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 welcome to our lesson.

Today's lesson is all about partitioning numbers, and it's about partitioning the numbers from six to 10 in a systematic way.

And today we're going to focus in particularly on the numbers eight and nine.

So let's look at how our lesson's going to shape up.

We've got some key words in our lesson today.

So I'm going to say them, and then you are going to say them back.

So my turn, partition.

Your turn.

My turn, systematic.

Your turn.

My turn, part-part-whole model.

Your turn.

Now, some of those words you might have seen before, but that word systematic, that's an interesting one.

We're going to be finding out what systematic means as we go through our lesson today.

So there are two parts to our lesson.

In the first part we're going to be partitioning numbers, and then in the second part of our lesson we're going to be being systematic.

So we'll find out more about that later.

So let's get on and partition some numbers.

And today we've got Andeep and Izzy who are going to help us with our learning.

So Andeep and Izzy are partitioning.

They're partitioning eight counters into two parts.

How many ways could there be? Andeep says, "There are eight counters," and Izzy says, "I think there will be eight ways to partition them." What do you think? Do you think there'll be eight ways, do you think there'll be more ways, or do you think there'll be fewer ways? Let's have a look and see what Andeep and Izzy do.

So Andeep and Izzy are partitioning, and they found two ways to do it.

And if you want to have a look at those two ways, we've got some darker red counters and some lighter yellow counters in each set, haven't we? I wonder what you notice.

Andeep says, "I have five as a part," and we can see those dark red counters in Andeep's set, he's got five of those.

Izzy says, "I have five as a part, too." Izzy's five though a yellow, aren't they? They're the paler, lighter coloured counter.

So she's got five yellow counters.

Eight is the whole, five is a part, and the other part is three.

So let's say that together.

Eight is the whole, five is a part, and three is a part.

Can you say that too? Your turn.

Well done.

And can you see the five in each set of counters, and the three, so and Andeep's five darker red counters and three lighter yellow counters? And Izzy has five lighter yellow counters and three darker red counters.

They've shown their ways on part-part-whole models.

So we can see eight, and five, and three.

Eight is the whole, and five and three is the parts.

And there, can you see, they're the other way round? Let's see what Andeep and Izzy have to say about this.

Andeep says, "I have five as a part and three as a part," and we can see that in his counters, and we can see that in the two parts in his part-part-whole model.

Izzy says, "I have five as a part and three as a part too." Andeep says, "Are our ways the same? Have they partitioned these counters in the same way then?" Izzy says, "Well, they look similar.

They've both got five and they've both got three." Izzy says the whole is the same, but the parts have swapped, and we can see that in the counters, the colours of the counters have swapped.

And in the part-part-whole model, we can see that Andeep has five and three, and Izzy has three and five.

Andeep and Izzy have represented these on a number line.

So their same ways of partitioning eight, they've represented on a number line.

Andeep says, "What is the same?" Can you see what's the same on these two number lines? Izzy says "The whole is the same," and the number eight there is the same whole on both number lines, and we've put a circle around it, that is our whole.

Andeep says, "Yes, eight is the whole, five is a part, and three is a part." And on both the number lines, we can see a jump of five and a jump of three, can't we? So that is what's the same.

I wonder what is different? And Andeep's asking, "What is different then?" And Izzy says, "The parts are in a different order." She says, "It doesn't matter if we do the jump of five first, or three." And you can see on that top number line, we've got to jump of five and then a jump of three, and we've landed on eight.

And on the bottom number line, we've got a jump of three and then five, but we've still landed on eight as our whole.

They've tried a different way to partition the counters, and they've represented it in a part-part-whole model, as well as their counters.

What do you see there? Andeep says, "Eight is the whole." We've still got eight counters, we've still got eight as the whole in our part-part-whole model.

Izzy says, "Four is a part, and four is a part." So the eight counters represent all the counters in the set, the whole, the four represents one part, and the other four represents the other part.

So how can this be represented on a number line? Well, you can see there, we've got our number line, and we've got our whole of eight marked with our green circle.

What do you think the jumps are going to look like? We partitioned eight into four and four.

