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 in today's lesson we're going to be learning about the equal sign and by the end of the lesson you should be able to understand how it is used within equations to show how the wholes or the sum and the addends are equal.

Okay, and you should feel really confident with that by the end of today's lesson.

So let's get started.

So let's look at the keywords for today, our important words for our learning.

So is equal to, my turn, is equal to your turn.

Okay, then we've got equals symbol and there is an equal symbol there, isn't there? So my turn, equal symbol, your turn.

Then equation, my turn equation, your turn.

And then sum, my turn sum, your turn.

Well done.

So in the first part of our lesson today, we are going to think about the use and learn to understand the use of the equal sign in an equation.

Okay, and then we'll move on to moving part-part-whole models to represent equations.

In this lesson you'll meet Jacob and also Sophia, they will help us with our learning today.

So Jacob and Sophia have some cakes.

They partition the whole group into two parts, chocolate cakes and cherry cakes.

So where we can see what they're going to partition them, split them into chocolate cakes and cherry cakes.

Sophia says the parts together and the whole are the same.

Do you agree? The whole group is equal to the two parts, isn't it? And if we look here, we can see the whole group has been split into the two parts and then the two parts are equal to the whole group.

And there we can see they're being combined again, haven't they? When two groups are equal, we use this sign, okay? And Sophia says I can use this to show the parts and the whole are the same as each other.

There we go.

This symbol means equal to, and we can see two is equal to two And we can write it like that, can't we? And that just shows that two is the same as two isn't it? They're equal to each other.

The whole group is equal to the two parts.

So we've got the whole group there and it is equal to the two parts there.

The two parts are equal to the whole group.

So there's the two parts and they are equal to the whole group and we can see that is equal to sign symbol showing that both sides are the same, they represent the same amount.

So that's what Sophia is telling us there.

The equal sign shows that they're both the same.

We can represent this as an equation.

So nine is equal to five plus four.

Okay, and that's called an equation when you see the numbers like that.

We can also say five plus four is equal to nine.

What do you notice about the two equations? What's the same and what's different? That's right, they have the same numbers.

So that's the same but written in a different order.

That's different isn't it? That's right.

So you can see that they all have a nine and they all have a five and a four, but they're not written in the same order.

This equation, nine is equal to five plus four, shows that the whole group is equal to the two addends.

This equation five plus four is equal to nine, shows that the two addends are equal to the whole group.

And there we can see it with the pictures, can't we? You can see how the whole is equal to the two parts.

The two parts are equal to the whole.

What does a nine represent? That's right, the nine represents the whole group of cakes.

So wherever it's written in the equation, it still represents that whole group, doesn't it? What does a five represent? That's right, the five represents a five chocolate cakes doesn't it? And what does the four represent? The four represents a four cherry cakes, excellent.

So remember we can write the addends in any order.

Okay, so we can see nine is equal to five plus four, five plus four is equal to nine.

We can see we can swap the wholes in the parts over, but then Sophia says, "That means I can write different equations." Because she's going to think about swapping the order of the addends.

So there we are, we've got nine is equal to five plus four, but we can see now we've moved the chocolate cakes over and rearranged them.

So now how will the equation change? That's right, it will become four plus five because now instead of representing the chocolate cakes first, we are representing the cherry cakes first.

How will the second equation change then? So we've got five plus four is equal to nine, that's right.

It will change to four plus five is equal to nine, because this time you're putting the cherry cakes representing them first, aren't you? What does a nine represent then in these equations? The nines still represents a whole group of cakes.

So wherever it is written, it is representing the same thing in this equation, isn't it? The same, it's representing the whole group of cakes.

What does the four represent? That's right, the four still represent the four cherry cakes.

And what does the five represent? That's right, the five still represents the five chocolate cakes.

So you can rearrange an equation as long as both sides of the equation remain equal.

That's really important, isn't it? Each number in an equation has a name.

We know when adding each part is called an addend.

So we've got five plus four, and five and four are the addends.

Five is an addend, four is an addend.

When adding the whole has a name, the whole is called the sum.

And there we have it.

So nine is the sum in this equation.

The sum is equal to the two addends, isn't it? Sophia partitions these cups into two groups and then combines them again.

