Lesson video

Hello, I'm Mrs. Cayley.

And I'm going to help you with today's lesson.

So in today's lesson we're going to explain how odd and even numbers can be partitioned.

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

(mouse clicks) Here's the outcome of today's lesson.

I can explain how even and odd numbers can be partitioned.

Here are the key words for today's lesson.

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

Your turn.

My turn, even.

Your turn.

My turn, partition.

Your turn.

Well done.

Do you know what these words mean? So an odd number is a number that cannot be made of pairs or groups of two.

You've got an extra one.

Odd numbers end in one, three, five, seven or nine.

An even number is a number that can be made of pairs or groups of two.

Even numbers end in zero, two, four, six or eight.

Partition means that we're going to split a number into two or more parts.

So let's start on the learning.

Here's today's lesson outline.

We're going to explain how even and odd numbers can be partitioned.

We're going to start by partitioning odd numbers and then we will move on to partitioning even numbers.

Let's start on the first part of the lesson.

Here are some children that are going to help us today.

We've got Sofia and Jun.

I've made a number out of some cubes.

What number does this represent? Is it odd or even and how do you know? Jun said, "This is five.

I can count the cubes." Is that what you thought? Sofia said, "Five is an odd number.

It is not made of pairs." Can you see the extra one at the top? I've made a different number out of cubes.

What number does this represent? Is it odd or even and how do you know? Jun said, "This is eight.

I can count the cubes." Did you find that that was eight? Sofia said, "Eight is an even number.

It is made of pairs." Can you see the pairs there? So an odd number is not made of pairs.

An even number is made of pairs.

Five is an odd number.

Eight is an even number.

So can you see the number five? It has got some pairs, but it's got an extra one at the top.

This is not part of a pair.

Eight is made of pairs.

Can you see the pairs? Can you point to them? We've got one pair, two pairs, three pairs, four pairs, and you end up with a nice flat top.

So eight is an even number.

This represents five.

How can we partition five? So how can we split five into two parts? Choose two number shapes to make a number five.

You could try this with cubes or number shapes if you've got them.

So Sofia said, "I can use three and two as parts to total five." So here she's got three at the top and two at the bottom.

Can you see that that makes the number five? Jun said, "I can use one and four as parts to total five." So here he's got one at the top and four at the bottom.

That makes the number five.

What do you notice about the way that they've done it? What do you notice about the two numbers that total five? Are they odd or even numbers? Jun said, "I have one odd and one even number." Sofia said, "And I have one odd and one even number." Can you see the odd number is at the top and it's sitting on top of an even number with a flat top.

Let's try partitioning another odd number.

Do we have to have one odd number and one even number? So here we've got seven.

Seven is the whole.

And we've got a stem sentence.

If mm is a part, then the other part is mm.

So let's try partitioning the number seven.

If one is a part, then the other part is? What do you think it's going to be? Yes, it's six.

Can you see we've got one at the top and six at the bottom there? If two is a part, then the other part is, what do you think it's going to be? Yes, the other part is five.

Can you see two at the bottom and five at the top? Can we do it a different way? If three is a part, then the other part is? Yes, the other part is four.

Can you see we've got four at the bottom and three at the top? So we always had an even number at the bottom and an odd number at the top and then you can see that odd block at the top.

Which parts are odd and which are even? So I'm going to put a circle around the odd numbers.

One is an odd number, three is an odd number, and five is an odd number.

Let's put a rectangle around the even numbers.

Two is an even number, four is an even number, and six is an even number.

So can you see we've always got an odd number and an even number for the parts? There is always one odd part and one even part.

Do you think this is true for all odd numbers? Perhaps you could try it with some others to see.

Let's check your understanding.

Can you partition the number three into two even numbers? Who do you agree with? Jun thinks, "Yes, I can partition three into two and two." Sofia thinks, "No, I can only partition three into two and one." Pause the video and think about who you agree with.

Who did you agree with? It was Sofia.

Sofia is correct.

You can only partition three into two and one.

Two is an even number and one is an odd number.

So Jun was not correct.

You cannot partition three into two and two.

That would make four, wouldn't it? Here's a task for you to have a go at.

How many different ways can you partition nine into two parts? Use number shapes or make the numbers out of cubes and fill in the stem sentences.

When you filled in the stem sentences with the two parts, can you draw a circle around the odd numbers and a rectangle around the even numbers? So the stem sentence says if mm is a part, then the other part is mm.

Here's the second part of your task.

Can you choose some other odd numbers to partition into two parts? Use number shapes or make the numbers out of cubes and fill in the stem sentences.

Draw a circle around the odd numbers and a rectangle around the even numbers.

So you could try three, five, seven or nine, and see if you can partition them into two parts and fill in the stem sentences and think about whether the parts are odd or even.

So pause the video and have a go at your tasks.

How did you get on with your tasks? How many different ways did you partition nine into two parts? Did you use number shapes or make the numbers out of cubes? Did you fill in the stem sentences and draw a circle around the odd numbers and a rectangle around the even numbers? So this is what I found out.

If one is a part, then the other part is eight.

If two is a part, then the other part is seven.

If three is a part, then the other part is six.

If four is a part, then the other part is five.

