Lesson video

Hello, I'm Mrs. Cayley, and I'm really looking forward to working with you today.

So in today's lesson, we're going to partition the numbers six and seven in different ways.

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

Here's the outcome of today's lesson.

I can partition the numbers six and seven in different ways.

Here are the key words for today's lesson.

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

Your turn.

My turn, whole.

Your turn.

My turn, part.

Your turn.

Do you know what these words mean? So partition means we're going to split a whole into parts.

Whole means we've got the whole thing.

We've got all of it.

And part means we've only got a small piece of the whole.

Here's today's lesson outline.

We're going to partition the numbers six and seven in different ways.

We'll start off by partitioning numbers and then being systematic.

So let's start on the learning.

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

We've got Alex and Aisha.

Alex and Aisha have six cubes in total.

They are splitting them into two parts.

How many could there be in each part? I wonder what it could be.

So Alex said there are six cubes.

I know six is five and a bit.

Aisha said five could be a part and one could be a part.

And we can show this on our fingers, can't we? Alex and Aisha have represented this using a part-part-whole model.

So I can see we've got the five cubes and one more cube.

Can you see it on the part-part-whole model as well? Six is the whole.

Five is a part and one is a part.

So the six represents all the cubes in the set.

That's the whole.

The five represents one part and the one represents the other part.

Alex and Aisha have represented this as a bar model.

Can you see the whole in the parts on the bar model? Alex said six is the whole.

Aisha said five is a part and one is a part.

Alex has noticed that six is an even number.

I wonder what the parts are.

Are they even or odd? Aisha said the parts are both odd.

Is that what you thought? So two odd numbers can be combined to make an even number.

Six has been partitioned into five and one.

Alex and Aisha have represented this on a number line.

Can you see the parts are now represented as a jump on the number line? So we've got five and one as the parts and we've got six as the whole.

Alex said six is the whole.

Aisha said five is a part and one is a part.

Six has been partitioned into five and one.

Aisha and Alex have swapped the two parts.

So now we've got one as a part and five as a part.

Is six still the whole? Is it the same? Aisha said the whole and the parts are still the same.

Six can be partitioned into one and five or five and one.

It still makes six, doesn't it? Alex and Aisha have represented these on a number line.

Can you see the two different ways that they've made? We've got one as a part and five as a part, or five as a part and one as a part.

Alex is asking what is the same? Look at the two number lines and think about what is the same about them.

Aisha said the whole is the same.

Can you see the whole is six both times? Six is the whole one is a part and five is a part.

Alex is asking what is different? Aisha said the parts are in a different order.

It doesn't matter if we do the jump of five or one first.

We still end up with six, don't we? Alex and Aisha have tried a different way to partition the cubes.

What have they partitioned six cubes into this time? That's right, they've partitioned it into four cubes and two cubes.

Six is the whole.

Four is a part and two is a part.

The six represents all the cubes in the set.

That's the whole.

The four represents one part.

The two represents the other part.

How can this be represented on a number line? I wonder what it's going to look like.

So, six is the whole, so that's where we're going to end up.

Four is a part and two is a part.

Can you think what it's going to look like on the number line? So, four is a part and two is a part.

Six has been partitioned into four and two.

Let's check your understanding.

Alex and Aisha are partitioning the number six.

Which bar model shows this? Can you see the way that they've partitioned six into two parts? Which bar model is correct? Pause the video while you have a think.

Which one did you think was correct? It was the first one.

Six has been partitioned into four and two.

Alex and Aisha have seven cubes in total now.

They are splitting them into two parts.

How many could be in each part? I wonder what it could be.

So Alex said there are seven cubes.

I know seven is five and a bit.

I wonder what the bit's going to be.

Aisha said five could be a part and two could be a part.

So here we've partitioned into five and two.

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

Alex said seven is the whole.

Aisha said five is a part and two is a part.

The seven represents all the cubes in the set.

That's the whole.

The five represents one part and the two represents the other part.

Alex and Aisha have represented this as a bar model.

Can you see the whole in the parts on the bar model? Alex said seven is the whole.

Aisha said five is a part and two is a part.

Alex has noticed that seven is an odd number.

I wonder whether the parts are odd or even.

So, Aisha has noticed that one part is odd and one part is even, because an odd and an even combine to make an odd number.

Seven has been partitioned into five and two.

