Lesson video

Hello, my name's Mrs. Hopper, and I'm really looking forward to working with you today in this lesson from our unit on comparing, ordering and partitioning two-digit numbers.

Have you done lots of work with two-digit numbers before? I wonder.

Well, I hope you're ready to work hard and think hard today, so let's make a start.

So in this lesson, we're going to be partitioning two-digit numbers in different ways.

So by the end of the lesson, you're going to be able to represent and interpret the structure of two-digit numbers on part-part-whole and bar models.

So we're going to look at partitioning those two-digit numbers in different ways, and we're going to be using part-part-whole models and bar models to record our work and our thinking.

So let's make a start.

We've got lots of key words in our lesson today.

We've got partition, combine, parts and whole.

So I'm going to say them, and then you're gonna have your turn.

So, my turn, partition.

Your turn.

My turn, combine.

Your turn.

My turn, parts.

Your turn.

My turn, whole.

Your turn.

Well done.

I'm sure those words are familiar to you, but they're going to be really useful to us in our lesson today, so listen out for them.

So we've got two parts to our lesson today.

In the first part, we're going to explore the structure of two-digit numbers, so look at what the different digits in a two-digit number represent, and in the second part, we're going to partition a two-digit number into three parts.

So let's make a start on part one of our lesson.

And we've got Izzy and Lucas helping us in our lesson today.

Lucas is using Base 10 blocks to show how the number 54 is made up.

So can you see what he's done there? He draws a part-part-whole model to show what he's done.

He says, "I can use a place value chart to show the value of each digit in the number 54." So there's his place value chart.

"54 is made up of 5 tens, or 50, and 4 ones." Now that we know what each digit represents, let's use the stem sentences to describe his part-part-whole model.

So let's have a look at the number.

There are 5 tens and 4 ones, and we could see those represented with the Base 10 blocks.

So there are 5 tens, which is 50, and 4 ones which is 4, and this is equal to 54.

So we're going to be using this stem sentence to help us to think about and describe our numbers in this lesson.

What does the 5 represent? Well, the 5 represents 5 tens, and it has a value of 50, and the 4 represents 4 ones, and it has a value of 4.

So our two parts are 50 and 4.

Izzy represents her number on this part-part-whole model.

"The whole always goes at the top of a part-part-whole model.

I'll write my numbers like this." 86 is 80 and 6.

Ooh, do we like that? Is she right? 80 and 6 combine to make 86.

Oh, she says, "I've spotted my mistake.

I can see that, when combined, the parts on my part-part-whole model lead to the whole." So just because we've turned our part-part-whole model round, our whole is still the circle that the other two lead into, so she's moved her numbers around now.

So she also says, "I can see that, when partitioned, the whole on the part-part-whole model leads to the parts." And we've turned the arrows round to show that the 86 leads out into the two parts, 80 and 6.

86 can be partitioned into 80 and 6.

Lucas represents his number on this bar model.

Let's use the stem sentences to find the missing number.

We can see the parts this time.

So there are 4 tens, which is 40, and there's our 40, and 7 ones, which is 7, and there's our 7, and this is equal to 47 altogether.

The 4 represents 4 tens and has a value of 40.

The 7 represents 7 ones and has a value of 7.

Time to check your understanding.

Which of the following numbers represents the missing number in the bar model? And you've got three choices there: A, B and C.

And you've got a bar model there with two parts, and you've got the stem sentences to help you.

Pause the video, and then we'll come back for some feedback.

How did you get on? So in our bar model, we can see there are 5 tens, which is equal to 50, and 6 ones, which is equal to 6, so this is equal to 56 altogether.

And that's C, isn't it? Let's complete the final stem sentences.

The 5 in 56 represents 5 tens and has a value of 50.

The 6 in the 56 represents 6 ones and has a value of 6.

Well done if you got that right.

Izzy represents her number on this bar model and hides one part.

Let's use the stem sentences to find the missing number.

So we've got 93 as our whole.

The 9 represents 9 tens and has a value of 90.

The 3 represents 3 ones and has a value of 3.

So our missing number in the part-part-whole model was 3.

90 and 3 combine to make 93.

Can you match the numbers to the correct part-part-whole model? We've got a missing part in two of our part-part-whole models, and a missing whole in one of them.

Can you match the numbers to the correct part-part-whole model? Pause the video, and then we'll come back for some feedback.

How did you get on? So 75 is the same as 7 tens, which is 70, and 5 ones, which is 5, so 75 was our missing whole.

78 is the same as 7 tens, which is 70, and 8 ones, which is 8.

So we had 78 as our whole, 70 as one part, so 8 ones was our missing part, 8.

