Lesson video

Hello, my name's Mrs. Cornwell, and I'm really excited to be working with you today.

We are going to use some of what you already know to help you with some new learning today and I'm really looking forward to helping you with that, so let's get started.

To today's lesson, which is called, Understand That Addends Can Be Represented In Any Order, and it comes from the unit, Additive Structures: Addition and Subtraction.

Okay, so we're going to be thinking again about the parts within a whole, okay? And finding out about how addends can be combined in different orders and how we can represent this.

And by the end of today's lesson, you should feel confident in knowing how to represent the addends within a whole.

So our keywords today, the words that will be important for our learning are partition, my turn, partition, your turn, and addend, my turn, addend, your turn, and combine, my turn, combine, your turn.

Well done and we'll find out a little bit more about those words in today's lesson, won't we? So the first part of today's lesson is called Identify an addend.

So we're going to talk about what they mean and what they are, find out all about them, and then we'll move on in the second part of today's lesson to recognise that addends can be written in any order.

So here we've got a whole group of cars, okay? The whole group has been partitioned into the parts shown, and there we can see two parts.

So it's been partitioned like that.

How have they been partitioned? How can you represent this so we can see that it's been partitioned into large cars and small cars? And how will we represent that? So remember we can describe to help us represent, can't we? So there are two large cars and three small cars.

I can represent this as 2 plus 3.

And there we can see 2 and the plus sign and 3.

And that shows that those parts will combine again to make the whole group.

What does each number represent? So what does a 2 represent? The 2 represents the two large cars and the 3 represents a three small cars.

When adding parts of a whole, each part is called an addend.

And we can see 2 plus 3.

Addend, 2 is an addend, and 3 is an addend.

What are the addends in this representation? So we can see that has been, that whole group, the parts have been represented as 4 plus 2.

So what do you think the addends are? That's right, it says there addend, addend, 4 is an addend, 2 is an addend.

What are the addends in this representation so you can clearly see two parts there, can't you? So it would be 5 + 3.

So what are the addends? So we know, there we go, 5 is an addend and 3 is an addend.

Jacob says he's partitioned this group into red apples and green apples.

He says that one of the addends is 4, is he right do you think? So let's describe to help us, there are two green apples and there are two red apples.

I can represent this as 2 + 2.

Jacob says now I can see that each addend is 2.

'cause the addends are the parts, aren't they? And there, addend, addend.

2 is an addend and the other 2 is also an addend.

So now it's time to check your understanding.

These pictures can be partitioned into two parts.

Each part is different to the other.

So in this case, in which group can you see an addend of three.

So pause the video now while you try that.

So how did you get on? Okay, so let's have a look.

So we can see the first set has a set of cats and there are two black cats and there's one tabby cat.

So we can see the addends.

There are two and one, okay, in the parts that we can clearly see.

In the next picture, we can see two purple cups and one clear cup.

So that would have addends of 2 and 1.

Okay, 2 plus 1.

Or you may have seen the cup with a straw and the two cups without a straw, but again that would've been two without a straw and one with a straw so the addends would've been 2 and 1.

So let's look at this last group then.

So we've got two green apples, there are two green apples and there are three red apples.

Okay, so we can see there are three red apples, three is a part so 3 is the addend, so well done if you've got that.

Okay, so let's think how could you represent that then? So the group of apples, the whole group of apples, how could we represent that using numerals and a plus sign? So pause the video while you try that.

Okay, so let's have a look.

That's right, two plus three because the 2 represents the two green apples and the 3 represents the three red apples.

Well done.

Using only the numbers shown, write an expression where one of the addends is 2.

So we can only use the number 0, 1, 2 or 3, and you can only use each number once.

Okay, so let's have a think about this then what could we write? You could write 2 + 0 couldn't you, 2 would be an addend there.

You could write 2 + 1.

Wonder what else you could put two with.

That's right, you could have 2 + 3 as well, couldn't you? Okay, or you could write 0 + 2, 1 + 2, or 3 + 2, so well done.

So now it's time to check your understanding again.

Okay, so write an expression that contains the addends 6 and 2.

So you'll need to use that plus sign as well, won't you? Okay, so pause the video now while you try that.

So let's see how we got on then.

You could have had, you could have written 6 + 2 or you could have also written 2 + 6.

You could have written them in any order there, but those are the two addends you needed to use.

So well done if you got those.

So the task for the first part of today's lesson then is use counters or cubes to make a whole group where one of the addends is 5.

You must not use more than 10 counters or cubes.

So only 10 or less.

Find as many different ways as you can and how do you know you've found all the different ways? Okay, so pause the video now while you have a try at that task.

So let's see how you got on.

