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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 partitioning two-digit numbers in a range of ways.

You might well have partitioned into tens and ones before, but we're going to think about other ways that we can partition our two-digit numbers.

We've got one keyword in our lesson today and that's partition.

So I'll take my turn, partition, and your turn.

Well done.

I'm sure you've used the word partition lots of times before, but it is gonna be really useful today.

So look out for it and make sure you use it when you're talking about your work today.

There are two parts to our lesson.

In the first part, we're going to be partitioning two-digit numbers into two parts, and in the second part, we're going to be partitioning two-digit numbers into three parts.

So let's make a start with part one of our lesson, and we've got Alex and Sam helping us with our learning today.

Sam uses base 10 blocks to represent the number 45, and we can see she's got her whole of 45.

She partitions it into tens and ones and records the numerals on a part-part-whole model.

So she's partitioned it into four tens and five ones, and then she's drawn her part-part-whole model.

45 is the whole, 40 is one part and five is the other part.

Alex moves one of the base 10 blocks.

Oh, can you see what he did? He says, "I found a different way to partition 45." Has he still partitioned 45? He has, hasn't he? We can still see four tens and five ones, but this time, he's partitioned it into 30 and 15.

He says, "I noticed that one part in each part-part-whole model is a multiple of 10." Ah yes.

So we had a 40 and five and now we've got 30 and 15.

Let's write the equations to show what the children did.

So that was how Sam partitioned it.

45 is equal to 40 plus five.

If we move one 10 block, we can make a pattern.

Aha.

So we moved it.

So now we had 45 is equal to 30 plus 15.

There's our next part-part-whole model to represent that.

And we can move another 10.

So what have we got now? We've got 45 is equal to 20 plus 25.

We've still got four tens and five ones.

So there's our part-part-whole model.

Can we move another one? We can.

So now we've got 45 is equal to 10 plus 35.

We've still got four tens and five ones.

We've still got 45 as our whole.

Alex wonders if he has found all the possible ways to partition 45 by moving the tens blocks, keeping his ones together.

He says, "I think I can move the last tens block to find one more way." Let's have a look.

Oh, so let's think about the one he's created.

He's moved his final 10 block across, so now he's got no tens and he's got 45 all in one part.

So his parts are zero and 45.

I think he might've found all the ways now.

There are other ways of partitioning the ones, but you have found all the ways of partitioning the tens.

So all those different ways are shown here in these part-part-whole models.

So working systematically, like Alex did, use base 10 blocks to find all the possible ways to partition 36 where one part is a multiple of 10.

So we're going to keep all our six ones together each time.

Record each way as a part-part-whole model and as an equation.

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

How did you get on? So we could have partitioned into 30 and six.

So there's our first way, 36 is equal to 30 plus six.

Then we could move one 10 across.

36 is equal to 20 plus 16.

And another one, 36 is equal to 10 plus 26.

And the final one, 36 is equal to zero plus 36.

Well done if you found all those ways.

Did you work systematically using your base 10 blocks? Sam uses base 10 blocks on a part-part-whole model to partition the number 64.

Each time she moves a 10 block, she writes an equation.

So we've got 60 and four and our whole is 64.

So 64 is equal to 60 plus four.

She's moved one 10.

So now 64 is equal to 50 plus 14.

This time 64 is equal to 40 plus 24.

Oh, she says, "I noticed that the first addend is decreasing by 10 and the second addend is increasing by 10.

Can you see that? 60 plus four and then 50 plus 14 and then 40 plus 24.

And that's because we're moving a base 10 block each time, aren't we? We're making one of our parts 10 less and the other one 10 more.

Now you can see that pattern highlighted in our equations.

What's the next equation she will write? That's right, 64 is equal to 30 plus 34.

Our first addend has got 10 smaller.

Our second addend has got 10 larger.

Alex continues the pattern and writes the next equation.

I'm not sure he's right though.

Can you explain why he cannot be correct? What do you think? He says 64 is equal to six tens and four ones.

When 64 is partitioned into a multiple of 10 and another part, that part must have a ones digit of four.

Ah, he spotted his mistake.

