equal to 54.

5 tens and 4 ones.

So our sum is 54.

24 plus 30 is equal to 54.

Time to check your understanding.

Which of these represents the equation shown? And our equation is 54 plus 30 is equal to something.

Which of the representations a, b, or c, represents that equation? Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

How did you get on? Which did you think it was? Did you spot that it was b? Our equation was 54 plus 30 and we can see in b that 54 has been partitioned into 4 ones and 5 tens.

And then we've got a 30 to add on.

In the other two, the representations weren't showing that we had 5 tens and 3 tens and 4 ones to combine to make our sum.

So b was correct.

Time for you to do some practise.

Can you use a part-part-whole model or a place value chart to solve the following equations? And then, you could use base 10 blocks to check that you are right.

So you've got three questions in a and three in b to find the sum.

And then in c and d, we've written our equations in a slightly different order.

So have a think, use the resources, have a go fill in the missing numbers, and when you're ready, we'll get together for some feedback.

How did you get on? So let's look at, a, first.

So we had a missing sum in each case, didn't we? So the first one is 15 plus 20, and we can use a part-part-whole model to partition the 15 into 5 ones and 1 ten.

So first, the two-digit number is partitioned into tens and ones.

So 15 partitioned into 5 ones and 1 ten.

Then, the tens are added using a known addition fact.

Well, we've got 10 plus 20, 1 ten plus 2 tens, so we know that's going to be 3 tens or 30.

And then finally, we can recombine our tens and our ones to find the sum.

So we know that we've got 30 as the total of our tens and another 5.

30 plus 5 is equal to 35.

And you could use the same strategy to solve the other equations.

And if you'd done that, you'd have worked out that 25 plus 20 is equal to 45.

35 plus 20 is equal to 55.

Did you spot that we were adding 10 more each time, 15 and then 25 and then 35, but we were always adding our 20 to those two-digit numbers? And what about in b? Can you spot a pattern here as well? We had 10 plus 36, 20 plus 36, and 30 plus 36.

So each time we were adding 10 more to 36.

So our sums are 46, 56 and 66.

So what about for c? Well, something is equal to 21 plus 50.

So we've put our sum at the beginning of our equation this time.

So we might have used a place value chart perhaps this time.

So first the two-digit number is partitioned into tens and ones.

So we've got 21, 20 plus 1 or 2 tens and 1 one.

Then, the tens are added using a known fact.

So in this case we're adding 50, we're adding 5 tens.

So we can see we've got 2 tens plus 5 tens, and we can use our known fact 2 plus 5 is equal to 7.

So 20 plus 50 must be equal to 70.

So we've got 7 tens now.

And finally, the tens and ones are recombined to find the sum.

And in our place value chart, we can see that straight away, 70 plus 1 is equal to 71.

So our sum is 71.

And can you spot a pattern as well here? We had 21 plus 50, now we've got 21 plus 60 and 21 plus 70.

I wonder what's gonna happen.

So you could use the same strategy to solve the other equations and our sums would be 81 and 91, and we could use the same strategy for d as well.

Again, we've got a missing sum in each of these.

For the first two, the sum is recorded at the end of the equation.

And for the last one, the sum is at the beginning of the equation.

But can you spot something here? We've changed the orders of the add ends, but in each of our equations we've got 43 and we're adding a multiple of 10.

We've got 43 plus 20, 30 plus 43, and 40 plus 43.

So 10 more each time.

So you'd see that our sums were 63, 73 and 83, and we know that the order doesn't matter because addition is commutative.

We can add the add ends in any order and the sum remains the same.

Okay, and on into part two of our lesson.

We're going to use known number facts to add multiples of 10.

Sam wonders which number facts she could use to help her solve each of the following? So she's got missing wholes in her part-part-whole model, and she's got parts of 20 and 26 and then 30 and 26.

Well, she says, 26 plus 20 is equal to 20 plus 6 plus 20.

She's partitioned the 26.

So she says I must add 2 tens and 2 tens.

I will use the fact 2 plus 2 is equal to 4, so 2 tens plus 2 tens is equal to 4 tens.

So let's use a stem sentence to help us.

2 tens and 6 ones, plus 2 tens is equal to 4 tens and 6 ones.

And 4 tens and 6 ones is equal to 46.

So we can say that 26 plus 20 is equal to 46.

