Lesson video

Hello, my name is 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, and welcome to today's lesson, which is called Add Parts to Find the Value of the Whole and Write the Equation, and it comes from the unit Additive Structures: Addition and Subtraction.

So in today's lesson, we're going to be adding parts to find the value of the whole.

We're going to be putting together the addends to find the sum to find out how many altogether and we'll be writing equations to match problems and solving problems using equations and part-part-whole models, so let's get started.

So our keywords today then are addend, my turn, addend, your turn, and sum, my turn, sum, your turn, and altogether.

My turn, altogether, your turn.

Well done, excellent.

(mouse clicking) Okay, so in the first part of today's lesson, we're going to combine the addends to find the sum and in this lesson, you'll meet Izzy and Jun, they will help us with our learning today.

So here's a problem.

There are three birds that are standing and two birds that are flying.

How many birds are there altogether? Izzy uses her stem sentences to help her find out.

(hums) is the whole, three is a part, and two is a part.

Three and two are the addends.

Where should she write the three and the two? That's right, she writes them in the parts of the part-part-whole model.

Could she have written them anywhere else? She could have swapped them around and written them in a different order, couldn't she? That's right.

Then she uses her stem sentences to find out how many birds there are altogether.

So we know that three plus two is equal to five and she represented it as an equation.

So she put three plus two and she put them together, combined them to make five and she wrote it as an equation like that, didn't she? Okay, so she also found out that two plus three is equal to five and wrote that as an equation as well, then she spotted that three is an addend, two is an addend, and five is the sum, and she can look at the equations and see where the addend and the sum are.

What does the three represent then? The three represents the three birds that are standing, doesn't it? What does the two represent? Yeah, the two represents the two birds that are flying, and what does the five represent? The five represents a number of birds altogether.

That's right, well done.

We must combine the addends to find the sum.

So we found out there were five birds altogether.

Izzy has found a way to check she is right.

She starts with the sum and partitions it into the addends.

So there's five, that was the sum wasn't it? Five is equal to three plus two, and there you can see she's partitioned it into three plus two and she represents it as an equation there.

We also can find out that five is equal to two plus three and she represents that as an equation.

Two is an addend, three is an addend, and five is the sum.

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

There are two dogs and five cats.

How many animals are there altogether? Jun is trying to solve this problem.

Explain what he can do to help him.

So first, he must describe the story to find the addends.

So he can say that there are two dogs and there are five cats.

Two is a part and five is a part, then he can represent them in a part-part-whole model, and there is a part-part-whole model, and he puts the addends in the parts two and five or he could have written them the other way around.

So Jun uses his part-part-whole model to help him to solve the equation, to solve the problem.

So he's got five plus two and he combines the addends to find out that they are equal to seven or he could have combined them the other way around and said two plus five is equal to seven.

What equation should he write? That's right, he should write two plus five is equal to seven.

Explain what each part of the equation represents.

That's right, the two represents the two dogs, the five represents the five cats, and the seven represents the whole group of animals, doesn't it? To find out how many altogether, you must count both the addends.

Izzy drew this part-part-whole model to represent this group.

Do you agree that it is right? Explain how you know.

Remember, you can use your stem sentences to help you.

So there are seven animals, there are two dogs and five cats.

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

The addends are two and five.

So they need to go there, don't they? To find out how many altogether, you must count both the addends.

So we can see that when you've combined the addends and count them, the whole amount, the sum is seven and we can represent it two plus five is equal to seven.

So Izzy is saying, "I was not right, seven is the whole and not five." She had the right numbers, but she hadn't put them in the right parts of the part-part-whole model, had she? There are four apples and two oranges.

How many pieces of fruit are there altogether? So there are four apples and two oranges, four and two are the addends, so they go in the parts of the part-part-whole model, and we've got four plus two is equal to (hums) or two plus four is equal to.

(hums) To find out how many altogether, you must count both the addends.

So we can see when we count both the addends, they come to six, don't they? So six must be the sum.

There are six pieces of fruit altogether.

Now, partition the whole to prove that you are right, so start with the whole amount and partition it.

So we can see that six partitions into four plus two, doesn't it? Six is equal to four plus two and six is also equal to two plus four.