Well, there's one jump of four, and there's the other jump of four.

Eight is the whole, four is a part, and four is a part, and we can represent that with the two jumps of four on the number line, jumping up to our whole of eight.

Andeep says, "Eight is the whole, four is a part and four is a part." And Izzy says, "The two parts are the same." So this time, the two parts of eight are the same, one part is four and the other part is four.

And she says, "If we swap the parts around, it will still look the same, won't it?" We might change the colour of our jumps, but we'll still have a jump of four, and another jump of four.

The parts will look the same.

So what do you notice here? We've got the top number line with our jumps of four and four, getting to eight.

And the bottom number line, we've got a jump of five and then a jump of three, and we still landed on eight, because we know that four and four are two parts which together make eight, and five and three are two parts which together combine to make eight.

Andeep says, "Eight is the whole in both of them." Ooh, Izzy's noticed something.

I wonder if you spotted this? As one part gets bigger, the other parts get smaller.

That's interesting, isn't it? So have a look.

So we've got our four and our four on the top number line.

Then on the bottom line, our first jump has got bigger.

It's now five.

But our second jump has got a bit smaller.

Because we've already jumped five, we haven't got as far to jump on to get to eight this time.

That's interesting.

I wonder if we can see that later on in the lesson too? So they're partitioning their eight counters into two parts again.

Have they found all the ways of doing it? Andeep says, "There are six ways to do it." So you can see his ways, and you can see Izzy's ways on the other side.

Izzy says, "I think there are more ways to partition eight." What do you think? Okay, so let's have a check and think about how we represent these parts.

So can you draw a part-part-whole model to represent these counters and then say the stem sentence? So the stem sentence, "Mm, is the whole, mm is a part, and mm is a part." So have a go at drawing the part-part-whole model to represent these counters, and then say the stem sentence.

Pause the video now and then we'll think about it together.

How did you get on? Let's have a look.

So there is our part-part-whole model.

There are still eight counters in our whole.

This time, one part is six, so the darker red counters is a part of six, and the pale yellow counters are a part of two.

So can we say the stem sentence together? Eight is the whole, six is a part, and two is a part.

I'll say it and then it's your turn.

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

Your turn, you say it now.

Well done.

So we've used a part-part-whole model to represent the counters, and we've represented it in words by saying our stem sentence.

So can you think of any other ways to partition eight counters? So we've looked at how we can show our partitioning.

And remember, Izzy and Andeep weren't sure they'd found all the ways, so let's have a look.

Ooh, Andeep says, "We could have zero as a part." So he could have zero yellow counters and eight red counters.

One part is eight, and one part is zero.

We can't see any yellow counters.

There are none of them.

Izzy says, "I can show that, too." So she's got all yellow counters and no red counters.

I can say one part is zero and one part is eight.

And this time, her eight are all the yellow counters and her zero is no red counters.

She says, "I think there are more ways to partition them." So they'd found some before, and now they've found some ways of partitioning into zero and eight.

I wonder if they've got them all yet? Okay, so we've got some mistakes here to spot.

So they've had a go at doing some partitioning.

They've shown it with the counters, and they've tried to make some part-part-whole models.

So you're going to have a look and see if you can find the mistakes in their recording.

So pause the video and have a go, and then we'll talk about it together.

How did you get on? What did you notice in the first one? So we can see four darker red counters and four paler yellow counters.

So we split our whole of eight into four and four.

One part is four and the other part is four.

But our part-part-whole model doesn't quite look right, does it? I think we've managed to get the whole in the wrong place, haven't we? We've said that eight is a part, but we know that eight is the whole.

So we need to swap those two numbers over.

Eight is the whole, four is a part, and four is a part.

What about the second set of counters? So what can we see there? We can see seven red counters, seven darker red counters, and one paler yellow counter.

So we've got our whole is eight, that's correct.

But look at those two parts.

I'm not so sure about those.

We know one part is seven, but the other part can't be seven as well.

Not enough counters.

Let's have a think.

So one part is seven, but the other part isn't seven, is it? The other part is one.

So eight is the whole, seven is a part, and one is a part.