So that means that 80 must be our missing part in the final part-part-whole model.

88 was our whole, and 88 is the same as 8 tens, which is 80, and 8 ones, which is 8, so our missing part there was the 80.

Lucas represents his number on this part-part-whole model.

What mistake has been made? Can you spot it? He says, "I'll use a place value chart to help me find my mistake." He says there are 5 tens, which is 50, and 3 ones, which is 3.

This is equal to 53 altogether.

Mm, have you spotted it? The 5 represents 5 tens and has a value of 50.

The 3 represents 3 ones and has a value of 3.

Oh, Lucas says, "I forgot to think about the value of each digit." He got his 5 and his 3 the wrong way round.

He didn't think about what they represented in the two-digit number.

We need to be really careful with that, don't we? Which is representing the tens and which is representing the ones? Izzy represents the same number in a different way.

Is she right? Oh, she says, "I've spotted my mistake.

In 53, the 5 represents 5 tens, so I must write either 5 tens or 50." So the 5 represents 5 tens, so it needs to be 50, or 5 tens.

And we've got our 3 for our 3 ones.

Time for you to do some practise.

Use the stem sentences to help you find the missing numbers.

So we've got some missing wholes, and we've got some missing parts.

We've got some bar models and some part-part-whole models.

So there's our stem sentence.

And for the second part, you're going to circle the representations which are incorrect, so can you spot the mistakes? Pause the video, have a go at the tasks, and then we'll get together for some feedback.

How did you get on? So we had to use the stem sentences to find the missing parts and missing wholes in these representations.

So let's have a look at A.

We had a parts of 90 and 2.

There are 9 tens, which is 90, and 2 ones, which is 2, and this is equal to 92 altogether, so our missing whole was 92.

In B, there are 6 tens, which is 60, and 1 one, which is 1, so this is equal to 61 altogether, so our missing part was our 1 one.

What about C? We had 87 as our whole.

There are 8 tens, which is 80, and 7 ones which is 7, and it's equal to 87 altogether, so what was our missing part? That's right, our missing part was the 80, the 8 tens.

And in D, our whole was 59, and one of our parts was 9, so what was missing? So there are 5 tens, which is 50, and 9 ones which is 9.

This is equal to 59 altogether, so we were missing the 5 tens or the 50.

So in E, we were missing a whole, and we knew our parts were 30 and 5.

So there are 3 tens, which is 30, and 5 ones, which is 5, and this is equal to 35 altogether.

And for F, we were missing a part.

We knew our whole was 73 and one of our parts was 7 tens.

So there are 7 tens, which is 70, and 3 ones which is 3, so this is equal to 73 altogether.

So we knew about the 7 tens, but we didn't have the 3 ones, so that was our missing part.

And in part two, we had to spot the mistake.

So did you spot that B, C and D were incorrect? In B, 62 is the same as 6 tens, which is 60, and 2 ones which is 2, so the parts should be 6 tens and 2 ones, not 2 tens and 6 ones.

And there we have corrected it.

Or you could have said that there are 2 tens, or 20, and 6 ones, and this is equal to 26 altogether.

So we could have changed the parts or we could have changed the whole.

What about C? 39 is the same as 3 tens and 9 ones, so the parts should be 30 and 9, not 3 and 9.

We've got to remember that our tens digit represents 30, represents 3 tens.

And in D, there are 2 tens, or 20, and 7 ones.

This is equal to 27 altogether.

We don't have to write the 20 as 2 and a 0 when we're writing it as a two-digit number, because we know that the 0 is where the ones go.

So 20 and 7 is equal to 27.

And on into the second part of our lesson.

We're going to be partitioning a two-digit number into three parts.

So Lucas wonders if he can partition his number into three parts.

So his whole is 58.

58 is the same as 5 tens, which is 50, and 8 ones.

"I will partition the ones from the tens." So he's got his 8 ones.

"Now I will partition the 5 tens," he says.

So he's partitioned his 5 tens into 20 and 30.

"I wonder how I can check if I'm right," he says.

Well, "We know that 2 tens plus 3 tens is equal to 5 tens, or 50.

50 and 8 ones will be equal to 58.

I was right," he says.

Lucas partitions the number 58 in a different way.

Let's see what the missing part is now.

"58," he says, "is the same as 5 tens, or 50, and 8 ones." I've still got the 8 ones, but they're in a different place.

So there are the 8 ones.

"I've partitioned 3 of my 5 tens, so how many tens are missing?" he says.

"If 5 tens is the whole and 3 tens is a part, then 2 tens is a part." There's the 2 tens, or 20.