So (hums) is the whole, (hums) is a part, and (hums) is a part.

So we've got six is the whole, two is a part, and four is a part.

So we can see, what does each number represent? The six represents the six pieces of fruit in the whole group, doesn't it? The four represents the four apples, that's right, and the two represents the two oranges.

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

There are five pens and three pencils.

How many there are there altogether in this whole group of pens and pencils? Represent the problem as a part-part-whole model and write the equations to find the sum.

So pause your video now while you do that.

Okay, so let's have a look together.

So there's a part-part-whole model and we can see there at the addends.

We've got five and we've got three, haven't we? And we're trying to find the.

How many altogether, the sum.

So five plus three is equal to, or three plus five is equal to.

So those are the equations we write and then we need to count both the addends, both altogether to find out the sum, the whole amount.

So we can see when we count together three and five or five and three, the whole amount is eight, so eight is the sum.

So now, the second part of your check is to write two different equations to check you are right.

So we've seen two equations, you need to write equation to check that.

Pause the video while you do that now.

Okay, so let's have a look then.

So you could have written eight is equal to, that's right, five plus three.

You could have also said eight is equal to three plus five, well done.

I know I'm right because when I partition eight, five is a part and three is a part, so we knew the equations that we did to find the sum, how many altogether were correct.

So now, explain what each number in the equation represents.

So you've got some stem sentences to help you.

The eight represents (hums), the five represents (hums), and the three represents (hums).

So pause the video while you complete those.

Okay, so let's have a think then.

The eight represents the whole group of eight pens and pencils, the five represents the five pens, and the three represents the three pencils.

Well done, excellent.

So there are three fingers held up on one hand and four fingers held up on the other hand.

How many fingers are held up altogether? So what equations could we write to find out? So we've got a part-part-whole model there and first, you must describe the story.

So there are three fingers held up on one hand and there are four fingers held up on the other hand.

Three and four are the addends.

Three plus four is equal to, or four plus three is equal to.

How will we find the sum, do you think? That's right, to find out how many altogether, you must count both the addends.

So three plus four is equal to seven and four plus three is equal to seven.

Represent the problem on a part-part-whole model.

Where will the different numbers go? Where will each part of the equation go? So we know that three and four are the addends, they're the parts, and seven is the sum, that's right, and we can swap the addends around, can't we? What does each number represent? That's right, the three represents the fingers held up on one hand, the four represents the fingers held up on the other hand, and the seven represents the numbers of fingers held up altogether.

Excellent.

So three and four are the addends, seven is the sum, that's right.

Now, partition the whole amount to prove you're right, so let's do that together.

So this time we start with the whole amount, the sum, don't we? And we say seven is equal to three plus four, that's right.

Seven is equal to three plus four.

Seven is also equal to four plus three, so we know we're right, don't we? What does each number represent? That's right, the seven still represents the numbers of fingers held up altogether, doesn't it? And the three still represents the fingers held up on one hand and the four still represents the fingers held up on the other hand, that's right.

Jun has been writing equations to represent this picture, but only one of them is right, okay? So let's find the right one and explain why the others can't be right, so let's look together.

So we can see three plus two plus five.

So is that representing the picture? Well, we know that plus, when we use plus, we are combining the addends, aren't we? So have we got an addend of three and an addend of two and an addend of five? No, we haven't, have we? So that one's not right, and it doesn't have an equal sign, so it can't be an equation, can it? Let's have a look at the next one then.

So we've got three is equal to two plus five, okay? So we've got.

They're saying three is a sum and the addends are two plus five.

Do we think that's right? No, three is not equal to two plus five.

I know because five is greater than three, isn't it? So we know that five can't be a part of three because it's greater than three.

Okay, so let's look at the next one now.

So we've got five is equal to three is equal to two.

Okay, so what do we think about that? That's right, the equal sign means all the numbers are equal, but those numbers aren't all equal, are they? And what about the last one? Five is equal to two plus three.

That's right, five is equal to two plus three.

When you combine the addends, two and three, they will add up to five altogether.

