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 "Understanding Part-Part-Whole Relationships", and it comes from the unit "Additive Structures: Addition and Subtraction".

So in today's lesson, we're going to look at the relationships between equations, part-part-whole models and the problems that they represent.

So by the end of today's lesson, you should feel much more confident representing problems by writing equations and also by looking at equations and being able to think about the problems that they represent.

Okay, so let's get started.

So our keywords for today are equation, my turn, equation, your turn and part-part-whole model, my turn, part-part-whole model, your turn.

Okay, well done.

So in the first part of today's lesson, we're going to explore the relationships in equations.

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

They will help us with our learning today.

So Jacob has five chocolates.

He arranges them between the two plates like this.

Let's see what he does.

He drew a part-part-whole model to show what he had done.

So there's his part-part-whole model and he puts in the numbers like that, doesn't he? So complete the stem sentences, mm is the whole, mm is a part and is mm a part.

That's right.

Five is the whole, two is a part and three is a part.

What does the five represent? That's right.

The five represents a whole group of five chocolates, doesn't it, that has been partitioned.

What does the two represent? That's right, the two represents the two chocolates on one plate, doesn't it, on that first plate.

And what does the three represent? That's right, the three represents the three chocolates on the other plate.

Well done.

So, complete the stem sentences.

Mm is equal to mm plus mm.

And then we're also going to complete this stem sentence, mm plus mm is equal to mm.

Okay, and we've got a part-part-whole model and the picture there to help us.

So that's right, we can say five is equal to two plus three, and we can also say two plus three is equal to five.

That's right.

Write some equations to represent this.

Okay, so we know the wholes and the parts, so we could say five is equal to two plus three, and we could also say five is equal to three plus two.

And we could say two plus three is equal to five and three plus two is equal to five.

So mm and mm at the addends, what were the addends in that, those equations? That's right, two and three are the addends.

And what was the sum? That's right.

Five was the sum, wasn't it? Because that's the whole amount.

Well done, that's excellent.

Jacob partitions in a different way.

Think about the wholes and the parts.

So you could draw a part-part-whole model like that.

Mm is the whole, mm is a part and mm is a part.

That's right, so the whole group is five, isn't it? And it's been partitioned.

So we've got five is a whole, four is a part and one is a part, and there it is on the part-part-whole model.

Sofia says when the chocolates are partitioned, there cannot be more than four chocolates on one plate.

Is she right? Let's see.

So she's partitioning the chocolates there.

Oh, that looks like more than four on one plate.

She put the whole group on, and she's also put them on the other plate, so she is not right.

All five chocolates could be put on the same plate, couldn't they? And there would be no chocolates, zero chocolates on the other plate.

So how could we write four equations to represent that, then? So let's think about the whole amount and the parts.

So we could say zero plus five is equal to five and five plus zero is equal to five.

That's what the plates are showing us.

And we could also say five is equal to zero plus five and five is equal to five plus zero.

So now it's time to check your understanding.

Which part-part-whole model represents the picture? So there's three part-part-whole models, so pause the video now while you choose the one that represents that picture.

Okay, so let's have a look.

So we know that we have got four chocolates on one plate and one chocolate on the other plate.

So those are the parts.

And what is the whole amount? That's right, it's five.

So it will be that part-part-whole model there.

Five is the whole, four is a part and one is a part.

Sofia wants to represent each of these equations with counters on a part-part-whole model.

Okay, she's got a stem sentence there to help her, hasn't she? Mm is a sum, mm is an addend and mm is an addend.

Use counters to show how you would represent each equation.

So we've got nine is equal to three plus six.

So there's nine counters.

Where would you put them? Because that's the whole amount.

Nine is the sum, isn't it? And then we can see that three is an addend and six is an addend.

That's right, that represents a whole amount.

And then we could say nine is equal to three plus six.

It's being partitioned.

What about nine is equal to six plus three, how could we show that? So let's use our stem sentence.

Nine is a sum, six is an addend and three is an addend.

So we would have nine there in our whole amount and we'd partition it into it's equal to six plus three.

Well done.

So now we've got six plus three is equal to nine, haven't we? Okay, so the stem sentence is swapped around slightly.

Mm is an addend and mm is an addend, mm is the sum.

So there's our nine counters and we can see six is an addend, three is an addend, and nine is the sum.

So in our part-part-whole model, we would have six is an addend, three is an addend and they combine to make the sum.

Six plus three is equal to nine.

And we could also have three plus six is equal to nine.

So let's do, use our stem sentence again.

Three is an addend and six is an addend, nine is a sum, so it will be three plus six is equal to nine.

Well done.

So there are four cats.

Some cats are sitting on the red cushion and some are sitting on the white cushion.