So we can see two clear parts in those cups, can't we in that whole group? So there, how was the group partitioned? That's right, the whole group was partitioned into two parts, wasn't it? Cups with straws and cups without straws.

She writes four equations to represent this.

What is the sum in each of these equations? So let's look at what she writes and then you've got to think, how do you know? How do you know that the number represents a sum in each equation? So we've got five is equal to two plus three.

So what's the sum in that equation? That's right, five is the sum because it represents the whole group of cups, doesn't it? Well done and it is equal, you can see to the two addends.

What about this equation then? What's the sum here? That's right, it's still five, isn't it? Five is still equal the two, the two addends and it represents the whole group, just being written in a different place.

The other side of the equals sign.

What about here then? That's right, five is still the sum, isn't it? Because it still represents the whole group of cups and it is still equal to the two addends.

And what about this one, three plus two is equal to five? That's right, you've got it.

Five is still equal to the sum.

It's still the sum isn't it? Five, it represents a sum because it is equal to the two addends isn't it? It represents the whole group when those two addends are put together.

The sum is the whole group, it is equal to the two addends.

So now it's time to check your understanding.

So what is a sum in these equations and explain how you know.

So we've got two equations, we've got seven is equal to six plus one, and we've got six plus one is equal to seven.

Okay, so pause your video and you've got to decide what the sum is.

Is it six, or is it seven, or is it one? Pause your video now while you try that.

Okay, so let's do it together then, let's try it together.

So we've got seven is equal to six plus one.

So we know the sum is equal to the addends, isn't it? Okay, so the addends are six plus one.

Okay, in both equations.

So the sum must be seven.

Seven is the sum because it is equal to the two addends in both equations, isn't it? Jacob writes an expression to represent the addends in this picture.

Okay, I wonder what they are.

What expression could he write? That's right, there are four empty cups, aren't there? So we can write four to represent the four empty cups plus two because there are two cups with juice.

So he could also have written two plus four, couldn't he? Because instead of looking at the empty cups first, he could have represented the cups with juice first, couldn't he? Then he writes the sum.

What will he write, do you think for the sum? Remember when adding the whole is called the sum, isn't it? So that's what you are thinking about.

That's right, six is the whole group.

So six is the sum and it's equal to the two addends, isn't it? So when adding the two addends are equal to the sum and we can see there we've got an equal sign which is going to show us that whatever we write on each side of it are equal.

So let's arrange the addends and the sum to make four equations.

So we've got the addends, two plus four and also we've got them written in a different order, four plus two and we've got the sum six.

So let's think about how we can arrange them.

Remember in an equation, both sides must remain equal to each other.

So we could put six there, couldn't we? We could start with six there.

And what will six be equal to? So six is a sum, that's right is equal to the two addends.

So we could write six is equal to four plus two.

We could also write six is equal to two plus four.

That's right.

Okay, 'cause it doesn't matter which way around you write those addends.

I wonder how else we could write the equation.

That's right, you could start with the addends, couldn't you? You could say four plus two is equal to six, or you could say two plus four is also equal to six, couldn't you? Well done, so now let's think about what each number represents.

The six represents the whole group of six cups.

That's right.

The four represents the four empty cups and the two represents the two cups with juice.

That's right, well done.

So although the equations have been rearranged, each number still represents the same part of the picture.

So Jacob writes an equation to represent this picture.

What mistake has been made? So he has written two is equal to three plus five.

What is his mistake? He says, "I will think about what each number represents to help me." That's a good idea, isn't it? So let's think about that.

The two represents the two cups with straws.

The three represents the three cups without straws and the five represents a whole group.

It is the sum, isn't it? It is equal to the two addends.

Five is the sum.

So Jacob should write, five is equal to two plus three, that's right.

So now it's time to check your understanding.

So rearrange this equation so that both sides remain equal and tick the correct equation.

So five is equal to two plus three.

So which of those if you rearranged it would still be equal? So would represent the same.

Okay, so pause the video while you try that.

Okay, so let's have a look.

So we've got five, sum is equal to the two addends two plus three.

Okay, so which one of those do you think could represent the same? That's right, we've got the same addends, haven't we? Two plus three, and we've got the same sum five and we can see they've just been swapped around, so they're on the other side of the equal sign, but they're still equal, well done.

