Lesson video

Hello, my name's Mrs. Hopper and I'm here today to work with you on your maths.

I'm really excited to be working with you.

I hope you're ready to have lots of fun, lots of different ways to represent our maths and to think about our maths.

So let's make a start.

So let's get started on our lesson today, which is all about partitioning the numbers six to 10 into two parts, and it's part of our unit on composition of the numbers six to 10.

So let's have a look at what we're going to be doing with our partitioning today.

Well, we've got some keywords to work with and I think you might have come across these before, but they're going to be useful to us today, so it's worth rehearsing them.

So I'll say the word and then you say it back.

So my turn, partition, your turn.

My turn, whole, your turn.

My turn, part, your turn.

Well done.

So partitioning is all about breaking our numbers up.

We're taking the whole and we're partitioning it, breaking it into those parts.

So look out for the keywords as we go through our lesson today.

So two parts to our lesson.

And in the first part, we're going to be thinking in particular about the number 10.

So we're going to be thinking about how we can partition 10 and then we'll look at other numbers in the second part of our lesson.

So let's get started with partitioning 10.

And we've got Sam and Lucas helping us with our learning today.

So Sam and Lucas are partitioning 10 counters into two parts.

How many ways could there be I wonder? Well, Lucas says, "There are 10 counters" and Sam says, "I think there will be 10 ways to partition them." Maybe that's right.

If there are 10 counters, there are 10 ways to partition them.

I wonder if you've ever partitioned any other numbers.

What did you find about how many different ways there were to partition them? Maybe you can think about that as we think about how we're going to partition 10.

So Sam and Lucas are partitioning 10 counters into two parts and they found two different ways to do it.

If you have a look at their ways, what do you notice about them? I wonder what Lucas and Sam are going to tell us about the two ways they've partitioned 10.

Lucas says, "I have six as a part," and if we look at Lucas's counters, we can see that six of them are in the darker red colour.

So six is a part.

Sam says, "I have six as a part too." Are Sam's six the red counters? Oh, they're not, are they? Sam's got the lighter yellow-colored counters.

They're her part that represents six.

So 10 is the whole, six is a part and four is a part.

And we can say that about Lucas's counters and about Sam's counters.

So they've shown their ways on part-part-whole models.

So we can see that the whole for both of them is 10.

So let's have a think about the parts.

Lucas says, "I have six as a part and four as a part." And we can see that in his part-part-whole model.

Sam says, "I have six as a part and four as a part too." I wonder if you can spot what's going on there.

So Lucas says, "Are our ways always the same?" Well, Sam says, "They look similar," so they've got things about them that are the same.

Sam says, "The whole is the same but the parts have swapped." So can you see that Lucas had six red and four yellow counters as his parts and Sam has got four red and six yellow counters as her parts? So the colours have swapped in the counters and the numbers have swapped in the part-part-whole models.

Lucas and Sam have represented the parts on number lines this time.

So can you see the different ways that they partitioned their number in the parts on the number line, I wonder? Lucas says, "What is the same?" And Sam says, "Well, the whole is the same." We've still got a whole of 10.

We're counting right the way up to 10 on our number line and we've put a circle around the 10 to show that.

10 is the whole, six is a part and four is a part.

And we can say that about both the number lines as well, can't we? Both of them have a jump of six and a jump of four.

"So what is different?" asks Lucas.

Ah, Sam spotted it.

Sam says, "The parts are in a different order." Sam says, "It doesn't matter if we do the jump of six or four first." We're still going to end up at 10 if we do a jump of six and a jump of four in either order.

Lucas and Sam have tried a different way to partition the counters and you can see they've recorded it and represented it in a part-part-whole model as well.

What do you notice this time? Lucas says, "10 is the whole." Yep, we can see that.

10 counters and we've got a 10 in the whole of our part-part-whole model.

Sam says, "Five is a part and five is a part.

"It's like my hands, "Sam says.

Five and five and 10 fingers all together.

The 10 represents all the counters in the set.

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

How can we represent this on a number line? So we've got our number line and we've got our whole of 10 mark there.

How can we represent the parts being five and five on the number line? Well, there's one jump of five and there's the other jump of five.

"10 is the whole," says Lucas.

"Five is a part and five is a part." And Sam says, "The two parts are the same.

If we swap the parts, it will still look the same." 10 is the whole, five is a part and five is a part.

So what do you notice about these two number lines? So on our top number line, we've got two jumps of five.

