Lesson video

Hello, my name's Mrs. Cornwell and I'm going to be helping you with your learning today.

We're going to be using some of the things you already know to help you with some new learning, and I'm really looking forward to working with you today.

So let's get started.

So welcome to today's lesson and it's called Understand the Relationship between Addition and Subtraction.

And it comes from the unit, additive structures, addition and subtraction.

So in today's lesson, we're going to represent both addition and subtraction, and we're going to look at the link between them, okay? How they're related.

So let's get started with that.

So our keywords today are subtraction, my turn, subtraction, your turn, and addition, my turn, addition, your turn.

That's right, well done.

So in the first part of today's lesson, we're going to explore and represent subtraction problems. So in this lesson we'll meet Jun and Izzy and they're going to help us with our learning.

So we can use counters to represent and solve problems. There's a problem.

Let's see how we can do that.

There are five dogs.

Three are standing up.

How many are not standing up? Izzy wants to represent this problem with double-sided counters.

Collect some counters so you can help her.

How many counters will she need? That's right.

She'll need five counters because there are five dogs.

What do these counters represent? The counters represent the whole group of five dogs in a subtraction equation.

This is the minuend and there's five.

If we were writing an equation, how will she represent the three dogs that are standing up? That's right.

She turns over three counters.

This is the part to be partitioned in an equation, the subtrahend.

So we've got five minus three.

Two of the group remain.

This is the difference.

That's the dogs lying down.

Let's help Izzy represent this on a bar model.

So five minus three is equal to Mm.

So where will we put the minuend? And there's Izzy reminding us Remember the minuend is the whole group.

That's right.

So it goes there.

Where will we put the subtrahend? Remember the subtrahend is the part to be subtracted so we can put it in either part.

But that part's larger, isn't it? So we'll put the larger amount in there.

Now we can find the difference.

Five minus three is equal to two.

You can see there were two remaining so we can write the numbers into to represent that, can't we? So five was the whole group and then three was the part that was subtracted and the difference was two.

Well done.

Jun wants to represent this problem with counters.

There are six boxes.

One box is open.

How many are not open? How many counters will I need, he asks.

That's right.

He'll need six counters won't he? How will I represent the counter to be partitioned from the whole? That's right.

He turns over one counter to represent that.

So how will we represent that as an equation? That's right.

We'd say six minus one is equal to.

Now you've subtracted the one box from the whole group.

You can see how many are in the rest of the group.

There were five, weren't they? Well done, draw a bar model to represent this.

So six minus one is equal to, where will we put the minuend? That's right, six is the whole group.

It's a minuend.

Where will we put the subtrahend? We subtracted one, didn't we? So we can put that in the smaller part.

And so how many are remaining? Now we can find the difference.

And we know it was five, don't we? Well done.

Explain what each number represents from your story.

So we know, don't we, that the six represented the whole group of boxes.

The one represented the open box to be subtracted and the five represented the boxes that were remaining, well done.

So now it's time to check your understanding.

Use counters to solve this problem.

There are seven teddies in a toy box, two are large teddies.

How many are not large teddies? So pause the video while you try that.

So let's see how we got on.

You needed to get seven counters to represent your seven teddies.

Then you turn over two counters to represent the two large teddies.

Now you can see how many teddies are not large.

Now it's time for the second part of your check represent this equation as a bar model.

So we had seven minus two is equal to, didn't we? So pause the video while you think about how you would put that, represent that as a bar model.

Okay, so let's see what we did.

So we had seven to represent the seven teddies, didn't we? That was the minuend, the whole group.

And then there were two teddies that were subtracted or partitioned.

Okay? And the subtrahend is the part to be partition, two was the subtrahend.

Okay, and we needed to find the part remaining.

And we can see when we subtract say seven minus two, there's five remaining.

The difference is the part remaining.

So well done if you've got that.

So let's tell a subtraction story to represent this picture.

When we subtract, we must start with the minuend.

My story must begin with a whole group of drinks, altogether there are hmm drinks in the whole group.

That's right.

There are altogether there are nine drinks in the whole group.

There were nine drinks in a cafe.

So Izzy's making up the story here, isn't she? So that's the first part of our story.

There are nine drinks in a cafe.

Then we must subtract a part.

And there's Izzy.

She says, "I think I will partition the drinks with straws." Three drinks had straws.

Now we can ask a question.

How many did not have straws? Six drinks did not have straws.

So when we subtracted partitioned, one part, we could clearly see the remaining part, couldn't we? The difference, Jun thinks he can make up a different subtraction for this story.

Is he right? There were nine drinks in a cafe.

I think I will partition the drinks without straws says Jun, six drinks did not have straws.

How many drinks had straws? So he's subtracted the other part of the whole, hasn't he? And then he found out that three drinks did have straws.

Let's write an equation to represent each problem.

So there we've got nine is the whole group, the minuend nine subtract three is equal to six.

But you could have also said nine subtract six is equal to three.

It depended which part you chose to subtract, didn't it? So now it's time to check your understanding again, tell a subtraction story to represent this picture and write the equation.

So pause the video now while you try that.

Okay? And let's see how you got on.

So you may have said there are six bananas altogether in the whole group.