So when we're using our part-part-whole models, we need to be really careful that we are representing our counters or our drawing accurately on our part-part-whole model, making sure that our wholes and our parts are recorded correctly.

It's time for you to have some practise.

So you're going to partition eight counters and record it in your own way.

So you could use part-part-whole models, you could use bar models, or you could use number lines.

And Alex is challenging you, can you find all the ways to partition eight counters? And for the second part of your task, you're going to complete this table.

So we've got lots of pictures of counters there.

In each row, you've got eight counters.

And then in the first row, it says zero counters are yellow and eight counters are red.

So could you make your counters, or colour in the counters to show that there are zero yellow counters and eight red counters? And then you're going to go all the way down and colour the counters in different ways and record the number of yellow and the number of red.

And at the very bottom row, we say we've got eight yellow counters and zero red counters.

Hmm, I wonder if that gives you a clue as to how you might organise your recording? So we go from zero all the way to eight in the yellow, and in the red column, we go from eight all the way down to zero.

Hmm, I wonder what your table will look like when you've finished? So pause the video now and have a go at your tasks.

So task one was all about partitioning eight in your own way.

So you might have chosen to use part-part-whole models.

I wonder if yours looked like this? How many ways did you find to partition the eight counters into two parts? Did you find all the ways? How do you know you found all the ways? So we've got lots of different ways here of partitioning eight counters into two parts and recording it in a part-part-whole model.

So in the second part I challenged you to find lots of different combinations, different ways of partitioning your counters, and I gave you the first one, which was zero yellow counters and eight red counters.

So we can see there, we've coloured them in so that they're all red counters.

I wonder if you notice anything in the way the table has been completed? Can you see something happening there? And in the columns you can see those numbers, zero, one, two, three, four, five, six, seven, eight.

And then in the red column, eight, seven, six, five, four, three, two, one, zero.

Hmm, this is something we're gonna be thinking about in part two of our lesson.

So well done.

Let's move on.

So the second part of our lesson is all about being systematic.

Hmm, now remember that last practise task we did where we saw the patterns in the counters? Let's think about that in the second part of our lesson.

So this time, Andeep and Izzy are partitioning nine counters into two parts.

I wonder how many ways there could be? Andeep says, "We found nine ways to partition eight counters." And Izzy says, "I think there will be more ways to partition nine counters." I wonder if she's right.

I wonder if she's thinking, there are more counters so there must be more ways.

Hmm.

I wonder if you can think back to when you've partitioned smaller numbers? What did you notice about how many ways there were to partition them? So they're partitioning their nine counters into two parts.

Andeep finds one way, and then Izzy swaps the parts.

So if we look at their first row of their counters, Andeep has got eight red counters and one yellow counter, and Izzy's got one red counter and eight yellow counters.

And Andeep says, "We found eight ways to do it," because each one has been swapped over.

So Andeep found four ways, Izzy swapped them 'round and found another four ways.

Izzy says, "I think there are more ways to partition them." Can you think of any other ways to partition nine counters? Andeep says, "I found eight and one as the parts, seven and two, six and three, five and four." And Izzy says.

Ooh, can you spot those are the other way 'round? "I found one and eight as the parts, then two and seven, three and six, four and five." So they swapped them around, didn't they? Can you see any that they've missed? Izzy says, "I think there are more ways to partition them." And Andeep says, "We could have zero as a part." They haven't used zero as a part yet, have they? Andeep and Izzy have used a table to show partitions of nine.

Have they found all the ways of partitioning nine? So in the first column we've got the yellow counters, and in the second column we've got the red counters.

So if we look across that first row, we've got zero yellow counters and nine red counters.

And if we have zero as a part and nine as a part, the whole will be nine.

The second row we've got one yellow counter and eight red counters.

So one is a part and eight is a part, and our whole will be nine.

So we've got lots of parts and parts there that combine to make nine, but have they found all of them? So Andeep says, "We found five ways to partition nine counters." Izzy says, "I think there will be more ways to partition nine counters." Have we used the trick that Izzy used yet, I wonder? Can you think of any other ways? Ah, Izzy says, "We could swap the parts around." Right, time for you to have a think.