So 64 must be equal to 20 plus 44.

Well spotted, Alex.

Time to check your understanding.

Which of the following equations will come next in the pattern? So we've got a pattern there of partitioning 64.

Is it A, B, or C that will be the next equation in the pattern? Pause the video, have a go, and when you're ready, we'll come together for some feedback.

How did you get on? Did you spot that it was B? When 64 is partitioned into a multiple of 10 and another part, the other part must have a ones digit of four and the tens digits must sum to 60.

So to continue the pattern, the first addend must decrease by 10, whilst the second addend increases by 10.

Well done if you spotted that.

Alex partitions the number 59 and hides one part from Sam.

Let's help her find the missing part.

Hmm, she says both the whole and the known part have nine ones.

So the missing part must be a multiple of 10.

Oh, good thinking, Sam.

59 is partitioned into something and 39.

She says the whole has five tens and the known part has three tens.

The missing part she says must be two tens or 20 because 20 plus 30 is equal to 50.

And there she is, she's right.

So she used her knowledge of known facts totaling five to work with the tens.

She had three tens and she knew she needed to add another two tens.

The children play I'm thinking of a number.

So Sam says, "I'm thinking of a number, I add 20 to it and I reach 56.

What was my number? Ooh, how are we going to think about this? Alex says, "I can write a missing number equation." So there's the number Sam was thinking of that we don't know.

I add 20 to it and I reach 56.

So something plus 20 must be equal to 56.

He says, "The missing number must have six ones because we're only adding a multiple of 10 to it." So we know it must have six ones.

Three plus two is equal to five.

So three tens and two tens equals five tens.

So the missing number must have three tens.

So the missing number must be 36.

36 add 20 is equal to 56.

And we can use our three stages.

Three tens and six ones plus two tens is equal to five tens and six ones and five tens and six ones is equal to 56.

Time to check your understanding.

Can you find the missing part in the part-part-whole model? Remember, you could use base 10 blocks to help you to see what the problem looks like.

Pause the video, have a go and we'll come back for some feedback.

How did you get on? Well, both the whole and the known part have eight ones.

So the missing part must be a multiple of 10 because the ones haven't changed.

The whole has seven tens and the known part has two tens.

I know that two plus five is equal to seven.

So two tens plus five tens must be equal to seven tens.

So the missing part must be five tens or 50.

And when we put those in, we can see that when we combine our base 10 blocks, we've got seven tens and eight ones, which is 78.

Well done if you spotted that.

Time for you to do some practise.

So for question one, Alex partitions the number 53 into 50 and three.

He moves one tens block from one part to the other and writes the new equation.

Can you use base 10 blocks on a part-part-whole model to continue his pattern and write the equations to represent each move? So what will it look like each time he moves a 10 block from the multiple of 10 into the part with the ones? And for question two, can you fill in the missing numbers to complete the pattern? We've got part-part-whole models there.

Can you complete them? And in question three, can you work systematically to partition the number 76 in as many ways as you can where one part is a multiple of 10? Write an equation to represent each way you found.

And what pattern do you notice? Pause the video, have a go at your tasks and when you're ready, we'll get together for some feedback.

How did you get on? So in the first question, Alex was partitioning 53.

So he started with five tens and three ones.

Then he moved one 10 at a time.

So we've got 53 is equal to 40 plus 13, 30 plus 23, 20 plus 33, 10 plus 43 and zero plus 53.

What did you notice? Did you notice that the first addend decreases by 10, whilst the second addend increases by 10? Because we are moving a 10 from one part to the other each time.

And you can see that pattern of our first addend decreasing by 10 and our second addend increasing by 10.

In question, two you had a first part-part-whole model of 49 partitioned into 40 and nine.

And remember, we're thinking about multiples of 10 each time.

So if one part is 30, the other part must be 19 and we can continue the pattern.

20 and 29, 10 and 39, 0 and 49.

And for question three, you are partitioning 76 in lots of different ways.

So 76 is equal to 70 plus six, 60 plus 16, 50 plus 26, 40 plus 36, 30 plus 46, 20 plus 56, 10 plus 66 and zero plus 76.

