Lesson video

Hello, I'm Mrs. Cayley and I'm going to help you with your learning today.

So today we're going to be partitioning the numbers one to five in a systematic way.

So let's have a look at today's lesson outcome.

Here's the outcome of today's lesson, so by the end of the lesson, you'll be able to do this.

I can partition the numbers one to five in a systematic way and know when I have found all the possible combinations.

Here are keywords for today's lesson.

Can you repeat them after me? My turn, partition.

Your turn, my turn part-whole model.

Your turn.

My turn, combination.

Your turn, my turn, systematically.

Your turn.

My turn, table, your turn.

So you might have seen some of these words before.

Our first word is partition.

This means we're going to split a whole into parts.

Then we've got part-whole model.

This is a representation showing the whole and the parts.

Then we've got combination.

This means different ways that we've used to partition the numbers.

Then we've got systematically.

This means that we're finding all the combinations in a good order, in a sensible order, in a good system so that we can make sure that we haven't missed any out.

Then we've got the word table, and I don't mean the table that you do your work on.

I mean the table where we put information or numbers in rows and columns so that we can make sure that we've got them all.

Here's the lesson outline for today's lesson.

We're going to partition the numbers one to five in a systematic way.

So we'll start off by partitioning numbers and then we'll move on to partitioning numbers in a systematic way.

Here are some children that are going to help us with today's lesson.

We've got Alex and Sam.

Let's start on the learning.

Sam and Alex have five counters in total.

Some are red and some are yellow.

How many could there be of each colour? Now, if you've got some counters, you could try this yourself, especially if you've got the counters that have got different colour on each side.

So you need five counters in two different colours.

How many could there be of each colour? Here's one way that Sam and Alex have found to do it.

They've got three red counters and two yellow counters.

Sam said there are five counters, so that's the whole Alex said three are red and two are yellow.

Sam and Alex have represented this as a part whole model, so we've got five as the whole and the parts are three and two.

Sam said five is the whole.

Alex said three is apart and two is apart.

You can see it on the part whole model as well.

The five represents all the counters in the set.

That's the whole.

The three represents the three red counters and the two represents the two yellow counters.

Sam and Alex have five counters in total.

Some are red and some are yellow.

How many could there be of each colour this time? So they're going to try to do it in a different way.

Can you think of a different way? Here's a different way that they found, this time we've got two red counters and three yellow counters.

Sam said there are five counters, so that's the whole, Alex said two are red and three are yellow.

Sam and Alex have represented this as a part-whole model.

Sam said five is the whole.

Alex said two is a part and three is a part.

Can you see that on the part-whole model? The five represents all the counters.

That's the whole.

The two represents the two red counters.

The three represents the three yellow counters.

Sam and Alex have five counters in total.

Some are red and some are yellow.

How many could there be of each colour this time? So they're going to try to do it a different way.

Can you think of a different way? This time they've got one red counter and four yellow counters.

Sam said there are five counters, so that's the whole.

Alex said one is red and four are yellow.

Sam and Alex have represented this as a part whole model.

Sam said five is the whole.

Alex said one is a part and four is a part, and you see that on the part whole model.

The five represents all the counters.

That's the whole.

The one represents the one red counter.

The four represents the four yellow counters.

I wonder if there's a different way they could have done it.

Some and Alex have five counters in total.

Some are red and some are yellow.

How many could there be of each colour this time? They're going to try to do it a different way.

This time they've got four red counters and one yellow counter.

Sam said there are five counters.

That's the whole Alex said four are red and one is yellow.

Sam and Alex have represented this as a part whole model.

Sam said five is the whole, and Alex said four is a part and one is a part.

We can see that on the part whole model.

The five represents all the counters.

That's the whole.

The four represents the four red counters.

The one represents the one yellow counter.

They're going to try a different way of doing it.

Sam and Alex have five counters in total.

Some are red and some are yellow.

How many could there be of each colour this time? Can you think of a different way they could have done it? And they've got five yellow counters.

Sam said there are five counters.

That's the whole.

Alex said zero are red and five are yellow.

I wonder what the part-whole model's going to look like.

Sam and Alex have represented this as a part-whole model.

Is that what you thought it would look like? Sam said five is the whole.

Alex said zero is a part and five is a part.

The five represents all the counters, that's the whole.

The zero represents zero red counters.

That's one of the parts.

The other five represents the five yellow counters.

That's the other part.

I wonder if there's any other way Sam and Alex could have done it? Let's check your understanding.

Sam and Alex have found one more way to partition five counters.

There are no yellow counters.

How many red counters will there be? Pause the video and think about what this one might look like and you could try to make it with your counters or draw it.

What did you think this one's going to look like? It's got five red counters and zero yellow counters.