So what about the next one? Can we use the same thinking? 26 plus 30.

Well, 26 can be partitioned into 20 and 6, and then we've got a 30 to add.

So she says I must add 2 tens and 3 tens for the 20 and the 30.

I will use the known fact 2 plus 3 is equal to 5.

So 2 tens plus 3 tens is equal to 5 tens.

Let's use our stem sentence.

2 tens and 6 ones, so 26, plus 3 tens, so that's the number we're adding our other add end is equal to 5 tens and 6 ones.

So we had 2 tens and 3 tens, which is equal to 5 tens.

And we've got our 6 ones.

And that's equal to 56.

So 26 plus 30 is equal to 56.

Time to check your understanding.

Can you match each part-part-whole model to the fact that you would use to solve it to find the missing whole.

So pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? So did you spot that our first part-part-whole model matches with that first set of equations? So we can use 3 plus 2 as equal to 5 because we've got 35 and 20, we've got 3 tens and 2 tens, 30 plus 20 is equal to 50.

And then we would add in our ones that we partition from the 30.

What about the next one? Ah, so the middle bar model matched with the equations on the right, we've got 50 and 32 or 32 and 50, so we can use 3 plus 5 is equal to 8 to add our 30 and our 50, which will be equal to 80.

And then we'd recombine with our 2 ones.

So our last part-part-whole model must match with the middle equations.

We've got 50 and 23 or 23 and 50.

So we've got 2 tens and 5 tens to combine.

So 2 plus 5 is equal to 7, 20 plus 50 is equal to 70.

And then we'd recombine with our 3 ones.

Well done if you've spotted all of those.

Now, let's find the number of facts to help us to solve these.

Let's look at this one first.

We've got 54 plus 30, so we're going to partition our two-digit number with tens and ones into 50 plus 4.

And then we're going to add the 30.

So can you see that we've got 5 tens and 3 tens to combine.

So we'll use the fact 5 plus 3 is equal to 8.

So 5 tens plus 3 tens must be equal to 8 tens.

So let's think about those three stages.

Partitioning our two-digit number with tens and ones, adding our multiples of 10 and then recombining with the ones.

So we've got 5 tens and 4 ones, plus 3 tens is equal to 8 tens and 4 ones.

So 54 plus 30 is equal to 84.

What about the next one? Can you think through those three stages that we had? So we've got 24 plus 30, so we're going to partition our two-digit number with tens and ones into 20 plus 4, and then we're going to add 30 and we're spotting that we must add 2 tens and 3 tens.

So we can use 2 plus 3 as our known fact.

2 tens plus 3 tens is going to be equal to 5 tens.

So let's think about the whole equation.

2 tens and 4 ones, plus 3 tens is equal to 5 tens and 4 ones.

24 plus 30 is equal to 54.

We partitioned, we added our tens and then we recombined with our ones.

Sam thinks she can use the known fact 5 plus 4 is equal to 9 to solve this efficiently.

Is she right? We've got 34 plus 50 is equal to something.

Let's check says Alex, "Remember, partition, add the tens, and then recombine.

So we're going to partition first.

34 is equal to 30 plus 4.

We've recorded it with the four first here, but that's okay.

We can combine our parts in any order.

We're going to add the tens.

So to add the tens, I need to know the fact 3 plus 5 is equal to 8, not 4 plus 5 is equal to 9.

Ah, she spotted it.

We've got 3 tens in 34 and we've got to add 5 tens in 50.

So we add the tens.

30 plus 50 is equal to 80, and then we're going to recombine 80 plus 4 is equal to 84.

And Sam says, "I've spotted my mistake, I didn't focus on the tens digits." She thought that the four was 4 tens and it isn't? It's four ones, isn't it? So we must be really careful that we focus on the tens digits when we are looking for that known fact that we're going to use when we're adding a multiple of 10.

So over to you to check your understanding.

Which known fact will you use to solve the following? So we've got a part-part-whole model with a missing whole, and we've got parts of 31 and 40.

So which known fact will you use to solve this? Pause the video, have a go, and when you're ready we'll get together for some feedback.

How did you get on? Did you spot that it was, a, 3 plus 4 is equal to 7, 31 plus 40 is equal to 30 plus 1 plus 40, so I must add 3 tens and 4 tens.

We can use the fact 3 plus 4 is equal to 7, so 3 tens plus 4 tens is equal to 7 tens.