Alex and Aisha have tried a different way to partition the cubes.

What do they partition seven cubes into this time? That's right, they've partitioned seven into four and three.

Can you see it on the part-part-whole model? Alex said seven is the whole.

Aisha said four is a part and three is a part.

So the seven represents all the cubes in the set.

The four represents one part and the three represents the other part.

How can this be represented on a number line? So I wonder what our jumps are going to be this time and what the whole's going to be.

So Alex said seven is the whole.

Aisha said four is a part and three is a part.

How will that look on the number line? So the first jump is going to be four and the second jump is three.

Is that what you thought? So seven has been partitioned into four and three.

What do you notice here? Have a look at the number lines and see what you notice.

What's the same and what's different about them? So Alex said seven is the whole for both of the number lines and Aisha said four is a part and three is a part.

The order of the jumps doesn't matter.

So the two parts have been swapped round, haven't they? The order of the jumps doesn't matter.

Let's check your understanding.

Alex and Aisha are partitioning seven cubes.

Who is correct? Can you see how they've done it on the number line and with the cubes? So Alex said seven can be partitioned into one even and one odd part, and Aisha said seven can be partitioned into two even parts.

Pause the video while you think about who is correct.

Who did you think was correct? It was Alex.

Seven can be partitioned into one even and one odd part, because in this example, six is an even number and one is an odd number.

Aisha was not correct.

Seven can't be partitioned into two even parts 'cause two even numbers combine to make an even number.

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

Can you find six cubes or six objects? Use six cubes.

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

So we've given you some examples here.

Can you try to find all the different ways and record them on the part-part-whole models? Here's the second part of your task.

Can use six cubes again and partition them into two parts.

This time record your combinations on number lines.

So we've given you some number lines here to try or you could draw your own.

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

How did you get on with your tasks? How many ways did you partition six cubes into two parts? So here, I've got some examples.

I've got six as the whole each time and for my parts I've got six and zero, five and one, four and two, three and three, two and four, one and five, and zero and six.

Did you find all the ways? Can zero be a part? Here's two examples where zero is a part.

Alex said zero could be a part.

Aisha said we might not be able to see it.

So when we're partitioning cubes or another object, we won't be able to see the part that's got zero.

How did you get on on the second part of your task? Did you record some combinations on number lines? Here are some examples.

So can you see that we've got six as the whole each time and we've got different parts? So I tried one as a part and five as a part, two as a part and four as a part, three as a part and three as a part, four as a part and two as a part, five as a part and one as a part, and six as a part and zero as a part.

Did you find any of those? Let's move on to the second part of the lesson, being systematic.

Alex and Aisha have six counters in total.

Some are red and some are yellow.

You might have some counters that you could try this with or another object.

How many ways could they be partitioned into two parts? Here's one example.

It's been partitioned into three counters and three counters.

Alex said there are six counters.

Aisha said three are red and three are yellow.

Alex and Aisha have represented one way as a bar model and a part-part-whole model.

Alex said six is the whole.

Aisha said three is a part and three is a part.

So the bar model and the part-part-whole model are both showing the same way to partition six into three and three.

Six is the whole, three is a part and three is a part.

Could there be a different way? Yes, I'm sure you can think of other ways to partition six counters.

Alex and Aisha partition six counters in different ways.

If you've got six counters you could try this as well.

So here we've got four red counters and two yellow counters.

Here, we've got three yellow counters and three red counters.

Here, we've got five red counters and one yellow counter.

Here, we've got five yellow counters and one red counter.

Here, we've got six yellow counters.

Here, we've got two yellow counters and four red counters.

And here, we've got six red counters.

Alex said we found seven different ways.

Aisha is asking did we find all the combinations? I wonder how we could check.

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

Aisha said we could be systematic.

Alex and Aisha have put them in a systematic order.

This means they've put them in a really good order where you can see the pattern going up or down by one each time, and then you can check that you've got all the combinations.

Alex said, I can see we found all the combinations.

Aisha said it looks like there are no other possible ways.

Can you think of any other possible ways? How can we know we have all the combinations? So here, we can see we've got zero yellow counters and six red.

Then we've got one yellow and five red.

Then we've got two yellow and four red.

Then we've got three yellow and three red.

Then we've got four yellow and two red.

Then we've got five yellow and one red.

And finally, six yellow and zero red.

So we can see that there are no other combinations.