Sam said there are five counters.

That's the whole.

Alex said five are red and none are yellow.

Zero are yellow.

I wonder what this is going to look like on a part-whole model.

Perhaps you could try to draw it on a piece of paper.

How could they represent this as a part-whole model? Sam thinks five is the whole and five is a part and zero is part.

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

Alex thinks zero is the whole and zero is a part and five is a part.

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

Who do you think's correct? Pause the video and try to decide.

That's right, Sam was correct.

Five is the whole, five is a part and zero is a part.

Alex used part-whole models to show their ways.

Here's the ways that they found.

Can you see five is the whole every time and we've got different parts.

Sam said there are different ways to do it.

Alex is asking a question, did we find all the ways? What do you think Sam said, how do we know? How could we check? Alex said, I tried all the numbers.

So if you look carefully at the part-whole models, he's tried the numbers three and two and then he is got two and three.

Then he's tried the numbers four and one and then he is got one and four and he's tried the numbers five and zero and he's got zero and five.

Do you think that's all the possible numbers? Let's check your understanding, is Sam right? Sam thinks if five can be partitioned into four and one, then it can also be partitioned into one and four.

Do you think she's correct? Pause the video while you think.

Yes, she is correct.

You can see on the part whole models can't you, five can be partitioned into four and one or one and four.

The numbers have just been swapped round.

Alex is asking a question, are they the same or different? Well, it's the same numbers, but they've been swapped round.

The parts have just been swapped round.

The parts might represent different colours.

So we had the yellow and the red counters earlier, so they might represent different colours.

Here's a task for you to have a go at.

Can you find four counters? If you haven't got counters, you could use a different object or you could draw them on a piece of paper.

How many ways can you partition them into two parts? Record your combinations on part whole models.

You could use two different colours of counters or you could just split them into different parts in different ways.

Alex wants to know, did you find all the ways? So see if you can think about this while you are doing it.

Here's the next part of your task.

Can you use three counters? How many ways can you partition them into two parts? Record your combinations on part whole models, and Alex is wondering, did you find all the ways? So pause the video and have a go at these tasks.

How did you get on with the tasks? So first of all, I asked you to partition four counters in different ways.

Here's some ways that I found I partitioned four into four and zero, three and one, two and two, one and three and zero and four.

Alex wants to know, did you find all the ways? I wonder how we could check.

Did we use all the possible numbers? Well, I can see that we've used four as a part, three as a part, two as a part, one as a part and zero as a part.

So that's all the possible numbers.

How did you get on with three counters? How many ways did you manage to partition three counters into two parts? So here you can see that I have partition three into three and zero, two and one, one and two and zero and three.

Did you find all the ways? Well, I can see that we've got three as a part, two as a part, one as a part, and zero as a part.

So we've used all the possible numbers up to three.

Let's move on to the second part of the lesson.

We are going to partition numbers in a systematic way.

That means we're going to use a good order or a good system to make sure that we found all the possible combinations.

Sam and Alex partitioned five counters in different ways.

Do you remember earlier Sam and Alex were partitioning five counters.

They partitioned five counters in different ways, and here we've recorded them on part whole models.

Alex is asking a question, did we find all the combinations? I wonder if they tried all the numbers up to five.

Here's the ways that they tried.

How many ways did Sam and Alex find? How many rows of counters have they got? Let's count them together.

One, two, three, four, five, six different ways of partitioning five counters.

So we've got six rows of counters.

Alex said, we found six different ways.

Sam is asking, did we find all the combinations? I can see they've got three red counters and two yellow counters.

Then they've got that the other way round.

Two yellow counters and three red counters.

Then they've got four red counters and one yellow counter and four yellow counters and one red counter.

Then they've got five yellow counters on their own with no red counters.

Then they've got five red counters with no yellow counters.

I wonder if that's all the combinations.

Maybe they could put them in the sensible order.

Alex thinks we could put them in a sensible order to check.

Sam said we could be systematic.

Sam and Alex have put them in a systematic order.

It's in a sensible order now, Alex said, I can see we found all the combinations.

Sam said, it looks like there are no other possible ways.

How can we know if we have all the combinations? So we started off with zero yellow counters and five red counters.

Then we had one yellow counter and four red counters.

Then we had two yellow counters and three red counters.

Then we had three yellow counters and two red counters.

Then we had four yellow counters and one red counter, and finally we had five yellow counters and zero red counters.

I think we found them all, haven't we? Alex said we could put the combinations in a table.

Now the combinations have been put in a table.

So we've got our yellow counters and our red counters and we've counted them up and put the numbers in the table.

So when we've got zero yellow counters, we've got five red counters.