Our two parts were both five.

And on the bottom number line, we've got one part is six and the other part is four.

So we've got a jump of six and a jump of four.

I wonder if you can look at the two number lines together and see if you can notice anything.

Well, Lucas says, "10 is the whole," but Sam spotted that as one part gets bigger, the other part gets smaller.

So have a look at the top number line.

You can see we've got two jumps of five.

They're both the same size, aren't they? On the bottom number line, one of our jumps of five has become a jump of six.

And so the other jump has to be smaller because we've jumped further with our first jump.

And Sam says, "The part of six is one more than the part of five.

So the part of four has to be one less than the other part of five." We've added one to one part.

So we have to take away one from the other part so that our whole still stays as 10 times.

Check your understanding.

I'd like you to draw a part-part-whole model to represent these counters and say the stem sentence.

Let's just practise that stem sentence together, shall we? And we can see it at the bottom of the slide there.

Hmm Is the whole, hmm is a part and hmm is a part.

You're going to have a go at drawing the part-part-whole models to go with both of those sets of counters and then say the stem sentence that matches.

So pause the video and then we'll have a look at it together.

How did you get on? So we could see that in both cases, we had 10 counters to start with.

So our whole is 10 and we've seen that in the top of our part-part-whole model.

And then in this set of counters, we've got eight dark red counters and two paler yellow counters.

So our parts are eight and two.

So let's say the stem sentence together.

10 is the whole, eight is a part and two is a part.

Well done.

Let's look at the other side of the page now.

What can we see here? Well, we can still see we've got 10 counters in our whole, but this time, we've got two darker red counters and eight lighter yellow counters.

So we've still got the parts as being two and eight, the same two parts but this time, we've swapped them over.

So let's say that stem sentence to match our second part-part-whole model.

So 10 is the whole, two is a part and eight is a part.

We've still got the same parts but we've swapped them over and our whole is still going to be 10.

So Lucas and Sam are partitioning 10 counters into two parts.

Have they found all the ways? Let's have a look at how they found these ones first.

Can you see them being a bit more systematic this time? You might have heard about being systematic, finding a pattern in something or putting things in order so that you can check that you found all the ways.

So let's have a look and see what they've done here.

So we started off with all 10 counters being yellow counters.

So we've got 10 as a whole for our yellow counters and zero part for our red counters, haven't we? And then we sort of turned over one counter.

So we've now got one red counter and nine yellow counters.

Then they've turned over another counter to make two red counters and so on.

So they've gone from zero red counters and then one, two, then three, then four, and then five red counters.

So they've got a pattern to follow, they're being systematic.

So let's see what they've got to say about the ways that they found.

Lucas says, "I think there are more ways to partition 10." And Sam says, "Well, we could swap the parts around and then we'll find more." So how many different ways will there be to partition 10 counters into two parts? Let's have a think about that with Lucas and Sam.

Lucas says, "We found seven ways to partition six counters." Oh, that's interesting, isn't it? Seven ways to partition six counters.

Sam says, "We found eight ways to partition seven counters." Eight ways to partition seven counters.

That's interesting too.

So they found nine ways to partition eight counters.

And then Sam says, "And we found 10 ways to partition nine counters." Does this give us any clues about how many ways there might be to partition 10 counters, I wonder? Lucas says, "I'm not sure how many ways there will be for 10.

Sam says, "I think there is one more way than the number of counters." Oh, that's interesting to think about.

Let's have a think about that.

So there were six ways to partition five and they said there were seven ways to partition six and then there were eight ways to partition seven, nine ways to partition eight, 10 ways to partition nine.

So what would that mean for 10? Sam thinks it's one more than the number of counters.

So what's one more than 10? So here are some ways to partition 10 into two parts.

What's going to come next do you think? Can you see a pattern? Can we see that Sam and Lucas have been systematic, have ordered their ways of partitioning 10 to help us to think about what would come next.

So let's look.

To begin with, we've got all the red counters, so 10 red counters and no yellow counters.

And then in the next row, we've got one yellow counter and all the rest red.

We can still see there's 10 'cause they line up with the 10 counters in the top row.

And then after one yellow counter, we've got two yellow counters and the rest red, then three yellow counters and the rest red and then four yellow counters and then five yellow counters.

So the question we're asked is what will come next? So we've got five yellow counters and the rest red.

What do you think is going to be next? I think we're going to find yes, six yellow counters and four red counters.