Only if we look at the picture, we can see we've got one part that's got three cups, one part that's got two cups, and when we combine them, there are five cups altogether, so we know we are right.

Okay, so time to check your understanding now.

So there are three pebbles in one box and one pebble in the other box.

How many pebbles are there altogether? What equation could we write to find the sum, okay? So if you have a look here, we can see we've got four is equal to three is equal to one, three plus one plus four, and one plus three is equal to four.

So pause the video while you think about that now.

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

Okay, so four is equal to three is equal to one.

Well, those numbers aren't all equal, are they? So that can't be right.

What about this one, the middle one? Three plus one plus four.

Well, we've got three addends there being combined, but we haven't got an equal sign, have we? So it's not telling us that it's equal to anything, it's not an equation.

What about this last one then? One plus three is equal to four.

Well, we can see that there's one pebble in one pot and there's three pebbles in the other pot and they are equal to a whole group of four.

The whole group is four, isn't it? So we know that that one's right, well done.

(mouse clicks) The second part of your check is here.

Jun was playing with a dice.

He threw these numbers on his dice.

Which equation represents the amount shown altogether? Okay, so you've got four equations there, okay? So have a look at those and then pick the right one and explain why the others can't be right.

Pause your video while you do that.

Okay, so what did we think? So this first one, three plus three plus.

Is equal to six.

Can that be right? No, that's not right, is it? There are three spots on one die and six spots on the other die.

So the addends must be three plus six, so it's not three plus three, is it? Okay, what about the next one? So we've got six plus three is equal to nine.

Have we got an addend of six and an addend of three? Yes, we have, haven't we? And are they equal to nine? This is the sum, nine.

That's right, so that one's right, the addends are three plus six.

We can write the addends in any order.

When we count the spots, there are nine altogether.

What about this next one then? Eight is equal to five plus three.

There are three spots on one die and six spots on the other, so the addends must be three plus six, not five plus three, so we know that one's not right, and what about this last one? Six is equal to three plus nine.

That's right, I know nine is greater than six, so six can't be the amount altogether.

Well done, that's excellent.

So now, here's your task for the first part of today's lesson, okay? So roll two dice and add the numbers shown to find out how many spots there are altogether, okay? And here's Izzy telling us how to do it.

She's saying, "I will roll both dice and record the numbers shown.

I will draw a part-part-whole model to show the addends.

I will combine them and count how many spots there are altogether, then I will record the equation that represents this." When you have written six equations, look at the part-part-whole models and see if you can write an equation to check that the addends are equal to the sum.

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

So let's see how we got on.

You may have done this.

So there's Izzy and she's saying, "I rolled three and five.

I drew a part-part-whole model to show the addends." It would be three and five, wouldn't it? And there's her part-part-whole model and then she put the addends in, "I recorded the addends," and it doesn't matter which order you record them, does it? And then she wrote three plus five is equal to eight.

She said, "I counted both parts to find how many spots there were altogether." So well done, you've worked really hard in this first part of today's lesson.

(mouse clicks) So now, we're going to move on to the second part of today's lesson, which is represent and solve problems. So there are three tennis balls in one tub and four tennis balls in the other tub.

How many balls are there altogether? So Jun says, "I will use counters to represent the tennis balls." So there, he's replaced the balls with counters.

"I'll write the equation." So he writes, four plus three is equal to.

Four is an addend, three is an addend.

"To find out how many altogether, I will count both the addends," says Jun and you can see he puts them together and now, he's going to count them up and he finds that there are seven tennis balls altogether.

"I can represent this on a part-part-whole model," says Jun.

So there, we can see the question mark is representing the sum, how many altogether that they're trying to find.

So he writes four plus three is equal to, and he puts those on a part-part-whole model and he uses the counters to help him as well.

He gets four counters and three counters and then when he combines them and counts them both up, he finds out that there are seven altogether.

Four plus three is equal to seven.

He could have also done it the other way around, couldn't he? He could have swapped the addends and said three plus four is equal to seven.

He could also check he was right.

He could partition the seven, couldn't he? So if he partitions seven, it should be three plus four and we can see there that it is when he partitions that seven into two parts, and then he can partition it a different way.

Seven is also equal to three plus four there.

