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 finding missing addends when adding two-digit numbers.

Addends are the numbers that we add together when we do an addition, but this time one of our addends is going to be missing and we're going to have to work out what the missing number is.

So let's make a start, see what's in our lesson.

We've got two keywords.

We've got addend and digit.

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

Are you ready? My turn, add end.

Your turn.

My turn, digit.

Your turn.

Lovely, well we just talked about addends are the numbers that we add together.

And digits are the numbers we use in the way we record the numbers in our calculations.

So let's look out for those keywords as we go through our lesson today.

There are two parts to our lesson.

In the first part, we're going to be finding the missing addend, and in the second part, we're going to be using knowledge of equality of things being equal to each other.

So let's make a start with part one, finding the missing addend.

And in this lesson we've got Andeep and Izzy helping us with our learning.

Izzy solves an equation, then she hides a digit from one of the addends.

Ah, so she's just hiding one of the digits in our two-digit number.

She wants Andeep to find it.

So she solved the equation.

She knows the equation is correct, but what's missing under her purple rectangle? Let's have a look see how Andeep's gonna go about solving this problem.

Andeep says "The whole has 7 tens and 6 ones." It's 76, isn't it? 34 plus hm 2 is equal 76, so the whole has 7 tens and 6 ones.

He says, "I will partition to see the tens and ones I already have." Good thinking, Andeep.

So by partitioning what he's got already, he knows he's got 34, 3 tens, 30, and 4 ones, and then he's got something and 2.

And he knows that the whole is 76, 7 tens and 6 ones.

He says, "Well, 4 ones plus 2 ones is equal to 6 ones, so we don't need any more ones." We've got the ones in our addends and they are equal to the ones in our sum.

4 plus 2 is equal to 6, so we don't need any more ones, so our missing digit must be a tens digit.

One part has 3 tens and the whole has 7 tens.

Andeep says, "I know that 3 plus 4 is equal to 7, so 3 tens plus 4 tens must be equal to 7 tens." So we're missing 4 tens, 40, so what's our missing digit? Ah, he says, "The missing digit must be 4, 4 tens, or 40." But in our number, we don't record the 40, do we? We record a missing digit of 4.

So there we go.

Our whole equation is 34 plus 42, and we can see that partitioned 30 and 4 plus 40 and 2.

The missing digit 4 represents 4 tens, which is worth 40.

Time to check your understanding.

Which digit is missing from this equation? Remember to partition to help you find out.

So is this equation missing a 2, a 5, or a 4? Have a think, work through it, pause the video, and when you're ready for the answer and some feedback, press play.

What did you think? Did you use Andeep's way of working? And if you did, you'd have worked out that the 5 digit was the one that was missing.

So let's have a think.

If we partition 20 and 3 plus something and 2 is equal to 75, the whole has 7 tens and 5 ones.

Let's look at the ones we've got.

3 ones plus 2 ones is equal to 5 ones, so we don't need any more ones, so we need to look at the tens.

One part has 2 tens and the whole has 7 tens.

2 tens plus 5 tens equals 7 tens.

20 plus 50 is equal to 70.

So the missing digit must be a 5 representing 5 tens, which is worth 50.

Well done if you've got that right, and well done if you used Andeep's thinking to help you.

Now Andeep solves an equation and then hides a digit from one of the addends, and Izzy wants to find it.

So this time we've got 24 plus 7 something is equal to 95.

What's missing this time, do you think? Let's see how she works out the missing digit.

So Izzy says, "The whole has 9 tens and 5 ones, 95." Let's partition what we've got.

So 24 is partitioned into 20 and 4, and 70 something is partitioned into 70 and there's something we don't know about.

Izzy says, "Well, 20 plus 70 is equal to 90." And that's the number of tens we've got in our sum, so we don't need any more tens.

So we are looking at ones, aren't we? One part has 4 ones and the whole has 5 ones.

And what fact you could use to help you there? Well 5 is one more, isn't it? 4 plus 1 is equal to 5, so the missing ones digit, we know it's a ones digit that's missing, is a 1.

So our missing digit is a 1, and it's representing the 1 one in 71.

24 plus 71 is equal to 95.

Time to check your understanding.

Which digit is missing from this equation? Is it a 2, a 5, or a 4? Remember to partition like Izzy and Andeep have been doing to help you find out.

Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

How did you get on? Did you spot that we had a 2 missing this time? Let's have a look at how we can partition to help.

So what we know about is 20 and 3, and 40 and something.

We know that 4 must be in the tens place because we've got a digit missing afterwards.