He says, "I'll combine the parts to check I'm right." So 3 tens add 2 tens is equal to 5 tens, which is 50.

He says, "I still have 5 tens, or 50, and 8 ones, so I know I am right." Izzy represents the same number on a bar model.

So we can see that our whole is 58, and one of our parts is the 8 ones.

Let's partition 50 in a different way.

"I still have 8 ones, but I will partition the 5 tens in a different way," she says.

"I will use known facts to help me.

I know that 5 is the same as 1 plus 4, so I know that 5 tens is the same as 1 ten plus 4 tens." So there's 1 ten, or 10, and 4 tens, 40.

And Lucas says, "You can check you are right by combining the numbers again." There we go, 1 ten plus 4 tens, or 10 plus 40, is equal to 50.

So which of the following will complete the bar model correctly? We've got a whole of 68, one part of 20 and one part of 8.

So is it A, B or C? Pause the video and have a go, and then we'll get together for some feedback.

How did you get on? Did you spot that it was 40, 4 tens? 68 is the same as 6 tens, or 60, and 8 ones.

We had 8 ones and 2 tens, so there must be 4 tens, or 40, missing.

So 20 add 40 is equal to 60.

So now we've got our 60, our 6 tens, and our 8, so we've got a whole of 68.

This time, Izzy partitions the tens from the whole.

So she's got her whole as 58, and one of her parts is 50, all the tens.

"Now, I need to partition the ones," she says.

"I could use my number pairs to 8." So she's partitioned her ones into 1 one and 7 ones.

Oh, is she going to do another one? She could have 2 ones and 6 ones, she could have 3 ones and 5 ones, or she could have 4 ones and 4 ones, 5 ones and 3 ones, 6 ones and 2 ones, 7 ones and 1 one.

And all of those pairs have a total of 8, so we know that we've still got 5 tens and 8 ones, so our whole will still be 58.

Lucas combines the parts of Izzy's new bar model to reach the whole.

So our whole this time is 67, and we've got parts of 50, 1, and 7.

What mistake has been made? Lucas says, "I added the 1 as 1 ten instead of 1 one." Ah, so Lucas hasn't found the correct whole has he? He thought that these two combined to make 60.

"The 1 represents 1 one, so I must combine it with the ones and not with the tens." So 1 one and 7 ones is equal to 8 ones, so our whole must be 58.

So which of the following will complete the bar model correctly? Our whole is 68, and we've got a part of 60 and a part of 2.

So which of the numbers will correctly complete the bar model? Is it A, B or C? Pause the video and have a go, and we'll get together for some feedback.

How did you get on? Well, we had to combine 2 with something to equal 8, 'cause we know we've got 8 ones in our whole.

So 2 add 6 is equal to 8, so B was correct.

6 was the correct number to make our bar model complete and to give us the correct whole of 68.

68 is the same as 6 tens, or 60, and 8 ones.

We had 6 tens and 2 ones, so there were 6 ones missing.

Time for you to do some practise now.

How many different ways can you find to complete the representations correctly? So we've got a whole of 87, and in the bar model, we've got one part of 80 and two other parts, and in B, we've used a part-part-whole model, but we've got three parts.

The whole is still 87, but one of our parts is 7.

So how many different ways can you find to complete the representations correctly? Remember to work systematically to make sure you find all the possibilities.

So you could just try lots of different numbers, but is there a way that you can work in an order so you could find all the ways of completing the bar model and the part-part-whole model? Pause the video now, and then we'll get together for some feedback.

How did you get on? So 87 is the same as 8 tens, which is 80, and 7 ones, which is 7.

There are 7 ones missing from the bar model, so we must use our number pairs to 7.

So our two parts have got to combine to equal 7.

So we could have had 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1.

Lots of different ways we could have completed our bar model.

And what about B? 87 is the same as 8 tens, which is 80, and 7 ones, which is 7.

There are 8 tens missing from the part-part-whole model, so we must use our number pairs to 10 to help us find pairs that equal 80.

Pairs of tens this time, isn't it? So pairs of tens that combine to equal 80.

So we could have had 10 and 70, 20 and 60, 30 and 50, 40 and 40, 50 and 30, 60 and 20, or 70 and 10.

Lots of different combinations again.

I hope you found them all.

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

We've been partitioning two-digit numbers into tens and ones, making two parts and maybe more than two parts.

So what have we learned about? We've learned that two-digit numbers can be partitioned into tens and ones, and that the order of the digits indicates their value.

And we've looked at partitioning into not just tens and ones, but then partitioning the tens again or partitioning the ones again.

Thank you for your hard work.

I hope you've enjoyed partitioning numbers, and I hope that I get to work with you again soon.

Bye-bye.