I can see we've always got one odd number and one even number as the parts.

How did you get on with the second part of your task? Did you choose some other odd numbers to partition into two parts? And did you use number shapes or make the numbers out of cubes? So I chose to partition the number five and I found if one is a part, then the other part is four.

If two is a part, then the other part is three.

If three is a part, then the other part is two.

And if four is a part, then the other part is one.

Did you notice we've always got one odd part and one even part? Let's move on to the second part of the lesson.

We will be partitioning even numbers.

So we've already found out that odd numbers can only be partitioned into one odd and one even number.

But what about even numbers? So here we've got the number six.

How can we partition six? Can you think of any ways? Let's partition six.

Can we use one odd and one even number? So six is the whole.

Let's try having one as a part.

If one is a part, then the other part is? It's five.

Let's try a different way.

If two is a part, then the other part is? It's four, if three is a part, then the other part is? It was three.

Which parts are odd and which are even? Let's put a circle around the odd numbers.

So I can see one is an odd number and five is an odd number.

Three is an odd number and three is an odd number.

Which ones are even? Let's put a rectangle around the even parts.

Two is an even number and four is an even number.

What do you notice about the parts? Are they odd or even? I can see that the parts are either both of them are odd or both of them are even.

So this time both parts are odd or both parts are even.

Is this true for other even numbers? So here we've got the number four.

Four is the whole.

I wonder how we can partition the number four.

Can you think of any ways? So we could partition four into one and it's three if two is a part, then the other part is? It's two, so which parts are odd? I can see one is an odd number and three is an odd number.

They're both odd.

Which parts are even? I can see two is an even number and two is an even number, so they are both even.

Let's check your understanding.

Can you partition eight into two odd numbers? Who do you agree with? So Jun said, 'Yes, I can partition eight into five and three." Sofia said, "Yes, I can partition eight into six and two." Who do you agree with? Pause the video while you have a think.

Who did you agree with? Well, they have both partitioned eight.

Jun has partitioned eight into two odd numbers, five and three.

They're both odd numbers.

I can see that they slot together to make an even number.

Sofia did partition the number eight into two parts, but her parts are both even.

Why can't we make an even number from one odd part and one even part? When one part is odd and the other part is even, there is always an odd cube, which is not part of a pair.

So can you see here we've got an even number at the bottom of all of these numbers? They've got a nice flat top.

And then we've got an odd number on the top.

So with the odd number, you've got the extra cube at the top.

So the odd cube is at the top and that makes the whole number an odd number.

When both parts are odd numbers, why is the whole an even number? When both parts are odd, the odd cubes make a pair.

So here we've got an odd number.

I can see the odd one at the top.

And when you put another odd number, those two odd cubes go together to make a pair.

Here we've got another odd number.

It's five.

And we've put another odd number on the top.

It's three.

Can you see the two odd cubes go together to make a pair? Here we've got another odd number.

And then another odd number on top.

Can you see the two odd cubes go together to make a pair? So they slot together like a jigsaw, don't they, to make an even number.

Here's a task view to have a go at.

How many different ways can you partition eight into two parts? Use number shapes or make the numbers out of cubes and fill in the stem sentences.

When you filled out the numbers on the stem sentences, can you draw a circle around the odd numbers and a rectangle around the even numbers? So the stem sentence says if mm is a part.

Then the other part is mm.

Here's the second part of your task.

Can you choose some other even numbers to partition into two parts? Use number shapes or make the numbers out of cubes.

Fill in the stem sentences.

And can you draw a circle around the odd numbers and a rectangle around the even numbers? So again, the stem sentence says if mm is a part.

Then the other part is mm.

So you could choose an even number like four, six, eight, or 10 and see if you can partition it into two parts and then decide whether the parts are odd or even numbers.

So pause the video and have a go at your tasks.

How did you get on with your tasks? First of all, we asked you to partition eight into two parts and we asked you to use number shapes or make the numbers out of cubes to check.

Did you fill in the stem sentences and draw a circle around the odd numbers and a rectangle around the even numbers? So I have partitioned the number eight in four different ways.

If one is a part, then the other part is seven.

If two is a part, then the other part is six.

If three is a part, then the other part is five.

And if four is a part, then the other part is four.

Can you see that the parts are both odd or both even? Here's the second part of your task.

Did you choose other even numbers to partition into two parts? I chose to partition four and this is what I found.

If one is a part, then the other part is three.

If two is a part, then the other part is two.

And if three is a part, then the other part is one.

Which number did you choose and what did you notice? Did you notice that the two parts are both odd or both even? We've come to the end of our lesson.

Well done, everyone.

Today we were explaining how even and odd numbers can be partitioned and this is what we found out.

When an odd number is partitioned into two parts, one part is even and the other part is odd.

I can see on the picture that the number seven has been partitioned into four and three and can you see four is an even number, and that's at the bottom, and three sits on top? When an even number is partitioned into two parts, both parts will be odd or both parts will be even.

So I can see there we've got the number eight and it's been partitioned into two even numbers, two and six, and they sit nicely on top of each other.

Or two odd numbers, we've got five and three, and they slot together to make an even number.

Well done, everyone.

See you next time.