The whole has 6 tens and 5 ones.

It's 65.

So 2 plus 4 is equal to 6.

So 20 plus 40 must be equal to 60.

Well, that's all the tens accounted for, so we don't need any more tens.

We're missing a ones digit.

One part has 3 ones, the 23, and we know there are 5 ones in the whole, 65.

And we know that 3 plus 2 is equal to 5, so the missing digit must be a 2 representing 2 ones in the 42.

Well done if you use that thinking to be able to work out what the missing digit was.

Andeep says, "The missing digit in this equation is a 5." Is he right? Not sure he is.

What mistake has been made? He might want have a think before Izzy and Andeep get into thinking about it.

Izzy says, "The whole has 7 tens and 8 ones." So if we partition what we know about, we've got some number of tens and 6, and 30 and 2, and the total is 78.

"6 plus 2 is equal to 8, so we don't need any more ones," she says.

We've got 8 in our sum, 78.

Andeep's mistake was that he thought 8 tens were needed, so he added 5 tens and 3 tens to reach 8 tens.

He knew about 30, he thought we needed another 50.

We don't, do we? We're looking for 7 tens, not 8 tens.

Ah, Andeep says, "The whole has 7 tens and one part has 3 tens, so I should have added 4 more tens." So the missing digit was a 4 and not a 5 representing 4 tens or 40, and 40 plus 30 is equal to 70.

And that's the number of tens we have in our sum.

Well done for correcting your mistake, Andeep.

This time when Andeep solves his equation, he hides both of the digits in the missing number.

Ooh, so 24 plus something is equal to 59, but we've got some stem sentences to help us here.

So do you remember in all the examples we've seen so far, we've thought about what the whole has.

So the whole has mm tens and mm ones.

What do we have already? Well, we have mm tens and mm ones already, so let's think about what the whole has and what we have already, and that might help us to work out what's missing.

So let's partition to find the missing addend.

So the whole has 5 tens and 9 ones for 59.

We have 2 tens and 4 ones, 24.

So what is missing? Well, we can use some more stem sentences.

We know we have 2 tens and our sum has 5 tens.

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

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

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

So we must have 3 tens missing in our missing addend, and that's 30.

And 4 ones plus some ones is equal to 9 ones.

Well we know that 4 plus 5 is equal to 9, so we must be missing 5 ones.

So the missing addend is 3 tens, which is 30, and 5 ones.

And if we recombine those, we get our missing addend of 35.

24 plus 35 is equal to 59.

Right, time for you to have a go.

You've got the stem sentences there to help you.

Can you find the missing addend from the equation? Something plus 37 is equal to 68 and we've started the partitioning of the addends to help you.

So pause the video, use the stem sentences to find the missing addend.

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

How did you get on? Let's see how the stem sentences can help us.

So the whole has 6 tens and 8 ones.

We have 3 tens and 7 ones in our 37, so we know that 3 tens add some tens has got to equal 6 tens.

Well, 3 tens add 3 tens is equal to 6 tens, so our missing tens value is 3 tens or 30.

We've got 7 ones and we need some more ones to equal 8 ones.

7 plus what is equal to 8? Well, we know that 7 plus 1 is equal to 8, so we must have 1 missing from our ones digit of our missing addend.

Now we can recombine them.

The missing addend is 30 and 1, which is 31.

31 plus 37 is equal to 68.

Well done if you worked that out.

And I hope the stem sentences were useful.

Maybe you could make a note to use those when you get into your own practise.

Izzy's going to use the first equation here to help her to solve the second equation.

So she's going to use a to help her to solve b.

What do you notice about a and b? Izzy says, "The sum of b is 10 more than the sum of a." So the sum of b, and can you see our sums are written first this time.

The sum of b is 83 and the sum of a is 73.

Yes, that's right.

83 is 10 more than 73.

Izzy says, "Both equations have one addend of 52, so I know that the missing addend in b must be 10 more than 21." So the 52 parts are the same.

52 plus 21 is equal to 73.

We want something that we can add to 52 to equal 83.

So I think Izzy's right.

It's got to be 10 more, hasn't it? So our missing addend must be 31.

And if we double check that we've got 30 and 1, and 50 and 2, 30 plus 50 is equal to 80, and 1 plus 2 is equal to 3, 83.

Great thinking there, Izzy.

Really good reasoning.

Well done.

Izzy writes a missing number equation.

She sets Andeep a challenge.

Oh, I wonder what her challenge is.