Well done, excellent.

Izzy wants to find out what the sum of two and five is.

She uses counters on a part-part-whole model to help her.

What mistake has been made? So you can see her counters there next to her part-part-whole model.

That's right, instead of combining the addends to find the sum, she has represented both the sum and the addends.

So it looks like 10 altogether, doesn't it? So you've got to remember that you can have the counters that can either be in the whole and then you move those counters into the parts or you have the counters in the parts and you move them into the whole, but you don't have the whole and parts together, do you? So there, that's how it should have been or like that.

Jun writes this equation for Izzy to solve.

Something, (hums) is equal to three plus four.

"Am I trying to find the addends or the sum?" He wonders.

"I will draw a part-part-whole model to help me." So three and four are the addends.

You can use counters or draw circles to represent the addends.

To find out how many altogether, you must count the addends, and we can see there's counters to represent the addends that aren't there, and then when you combine them, you can see that they come to seven altogether.

Izzy, writes this equation for Jun to solve.

Four plus two is equal to (hums).

How do you think Jun could solve it? He says, "I can't solve this.

I can't see any objects.

I could use counters to represent the numbers." So he knows he needs to get counters to represent the four and the two and he also says, "I could draw something to represent the numbers," if he didn't have any counters available.

So here we are, let's see what he does.

He's going to use counters, first of all, to represent the addends.

So four counters to represent the four and two counters to represent the two.

How will we find the sum? That's right, to find out how many altogether, we must count both the addends, so let's have a look.

We have four, we don't need to count those 'cause we already know that's four, don't we? So we can start our count up four, we can use our stem sentence.

So I can start my count up four and I count four, five, six.

So we know that six is the amount altogether, it's the whole amount, the sum.

Now, Jun says, "I will draw circles to represent the addends." So there's four again and two, he's drawn circles to represent the four and the two.

How will we find the sun this time? That's right, to find out how many altogether, we must count both the addends, okay? So let's see.

So we've got four, we don't need to count them 'cause we already know it's four.

I start my count from four and I count.

So four, five, six.

So the amount, the sum, is still six, that's how many there are altogether.

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

Solve this equation.

Remember, you can use counters on a part-part-whole model or draw to help you.

So we've got five plus two is equal to (hums) and then when you've solved that, have a try at the equation underneath.

You've also got (hums) is equal to five plus three, okay? So you could use counters or objects if you've got some available or you could draw to help you, couldn't you? Okay, pause the video while you try that.

Okay, let's see how we got on.

So you could get five counters, couldn't you? And then two more counters and then to see how many altogether, you would count them all up and you'd find out there was seven altogether.

Now, let's sort this other equation here.

(hums) this looks a bit more tricky because the missing number is at the start, isn't it? But we know the missing number is equal to five plus three, so what should we do? That's right, we draw five circles or get five counters and three circles or three counters and then to find out how many altogether, we count both the addends, don't we? So we know that there are eight, well done.

Write an equation to represent this story.

There were five children in the classroom and two children in the playground.

Altogether, there was seven children.

So we know five and two are the addends, five plus two is equal to, and to find out how many altogether, we must count both the addends.

So we've got five and then we start from five, don't we? I start my count from five and I count five, six, seven.

Well done, seven is the sum.

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

Write an equation to represent this story.

I have six pennies in one pocket and three pennies in my other pocket.

Altogether, I have nine pennies.

So pause the video now, okay? While you think about what equation you can write to represent that problem.

Now, when you've done it, think about how you can solve it.

Think about what we've done already that can help you to solve those equations and to find out how many altogether.

Pause the video now.

Okay, so let's have a look.

So six and three are the addends, aren't they? They're the parts and we're trying to find out how many altogether.

So we could write six plus three is equal to, okay? And then how can we find out what six plus three is equal to? So to find out how many altogether, we must count both of the addends.

So we could draw six circles, couldn't we? Or get six counters? And then we could count three more.

So six and seven, eight, nine.

So six plus three is equal to nine.

Nine is the sum.

So Jun writes this equation for Izzy to solve.

One plus two plus four is equal to.