How many cats could be on each cushion? And Sofia says you could use counters to represent the cats to help us with that, couldn't you? So draw a part-part-whole model to show what you think and describe what each part represents, then write four equations to represent it.

So how many cats could be on each cushion, so you could partition them like this.

Let's look at the different possibilities.

You could have one on the red cushion.

There are, there is one cat on the red cushion and there are three cats on the white cushion.

How could you represent this on a part-part-whole model? That's right, four was the whole, the four represents a whole group of four cats.

One is a part and three is a part.

The one represents the one cat on the red cushion.

The three represents the three cats on the white cushion.

You can write these equations to show the story.

Four is equal to one plus three, four is equal to three plus one, one plus three is equal to four, and the last one, three plus one is equal to four.

Excellent, let's have a look at another possibility.

So we could have partitioned like this.

We could go there are two cats on the red cushion and there are two cats on the white cushion.

How could you represent this on a part-part-whole model? There's our part-part-whole model.

That's right, we've got four.

The four represents a whole group of four cats that's been partitioned, doesn't it? And then we've got two, two is a part.

The two represents the two cats on the red cushion and two is a part.

The other two represents the two cats on the white cushion.

How many equations can you write for this story and why? I wonder if we'll get the same amount of equations.

So we've got four is equal to two plus two.

Can we swap the addends around on that equation? No, we can't, can we? Because they're both two, so we would just end up with the same equation again, wouldn't we? So we can only have that one when we partition the four and then we can have two plus two is equal to four.

So we only get two equations for that because the two addends are both the same number.

Okay, let's have another, a look at another possibility here.

So you may have said that there are three cats on the red cushion and one cat on the white cushion.

How could you represent this on a part-part-whole model? Okay, so what would the whole amount be? That's right, it will be four.

And then the four represents a whole group of cats, of four cats.

And then there's three is a part.

The three represents the three cats on the red cushion and one is a part.

The one represents the one cat on the white cushion.

You can write these equations to show the stories.

I wonder what equations we can write.

That's right, you can have four is equal to three plus one.

Four is equal to one plus three.

Three plus one is equal to four and one plus three is equal to four.

Excellent.

Jacob and Sofia both draw a part-part-whole model to represent this possibility.

Who is right? So we can see there are four cats on the red cushion and no cats on the white cushion.

Okay, so whose part-part-whole model is right? So we can see there Jacob has put zero in the whole amount.

That would mean there was zero cats altogether.

So that can't be right, can it? And then he's partitioned the zero into zero and four.

The whole has to be larger than the parts as together, the parts make the whole.

So Jacob cannot be right, can he? Because zero plus four will not combine to be equal to zero.

And there's Sofia's part-part-whole model.

Could hers be right, do you think? That's right.

It doesn't matter how a part-part-whole model is drawn as long as together the parts make the whole and the whole splits into the parts.

So Sofia is right, isn't she? We can see that the four, it's been written in a different way.

It's been arranged in a different way, but we can see the four is still the whole and the zero and the four are still the parts.

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

Which part-part-whole model is incorrect? Explain how you know.

Okay, so pause the video now while you have a think about that.

So what did we think? Look carefully at the part-part-whole models.

So we can see the first one has four as the whole.

two is a part and six is a part.

Can that be right? No, that's the one that's incorrect, isn't it? Because four is the whole, and so it has to be equal to two and six when they're combined, doesn't it? Okay, and we can see that six is larger than four.

Okay, so six can't be a part of four.

Four is smaller than six, so when six and two are combined, the whole amount cannot be four.

Let's look at each of the part-part-whole models and complete the stem sentences together.

So these are the part-part-whole models and equations that we use to represent the cats on the cushion.

So the stem sentences are mm is the whole, mm is a part and mm is a part.

And then we've got mm is an addend, mm is an addend, mm is a sum.

So let's look at the first part-part-whole model.

That's right, four is a whole, one is a part and three is a part.

And then what are the addends and the sum? One is an addend, three is an addend, four is the sum.

Excellent.

Okay, and then looks, let's look at this part-part-whole model.

What do we think? That's right, four is the whole, two is a part and two is a part.

And then two is an addend, two is an addend, four is the sum.

And finally, let's look at this part-part-whole model.

What do we think? That's right, four is the whole, three is a part and one is a part.

Three is an addend, one is an addend and four is the sum.

Excellent.

So now here's a task for the first part of today's lesson.

So you must use a set of six counters.

We can see them there.

And Jacob's telling us what to do, so I will partition the whole group of six counters on my part-part-whole model, then draw it, writing in the numbers to represent the parts and the whole.

I will use my stem sentences to help me write four equations to represent my part-part-whole model, okay? And then when you've done this, partition your counters in a different way and repeat.

How many ways can you find? So pause the video now while you try that.

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

You may have done this.

So six counters in the whole, and you may have partitioned it like that.

Six is equal to five plus one.