And the first addend decreases by 10 while the second addend increases by 10 because we're moving 10 from one part to the other.

You may have written your equations the other way round, six plus 70, 16 plus 60, in which case it would've been your first addend that was increasing and your second addend that was decreasing.

But we know that it doesn't matter which way round because whichever way round the addends are, the sum will be the same.

And there you can see those patterns of the multiples of 10 decreasing and our two-digit number with a six in the ones increasing by 10 each time.

And on into the second part of our lesson.

We're going to partition two-digit numbers into three parts.

So Alex uses base 10 blocks to partition the number 56 into more than two parts.

He says, "I will move the tens blocks so that this time two parts are multiples of 10." So he's got 56 as his whole.

So he's going to have four tens and one 10 and the six ones, he's gonna keep them together at the moment.

He records it as an equation.

56 is equal to 40 plus 10 plus six.

Sam moves one tens block and writes a new equation.

I wonder what she wrote.

Alex says, "I think she did this." Can you see the tens block move? So now we've got 56 is equal to 30 plus 20 plus six.

Is there another possibility? Alex says, "She could have done this." Oh, that's interesting, isn't it? This time we've got 56 is equal to 30 plus 10 plus 16.

"Or this," he says.

56 is equal to 50 plus zero plus six.

And that would be like using just a two-part part-part-whole model and having 50 and six, wouldn't it? But we've got three parts and we know one part is zero this time.

Alex says, "I notice that the tens digits always sum to 50." Well, they must do mustn't they because our whole is 56.

Over to you to check your understanding.

Can you move one tens block to find a new way to partition 56 when two parts are multiples of 10? So we're going to keep our six ones on their own.

And can you record the equations that you make? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, there were two possibilities.

You could have done this and shown that 56 is equal 20 plus six plus 30, or you could have done this: 56 is equal to 40 plus six plus 10.

Now, you may have ended up with your 20s, 30s, 40s and tens in different parts of your part-part-whole model.

But we know that we can combine the addends or the parts in any order and the sum will remain the same.

Alex continued to partition 56 and he drew these part-part-whole models to show what he had done.

Which one cannot be correct? He's got two right, but one is wrong.

Can you spot the one that's wrong? Well, 56 is equal to 50 plus six.

So when 56 is partitioned, the tens digits must sum to 50 and there must be six ones.

Can you spot one where that isn't true? Let's look at this one.

20 plus 30 is equal to 50.

So the third part should be six ones and not 16.

Can you see, we've already got our five tens in our multiples of 10, so we've got an extra 10.

The sum for this one would be 66.

Over to you to check your understanding.

This time, we've got a whole of 58.

Can you spot which of these ways of partitioning is not correct? Can you spot the mistake? Pause the video, have a go and when you're ready, we'll get together for some feedback.

Did you spot that it was A that was not correct? 58 is equal to 50 plus eight, so there must be eight ones and the tens must sum to 50.

In A, the two represents two ones and not two tens.

So the tens do not sum to 50.

We've got an eight and a two and 30, which would give us a sum of 40, wouldn't it? This time Alex puts the tens blocks together in one part and partitions the ones blocks when he partitions 56.

Oh, let's have a look at this.

Let's see what he does.

There are his five tens and they're going to stay together this time.

He says, "I could partition six into one and five." So we've got one and five.

So 56 is equal to 50 plus one plus five.

"Or into five and one," he says.

And he's just swapped the parts around and we know that the sum will remain the same.

56 is equal to 50 plus five plus one.

Sam partitions the ones in a different way.

And again, she's moved the parts around as well.

She says 56 is equal to three plus 50 plus another three because she knows that three plus three is equal to six.

She draws a part-part-whole model to show what she's done.

Alex says, "That can't be correct.

I can't see six ones." And Sam says, "I know that three plus three is equal to six." So the ones sum to six.

There are six ones.

There's the 50, three ones and another three ones.

So we've got a whole of 56.

So I think Alex needs to look again, doesn't he? Because she was right.

Her parts did sum to 56 as the whole.

Over to you to check your understanding.

