Lesson video

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

We're 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.

So welcome to today's lesson, which is called Combine Addends, Using the Addition Symbol, and it comes from the Unit: Additive Structures, Addition and Subtraction.

So in today's lesson, you're going to learn how to partition a whole in different ways and use the addition symbol to represent recombining the parts to show how that's done.

And so by the end of today's lesson, you'll be able to represent the parts of the whole and you'll know how to confidently do that, and you'll know how to combine them using the addition symbol, the plus sign as well.

So let's get started.

So the words are going to be important for our learning today, the keywords are partition, my turn, partition, your turn, and whole, my turn, whole, your turn, and parts, my turn, parts, your turn, and plus, my turn, plus, your turn.

And combine my turn, combine, your turn.

Well done, that was excellent.

So in the first part of today's lesson, we're going to partition a whole in one way and describe it using the plus sign.

In this lesson you will meet Jacob and you will also meet Sofia.

Jacob and Sofia have made some chocolate cakes and some cherry cakes, can you see them there? They're in the tray, aren't they? They want to partition the whole amount into two parts.

I wonder how they'll do it.

They partition them like this.

They partition them into the chocolate cakes and into the cherry cakes.

When you partition a whole, you can describe the parts.

There are four chocolate cakes, and two cherry cakes.

There's the 4, and there's the 2.

We can represent this as 4 plus 2, and there's a plus sign in the middle, that's called a plus sign.

The 4 represents the 4 chocolate cakes.

The 2 represents the 2 cherry cakes.

And the plus sign shows the two parts will combine to make the whole.

Jacob and Sofia are playing with these toy cars.

They partition the whole group into two parts.

I wonder how they'll do that.

How do you think they will partition them? Think about what's the same and what's different in the whole.

Do you see any parts? That's right, they partition the cars like this.

Is this how you did it? Small cars and large cars.

Describe the parts.

There are 3 small cars and 2 large cars.

We can represent this as 3 plus 2.

And there we have 3 plus 2.

What does the the 3 represent? That's right, the 3 represents the 3 small cars, doesn't it? What does the 2 represent? The 2 represents the 2 large cars, doesn't it? Yes.

And the plus sign in the middle there shows it will combine to make the whole, the two parts combine again, and they make the whole again, don't they? Complete the stem sentences.

So we can see here we've got some black cats, haven't we? How many have we got? That's right, we've got four black cats and we've got a tabby cat as well, haven't we? So let's complete the stem sentences.

There are mm black cats and mm tabby cats because it's important to describe, to help us know how to represent the parts.

There are 4 black cats and there is 1 tabby cat.

That's right, we can represent this as mm plus mm, that's right, 4 We can represent this as 4 plus 1.

There's the 4 plus 1.

What does the 4 represent? That's right, the 4 represents the 4 black cats.

What does the 1 represent? The 1 represents the 1 tabby cat, that's right.

The plus sign shows that the parts will combine to make the whole.

so now it's time to check your understandings.

So use the stem sentences to describe the parts.

Okay, so we've got the stem sentences there and it says there are mm cups with straws and mm cups without straws.

We can represent this as mm plus mm.

So pause the video now while you have a try at that.

Okay, let's see how you got on.

So there are mm cups with straws and mm cups without straws.

So we can see there that there are 2 cups with straws and there are 3 cups without straws, that's right.

So we can represent this as 2 plus 3, excellent! And there's 2 plus 3, that's how we write it with numerals and the plus sign.

Okay, so we're going to think about what the numbers represent now.

So we've got the 2 represents the mm and the 3 represents a mm.

So pause the video again now while you have a try at that, completing in the stem sentences.

Okay, and now let's go through it together.

The 2 represents the 2 cups with straws, that's right.

And the 3 represents the 3 cups without straws.

Excellent, well done! Now complete the stem sentences to describe the parts here.

So we've got a different picture, haven't we? And the stem sentence is, there are mm full cups, and mm empty cups.