She says, "Complete the equation using only the digits shown." So we've got 58 is equal to something plus something, and they're 2 two-digit numbers.

And we can only use the digits 1, 2, 3, and 7 to fill in those missing ends.

I wonder what Andeep is going to do.

Andeep says, "The whole has 5 tens, so my tens digits must sum to 5." Great thinking, Andeep.

Can you see two numbers in there that are going to sum to 5? Think I can.

Ah, that's right.

2 plus 3 is equal to 5.

So the tens digits must be 2 and 3.

So there we are.

He's put the 2 and the 3 as his tens digits.

What are we left with? The whole has 8 ones, so my ones digits must sum to 8.

What's he got left? He's used the 2 and the 3.

He's got the 1 and the 7 left.

1 plus 7 is equal to 8, so the ones digits must be 1 and 7.

There we go.

Oh, Izzy says, "Are there any other possible equations that could be made?" Well we've got 58 is equal to 21 plus 37.

Can we write that in a different way? So we could also say that 27 plus 31 is equal to 58.

What did we do there? We swapped the ones digits over, didn't we? "Or we could say," says Andeep.

What's gonna happen this time? Oh, 37 plus 21.

We swapped the tens digits over, haven't we? Because we've kept our 3 and our 2 as tens and our 7 and our 1 as ones, we know that the sum will stay the same time.

Time to put all this into practise for you.

I wonder if you can remember all the things that Izzy and Andeep have been thinking about and those stem sentences maybe? So for question one, you're going to partition the numbers to find the missing addend from each equation.

Do you notice any patterns that might help you to solve each one? Look for a pattern in the equations in a and the equations in b.

Maybe you can use some reasoning as well.

And in question two, you're going to use the digit cards shown to complete the equation.

How many different ways can you find? Think about what Andeep was just doing.

Pause the video, have a go at those two 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.

Let's look at a first.

Remember we were solving these equations using partitioning, but seeing if we could find any patterns.

Well, I'm looking at those sums 'cause the sums are written first in a.

We've got 64 is equal to some, 74 is equal to something, 84 is equal to something, and 94 is equal to something.

Hmm, I wonder if there's any thinking we can do there? Well, 64 is equal to 21 plus 43.

If we partition that we've got 20 and 1, and we are looking for 6 tens, so 60.

So we need to add 4 more tens on.

2 tens plus 4 tens is equal to 6 tens, and we had 1 one.

1 one plus some ones is equal to 4 ones.

Well, 1 plus 3 is equal to 4, so 21 plus 43 must be equal to 64.

The next sum was 74.

Now, we'd worked out that one of our missing addends was 43.

We've got that 43 again.

This time we need our sum to be 10 more than it was before.

So we need 10 more in our missing addend.

So 31 plus 43 is going to be equal to 74, and we could use partitioning to check that as well.

What about the next one? 84 is equal to 31 plus something.

Ah, we've got that 31 repeated, but can you see 84 is 10 more than 74.

Our 31 is the same, so our missing addend has got to be 10 more.

So it's got to be 10 more than 43, which is 53.

And again 94 is 10 more than 84.

We've got that 53 staying the same, so our other addend must be 10 more than the one we had before, which was 31, so it must be 41.

Yes, I noticed that in each equation in set a when the sum increased by 10 and one addend was the same, the other addend increased by 10.

And you could use your partitioning strategies just to check that your thinking was right on those as well.

Well done if you spotted that though and if it saved you some partitioning.

Let's have a look at b.

Let's look at the sums again.

We've got 89, 79, 69, and 59.

Oh, they're getting smaller by 10 each time, aren't they? So let's have a look at the first one.

28 add something is equal to 89.

Well, it's 61 isn't it? We've got 28, which is 2 tens and 8 ones.

I need 8 tens in my sum, so 20 plus 60 is equal to 80.

And I need 9 ones in my sum, and I've got eight ones already, so 1 more one.

Let's look at the next one.

This time our sum is 10 less.

89 has decreased to 79, but my 61 addend is the same, so my other addend must be 10 less.

So 28 decreases to 18.

18 add 61 is equal to 79.

In the next one, my 18 is the same.

I've got that part which is the same, but my sum, my whole, is 69, it's 10 less again.

So my other addend must be 10 less than it was before.

So 61 comes down to 51.

18 plus 51 is equal to 69.

And then finally, ooh, now this is interesting.

69 has decreased by 10 to 59 and my 51 has decreased by 10 to 41, so this time my 18 can stay the same.

18 plus 41 is equal to 59.