You may have also said six is equal to one plus five.

You could have said five plus one is equal to six or you may have said one plus five is equal to six.

So well done.

You may have also used counters to show these equations.

So you could have said it's six is equal to two plus four, six is equal to four plus two, two plus four is equal to six and four plus two is equal to six.

And you could have said six is equal to three plus three.

So three plus three is equal to six.

So, well done.

You've worked really hard in this first part of today's lesson, haven't you? So the second part of today's lesson is called make links between equations and problems. Sofia is playing with seven toy cars.

She wonders how many different ways she can split them between the garage and the car park.

"I will use double-sided counters to represent the cars," she says.

So there are some double-sided counters.

She uses the yellow side of the counters to represent the cars in the garage and the red side of the counters to represent the cars in the car park.

So there's the yellow ones, represent the cars in the garage and the red ones represent the cars in the car park.

What story did these counters represent, then? There are three yellow counters and four red counters.

The three yellow counters represent the three cars in the garage.

The four red counters represent the four cars in the car park.

Jacob says, "There are only two numbers, so this cannot be represented on a part-part-whole model." Is he right? Sofia reminds him, "You must remember to think about the whole amount." So he's looked at the counters, but he's only looked at the parts.

He hasn't thought about the whole, has he? So, mm is the whole, three is a part and four is a part.

That's right, so seven will be the whole amount, won't it? Because we know the addends, three plus four are equal to seven.

Tell the story to explain what these counters represent.

So there are seven counters.

There are two yellow counters and five red counters.

So we know what the red counters represent, don't we? And we know what the yellow counters represent.

That can help us to tell a story.

The two yellow counters represent the two cars in the garage.

The five red counters represent the five cars in the car park.

The whole group of seven counters represents how many cars there are altogether.

Draw a part-part-whole model to represent this.

Use your stem sentence to help you then tell the story.

So we have got our part-part-whole model there.

Seven is a whole, five is a part and two is a part.

Or you could have said two is a part and five is a part.

Write four equations to represent this.

Explain what each number represents from your story.

So we could say seven is equal to five plus two, seven is equal to two plus five.

We could also say five plus two is equal to seven and two plus five is equal to seven.

So here's our story.

There are seven cars, five are in the car park and two are in the garage.

We know that the seven represents a whole group of cars.

The five represents the five cars in the car park.

The two represents the two cars in the garage.

Well done.

So tell the story to explain what these counters mean, then.

What do they represent? So Sofia's saying this is more tricky.

There are seven counters, so there must be seven cars altogether.

Seven must be the whole.

There are seven yellow counters, so there must be seven cars in the garage.

So that's one part, isn't it? There are no red cars, so there are no cars in the car park.

So in the other part of the part-whole model, we have to write zero because the whole group is one of the parts this time, isn't it? We can write these equations.

Seven is equal to seven plus zero.

Seven is equal to zero plus seven.

Seven plus zero is equal to seven and zero plus seven is equal to seven.

Excellent, so now it's time to check your understanding again.

Match the counters to the part-part-whole model that represents them.

Notice the number of red counters and the number of yellow counters.

Okay, so you'll have to look carefully, won't you? So pause the video while you decide which part-part-whole model represents those counters.

Okay, so let's have a look then.

So we can see there are two red counters, there are six yellow counters, and altogether there are eight counters in the whole group.

So it would be that one, eight is the whole, six is a part and two is a part.

Now let's look at the next group of counters.

Pause your video again while you have a try at that.

Okay, so this time we can see there are four red counters and two yellow counters, okay? And there are six counters in the whole group.

So it will be, that's right, six is the whole, two is a part and four is a part.

Okay, and now look at these counters.

Pause your video while you have a think about that one.

Okay, so what did we think? So there are three red counters, there are three yellow counters and there are six counters in the whole group.

So it will be that one, won't it? Six is a whole, three is a part and three is a part.

Well done, that was excellent work.

Jacob wants to make up a story that these counters could represent.

I wonder if you have some ideas to help him.

There are mm red counters and mm yellow counters.

There are mm counters altogether.

And Jacob is saying, "I want to make up a story about animals." So there are two red counters and five yellow counters.

There are seven counters altogether.

"The yellow counters can represent dogs," says Jacob, "And the red counters can represent cats." So Jacob thinks of this story.

I can see seven animals from my window, two are cats and five are dogs.

And then he says the seven counters represents the seven animals, doesn't it? The two red counters represents the two cats and the five yellow counters represent the five dogs.

Draw a part-part-whole model to represent the story.

So there's a part-part-whole model, and we know that there are seven animals altogether.

Seven is the whole, two is a part 'cause we've got two cats and five is a part, we've got five dogs.

And you could have also put those addends the other way round, couldn't you? Jacob represents his story as different equations.