That's right, there are 3 full cups and there are 5 empty cups.

We can represent this as mm plus mm, what would we say, all right there, I wonder? That's right, we can represent this as 3 plus 5, excellent! What does a three represent? That's right, the 3 represents the 3 full cups, doesn't it? What does the 5 represent? That's right, the 5 represents the 5 empty cups, and the plus sign shows that the parts will combine to make the whole.

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

Okay, so it says, "Complete the stem sentences to describe the parts." There are mm black cats and mm tabby cats.

Okay, so we can see we've got a different number there from last time, haven't we? And we can represent this as mm plus mm.

So pause the video now while you try that.

Okay, so let's go through it together.

There are mm black cats and mm tabby cats.

So we can see there can't we, the black cats? There are 5 black cats and 4 tabby cats, that's right.

We can represent this as.

That's right, it is 5 plus 4, excellent! So now describe the two parts that make the whole using the stem sentence to help you, okay? so it says, "There are mm forks and mm spoons." Now this is a bit more tricky, this picture isn't it, i wonder why? That's right, it's because the spoons and the forks are a bit more muddled up then, and the parts aren't as easy to see, are they? So, I wonder what we can do to help us.

That's right, sometimes, you may have to move the objects if you've got them in front of you or mark the parts in a picture to help you see them.

So let's see how we do that.

So you can draw a ring around each of the parts, can't you? So we're going to do the forks part first.

So we've got 1, 2, 3, 4, 5 forks, and that can help us to complete the stem sentence.

There are 5 forks, and now we have to see how many spoons there are.

So 1, 2, 3.

So there are 5 forks and there are 3 spoons.

How can we represent this? So we need to think about how we will represent this using numerals and the plus sign.

Mm plus mm.

we can represent this as mm plus mm.

That's right, we can represent it as 5 plus 3, excellent.

Explain what each number represents then.

So what does that 5 represent? That's right, the 5 represents the 5 forks, and the 3 represents the 3 spoons, doesn't it? Well done, excellent! The plus sign shows that the parts will combine to make the whole, so that's what that represents.

That the parts are being put together to make the whole again.

Now, either collect a set of pens and pencils or use the ones shown, and partition the whole group into two parts, and describe and write how you would represent it.

So we can see there, can't we? It says mm plus mm, there are mm pens and mm pencils.

So you're going to describe them, and that will help you know how to represent it.

We can represent this as mm plus mm.

When you have represented it using the plus sign, remember to say what each number represents 'cause that can help you check that you are right as well, can't it? So there are 4 pens and 3 pencils, that's right.

You may have, if you had the objects, move them into two parts that you could clearly see or you may have drawn a ring round them to count them couldn't you, or mark them in some way? So there are 4 pens and 3 pencils.

We can represent this as 4 plus 3, that's right.

And using the numerals and the plus sign, it would be 4 plus 3, that's right.

So now it's time to check your understanding again, okay? So you're going to match the representation, the picture, to the correct stem sentence.

And we can see we've got three options here, haven't we, to choose from? So let's look at the first picture, the first representation.

So we can see there, we have got a set of pens and pencils, and remember, we can describe to help us to decide how to represent them.

So have a look at the options.

We can represent this as 4 plus 3.

We can represent this as 1 plus 5, or we can represent this as 5 plus 2.

So pause the video now while you have a try and decide which one to match that group to.

What did you think? So let's describe the two parts within the whole group.

So we've got, there's 4 pencils, aren't there? There are 4 pencils and there are 3 pens, we can represent this as? That's right, 4 plus 3, well done.

Let's look then at the next representation, the next picture.

So now we've got a set of spoons and forks there, haven't we, okay? So pause the video there now, and remember to describe the picture to help you, and then match it to the correct stem sentence.

So let's have a look.

So we can see, I'm going to look at the forks first, I think.

So 1, 2, 3, 4, 5 forks.

And if I had this on a piece of paper, I would draw a ring around those so I could clearly see those parts.