So, yes, I noticed in each equation in set b when the sum decreased by 10 and one addend was the same, the other addend also decreased by 10.

In the last one though, we could see the addend that had decreased by 10, so we had to put in the one that was the same as before.

Well done if you spotted that.

Reasoning your way through these questions is a really good way of checking your partitioning or of finding an efficient way of calculating the answer.

And for question two you had to use the cards.

We have 97, 9 tens, so our tens digits needed to sum to 9.

Well, 2 plus 7 is equal to 9, so our tens digits must be 2 and 7, but we can write them in any order.

So 97 could be also equal to 70 something plus 20 something.

What about the ones? Well the whole has 7 ones, so my ones digits must sum to 7.

So that's my 3 and my 4.

3 plus 4 is equal to 7, so the ones digits must be 3 and 4, and we can write those in any order.

So we could have 3 and the 4 and then we could have 4 and the 3.

So the possible equations we could have would be 97 is equal to 23 plus 74, 97 is equal to 24 plus 73, 97 is equal to 73 plus 24, and 97 is equal to 74 plus 23.

As long as our tens digits are the 2 and the 7 and our ones digits are the 3 and the 4, we can have them in any combination and we can have the addends in any order.

Well done if you've got all of those.

And on into part two, we're going to be using our knowledge of equality of things being equal.

So the children are exploring with some base 10 blocks.

And can you see the equation they've got there? Hmm? They lay out the blocks to show this equation.

8 plus 5 is equal to 5 plus 8.

Do you notice something? Andeep says, "This equation is different to the others we've been solving.

It has an addition expression on each side." Ah yes, 8 plus 5 is equal to 5 plus 8.

The equal sign can show us that two expressions are equal.

It doesn't have to have something to calculate and an answer on the other side.

It can show us that two things are equal, and in this case it's two expressions.

Each side of the equation is equal in value.

We don't need to work out the sum of 8 and 5, we just know that if we've got 8 and 5 and 5 and 8, the sum will be the same.

And we know that we can change the order of the addends and the sum remains the same.

So 8 plus 5 is equal to 5 plus 8.

Izzy moves one of the base 10 blocks.

Let's look at what she does.

Ooh, did you see what happened? Let's look at it again.

Did you see that she moved one of the blocks from the 8 and put it in with the blocks for the 5? So instead of 8 plus 5, she's got 7 plus something.

Andeep says, "How does this change the other addend in the equation?" Did you see what happened to the 8 and what happened to the 5? What happened to the blocks? Ah, Izzy says, "We decreased one addend by 1, so to keep each side of the equation equal, the other addend must increase by 1." And you can see that with the blocks.

8 blocks has become 7 blocks, but 5 blocks has become 6 blocks.

We didn't lose any blocks or add any in, we just moved them.

So 8 plus 5 is equal to 7 plus 6.

And we can see that in the new arrangement of the blocks.

So now we're starting with 7 plus 6.

Andeep moved another block and decreased 7 by 1.

I wonder how this will change the other addend in the equation.

Shall we see what he does? Ha-ha.

So he's decreased the 7 to 6.

So now our first addend is 6.

So 7 plus 6 is equal to 6 plus? What happened to the number of blocks under the 6? It went up by one, didn't it? So one addend decreased by 1.

So to keep it the same, the other addend must increase by 1.

Each time one addend decreases by 1, the other addend increases by 1.

Time to check your understanding.

Izzy decreases 6 by 1, she moves another base 10 block over.

Complete the equation to show the missing addend.

So let's watch the base 10 block move and then you're going to complete the equation.

So there's the move.

Pause the video, complete the equation, and when you're ready for the answer and some feedback, press play.

Did you see what happened? Let's just look.

We started with 6 plus 7, now we've got 5 plus 8.

That's right.

To keep both expressions equal as one addend decreases by 1, the other must increase by 1.

So our 6 blocks became 5 and our 7 blocks became 8.

Izzy says we can use the same strategy to help find the missing number in equations with two-digit numbers as well.

Ooh, let's have a look.

So we've got 30 plus 25, we can see that in the blocks, and that's equal to 31 plus something.

Ooh, can you think what we could do with the blocks to help us here? Izzy says, "The addend of 30 has been increased by 1 to 31." So 30 has become 31.

She says, "If 30 has been increased by 1, then 25 must have been decreased by 1." So let's have a look at that with the blocks.

We're going to take one block from the 25 and give it to the 30, so now we've got 31 plus 24.

The missing addend is 24.

Let's move another base 10 block and predict the missing addend.