And what would be next? Seven yellow counters and three red counters.

Can you see, we're adding one yellow counter every time and the number of red counters is getting smaller each time by one.

So we've now got seven yellow counters and three red, eight yellow counters and two red, nine yellow counters and one red.

And what's our last row going to be? Did you get it? Yes.

All yellow counters and no red counters.

That looks quite organised, doesn't it? I think we've been quite systematic there.

Let's see what Lucas and Sam have got to say.

Lucas says, "As the number of yellow counters goes up.

." Sam says, "The number of red counters goes down." So let's read those two again.

As the number of yellow counters goes up, the number of red counters goes down and we can see each number changing each time we're adding one more yellow and we're taking away one red each time.

Can you see how many ways there are all together in that arrangement of counters? If you count the rows, do you remember they were saying that there would be one more than the number of counters? So there are 11 different ways to partition the 10 counters.

Okay, time to check.

Let's think about how we represent these.

We can represent with counters and we can represent with part-part-whole models.

So Lucas and Sam have done some, but I think they might have made a mistake.

So can you spot the mistakes they've made in recording their ways of partitioning 10 counters? So pause the video and have a look.

Did you spot it? Let's have a look together.

So Lucas has shown in his counters seven red counters and three paler yellow counters but I'm not sure his part-part-whole model shows that.

He's got a whole that's three.

I think he's recorded his part and whole the wrong way round, hasn't he? So we need to swap those.

So we show that 10 is the whole, seven is a part and three is a part.

And then that matches with his counters.

So let's have a look at Sam's.

So Sam's counters show that she's partitioned her 10 into three red and seven paler yellow counters.

So her part-part-whole model shows 10 is the whole, that's great, but then she's got both parts being seven.

I don't think that's right.

One part is seven but the other part isn't, is it? So we need to change one of the parts to three.

That's right.

Now, her part-part-whole model matches her counters.

Time for you to do some practise.

So you're going to take 10 counters and partition them and record them in your own way.

You could use part-part-whole models, you could use bar models or you could use the number line.

Can you find all the ways? Think about what we thought about, about organising your work, being systematic.

Can you find all the ways to partition 10? And then for the second part of your task, we've got a table for you to record your partitioning.

So you can see we've got part and part and whole.

The whole is always 10.

So we need to complete the table, complete those missing parts so that our two parts combine to make 10 each time.

So pause the video, have a go at your tasks and then we'll look at them together.

So you might have chosen to use part-part-whole models and Lucas is saying, "Did you work systematically?" Let's have a look at these ones.

So we can see that 10 is the whole in all those cases.

But if you look at the parts and the wholes, you can see that we've been quite systematic.

We started with one part is 10 and the other part is zero.

Then we changed it.

So that one part was nine and the other part was one and then eight and two, seven and three.

So you can see that one part is always going down by one number and the other part is always increasing by one number as well.

So I wonder if you found all that and how you decided to record yours.

So how did you get on with your table? Did you spot some patterns there as well? If you look down each column of parts, can you see the numbers go zero all the way up to 10 in the first column and from 10 all the way down to zero in the other column? So again, I wonder if you filled in your table going across the rows or whether you spotted the pattern in the columns and used that to help you.

However you did it, well done.

Let's move on to part two of our lesson.

So in this part, we're going to partition some different numbers, six to 10.

And we're going to think about partitioning in different ways.

So we can partition numbers into two or more parts.

We've partitioned some numbers into two parts here, but what numbers have been partitioned here and how do you know? So let's have a look.

We've got parts there.

So the first one has parts of five and one.

And then the second part-part-whole model shows parts of five and two.

Five and three.

Oh, I wonder what's going on here.

Let's see.

So the first one is six, five is a part and one is a part.

So the whole must be six.

So if five is a part and one is a part, what happens if one of our parts gets bigger? So five is a part and two is a part.

Our whole is seven, that's right.

Five is a part and three is a part and our whole is one more again, it's eight.

And then nine and then 10.

And we know that five and five, remember, Sam talking about her hands earlier, if five is a part and five is a part, the whole is 10.

Lucas says, "One part is always five in each model." And we can see that.

Sam says, "The other part is going up by one each time." We can see it going 1, 2, 3, 4, 5 across the slide.

So Lucas says, "So the whole has to go up by one each time." If you imagine cubes or counters, we'd have five in the part each time and then we'd have one and then two.