Alex said we could put the combinations in a table.

So here, you can see the combinations have been put in a table.

Can you see the yellow counters are going, zero, one, two, three, four, five, and six? They're in the right order.

And the red counters go, six, five, four, three, two, one, and zero.

What do you notice about the yellow and the red counters? So Alex said, as the number of yellow counters goes up, the number of red counters goes down.

So one part is going up and one part is going down.

Alex and Aisha use part-part-whole models to record their ways.

Can you see they've got six as the whole each time? And one of the parts is going up each time, starting from zero all the way up to six, and the other part is going down.

It starts at six and goes down to zero.

So we've got zero and six, one and five, two and four, three and three, four and two, five and one, and six and zero.

So we can see we've got all the possible ways.

Did we find all the combinations? Yes, I think we did.

Alex said, I can see from the table that we have them all.

So you can check this on the table.

Let's check your understanding.

Alex and Aisha 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 the missing numbers are.

What did you think the missing numbers were? So I can see we had zero and six and then we have one and five.

Then we have two and four.

Then we have three and three.

Then we have four and two.

And next, we have five and one.

Finally, we have six and zero.

Is that what you thought? Aisha said, as the number of yellow counters goes up, the number of red counters goes down, but the whole is always six.

Let's check your understanding again, which counters match the bar model? So have a look at the bar model there and think about which set of counters matches that bar model.

Pause the video while you have a think.

Which set of counters do you think matches the bar model? So I can see on the bar model that six is the whole, two is a part and four is a part.

So it's the middle set of counters.

We've got two yellow counters and four red counters.

We always had six for all of those sets of counters, but the middle one is showing the correct parts to match the bar model.

Alex said six is the whole, two is a part and four is a part.

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

Alex and Aisha partitioned seven counters in different ways.

Can you see the different ways that they found? Sort each set so they are arranged systematically.

So see if you can think of a really good order to do them in.

So one of the parts is going up, while the other part is going down.

Which one should you start with? When you have arranged them, play a game with your partner.

Take it in turns to hide one of the combinations.

You could cover it up with your fingers or you could move them out of the way if you've got them cut out.

Ask your partner to say which combination is missing and how they know.

So, here's an example of how to play the game.

Alex and Aisha play the game with the partitions of six.

So here are the partitions of six in a systematic order.

Aisha removes a combination.

Which combination have I removed and how do you know? Look carefully at the counters and think about which combination she has removed.

So Alex said the combination above the gap has two as a part and four as a part.

So the missing combination has two parts of three because it fits the pattern, and there it is.

So we got three yellow counters and three red counters.

Here's the second part of your task.

Can you complete the bar models to partition seven in different ways? Remember to be systematic.

So we've filled out the whole and one of the parts for you.

Can you find the other part? And remember you could use counters to check.

So pause the video while you have a go at your tasks.

How did you get on with your tasks? Here, we've got seven counters that have been partitioned into two parts.

The combinations have been ordered systematically.

Did you spot the two ways? So here's one way of doing it, starting with seven red counters, and then working all the way down to seven yellow counters.

And here's a different way you could have done it if you start with seven yellow counters and work all the way down to seven red counters.

How did you get on with the game? Your game might have looked like this.

Here, Aisha has ordered the combination systematically, but one is missing.

She said the missing combination is seven yellow and zero red counters, because as the number of yellow counters goes up, the red counters go down.

So I can see there's one combination missing at the bottom there.

Or your game might have looked like this.

Here, a different combination is missing.

Aisha said the missing combination is one yellow and six red.

The next combination has two as a part and five as a part.

One part is one less and one part is one more.

So as the number of red counters goes down by one, the yellow counters go up by one.

How did you get on in the second part of your task? Did you complete the bar models systematically to partition seven? And did you check with counters? So here, we've got seven is the whole, one is a part and six is a part, or two is a part and five is a part, or three is a part and four is a part part.

Then we can swap them round and we've got four is a part and three is a part, or five is a part and two is a part, and six is a part and one is a part.

How did you get on with that one? We've got to the end of our lesson.

Today, we were partitioning the number six and seven in different ways and this is what we found out.

There is more than one way to partition a number.

When a number is partitioned into two parts, the parts can be odd or even.

Even numbers can be partitioned into two odd parts or two even parts.

And odd numbers can be partitioned into one odd part and one even part.

Well done, everyone.

See you next time.