Can you find a new way to partition the ones in 56 and record the missing numbers in the equation? Pause the video, have a go, and when you're ready, we'll get together for some feedback.

How did you get on? Well, we've already partitioned the six ones into one and five, five and one and three and three.

So what was left? Now we can partition them into two and four or four and two, and we can record that as an equation.

56 is equal to two plus four plus 50, or four plus two plus 50.

Let's use what we know about partitioning numbers to find the one missing part.

Hmm.

Well, we know if we know the whole, then we can subtract the parts we know to find the missing part or we can count on to find the difference.

So we've got our whole of 75, we've got an unknown number, we've got five and we've got 40.

Sam says 75 is equal to 70 plus five.

So the tens must sum to 70 and the ones must sum to five.

One part has five ones and the other has four tens.

So there are some tens missing.

She says, "Four tens plus three tens is equal to seven tens." So the missing part must be three tens or 30.

75 is equal to 30 plus five plus 40.

What's different about the missing number this time? We've got 75 as our whole and it's equal to two plus 70 plus something.

Hmm, what do you notice? Well, Sam says 75 is equal to 70 plus five.

So the tens must sum to 70 and the ones must sum to five.

Well, one known part has two ones and the other has seven tens.

So we've got all our tens.

So this time there are some ones missing.

Two ones plus three ones is equal to five ones.

So the missing part must be three ones or three.

So there we have it, 75 is equal to two plus 70 plus three because two plus three is equal to five and we need five ones.

Time to check your understanding.

Can you match each representation to the number that would correctly complete it? So we've got missing parts in our part-part-whole models and missing parts in our equations.

So which number will complete each of those representations? 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 we were missing a one from our first part-part-whole model? 75 is equal to four plus one plus 70.

Our second equation, we were missing a 30.

We had 75 is equal to something plus 40 plus five.

Well, we know we've got our fives, but we've only got four tens, so we need another three tens or 30.

In the next part-part-whole model, 75 is equal to five plus 10 plus something.

Well, we've got all our ones, so it must be missing tens.

We need six more tens.

So we need the 60.

And let's just check.

Two should complete our final equation.

75 is equal to three plus 70 plus something.

We've got all the tens, we need two more ones.

So we needed our two.

Well done if you matched all those correctly.

thinking about your partitioning and what was missing from our parts.

Alex thinks he can use what he knows about partitioning numbers to solve this puzzle.

Hmm.

So what have we got? We've got one column and one row and we've got a 12, which is the middle of our column and the beginning of our row.

Each row and column sum to 62.

And you could only use multiples of 10.

Hmm.

That's interesting, isn't it? Let's see what Alex is going to do.

He says 12 is equal to one 10 and two ones, and 62 is equal to six tens and two ones.

So we've got the twos that we need.

He says, "I need more tens.

One 10 plus five tens is equal to six tens.

So I need five more tens," he says.

I could have.

Oh, 20 plus 30 because those five tens have to be in two parts.

So we could have 12 plus 20 plus 30.

Two tens plus three tens plus another 10 gives us our six tens and two ones is 62.

And he could have 30 plus 20 again in our column.

Three tens plus two tens plus one 10 plus our two twos is equal to 62.

Ooh, or he could have 40 plus 10.

Remember, he needs five tens to make six tens and then our extra two for 62.

So he could have 40 and 10 and he could have 10 and 40.

And that would mean that our column had a sum of 62 and our row had a sum of 62.

Or he could have 20 and 30 in the column.

And then he's used each multiple of 10 only once.

He says, I could have any two multiples of 10 that sum to five in each row and in each column.

So in our column, he's got 20 plus 30, two tens plus three tens, and in our row, he's got 40 and ten, four tens plus one 10.

Perhaps you could make some other puzzles like this.

You could choose a number to sum to and put one number into the grid to start you off.

Ah.

And here's a puzzle for you to have a go at.

So can you use what you know about partitioning numbers to solve this puzzle? Each row and column must sum to 55 and you can only use multiples of 10.

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

How did you get on? Well, 25 that we were given is equal to two tens and five ones and 55, which is the sum we were aiming for, is five tens and five ones.