So we're adding one more each time.

So our whole is going to go up by one each time.

So they're all five and a bit but the bit is different each time.

And you might have thought about your numbers as five and a bit, those numbers from six to 10 before.

Different one to have a think about here.

What could the whole be and what could the other part be? All we know now is that we've got one part that is two.

I wonder what we're thinking here.

Well, Lucas says, "The whole has to be two or more." 'Cause if we've got two as a part, then our whole probably has to be at least two.

If zero is a part, it would be two or it could perhaps be bigger depending on what our other part is.

Sam says, "The other part could be any number." It could be, couldn't it? So Lucas says, "We could try starting at two and going up." So if two is our whole, the other part would be zero because if one part is zero, then the other part is equal to the whole.

If our other part was one, the whole would be three.

If our other part was two, the whole would be four.

If our other part was three, the whole would be five.

Sam says, "The next whole in the pattern will be six because it is one more than five." So our two is staying the same each time.

Our other part is increasing by one, so the next one will be six.

"So the next missing part, she says, "has to be four." So yes, if that whole keeps going up by one, then our other part has to keep getting bigger by one as well.

And we can see we've got bigger by one again.

So our whole is seven and our other part is now five.

I wonder what'll be next? The whole is eight and our missing part has gone up by one to be six because we know that if eight is the whole and two is a part, then six is the other part.

So if nine is the whole and two is a part, then seven is the other part.

And finally, if 10 is our whole and two is a part, then eight is a part.

Did you spot those numbers getting bigger? Both of them by one each time.

So this time, we're told that the whole is the same for each of these part-part-whole models.

What could the whole be and how do you know? I wonder.

Sam says, "The missing part could be any number." Yep, I think she's right, isn't it? We could have any number 'cause we don't know what the whole is.

So we could have any other number as our missing part.

Wonder about the whole? What do you think about the whole though? Lucas says, "The whole will be seven or more." Sam says, "How do you know?" I wonder how he knows.

Do you know how Lucas can tell that the whole will be seven or more? Lucas says, "I can see that the biggest part is seven" and the whole is the same for all of them.

So Lucas thinks that it must be seven because we've got a part that is seven already.

So let's think, if the whole is seven, what would the other parts be? So let's put the whole in as seven.

So if the whole is seven and one part is zero, then the other part must be seven.

And then can you see that the part we knew was increasing by one each time going up and getting bigger by one each time? So our missing part must be getting smaller each time.

And I think we found all the ways of partitioning seven into two numbers there.

And if we think back to what they were saying, the number of ways to do it is one more than the number.

There are eight ways there.

So that must be all the ways of partitioning seven into two parts.

So the whole is the same for all of these.

What could the whole be and how do you know again? So Sam says, "Could the whole be 10?" Well, let's have a think.

"Yes," says Lucas.

"It could be any number more than seven." You remember he said it had to be seven because we had a part that was seven.

So the whole could be 10.

So there we go.

There's our whole being 10.

And I wonder, have we found all the ways of making 10 here? What will these missing parts be? Well, there we go.

So we know that if 10 is the whole and zero is a part, then the other part must be 10.

And we've got parts that go from zero all the way up.

1, 2, 3, 4, 5, 6, 7.

Those were our known parts and we can now fill in the missing parts because as our known part goes up by one, then the missing part must come down by one as well.

So what number has been partitioned here and how do you know? Well, we've got some parts there, but we don't know what the whole is.

So I wonder whether we can work out what the whole is.

Sam says, "The parts are all six or less." So all the numbers there are six or less.

Lucas says, "The parts combine to make six." So zero is a part and six is a part, the whole is six.

One is part and five is a part, the whole is six.

So I think we know that our whole has to be six.

And Sam says, "The whole is six." Six has been partitioned.

Has it been partitioned in all the ways it can? We've got zero to six, I think it has.

There are seven ways to partition six.

So numbers can be partitioned into more than two parts.

So let's have a look.

How many counters have we got here? We've got eight counters all together.

It can be partitioned into more than two parts.

Let's have a look.

So Lucas says, "The whole is eight.

Two and six could be the parts." So let's have a look.

There we go.

We've got two and six being our parts.

Sam says, "What if I split up the parts of six?" Oh, so she split her parts up here, hasn't she? What's she split them into? Oh, Lucas says, "Well, now there are three parts.