So we've got our 31 plus 24, and it's equal to 32 plus something.

Can you think what's going to happen? What we could do with the blocks to help us? Izzy says, "The addend of 31 has been increased by 1 to 32." So 31 has increased by 1 to 32, so what do we have to do to the 24? If 31 has been increased by 1, then 24 must have been decreased by 1.

So let's move one of those blocks across from 24 to 31, so now we've created 32 plus 23, well done.

The missing addend must be 23.

Time to check your understanding.

Move another base 10 block to increase 32 by 1 and then complete the equation to show the missing addend.

Think about how those blocks are going to move.

Pause the video, have a go, and when you're ready for the answer and some feedback, press play.

Did you see what happened? So if 32 has been increased by 1, then 23 must have been decreased by 1 because we've got to have the same number of blocks for our expression to be equal.

So we've moved one block across, and now we've got 33 plus 22.

32 has increased by 1 to make 33 and the 23 has decreased by 1 to equal 22.

Well done if got that right.

The missing addend must be 22.

To keep both expressions equal as one addend increases by 1, the other must decrease by 1.

I wonder what's different about this equation? We've got 50 plus 35 is equal to 60 plus something.

What's changing this time? Izzy says, "The addend of 50 has been increased by 10 to 60.

So the other addend must have decreased by 10." We've been changing things by 1 before, this time we're changing by 10, so the 50 has become 60.

So can you think what we can do with the blocks to show this? Ah, that's right.

So we can move one of the blocks from the 35 from the 50 to make our 60.

So what's then happened to our other addend? It's decreased by 10.

So 50 plus 35 is equal to 60 plus? 25, that's right.

The missing addend is 25.

"This is different because this time," she says, "the addend's change by 10 and not by 1." But we can use the same thinking.

If one addend is 10 more, the other addend must be 10 less for the expressions to be equal.

Time to check your understanding.

Can you use base 10 blocks to represent these equations? So can you continue the patterns and make the expressions equal on each side of the equation? And if you have got some base 10 blocks to help you, that would be great, otherwise you might be able to draw them.

And for question two, again, use base 10 blocks to represent these equations, and continue the patterns, and make the expressions on each side of the equation equal.

Look carefully to see what's changing and what's staying the same.

And for question three, represent one side of the equation with base 10 blocks and then move a block to complete the other side of the equation.

How many ways can complete the equation? Pause the video, have a go at the three questions, and when you're ready for the answers and some feedback, press play.

How did you get on? So in question one, we were balancing these equations, making sure they were equal on both sides of our equal sign.

43 plus 37 is equal to 44 plus 36.

43 has increased by 1 to 44, so 37 must decrease by 1 to 36.

Aha, then we've got 44 plus 36 is equal to 45.

One more plus 35, which will be 1 less.

So for c, 45 plus 35 is equal to 46.

That's gone up by one.

So the other addend must decrease by 1, 46 plus 34.

And for d, 46 plus 34 is equal to 47, which is one more than 46 plus 33, which is one less than 34.

Well done if you spotted those.

In each side of the equation as one addend increased by 1, the other add end decreased by 1.

And what about question two? Did you spot what was happening here? Were we changing things by 1 this time? We weren't, we were changing by 10 this time.

23 plus 64 is equal to 33, which is 10 more, plus 54, 10 less.

In b, 33 plus 54 is equal to 43, 10 more, plus 44, 10 less.

And in c, 43 plus 44 is equal to 53 plus 34, and 53 plus 34 is equal to 63 plus 24.

In each side of the equation as one addend increased by 10, the other addend decreased by 10.

And you can spot those patterns in those equations.

And for question three, you may have done something like this.

So we had 67 plus 32 is equal to something plus something, and we were going to move the blocks to change things.

So you might have moved a one.

So you made the 67 one less and the 32 one more.

So 67 plus 32 is equal to 66 plus 33.

Or you might have done this.

Ooh, so this time we increased our 67 to 68, so we decreased our 32 to 31.

Ah, you might have switched some tens around.

So you might have made 67 ten less and 32 ten more, or you might have made 67 ten more and 32 ten less.

Lots of different ways that you could change that equation by moving ones and tens, but keeping the overall sum the same.

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

We've been finding the missing addend when adding two-digit numbers.

What have we learned? We've learned that we can partition two-digit numbers to help find a missing digit or a missing addend.

We can use one equation to help solve another equation, and we can use the patterns in equations to help find a missing addend.

Thank you very much for your hard work and your mathematical thinking, and I hope I get to work with you again soon.

Bye-bye.