So you could have made 5 + 1, couldn't you? You could have also made 5 + 2, you could have made 5 + 3, couldn't you? I wonder what else you could have made? What might come next if you are working systematically you could have made 5 + 4, that's right.

And you could have also made 5 + 5.

Well done if you got those.

You could also have made 1 + 5, couldn't you? So you could have done, written the 1 first, the 1 addend first and then the 5.

You could have said 2 + 5, couldn't you? You could have said 3 + 5.

I wonder what's next.

You could have said 4 + 5, that's right.

And you could have said 5 + 5, okay.

And you may have had the 5 + 5 before from when you did it with the 5 as the first addend.

How do you know you found all the possible combinations then? That's right.

I could only use up to 10 counters.

So once I'd used 5 and 5 there were no possible, other possible answers, and I worked systematically.

So in order, 1, 2, 3, 4, 5 with the 5.

So I knew I hadn't missed any possible combinations.

So well done.

You've worked really hard in the first part of today's lesson.

So in the second part of our lesson then we're going to be looking at how addends can be represented in any order.

So here are two groups of cups.

Can you see them both there? What's the same about each group? That's right.

Both groups have three cups with juice and two cups without juice.

What's different about them both? That's right, one group has lined up the three full cups first, the three cups with juice first and the other has lined up the two empty cups first.

And if we move them here, hmm, what do we notice? That's right.

It's the same group of cups, isn't it? It's just been arranged in a different order, and there you can compare it there and see that the parts have just been swapped over.

So how could you represent each group then? And what do you notice about the addends when you do represent them? So let's use our sentences to describe, there are three cups with juice and two empty cups.

I can represent this as 3 plus 2, 3 plus 2 there.

Okay, we could also say there are two empty cups and three cups with juice.

I can represent this as 2 plus 3, 2 + 3.

So what do we notice about those addends there? What does the 3 represent? So in both pictures, the 3 represents the three cups with juice, doesn't it? And what does the 2 represent? In both cases, the 2 represents the two empty cups, doesn't it? But they haven't been written in the same way.

You can write the addends in any order, can't you? So you can combine the parts in any order because they still make the same whole.

So 3 + 2, or you could also write 2 + 3, and you can see it's exactly the same group, but the parts, the addends have just been swapped around, haven't they? They make the same whole.

So Jacob has partitioned his box of sweets into two parts, okay? You can see he's got two chocolates and he's got four lollies.

They look delicious, don't they? Okay, he says he can represent this as 2 + 4, and he uses the stem sentences to prove he is right.

So you might be able to do this when you represent parts of a group, you can use your stem sentences and prove you are right.

So he says there are 2 chocolates and 2 lollies.

So I know I can represent this as 2 + 4.

Jacob represented the chocolates first, didn't he? Sophia thinks there's a different way to represent this.

She says we can also represent this as 4 + 2.

Is she right? We can describe the pictures to prove it, can't we? So let's see, Sophia represented the lollies first.

There are 4 lollies and 2 chocolates.

So I know where you can represent this as 4 + 2, and there, that's how she's represented it.

I know the 4 represents the four lollies, so she knows that part, that addends, right? I know the 2 represents the two chocolates so she knows that part's right.

So you can combine the addends in any order because when combined they make the same whole and you can see she's just moved two chocolates to the other side now and the whole's exactly the same, but the addends, the parts have just been rearranged, haven't they? Let's use the stem sentences to help you write two expressions for this picture.

So we've got chocolate cakes, haven't we? And we've got cherry cakes.

So there are mm chocolate cakes and mm cherry cakes.

That's right, there are 4 chocolate cakes and there are 2 cherry cakes.

We can represent this as mm plus mm.

That's right, we can represent this as 4 plus 2, 4 + 2.

I wonder if you can represent it another way as well.

So we could think of the cherry cakes first and represent those first, couldn't we? We could say there are 2 cherry cakes and there are 4 chocolate cakes.

We can represent this as, that's right, 2 plus 4.

You can write the addends in any order because when combined they still make the same whole, don't they? Now it's time to check your understanding again.

So represent the picture in two ways and use your stem sentences to prove you are right.

So there's a picture there.

Okay? So you've got to think about how you'll represent it in two different ways, and don't forget to describe the picture and use those stem sentences to prove that you are right.

Pause the video now and have a go at that.

Okay, so let's have a look then.

So we can see that there are 5 black cats and there are 4 tabby cats, so we can represent it as 5 + 4.

There are 5 black cats and 4 tabby cats.

So I know you can represent it as 5 plus 4 because we can think about what those numbers, those numerals represent, can't we? Okay, could we represent it a different way? That's right.