Let's check with our stem sentence and complete the equation and find our missing whole.

3 tens and 1 one, plus 4 tens is equal to 7 tens and 1 one.

So 31 plus 40 is equal to 71.

Sam says both of these equations will have the same sum.

Is she right? She says, "When I partition the tens and ones, I can see that each equation has the same number of tens and ones to be added." So she's partitioned 24 into 20 and 4 and she's got to add 30.

And she's partitioned 34 into 30 and 4, and she's got to add a 20.

She's going to represent it with base 10 blocks.

So we can see there she's got 24 and she's got to add 30.

So we've got 20 plus 4 plus 30.

What about the next equation? Well, she's got 30 and 4 and she's got to add 20.

So we've got 30 plus 4 plus 20, and she says we can combine the add-ins in any order and the sum remains the same.

So we can see that in both of those equations, there's a 20 and a 30 and a 4 to combine.

So 20 plus 4 plus 30 is equal to 30 plus 4 plus 20.

And we can see that when we combine our tens and then recombine with our ones.

We've got a sum of 54 and the same for this one as well.

54 is equal to 54.

So both of those equations do have the same sum.

And she says, "I use the known fact 2 plus 3 is equal to 5, or 3 plus 2 is equal to 5 to solve both equations." And she applied that to her tens.

2 tens plus 3 tens is equal to 5 tens.

Time to check your understanding.

Which of the following equations will have the same sum as 62 plus 30? Pause the video, have a go.

And when you're ready, we'll get together for some feedback.

How did you get on? Ah, so, a, we'll have the same sum because we've just swapped the order of the add-ins and we know that they can be combined in any order.

So 62 plus 30 is the same as 30 plus 62.

Was there another one? There was, b, will also have the same sum.

This will have the same sum because both equations combine 3 tens, 6 tens and 2 ones.

And we can use the known fact 3 plus 6 is equal to 9, or 6 plus 3 is equal to 9 to add our tens and solve both of those equations.

So well done if you spotted that, both of those equations will have the same sum as our equation, 62 plus 30.

Time for you to do some practise.

So in one, you're going to use a known fact to solve the equations and write the fact that you used.

And then for two, how many ways can you complete the following? We've got 14 plus something is equal to something 4.

So we've got a two-digit number plus a multiple of 10 is equal to another two-digit number.

Pause the video, have a go at your practise tasks, and when you're ready, we'll get together for some answers and feedback.

How did you get on? So for question one, you had to fill in the missing wholes.

So did you find that the whole for 47 plus 20 was 67, 40 plus 32 was 72 and 23 plus 60 was 83.

But what facts did you use? Well, in the first one we had 4 tens and 2 tens.

So 4 plus 2 is equal to 6.

So 4 tens plus 2 tens is equal to 6 tens.

So our sum is 67.

In the second, we had 4 tens plus 3 tens, so 4 plus 3 is equal to 7.

So we could then recombine with our ones and we got the sum of 72.

And in the final one, we had 2 plus 6 is equal to 8 because we had 2 tens and 6 tens.

And when we combined that with our ones, we got a sum of 83.

What about two? So for two, you could have added any multiple of 10 as your second add end right the way up from 10 until you reached 80.

So let's have a look at how that would work.

So we could have had 14 plus 10 is equal to 24, 14 plus 20 is equal to 34, 14 plus 30 is equal to 44.

14 plus 40 is equal to 54, 14 plus 50 is equal to 64, 14 plus 60 is equal to 74, 14 plus 70 is equal to 84 and 14 plus 80 is equal to 94.

If we'd added any more, we wouldn't have had a two-digit number as asked sum.

Well done if you found all of those.

Did you work systematically in order to make sure you'd found all the possibilities? I wonder if you did.

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

So we've been adding multiples of 10 to two-digit numbers.

So what have we learned about? We've learned that when adding multiples of 10 to a two-digit number, the tens digit changes but the ones digit stays the same.

And we've learned that we can use number facts to help us to add multiples of 10 to a two-digit number.

Do you remember those three steps? We partitioned the two-digit number that had the ones, and then we used the known fact to add our multiples of 10, and then we recombined the multiples of 10 with the ones to get our sum.

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

I hope you've enjoyed the lesson and I hope I get to work with you again soon.

Bye-bye.