Okay, so there are 5 forks and there are 2 spoons.

So how did you represent that? That's right, we can represent this as 5 plus 2, can't we? Okay, and now let's look at the last picture, the last representation.

So have a think about that, how you will describe that whole group, and how you will describe the parts within it, okay? And then use that to help you find the correct stem sentence.

Pause the video now while you do that.

Okay, so what parts did you see? That's right, there are cups with straws and cups without straws, okay? so let's think about that.

So there is 1 cup with a straw, isn't there? And there are 1, 2, 3, 4, 5 cups without straws.

So we can represent that as 1 plus 5.

Excellent work, well done! So Sofia has six counters.

Some are red and some are blue.

Jacob wants to find out how many of each she has, and she gives him a clue.

She says, "I can represent it as 4 plus 2." Jacob thinks about the stem sentences to help him describe the counters.

He says, "There are 4 mm counters and 2 mm counters." We can represent this as 4 plus 2." So those are going to help him.

Could you make a group the same as Sofia's? Perhaps if you have some different coloured counters, you could use those stem sentences to help you.

So let's see how Jacob got on.

He said, There are 4 mm counters and 2 mm counters." So what possible options could there be? That's right, there could be 4 red counters and 2 blue counters.

And we can see the red counters there and the blue counters there.

And we can represent this as 4 plus 2, can't we? And there he's written it with numerals and the plus sign.

Now Sofia says, "That could be right, but that's not what my counters look like.

So I wonder what other option there could be." Jacob says, "I will have another try.

This time, he says, "There are 4 blue counters and 4 red counters." we can represent this as 4 plus 2 as well, can't we? And there he's written it using the numerals and the plus sign.

And then Sofia says, "Well done, now your counts look the same as mine." So he found it, didn't he? He tried the two possible ways and found the right way.

So your task for the first part of today's lesson is here.

So first of all, number one, share a box of two different coloured counters or cubes.

You must not use more than 10 counters in each turn, so don't get any more than 10 counters.

Jacob says, He's Partner 1, and he says, "I will make a whole group and use two different colours to show the two different parts." For example, and there you can see, he got a whole group of four there.

One part was red and one part was blue.

And then Sofia's there, she's Partner 2, and she says, "I will describe your parts using the stem sentences, then show you how I would write it." So, for example, with the counters that Jacob has there, she would describe it saying, "There are three red counters and one blue counter.

And then she would say, "I can represent this as 3 plus 1." Okay, so pause the video while you have a try at that.

Okay, so the second task in this first part of today's lesson is here, this time try this, and here's Jacob again.

And he's saying, "I will make a whole group, hide it, and then show how I can write it." So he's not showing Sofia group this time, he's going to make it and hide it from her.

And there he makes this group, and then he hides it.

But he writes down how he could represent it and that's to give Sofia a clue.

And then she says, "I will use the stem sentences to help me try to make a whole group with parts that look the same as yours." She knows she's got red and blue counters.

So she could say, "There is 1.

And then she could choose, couldn't she? There was 1 red counter and 2 blue counters.

I can represent this as 1 plus 2, or she might say it the other way round and say, "There is 1 blue counter and 2 red counters.

I can represent this as 1 plus 2." So pause the video now, while you try that with your partner.

Okay, and the third part of the task in today's lesson here is use numerals and the plus sign to describe each of these pictures.

So you've got some pictures that show a whole amount, but you can see two parts clearly within that amount.

So you've got to use numerals and the plus sign to write how you would represent each of those parts, okay? So pause the video now while you try that.

So let's see how you got on, on the Part 1 of our task.

So you may have done this.

Jacob says, "I made this group," and he's got a group of counters there, hasn't he? 5 counters in the whole group, okay? And then Sofia says, "I used the stem sentences to help me describe your group.

There are 3 red counters and 2 blue counters.

I can represent this as 3 plus 2." Well done, okay, so let's see how you got on with the second part of today's task.