There are four pens and three pencils shown here.

I can represent this as four plus three or three plus four.

These are the addends and there we are four plus three or three plus four.

The whole group has seven things we can write with.

This is the sum.

So seven is the sum, the addends are equal to the sum and the sum is equal to the addends, isn't it? Let's use the addends and the sum to write four different equations to represent this picture then.

Okay, so we can see we've got the addends there, four plus three and we've also rearranged it, swapped it round three plus four and we've got the sum seven.

And we know the addends have to be equal to the sum, don't they? Okay, so let's think about how we would represent this in an equation.

We could have four plus three, we could pick that one first, couldn't we? And we could say it is equal to.

That's right, four plus three are the parts, the addends.

So they're equal to the whole group of seven.

Seven is a sum.

What else could we have? Could we swap those addends around? That's right, we could say three plus four is also equal to seven.

Could we write another two equations? I wonder, could we start with a different number this time? That's right, we could start with seven, couldn't we? And say seven is equal to four plus three, couldn't we? And we could also say seven is equal to three plus four.

Excellent, well done.

So now we're going to check your understanding again, write the addends and the sum to represent this picture first of all.

So pause the video while you do that.

Okay, so what did you write? Let's see.

So four plus one are the addends or you could have one plus four, are the addends.

You could rearrange them and the sum would be, that's right, five.

Okay, so now the second part of your check is to use those addends and the sum to write four different equations to represent this picture.

And remember both sides of the equation must be equal.

Okay, so pause the video now while you try that.

Okay, so let's see how we did.

Which did you decide to write first to represent first the addends or the sum? Let's see.

So I think I'll start with four plus one is equal to, so the two addends are equal to the sum.

So it must be five, that's right.

Could we have written that a different way? We could swap it round.

Change the order of the addends, couldn't we? And we could say one plus four is equal to five.

How else could we write it? We could write five is equal to one plus four, couldn't we? Or we could also say five is equal to four plus one.

Excellent, well done if you've got those.

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

First write the addends and the sum for each picture.

So like we did in the check, then use them to write four equations for each one.

So before you write the equations, write what the addends are, okay with a plus sign and write your sum for each picture and then you can rearrange those to write the equations.

So pause the video now while you try that.

Okay, and let's see how you got on with that.

Okay, so let's look at the addends here.

So we've got four plus two, 'cause we've got four chocolate cakes and two cherry cakes.

Or you could also represent it as two plus four.

And the sum, the whole amount is six, that's right.

So we could write four plus two is equal to six.

That's right.

We could write two plus four is equal to six.

We could write six is equal to four plus two.

And what's the last one? We could write six is equal to two plus four as well.

Well done.

Okay, so what are the addends and the sum for this next picture? That's right, we've got five plus three or three plus five.

And the sum, the whole group is eight.

Okay, so how would we write that? We could say five plus three is equal to eight.

We could say three plus five is equal to eight.

And then we could put the sum first, couldn't we? Because the whole is equal to the part.

So we've got, we could say eight is equal to five plus three and eight is also equal to three plus five, excellent.

With the cups we've got two plus three or we've got three plus two.

Okay, and the sum that's right is five.

So we could represent it as two plus three is equal to five.

We could swap the addends around and say three plus two is equal to five.

And then we could start with the whole group.

The sum, couldn't we, we could say five is equal to two plus three or five is equal to three plus two, excellent.

And then the last one we've got four plus three, 'cause we can see four red apples and three green apples and we can swap it round as well and have three plus four.

And we've got the seven in the whole group.

Seven is the sum.

Okay, so we've got, we could say four plus three is equal to seven.

We could say three plus four is equal to seven.

We could say seven is equal to four plus three.

And finally, seven is equal to three plus four.

Well done, excellent.

And you've worked really hard.

So in the second part of today's lesson, we're going to use part-part whole models to represent equations.

So Jacob has a pot of pebbles there and he sorts them between two pots like this.

What number would represent the whole amount do you think? And what numbers would represent the parts? Six is the whole, two is a part, and four is a part.

And we know six is a whole because when you combine the addends two and four, then they would combine to make six as the whole group wouldn't they? Sophia sorts 'em in a different way.