Eight is still the whole, two is a part, three is another part, and three is another part." So numbers can be partitioned into more than two parts.

So can we show that on a part-part-whole model? Maybe it's a part-part-part-whole model or even a part-part-part-part-whole.

We'll just call it a part-part-whole model.

Let's have a look and see.

What could the parts be? So our whole is eight counters, we've got one part which is five.

So the other part must be three.

So eight is the whole, five is a part and three is a part.

But we could change that part of three into a two and a one.

So we could partition eight into five and two and one.

I think we can still partition that even further.

We're going to keep our five, but we could split those two up, couldn't we? Let's have a look.

There we go.

So now we've split our whole of eight into five as a part and three parts that are all equal to one.

So five is a part, one is a part, one is a part and one is a part.

So Lucas says, "Five is a part.

So the other parts will make three" as we know that if five is a part, then three is the other part.

But we can then partition the part into ever smaller pieces.

And Sam says, "All the parts will combine to make eight." It doesn't matter how many parts we've got, we put them all together and we have a whole of eight again.

So we can partition numbers into more than two parts.

So can you spot the mistakes? The whole is nine and one part is six.

So are our part-part-whole models correct? Pause the video, have a look and we'll come back and talk about it.

How did you get on? Lucas says, "The parts should combine to make nine." So in this first part-part-whole model, we've got nine is the whole, six is a part and three is a part.

And we know that six and three combined are equal to nine.

So the first one is correct, but let's look at the second one.

Sam says, "Some of these make more than nine." So in the second one where we've got three parts, we've got nine is the whole, six is a part, three is a part and three is a part.

Well, we know that six is a part and three is a part combine to make nine as a whole.

So we've got too many there.

We've got an extra three in that second part-part-whole model.

So we need to be careful if we go into more than two parts to make sure that we've still got our whole the same as it should be, nine in this case.

Ah, Sam's corrected it for us.

So Sam realised that we should have partitioned the three and we can partition the three into two and one and now six and two and one combine to equal nine.

Time for you to do some practise now.

Can you complete these tables to partition eight and nine? So we're thinking about eight on the left-hand table and nine on the right-hand table.

And you're going to complete that to find all the different parts to equal eight and nine.

And then for the second part of your task, you're going to partition 10 counters into more than two parts in different ways.

So you might partition into three parts or four parts.

So you might want to get some counters to help you.

Can you partition 10 counters into more than two parts in different ways? So pause the video, have a go and then we'll come back and discuss them.

So how did you get on? Did you complete the tables to partition eight and nine? Did you spot the patterns? Did you see that we'd been systematic in the way we set up our tables? So when we're thinking about eight, we can go from zero is a part and eight is a part.

And then we can make one number go up by one and the other number come down by one all the way down to eight is a part and zero is a part.

And then the same with nine.

So we can make sure that we found all the different ways to partition eight and nine, not left any out and not repeated any.

Now, you might have had lots and lots of different examples of partitioning 10 into more than two parts.

So here are some examples with three parts.

So if 10 is a whole and six is a part, then we can have another part of two and another part of two.

So six and two and two together combine to equal 10 as our whole.

And another example might be to say we've got 10 and one part is five.

We know that five and five is equal to 10, but we can partition that other five into three and two to create our 10 as a whole.

And here are some examples with four parts.

So if 10 is the whole, we can have five as a part and then we can have three other parts of two and two and one and we'll still have a total of 10 as our whole.

And then the other example we've got there shows 10 as the whole, six is a part and then two and one and one are the other parts.

But we can see in both of those that we know that if six is a part, then four is the other part and our three smaller parts combine to make four.

And if five is a part, then the other part will be five and we can see that two and two and one combine to make five.

I hope you had fun partitioning your numbers and particularly partitioning 10 into more than two parts.

Well done, you've worked really hard in your lesson today and I've really enjoyed learning about partitioning the numbers six to 10 in different ways with you.

So let's just think about what we've learned today.

So we've learned that each of the number six to 10 can be partitioned into two parts in different ways.

And we've even looked at partitioning into more than two parts, haven't we? A part-part-whole model or a bar model can be used to represent the whole and the parts.

And we've also learned that if we know one part, we can find the other part and we can even work out what the whole is going to be.

And you've also done some work in being systematic, in organising your work so that we can see patterns and use those to help us to make sure we found all the ways to partition numbers.

Thank you for your hard work today and I hope I'll get to work with you again soon.

Bye-Bye.