So you may have done this, and there's Jacob saying, "I made a whole group with these two parts, and I hid it from my partner and represented it as 3 plus 4." So he made a group with 3 of 1 colour counter and 4 of another colour counter, didn't he? Okay, and then Sofia uses the stem sentences to help her.

She says, there are 3 mm counters and 4 mm counters." And she's going to use that to find out what Jacob's group looks like.

So she says, "There could be 3 red counters and 4 blue counters." So there we are, 3 red counters and 4 blue counters.

There could also be 4 red counters and 3 blue counters as well, couldn't it? That could also be represented by 3 plus 4.

And there we are.

And Jacob says, "Well done.

I had 3 red counters and 4 blue counters." So the first option she chose was the right one, wasn't it? She found Jacob's group, well done! So the third part of our task now today it says, "Use numerals and the plus sign to describe each of these pictures." Okay, so we can see, first of all, we've got two hands, haven't we? And we can see there are three fingers showing on one hand and there are four fingers showing on the other hand.

So we can represent this as, I wonder? That's right, 3 plus 4, well done! Okay, and then let's describe the beads to help us how to represent those.

So there are 4 red beads and there are 4 white beads.

So we can represent this as, 4 plus 4, that's right.

And then on the tens frame, let's have a look, there are 5 blue counters and there are 3 red counters.

We can represent this as 5 plus 3.

The apples, now, they're a bit more tricky, so you may have had to put a ring around those or mark them in some way to help you count them, and see the parts.

So let's have a look.

I'm going to look at the red apples first.

So we've got 1, 2, 3, 4, 5, 6 red apples.

So there are 6 red apples and there are 3 green apples.

So we can represent this as 6 plus 3, that's right.

And then this next one, oh, this is a bit more tricky because I can't see two parts in those cherry cakes.

So I can see 4 cherry cakes and then I can't see any other cakes.

So here we could say, "4 plus 0." We can represent this as 4 plus 0 'cause 4 is one part and there isn't another part, is there? So there's 0.

Okay, and then we've got here some cups with juice and some cups without juice.

And we've also got some cups with straws and cups without straws.

So there may be a few ways we can represent this, let's think how we may be able to represent it.

So first of all, we could think about, hmm, let's have a look.

4 plus 3, what would that represent? That's right, if you wrote 4 plus 3, you would be thinking about the 4 cups without straws.

The 4 represents the 4 cups without straws, and then you would be representing the 3 cups with straws, and that would be 4 plus 3.

How about if we look and see the cups with juice and the cups without juice? How would we represent that? So we can see there are 1, 2, 3, 4, 5 cups with juice, and 2 cups without juice, aren't there? So we could represent that as 5 plus 2.

Well done, excellent, you've worked really hard in the first part of today's lesson.

So now, let's go on to the next part of the lesson.

So we're going to partition wholes in many ways, just instead of separating them partitioning in one way, we'll look at a few different ways to partition a whole, and we'll still describe it using the plus sign.

So Jacob here, wants to partition this whole group into two parts.

Okay, so he is got a group there of apples.

How many apples has he got, do you think? That's right, it's 5 apples, isn't it? And Sofia says, "These all look the same, so I can't partition them into two parts." Is Sofia right? So Jacob says, "You can partition the whole group into two separate parts, you've got two plates there." I think he's going to partition them between the two plates.

So you could say, 1, 2 on that plate, and 1, 2, 3 on that plate.

And he's partitioned the whole group, hasn't he? And Jacob says, "How can I represent this?" I wonder how we would represent it? Remember, you can describe the parts to help you.

There are mm apples on Jacob's plate, and mm apples on Sofia's plate.

So that's right, there are 2 apples on Jacob's plate and there are 3 apples on Sofia's plate.

We can represent this as? That's right, 2 plus 3, 2 plus 3.

The 2 represents, that's right, the apples on Jacob's plate, the two apples on Jacob's plate, and the three represents the apples on Sofia's plate, the three apples on Sophia's plate, that's right, and the plus sign tells us that the parts will combine to make the whole.