(hums) How can you find the missing number? So that's a bit different from the equations we've seen so far, isn't it? What are the addends? And can you draw a part-part-whole model to help you? So let's think about this.

So how many parts would you need in your part-part-whole model? Is that right? Do we think that's going to represent it? It's got a four and a one and a two, hasn't it? So let's look together to see.

There are three addends, aren't they? 'Cause it's.

Aren't there? Because it says one plus two plus four.

So that's three addends that are going to be equal to the sum.

So our part-part-whole model has to have three parts, doesn't it? There must be three parts in the part-part-whole model.

We know when the addends combine, they are equal to the sum.

So to find out how many altogether, you must count all the addends.

So we've got an addend that's one and two and four and we can see we've put counters there to represent them as well, and then to find out how many altogether, you must count all the addends, and we can see that the sum is seven.

So now, time to check your understanding again.

Find the sum in this equation.

Two plus three plus four is equal to.

Remember, you can use a part-part-whole model to help you.

So pause the video while you try that now.

Okay, and let's see how we got on.

There must be three parts in the part-part-whole model.

If you draw one wasn't there because there are three addends.

So the three addends are two plus three plus four and you may draw circles to help you or there are some counters there to help us as well.

To find out how many altogether, you must count all the addends.

So that's right, when you count all of those up, you see that there are nine altogether, aren't there? Well done.

Okay, so here's your task for the next part of the lesson.

So combine the addends to find the sum, then fill in the missing numbers, okay? So you can see you've got some part-part-whole models there and you've got some equations underneath with a missing number, okay? So you've got to find the missing number, okay? Solve the equations and then put the numbers in the correct places on the part-part-whole model to represent the equations underneath, okay? And explain what you notice about each pair of equations.

So pause the video now while you do that.

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

Okay, so we have got here four plus three is equal to.

So we can see four plus three are the addends, aren't they? And we're trying to find out what they're equal to.

So we know to find out how many altogether, we count both the addends.

So we can see four plus three would be equal to seven, can't we? And then underneath, if you have a look, we can also see we've got a.

If we think about what's the same and what's different about that pair of equations, we've also got a three and a four, haven't we? So that can help us.

That's right, because we know if four plus three is equal to seven, three plus four must be equal to seven as well.

Okay, let's look at the next set of equations.

So we've got (hums) is equal to eight plus one.

So we know eight plus one are the addends and so we're trying to find the sum.

So there's eight plus one and to find how many altogether, we count both the addends.

So we know that it will be nine.

What do you notice about this next equation underneath? That's right, it's got the same numbers.

Instead of eight plus one, it's got one plus eight and so we know if eight plus one is equal to nine, one plus eight must be equal to nine as well.

Excellent, now, let's look at the next set.

So we've got something, (hums) is equal to six plus two.

So we need to put our six and our two in, don't we? And we know it doesn't matter which way around you draw your part-part-whole model, but the addends or their parts that come from the whole, that partition from the whole.

So we can write our six and hour two in, and we know to find out how many altogether, we need to count both the addends.

So we know that six plus two will be equal to eight, and then what you notice about this, the equation underneath.

That's right, it's got a six and a two, but in the other order.

So if six plus two is equal to eight and eight is equal to six plus two, two plus six must also be equal to eight, and we can see that from the part-part-whole model, can't we? Okay? (mouse clicks) And then if we look at this last set of equations, we've got seven plus two plus one is equal to, okay? So those are the addends and we need to write those in the part-part-whole model and think about how many altogether.

So we have seven plus two plus one, and we know to find out how many altogether, we count all the addends, don't we? So they will combine to make 10, won't they? That's right, and we know if seven plus two plus one is equal to 10, then 10 must be equal to one plus two plus seven because it's the same addends just in a different order.

So well done with that, and let's think about what did we notice.

The sum in each pair of equations is the same because you're combining the same addends each time, but in a different order.

So well done.

Excellent, you've worked really hard again.

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

In an equation, each addend represents a part.

You can combine the addends to find the sum.

To find out how many objects there are altogether, you must count both addends.

Okay, well done, you've worked really hard.

I've really enjoyed working with you and solving problems with you and writing equations today, that was excellent.