So there's a table here with partitioning.

What number has been partitioned here? Andeep says, "I think eight has been partitioned." And Izzy says, "I think nine has been partitioned." So who do you agree with? Pause the video and then we'll have a think.

Who did you agree with then? It's Andeep, isn't it? Eight has been partitioned.

I wonder what the clues are? Well, you might know your parts that combine to make eight, that's brilliant.

But I'm looking at that very first row.

There are zero yellow counters and eight red counters.

So zero is a part, eight is a part.

Eight must be all of the counters, because our other part is zero.

So yes, Andeep was right, eight has been partitioned.

Okay, so we talked about being systematic.

So in your task here, we want you to put the counters in a systematic order and complete the table.

Now, do you remember how the counters looked in the filled in table from the first part of the lesson, and you could see a pattern, you could see a pattern in the counters and you could see a pattern in the numbers in the table? And when we organise and order our numbers to create a pattern, we are being systematic.

So I wonder if you can look at all those counters and find a way of being systematic? So you might want to cut out the counters for yourself, or take some counters of your own, make the patterns of and see if you can be systematic and complete the table.

And for the second part of your task, you're going to have a look at the bar models we've used to partition nine and see if you can complete the missing numbers.

Can you see that there are some missing parts in the bar models? Can you work out what those missing parts are using your knowledge of the way that we can partition nine? So pause the video, and then we'll come back and talk about the tasks together.

Wow, look at that.

That looks a bit more organised than the first slide, doesn't it? Can you see that we've been systematic now? We've ordered the ways of partitioning nine so that we've started with zero and nine, and then we've gone to one and eight, and then two and seven.

So each time we've recorded, the number of yellow counters has increased by one, hasn't it? Look down the yellow counters and we can see zero one, two, three, four, five, six, seven, eight, and nine.

And do you remember in the first part of the lesson when we looked at the number lines and we saw that if one part got bigger, the other part got smaller? Well, let's have a look at those red counters.

So the yellow counters go up one each time, and the red counters go down a number each time.

So the red counters go from nine to eight, seven, six, five, four, three, two, one, and zero.

And can you picture that on a number line? Can you picture a jump of zero becoming a jump of one, so the jump of nine has to become a jump of eight because we've added one more yellow counter? So one of our red counters has had to go away, or has turned over to become a yellow counter.

So try to imagine that way of being systematic, of ordering the work, try to imagine what it would look like on the number lines as well.

Did you use your knowledge of different ways to partition nine to fill in the bar models? So in the first bar model, nine is the whole, one is a part, and eight is a part.

And can you see also in the bar models, can you see that systematic approach? So we've got one is a part and eight is a part, and then underneath it we've got two is a part and seven is a part.

So can you see that one part has got bigger and the other part has got smaller? And if we look through, we can see one part getting bigger, going from one, two, three, four, and then up on the next column, five, six, seven, and eight.

And the other part then gets smaller, eight, seven, six, five, four, three, two, and one.

So I wonder if you used your knowledge of pairs of numbers, or whether you used the order? And the systematic way that the bar models were written, did you use that to work out what the missing numbers were? Well done anyway, however you filled in those gaps.

You've worked brilliantly hard today and I've really enjoyed exploring partitioning the numbers eight and nine in different ways, and I hope that you can now partition more numbers from six to 10 in different ways, and knowing those number pairs will really help you with your work in the future.

So what have we learned about today? We've learned that partitioning can be represented on a part-part-whole model.

We've used them before, we've used them to represent our partitioning again today.

We also used number lines, and we used counters as well.

Being systematic helps you to find all the ways of partitioning a number, and being systematic meant recording things in order, making things into an ordered way, putting it into a table, looking for those numbers that go up by one each time, or go down by one each time.

And the ways of being systematic would help us to find anything that we'd missed or any that we'd maybe put in twice by mistake.

And the other thing we've learned is that the larger the number, the greater the number of combinations there are to make that number.

So we learned that there were more ways to partition nine than there were to partition eight.

You've worked really hard today, and I've really enjoyed learning with you today.

I hope to see you again.

Bye-Bye.