Okay, so, Sofia wants to partition the apples in a different way and she says, "I will use counters to represent my apples." That's a good idea, isn't it? So she's going to use counters.

So you can see she's put one counter there for each apple.

And let's think about how she's going to partition it then, what does she do? So we can see she partitioned it into four in one group, and one in the other group.

So there are four counters in one group and one counter in the other group.

So how would she represent that, I wonder, how will she represent this? That's right, it will be 4 plus 1, wouldn't it? Let's have a look.

Or she's partitioned it a different way now, how would she represent this? That's right, she would write 3 plus 2, wouldn't she? And now she's partitioned it a different way.

How would that be represented? That's right, 2 plus 3.

And then how about this one here? That's right, 1 plus 4.

Jacob says, "He has also partitioned the whole group." Is he right? Let's see what Jacob does.

So he goes, "Hmm, there are no counters in one part and five counters in the other part.

We can represent this as zero plus five." So he has partitioned it, he's right, isn't he? 0 plus 5 Jacob has partitioned the whole group, and we know all of the counters have gone into one part, and so there's zero in the other part, isn't there? So now it's time to check your understanding again.

So show how you would write what you can see for each of the following, using the plus sign.

So you're going to use use numerals again and the plus sign, okay? And you've got three representations, three pictures to describe.

So pause the video now while you try that.

Okay, so let's have a look then.

That first one, let's describe to help us.

There are two counters in one group and no counters in the other group.

We can represent this as 2 plus 0, excellent! Now, let's look at the next picture.

So there are four beads in one part and one bead in the other part.

We can represent this as 4 plus 1, that's right.

And then let's look at the domino.

There are two spots on one side and five spots on the other side.

So we can represent this as 2 plus 5.

That's right, well done, excellent! So Sofia takes the same nine counters that Jacob had, and she partitions them in a different way.

She hides the counters from Jacob, so he can guess how she did it.

She says, "I will give you a clue.

I can represent it as 2 plus 7." So that's her clue that she's given him.

and he says, "I wonder what each number represents." So he is going to think about what that two represents and what that seven represents.

So 2 plus 7, "The number 2 must represent the counters in one group." Did you think that? That's right, so there's 2.

And so what will the 7 represent then? "The number seven must represent the counters in the other group." That's right, excellent.

And then the plus sign shows that the parts combined to make the whole.

So now it's time to check your understanding again, which of the following represents 4 plus 2? Okay, so remember, describe the parts to help you, okay? And then you can think about what the numbers represent to check that you're right.

So pause the video now while you try that.

Okay, so how did we get on? So let's have a look at the first picture.

So there are four counters in one group, in one part, and four counters in the other part.

So would we represent that as 4 plus 2? No, we wouldn't, would we? So let's have a look at the Picture B here.

So there are two counters in one part and two counters in another part, and two counts in another part, and two counts in another part.

So we can see, we've actually got four parts there, haven't we? Okay, so we'd have to write four numeral for that, so that can't be right.

So let's have a look at this last example.

Okay, so there are four counters in one part, and there are two counters in the other part.

We can represent this as? That's right, 4 plus 2, excellent! The four represents the four counters in the first part, and the two represents the four counters in the second part.

Jacob and Sofia want to partition this group of pebbles, oh, so we can see a group of pebbles there.

You might be able to collect some pebbles to help you to try something like this.

So Sofia says, "I think I can write it as 2 plus 5." And Jacob says, "I think I can write it as 3 plus 4".

Who do you think is right? Describe the parts to prove it.

So let's look at what Jacob did, first of all.

Jacob noticed dark stones and light stones.

So he partitioned them into two parts.

You can see the two parts there, can't you? There are mm, dark stones and mm light stones.

That's right, there are 3 dark stones and 4 light stones.

I wonder how we'll represent that.

We can write this as 3 plus 4.