So we've got our ones.

We need more tens.

Two tens plus three tens is equal to five tens.

So I need three more tens in each row and column.

So you could have 20 and 10.

So 25 plus 20 plus 10 is equal to 55.

And we could have had 10 and 25 and 20.

So we could have used 10 and 20 in each row and each column to give us a sum of 55.

Or we could have swapped them around because we know that we can combine the addends in any order and the sum remains the same.

You could have had any two multiples of 10 that sum to three in each row and in each column.

So that's 20 and 10.

Or I suppose we could have had zero and 30, but we needed a multiple of 10 in each square.

So 20 and 10 were our solutions for this one.

Time for you to do some practise.

Question one asks you how many ways can you find to complete the part-part-whole models correctly? Remember to work systematically to find all the possibilities.

And for question two, you're going to find the missing number in each part-part-whole model or equation.

So pause the video, have a go at your tasks and we'll get together for some feedback.

How did you get on? So in question one, you had to complete the part-part-whole models in as many different ways as possible.

So in the first one, 76 is equal to seven tens and six ones.

Well, we've got the six ones there.

So you needed to partition the seven tens and you could use your pairs that sum to seven to find pairs of multiples of 10 that sum to 70.

70 and zero, 10 and 60, 20 and 50, 30 and 40, 40 and 30, 50 and 20, 60 and 10 or zero and 70 again.

And you might have decided that some of those were the same because they were just adding in a different order.

What about the second one? This time, there are seven tens there, but the six ones must be partitioned.

So you can use your pairs that sum to six.

Six and zero, five and one, four and two, three and three, two and four, one and five, zero and six.

And again, some of those were the same numbers but in a different order.

I hope you worked systematically there.

And for question two, you had to fill in the missing parts.

So in A, we had 87 as our whole and we had 80 and two, so we had the eight tens, but we only had two ones.

And we know that if seven is the whole and two is a part, then the other part must be five.

In B again, we had a whole of 87.

This time, one of our parts was the seven ones, so we were looking at the tens.

So we had two tens.

So if eight tens is the whole and two tens is a part, the other part must be six tens.

And for C, D and E, we had similar things, but written as an equation.

65 is our whole, 20 is a part and five is a part.

So we've got all our ones, so we need to think about our tens.

If six tens is the whole and two tens is a part, the other part must be four tens or 40.

And then for the other part, we had 65 was equal to two plus something plus 60.

Well, all our tens are there, so we're looking at our ones.

And if five is a whole and two is a part, the other part must be three.

So for D, the first part, our whole was 76, we had three tens and four tens.

So we had 30 plus 40.

Well, we know that that is equal to 70.

So our missing part must be the six ones.

And for the second part, our whole was 67, so we had four ones and three ones.

So we had our seven ones.

So the missing part was our six tens or 60.

Did you spot there that the numbers had been reversed? We had seven tens and six ones as our first whole and then six tens and seven ones as our second whole.

And in E, our whole to begin with was 98 and we had a missing part and 40 and eight.

So we have all our ones there.

So we're thinking about our tens.

And if nine tens is the whole and four tens is a part, the other part must be five tens.

And then, oh look, we've reversed those digits again.

We've gone from nine tens and eight ones to eight tens and nine ones.

So 89 is our whole.

This time, one of our parts was 80, all our tens.

So we knew that we needed nine ones.

And if four ones is a part, the other part must be five.

I hope you used your known number facts there to help you to think about what the missing parts were when we partitioned into three parts.

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

We've been partitioning two-digit numbers in different ways.

So what have we learned about today? Well, we've learned that two-digit numbers can be partitioned into two or more parts.

We can use known facts to help us partition a two-digit number into a multiple of 10 and another part.

And the patterns in the tens can help to predict new equations.

And we can also use known facts to help us partition both the tens and the ones in a two-digit number.

And that really helpful when we'll be partitioning into more than two parts.

Well done today.

Thank you for all your hard work.

Thank you for using your number facts.

I hope you've enjoyed exploring partitioning two-digit numbers in different ways and I hope I get to work with you again soon.

Bye-bye.