So he says, "Seven is equal to two plus five, seven is equal to five plus two." He also says, "Two plus five is equal to seven and five plus two is equal to seven." Sofia wants to make up a story that these counters could represent.

I wonder if you have some ideas to help her? So she completes the stem sentence.

There are seven counters altogether.

Two are red and five are yellow.

"I want to make up a story about toys," she says.

The yellow counters can represent teddies and the red counters can represent footballs.

The seven counters represents a group of seven toys.

That's the whole group, isn't it? The two counters represent two footballs.

The five yellow counters represent five teddies.

Sofia tells this story.

There are seven toys in my room, two are footballs and five are teddies.

She represents it like this.

And she put, draws a part-part-whole model to show the whole and the parts, and she writes four equations to show that how the sum and the addends are equal to each other.

What did you notice about the part-part-whole model she drew compared to the one that Jacob drew? That's right, they both have the same numbers but they're representing different stories, aren't they? Okay, so now it's time to check your understanding.

Which story could be represented by this part-part-whole model? Okay, so think about the whole and the parts.

So we've got, there are four sweets on a plate, two are yellow and six are red.

There are six sweets on a plate.

Two are yellow and four are red.

And there are six sweets on a plate, two are red and four are yellow.

So which of those stories could be represented by that part-part-whole model now? Pause your video while you have a think about that.

Okay, so let's have a look.

So there are four sweets on a plate, two are yellow and six are red.

So let's think about the whole and the parts.

So that would be four is a whole and two is a part and six is a part.

But we know that six is greater than four, so that can't be right, can it? So let's look at this second example, B, then.

There are six sweets on a plate, two are yellow and four are red.

Okay, so what would be the whole and the parts there? So six would be the, six is the whole, two is a part and four is a part.

So looks, let's look at our part-part-whole model.

And we can see that that is right, isn't it? Six is the whole and two is a part and four is a part.

And let's look at this last problem here, C.

There are six sweets on a plate, two are red and four are yellow.

So what is the whole and what are the parts? So we can see that six is the whole, two is a part and four is a part, so could that part-part-whole model represent that story? Yes, it could, couldn't it? So well done, that was excellent.

So who do you think is right? We've got a group, a whole group of cups here, haven't we? And Sofia says, "I think I can represent the cups as two plus five equals seven." And Jacob's saying, "I think I can represent the cups as three plus four equals seven." Let's draw a part-part-whole model and write the equations, then explain what each number represents and that's how we'll prove if we're right or not.

So Jacob says, "There are seven cups in the whole group, three cups with straws and four cups with without straws." So he represents it like that on a part-part-whole model.

Seven is the whole group, isn't it? Seven is equal to three plus four, the addends.

Seven is also equal to four plus three.

Three plus four is equal to seven, and four plus three is equal to seven.

So we can see that that part-part-whole model and equations represent that picture.

The seven represents a whole group of seven cups.

Three represents the three cups with straws.

The four represents the four cups without straws.

So Jacob says, "I have proved I am right." So let's look at what Sofia thought, then.

Sofia says there are seven cups in the whole group.

Five cups are green and two cups are clear.

So she's partitioned them in a different way.

So there's her part-part-whole model.

And here's her equations.

The seven represents a whole group of seven cups.

That's right, isn't it? The five represents the five green cups and the two represents the two clear cups.

So Sofia has also proved she was right, hasn't she? Well done.

So now it's the task for the second part of today's lesson and it's work with a partner time, okay? So we've got Sofia and Jacob are going to be partners there.

Sofia's saying, "I will partition a group of seven counters into two parts.

Then I will draw a part-part-whole model to represent this." And Jacob says, "I will make up a story to match your part-part-whole model then write four equations to represent it, telling my partner what each number in the equation represents." Okay, so pause the video now while you have a try at that.

You might have said seven is the whole, one is a part and six is a part.

There are seven cakes in the box, one is a cream cake and six are chocolate cakes.

And there we can see the counters representing that.

And the equations would be seven is equal to one plus six, seven is equal to six plus one, six plus one is equal to seven, and one plus six is equal to seven.

The seven represents a whole group of cakes.

The one represents a cream cake and the six represents the six chocolate cakes.

So you may have had lots of other examples as well, but that just shows you the one that Sofia came up with.

So well done, you've worked really hard again, haven't you, in the second part of today's lesson.

So now let's think about what we've learned in today's lesson.

So we've found out that drawing a part-part-whole model can help you to understand a problem or equation.

Moving counters or cubes within a part-part-whole model can also help you to understand a problem or equation.

Describing a problem or equation can help you understand it.

And you can tell a story to represent an equation or part-part-whole model.

So I've really enjoyed today's lesson.

We found out lots about solving problems and using equations to represent them, haven't we? And hopefully you should feel much more confident in your work when you are doing that now.