She sorts 'em like that.

What number would represent the whole amount now and what numbers would represent the parts? So is hmm the whole, hmm is a part and hmm is a part? Well we can see the parts there, can't we? So we could have one is a part, and five is a part.

So what would the whole group be? That's right, we would combine the addends to make the sum, wouldn't we? So we would have one and five.

So we know six would be the whole.

Six is the whole, one is a part, and five is a part.

What equations could Sophia write to represent this? So we've got six partitioning into one and five there.

So we could write six is equal to one, add one plus five or you can say add, can't you? Okay, oh, now she swapped them around there.

So how would we write that one? We could also say six is equal to five plus one, couldn't we? And there we have got one plus five and they are going to combine to make six, aren't they? One plus five is equal to six.

And then we've got swapped around five plus one is equal to six, well done.

The whole is equal to the two parts isn't it? Or the sum is equal to the addends.

The two parts are equal to the whole.

Okay, so here's Jacob's pots and he says, "This reminds me of something." Sophia says, "It makes me think of a part-part-whole model." It does look like one, doesn't it? Jacob decides to use a part-part-whole model to help him represent this group.

So he is got some hot drinks and some cold drinks in the whole group hasn't he? Where should you put the whole group, do you think? That's right, it goes in the top there because that's a part that's been partitioned isn't it? The whole group.

He partitions a group, where should he put the two parts? That's right.

And the whole group has been split, hasn't it? Is there a different way he could have represented them, do you think? Could he have arrange them differently? That's right, the parts can be partitioned in any order, can't they? So they could be swapped around.

What numbers could Jacob write in the part-part-whole model to represent the cups? So he could write seven, couldn't he? To represent the whole group and then four to represent the four in that part, the first part and three to represent the three in the other part.

Can any of the numbers be arrangement there do you think? When they're written as numerals like that? That's right.

The four and the three are the addends, they can be written in any order so we can swap them over, can't we? What does the seven represent? The seven represents a whole group of drinks, doesn't it? It's the sum in an equation.

What does the three represent? The three represents the three cold drinks, doesn't it? There were three cold drinks.

And what does the four represent? The four represents the four hot drinks, doesn't it? That's right.

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

So Sophia has this group of objects, okay, we can see she's got some pebbles or stones, hasn't she? Okay, which number would she use to represent the whole group? So you need to think about that and you need to think about which numbers she would use to represent the parts of the whole, okay? And then you need to record the numbers in the correct place on the part-part-whole model.

Okay, so perhaps you could draw your own or you may have one that you can fill in, okay? And you can explain to your partner which numbers you've used and why you've put them where you have.

So pause the video now while you try that.

Okay, so let's see how we got on with that then.

So let's see, think about which number we would use to represent the whole group.

That's right, it will be nine and it will go in the top there because that's a ball group, isn't it? What about the parts then? So you may have written a five and a four.

A five to represent the five dark stones and four to represent the four light stones.

Could any of the numbers be rearranged? That's right, you may have also written it like this and put the four and the five the other way round because we know the addends can be written in any order.

They represent the same parts of the whole, don't they? Well done, excellent.

Sophia draws this part-part-whole model to represent these equations.

So she's got these equations, one plus five is equal to six, five plus one is equal to six.

And she's also got six is equal to one plus five, and six is equal to five plus one.

So let's think about where she should write the sum in that part-whole model, which part of the equation is the sum? So it will go in the top there because six is the sum, isn't it? The sum represents the whole amount.

Where should she write the two addends then? She would write them in those bottom parts there, wouldn't she? The addends represent the two parts within the whole, right? You could have also written the one and the five the other way round because the addends can be written in any order and they're still equal to the sum, aren't they? Right, so now we're going to check your understanding again.

So repeat the same sentences to help you write the equations.

So we've got, hmm, it's equal to hmm, plus hmm.

Okay, pause the video and the part-whole model's there.

And it's got the numbers in to help you, hasn't it? So you can see the parts and the whole.

So off you go.

Okay, so let's have a think then.

So we could have, five is equal to two plus three, couldn't you? Or you could have also had five is equal to three plus two.

You could have swapped the order of the addends around.

Okay, so now there's another same sentence, and this time we've got hmm, plus hmm, is equal to hmm.