That's right, 3 plus 4.

So what does the 3 represent? That's right, the 3 represents those 3 dark stones, doesn't it? What does the 4 represent? The 4 represents the 4 light stones.

So there's Jacob saying, "He was right, he's proved he was right because he said what the numbers represent." Well done! Let's look at what Sophia did then.

So she noticed small stones and large stones, so she partitioned the same whole group, but in a different way.

She partitioned them into the two parts there, didn't she? Small stones and large stones.

So we can see, there are mm small stones and mm large stones.

So that's right, there are 5 small stones and 2 large stones.

We can represent this as? That's right, 5 plus 2, 5 plus 2.

And then Sofia can prove she's right because she can say, "What does the 5 represent?" The 5 represents the 5 small stones.

What does the 2 represent? That's right, the 2 represents the 2 large stones.

So there's Sofia saying, "She was right," so it was partitioned in a different way, the whole group of pebbles or stones, and it was represented as 5 plus 2.

So well done, if you notice that.

So now it's time to check your understanding again, which pictures can be represented by 6 plus 3? Okay, so pause the video now while you try that.

Okay, so let's have a look.

Let's describe the pictures to help us.

Let's describe the parts, so we can see there, can't we? The first picture, we can see there are 6 chocolate cakes and there are 3 cherry cakes.

We can represent this as 6 plus 3.

Yeah, that's right.

And then let's have a look at the next picture.

So we've got, there are 3 green apples and 3 red apples.

So we were would represent that as, that will be 3 plus 3, so it's not that one, is it? And then we've got, oh, let's have a look at the pebbles, we've got 1, 2, 3, 4, 5, 6 small pebbles and 3 large pebbles.

So we can also represent that as 6 plus 3, can't we? So well done, if you've got that, there were two pictures there that would represent 6 plus 3, wouldn't they? Okay, so here's this task for the second part of today's lesson.

Collect a group of six objects such as cubes or counters.

And there's Sofia, she's saying, "I will partition the whole into two groups in as many ways as I can.

Each time, I will use numerals and the plus sign to represent the parts." Okay, and you've got to think about why you're doing this, how do you know you found all the possibilities? So think about the way you'll work, to help you find all the different ways of partitioning.

And we've got an example here.

So for example, you could partition like that, and put two into one part and four into another part, couldn't you? And then you would represent it as 2 plus 4.

There we are, okay? So pause the video now while you try that.

So, here are all the possible ways you can partition 6 counters.

So we've got the 6 counters there, look, okay? And Sofia could have gone, or you could have gone, 0 plus 6, couldn't she? So she could have 0 in one part and then she could have 6 counters, all of the counters in the other part.

Then she could say, "1 plus 5," couldn't she? Then she could say, "2 plus 4." Hmm, do we notice anything about the way she's worked here? So what would come after 2 plus 4? So she had 1 plus 5, 2 plus 4, 3 plus 3, that's right.

And then what do we think may be next? 4 plus 2, 5 plus 1, and then 6 plus 0.

So each time she moved a counter from one set into the other set, didn't she? And so we could see, that she did it systematically.

So she knew she'd found all the possibilities.

She said, "I work systematically, so I know there's no more possibilities." So she worked in a certain order to help her, didn't she? So well done if you did that as well, excellent! You've worked really hard today, haven't you? So let's think about what we've learned in today's lesson then.

So first of all, when a whole amount is partitioned into parts, it can be represented using the addition symbol, the plus sign, can't it? And the plus sign shows that the parts combine to make the whole.

We can describe the parts to help us understand how to represent them.

And a whole group can be partitioned into different ways, can't it? Okay, so sometimes you can clearly see the parts and partition that way, but you can also find different ways to partition.

So you've worked so hard today, and you should be feeling much more confident now, about partitioning the whole into parts, and knowing how to represent how you combine them back to make the whole using that plus sign.

So excellent, well done! You've worked so hard, I've really enjoyed today's lesson.