When we've got one yellow counter, we've got four red counters.

When we've got two yellow counters, we've got three red counters.

When we've got three yellow counters, we've got two red counters.

When we've got four yellow counters, we've got one red counter, and when we've got five yellow counters, we've got no red counters.

I can see we found all the possible combinations.

What do you notice here? Have a look at the table.

Alex has noticed as the number of yellow counters goes up.

So can you see the yellow counters start with zero? Then one, two, three, four, five.

So those are going up.

What's happening to the red counters? Sam has noticed the number of red counters goes down.

So we are starting with five red counters and going down four, three, two, one, zero.

So as one number goes up, the other number is going down.

Sam and Alex use part whole models to record their ways.

Can you see their part-hole models here.

They've been put in a systematic order.

So as one number in the parts goes up, the other number goes down.

Alex is asking, did we find all the combinations? Alex said, I can see from the table that we have them all.

Let's check your understanding.

Sam and Alex used a table to record their ways.

They have spilt paint on some of the numbers.

What are the missing numbers? Pause the video and think about what those missing numbers are.

What do you think the missing numbers are? So first of all, we had zero yellow counters and five red counters.

Then we've got some paint spilt on the next one.

How many yellow counters and four red counters? So I wonder what that one's going to be.

It's one, one yellow counter and four red counters.

Then we've got two yellow counters and we've got a missing number there for the red counters.

It's three, three red counters.

Then we've got a missing number for the yellow counters and two red counters.

So I wonder what the missing number is there.

It's three yellow counters.

Then we've got four yellow counters and a missing number for the red counters.

It's one red counter.

Finally, we've got a missing number for the yellow counters and we've got zero red counters.

That's five, five yellow counters.

Sam has noticed as the number of yellow counters goes up, the number of red counters goes down.

Let's check your understanding again.

Sam and Alex have partitioned three in different ways.

So they had three counters.

Can you help them spot and correct their mistakes? So they've made a table with their combinations.

I wonder what mistakes they've made.

Pause the video and see if you can spot any and think about what they should have put.

Did you spot any mistakes in their table? So the whole is three and the parts parts are zero yellow and three red.

That looks right.

Then we've got one yellow and four red.

Not sure that's right.

So Alex said one yellow and four red counters makes five counters and they've only got three counters.

So that one's not right.

Then we've got two yellow counters and one red counter.

Yes, that's correct.

Finally, we've got three yellow counters and one red counter.

I don't think that makes three and a whole.

Sam said three yellow counters and one red counter makes four counters and we only need three counters.

I wonder what the answers should have been.

So in the second row we had one yellow counter.

I wonder how many red counters it should be.

That's right, two red counters and in the bottom row we've got three yellow counters and how many red counters should it be? That's right, zero red counters.

Now the whole is three.

Here's a task for you to have a go at.

Can you use the ways you found to partition four in task A to complete the table? Do you remember in task A, we asked you to partition four counters in different ways so you can look back at your combinations from then and use that to help you complete the table.

So I've started it for you by colouring some of the counters in and counting them up.

Can you finish off colouring the counters and fill in the numbers for the yellow and the red counters? This is the second part of your task.

Can you play this snap game with your friends? Can you see we've got the numbers.

Zero, one, two, three, four and five.

Can you cut out the cards and put them face down on the table and then say snap each time a pair is turned over that totals five? Check using your table or your part-whole models from earlier.

And when you finish playing the game, can you put your pairs in a systematic order to check that you have them all? So pause the video and have a go at your tasks.

How did you get on with your tasks? Did you complete the table showing the ways to partition four? So we had zero yellow counters and four red counters.

Then we had one yellow counter and three red counters.

Then we had two yellow counters and two red counters.

Then we had three yellow counters and one red counter, and finally four yellow counters and zero red counters.

Did you find them all? How did you get on with the Snap game? Did you find pairs that make five? Here's a pair that makes five, five and zero snap.

Here's another pair that makes five, four and one snap.

Here's another pair that makes five, three and two, snap.

Here's another pair that makes five, two and three, snap.

Here's another pair that makes five, one and four, snap.

Here's a different pair that makes five, five and zero, snap.

Here are the ways that we found to make five.

Did you put all your pairs in a systematic order to check you found them all? So we've got five and zero, four and one, three and two, two and three, one and four and zero and five.

Some of these look the same, don't they? They're just swapped round.

We've come to the end of our lesson.

Today, we were partitioning the numbers one to five in a systematic way.

This is what we found out.

Each of the numbers one to five can be partitioned in different ways.

We can work systematically to ensure all the possible ways of doing this are found.

Tables and part whole models can be used to record the different combinations systematically and to check that all the possible combinations have been found.

Well done everyone, see you next time.