You could look at the tabby cats first, couldn't you? And you could think 4 + 5.

Okay, and you can prove it.

There are 4 tabby cats and there are 5 black cats.

So I know you can also represent it as 4 + 5.

So well done if you've got those.

So now we've got a basket of balls, haven't we? Okay, so represent the addends shown in two different ways.

So we can see we've got some tennis balls, haven't we? And we've got some basket balls and we're going to represent them in two ways, but this is a bit more tricky isn't it? And there's Sophia, she's noticed that she says this seems a bit more tricky, I wonder why? So sometimes we have to move or mark the addends in a whole group, don't we to see them more easily because those balls are all in one basket, they're all caught, but you can't really count them very easily, so we'll have to move them or mark them in some way, won't we so let's try that.

So we can say 1, 2, 3, 4, 5 tennis balls, and then 1, 2 basketballs there.

Now we can see the parts more clearly, can't we? So now I can see the addends.

I will describe them using my stem sentences.

So there they are.

There are 5 tennis balls and 2 basketballs.

We can represent this as, that's right, 5 plus 2, 5 + 2.

We could also look at it the other way instead of looking at the tennis balls first we could look at and represent the basketballs first, couldn't we? We could say there are 2 basketballs and 5 tennis balls.

We can represent this as 2 plus 5.

Excellent, 2 + 5.

So you can write the addends in any order because when combined they make the same whole don't they? So now time to check your understanding again.

So represent the parts shown in two different ways.

So these are a bit harder to see these parts, aren't they? So perhaps you could get a group of pens and pencils to help you with this or you might be able to think about how you can easily count those parts.

So pause the video now while you have a try, and when you found out what the parts are and how many, you represent it in two ways.

So now let's try together.

So there are four pens and there are three pencils.

We can represent this as 4 + 3, that's right, there are also 3 pencils and 4 pens.

So you might represent the pencils first, in which case you would represent it as 3 + 4.

Well done.

That's excellent.

You can write the addends in any order because when combined they make the same whole, don't they? Yes.

Excellent.

So now we've got some teddies here, haven't we? So represent the parts shown here in two different ways.

So what parts can we see, I wonder? So there are 4 blue teddies and 3 cream teddies aren't there? So we can represent this as 4 + 3.

We could also look at the cream teddies first and say there are 3 cream teddies and 4 blue teddies.

So we would represent that as 3 + 4, that's right.

I wonder if we could see any other parts in that if we could have partitioned in a different way? That's right, you may have also noticed there are 2 large teddies and 5 small teddies, in which case you could represent it as 2 + 5.

That's right, and if you decided to look at the small teddies first, there are also 5 small teddies and 2 large teddies.

You could represent it as 5 + 2.

Excellent, well done.

The whole can be partitioned in different ways can't it? So sometimes there's often there's more than one way to partition.

So now it's time to check your understanding again.

So represent the parts shown in two or more different ways.

Okay, so look carefully at that set and decide how you could partition them, what parts you can see, and then you can write how you would represent that.

Okay, remember to use your stem sentences to check that you are right, okay, pause the video now while you try.

Now let's look at it together then.

So we could say there are 4 cats and 2 dogs.

So you might have noticed those two parts, 4 + 2, so we can represent that as 4 + 2.

We could have also looked at the dogs first, couldn't we, and said there are 2 dogs and 4 cats.

So in which case we'd write 2 plus 4.

I wonder if we noticed another way we could have partitioned them? That's right, you may have said there are 3 large animals and 3 small animals, and you would represent that as 3 + 3.

Excellent, the whole can be partitioned in different ways, can't it? That's right.

Well done.

Jacob picks up some cubes in one hand and some cubes in his other hand.

You can see them there, can't you? He says, I have three cubes in one hand and I have four cubes in the other hand, how can he represent this? I can represent this as 3 plus 4 he says, that's right, 3 + 4.

Jacob swaps his hands over how can he represent this now, and he says, he's noticed I still have 4 cubes in one hand and I still have 3 cubes in the other hand, I've just swapped them over.

So how would we represent that? That's right, I can represent this as 4 plus 3.

So even when they look the same, you can represent the addends in any order because when combined they still make the same whole.

Sophia and Jacob are tidying up the cubes and they partition them into two pots.

How can they represent the two parts in two different ways? So again, all the cubes look the same as each other, don't they? But we can, they have been partitioned.

So how can they represent the two parts? Let's think about what each number represents then.

So we've got Sophia here and she says I will represent the pot next to me first.

There are 4 cubes in one pot and 5 cubes in the other pot, and so she represents it as 4 + 5.

Then Jacob says I will represent the pot next to me first.