Okay, so pause the video and see if you can write two equations using that same sentence to help you.

And let's do that together now.

So, hmm, plus hmm, is equal to hmm.

We could have had two plus three is equal to five.

You could have had three plus two is equal to five.

So well done if you wrote those.

So now we've got to think about hmm and hmm at the addends and hmm is the sum.

So pause the video now while you think about that.

Okay, to complete those same sentences, remember you can use the part-part- whole model to help you.

What were the addends then? That's right, two and three are the addends, and five is the sum, well done.

Okay, so here's our next task.

So the first part of the task is match each part-part-whole model to the correct picture.

Okay, and can you draw a different part-part-whole models for each picture.

So you've got some pictures there, okay? And you need to match them to the part-part-whole models, or you might do it the other way around and match the part-part-whole models to the picture, okay? Thinking about what's the whole group, how many are in the whole group, and what are the parts, okay? And then when you've done that, you may draw a different part-part-whole model, thinking about what we know about the order of the addends.

And then the second part of our task today is to draw a part-part-whole model for each picture from task A.

So if you go back to the first task that we did in the first part of the lesson, you could draw a part-part-whole model to represent those pictures as well.

So pause the video while you try that.

Okay, so let's see how we got on now then.

So first of all, let's have a look and we can see that we've got the cars and they would match to that part-part-whole model there because we can see there are five in the whole group.

And we can see that the three represents the three small cars and the two represents the two large cars, doesn't it? Okay, and you may have written the part-part-whole model the other way around with the two and the three in a different order as well when you drew another part-part-whole model for the picture.

Okay, then let's look at the next one then.

So we've got the forks and the spoons, and we can see that in the whole group of cutlery.

We've got seven and then we have got two, which represents the two forks and five which represents the five spoons.

And when you did another drew another part-part-whole model for each picture, you could have swapped the five and the two, the addends around and written those the other way round, right? Okay, let's look at the cups and the juice now.

So we've got three is the whole, and we can see we've got a group of three cups there and then we've got three is a part and we've got zero is a part, isn't it? And we can see that we have got three cups, but then we have got no other part there, have we? So the three cups would be in one part and the zero would be in another part.

And when you drew a different part-part-whole model for that picture, then you could swap the zero and the three around, couldn't you? And finally got the pens and the pencils.

We can see that we've got four pens.

So the four represents the four pens, that's one of the parts, one of the addends and three represents the three pencils, that's the other addend.

And the whole group is seven.

That's right.

And then you could swap that around when you drew a different part-part-whole model.

And you could swap the order and put the three and the four the other way around, couldn't you? Okay, well done.

And then the second part of the task where you had to draw a part-part-whole model for each picture from task A.

So if we have a look here, there's our first picture from task A, and we could write, we know there's six in the whole group, four is a part and two is a part, isn't it? That's right, and then we can see here, you can also swap it around and swap those addends and put two and four in the other order.

That's right.

Okay, and then we can see here we've got eight as a whole group, five is a part and three is a part.

And we could have also represented the three oranges first, couldn't we? And then the five apples.

We can see here we've got five is the whole group, two is a part, and three is a part.

And we can think about the two represents the two purple cups.

We represented those first and the three represents the three clear cups, but we could swap those around, couldn't we? Rearrange the order and represent the three clear cups first? And then finally we've got seven in the whole group.

And we can see that the four represents the four red apples and the three represent the three green apples.

So those are the two addends, but we can rearrange those, can't we? You could have represented the three green apples first and then the four red apples.

So well done.

You worked really hard with that.

Okay, so let's see what we found out in today's lesson then.

So we found out we can write an equation to show that the whole is equal to the sum of its part.

So the whole is equal to the parts, isn't it? Okay, the equal sign represents is equal to, and it shows us which parts of the equation are equal to each other.

When adding the whole is called the sum.

The sum is equal to the two addends, isn't it? And the two addends are equal to the sum.

And you can rearrange an equation as long as both sides of the equation remain equal.

And that's really important, isn't it? And we've seen how we can do that.

So well done, you should know lots more now about representing addends and showing how they're equal to the sum, and how the sums equal to the addend.

So well done, I've really enjoyed working with you today.