There are five cubes in one pot and four cubes in the other pot.

So he will represent it as 5 + 4.

So they didn't actually swap the pots around this time, did they? But they just looked at them in a different way and in a different order.

So even when they look the same, or that the objects look the same, you can represent the addends in any order because when combined they still make the same whole, don't they? So now it is time to check your understanding again.

The children partition the cubes in a different way.

Okay, so we can see they've partitioned them between two pots, but there's a different amount in each pot this time.

So you've got to write two ways to represent them.

So pause the video now and try that.

Okay, so let's have a look together.

There are mm cubes in one pot and mm cubes in the other pot.

So I wonder which pot you decided to look at first.

So I'm going to look at this pot here.

There are 3 cubes in one pot and there are 6 cubes in the other pot.

So I could represent that as 3 + 6.

Now I'm going to look at the other pot first and I'm going to say there are 6 cubes in one pot and 3 cubes in the other pot.

So we can represent that as 6 + 3.

So the addends can be represented in any order because they combine to make the same whole, don't they? Sophia has 6 double-sided counters.

She wants to find out how many ways she can partition them into two parts.

I wonder how many ways I can find.

So you can see they're double sided.

They must be red on one side and blue on the other.

So she partitions them like this and then describes the parts.

She says there are 5 counters red side-up and 1 counters blue side-up.

We can represent this as 5 + 1.

Could we represent it another way do you think? Yeah, we can represent this also as 1 + 5, couldn't we? Could either look at the red counters first or the blue counter first.

Jacob partitions them like this in, so in a different way and then describes the parts.

He says there are 2 counters red side-up and 4 counters blue side-up.

We can represent this as, that's right, 2 + 4.

We can represent this as 4 + 2, that's right.

Sophia says she's partitioned the whole now, is she right? She says there are 6 counters red side-up and no counters blue side-up.

We can represent this as, can she represent that? Yes, that's right, she can say 6 + 0 can't she? Because there's 6 red side-up but there aren't any blue side-up.

So you have to write 0 for the blue counters and then we can represent this as, that's right, we can also swap the addends around.

We can write them in any order.

So we could say 0 + 6, well done.

So your task for this next part of the lesson then is here, collect a whole group of 8 double sided counters.

See how many different ways you can partition them into two groups.

And there's Sophia, she's saying I can use my stem sentences to help me, and Jacob says, I can think about what each number represents to help me.

So each time you partition, remember to write down how you can represent it in two different ways.

Okay, so you need 8 double sided counters.

If you don't have those, you could get 8 counters but use two different colours, couldn't you? Okay, so pause the video while you try that.

So let's see how we got on with that task then.

Sophia represented the 8 counters like this.

So she said each time I partitioned I represented it in two ways.

So she's going to write it in two ways, isn't she? 8 + 0 or 0 + 8, that's right.

Then she turned a counter over and she said I can write it as 7 + 1 or 1 + 7.

And wonder what will be next then.

So she turned another counter over and then she wrote 6 + 2 or 2 + 6, that's right.

And then I wonder what she'll do next.

That's right, turn another counter over so now she's got 3 + 5, 5 + 3, or 3 + 5, hasn't she? That's right, okay, and now she's turned another counter over and she's got 4 + 4, and you couldn't, you only write that once because obviously if you swapped it it would be the same expression, wouldn't it? Okay, so what's she going to do next then? So we've got, she turned another counter over and she's written 3 + 5 or 5 + 3, and then she's turned another counter.

Wonder what this will be, 2 + 6 or 6 + 2.

And what do you think she'll do next? And what will that expression be? That's right, so we've got 1 + 7 or 7 + 1.

And then finally turn the last counter over and we've got 0 + 8 or 8 + 0, that's right.

What do you notice about the way that we've represented the counters? Do you notice anything about what we've written there with the numerals and the plus sign? That's right, because I changed the order of this addend, says Sophia, I'd already represented these.

So you can see you've got there 8 + 0, 0 + 8, and then you've got the same thing again, haven't you? 0 + 8, 8 + 0.

So actually we didn't need to write the second lot did we because we'd already rep represented them when we swapped the addends around.

So well done.

You've worked really hard on that task.

So let's look at what we've learned in today's lesson then.

So we found out when parts of a whole are added together, each part is called an addend.

You can combine the parts in any order because they still make the same whole, don't they? So even if you rearrange them, the whole amount stays the same.

And you can write the addends in any order because when combined they still make the same whole.

So you can write and represent them either way round, can't you? So well done.

You've worked really hard in today's lesson.

And hopefully you are feeling much more confident now about how to represent those addends and you know how you can represent them either way round.

So, excellent.

I've really enjoyed today's lesson.