Three bananas are peeled, how many are not peeled? And then you would've said six minus three is equal to three.

Well done.

You may have also said there are six bananas altogether in the whole group.

Three bananas are not peeled.

How many were appealed? How would we write the equation to represent that then? The story's different, but the equation would actually be the same wouldn't it? Because whichever part you subtracted, they're both parts of three, aren't they? So it'll be six minus three is equal to three.

Well done.

Let's make up a story to match these counters.

So when we subtract, we must start with the whole group then partition one part to find the other part.

The whole group is, that's right.

Seven counters.

I think I will tell a subtraction story about fruit.

The three white counters can represent mm, three apples I think.

And then the four red counters can represent four oranges.

Yes, that's a good idea.

So there are seven pieces of fruit.

Here's my story.

Three are apples, how many are oranges? Or I could have said, how many are not apples couldn't I? Or is there a different story I could have told? That's right.

I could have said there are seven pieces of fruit, four are oranges, how many are apples or how many are not oranges? So it depended which part I chose to partition, which part I subtracted.

Okay, so Jun wants to make up a different subtraction story that these counters could represent.

Let's think of some ideas to help him.

There are mm counters altogether.

Mm are red and mm are white.

So we could have, there are seven counters altogether.

Five are red and two are white.

And then let's think of what they could represent.

So the seven counters could represent for example, a group of seven toys.

The two white counters could represent two footballs, and the five red counters could represent five teddies.

Okay, so now we need to think of a story that could match that.

So let's think there are seven toys.

Two are footballs.

How many are teddies? That would be a good subtraction story.

Could we write a subtraction equation to represent this? Seven minus two is equal to five.

That's right, well done.

There are seven toys, two are footballs.

How many are teddies? In Jun's story, the two footballs were subtracted.

Could Jun tell a different subtraction story for the counters, do you think? That's right, he could have said there are seven toys, five are teddies.

How many are footballs? He could have partitioned the teddies instead of the footballs, couldn't he? Write a subtraction equation to represent this.

So it would be seven minus five is equal to two.

That's right, well done.

So now it's time to check your understanding again, which counters will match this subtraction story.

There are six cats, two are kittens.

How many are not kittens? Okay, so pause the video while you think about that.

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

So there are six cats, so we need a whole group of six.

Okay? And then two of them have to be kittens and then you need to partition two off.

So let's have a look.

It could be that one because we've got six and two is a part, isn't it? Or it could be that one because that's six and two is a part.

So well done if you spotted those.

Okay, so let's look at the task for the first part of today's lesson.

Okay, Izzy's telling us here what to do, isn't she? I'll look at the picture and tell the story.

I'll use counters to represent it as a bar model.

So there we can see that this picture has three dogs.

And so she's making up a story.

There are three dogs altogether in the whole group.

One is standing, how many are not standing, okay? And then when she's represented it on a bar model with counters, she will write the equation and solve it.

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

So let's see how you got on.

You may have done this.

So there's a picture, the banana picture for example.

And you may have said there are six bananas altogether in the whole group.

Two are peeled, how many are not peeled? And so there's your counters to represent the bananas.

And we can see six is the whole group, the minuend, and then that represents the two that are peeled.

And the other part is the four that were not peeled.

So well done if you did that.

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

Excellent.

So the second part of our lesson is where we're going to look at how we can link addition and subtraction.

When we partition the parts of a whole group, it is called subtraction.

And there we can see the whole group has been partitioned into two parts there hasn't it? When we combine the parts of a group, it is called addition.

There we've combined them again, we can use addition and subtraction when we combine and partition the same group of objects.

Look at how this group of six pencils has been partitioned.

It has been partitioned into four and two.

What will the whole be? If we combine them again, I wonder, that's right.

It will be the whole group of six, won't it? We can use addition to combine then use subtraction to partition again, collect cubes and partition it into two parts.

And then say with me, taking apart subtraction and then put it together and say putting together, addition.

So let's try that.

Repeat saying the words with me.

Taking apart, subtraction, putting together, addition, taking apart, subtraction, putting together addition.

Izzy and Jun want to tell a story about this picture? Izzy says, "I think I can tell an addition story." Jun says, "I think I can tell a subtraction story." I wonder who's right.

They are both right.

If our story involves putting the parts together to make the whole, it will be an addition story.

If our story involves partitioning one part from the whole to find the other part, then it will be a subtraction story.

So it depends whether you combine or partition.

Let's tell an addition story.

In our story.

We must put the parts together to make the whole first we must describe the picture.

In addition, we describe the parts and put them together.

There are three dogs standing up and two dogs lying down.

How many dogs are there all together? And that's our addition story, isn't it? Three plus two is equal to five.

Let's tell a subtraction story, in our story.

We will start with the whole and subtract a part.

First we must describe the picture again, wasn't we? So in subtraction we describe the whole and then subtract apart to find the other part.

There are five dogs, two dogs are lying down, how many are standing up? And there we partition to find out, didn't we? And we can represent that as five minus two is equal to three.

We can see the dogs that are standing up Draw a bar model for is Izzy's equation.

Three plus two is equal to five.

So where will the parts go and where will the whole go? So that's right.

So three and two are the parts and they were combined to make the whole.

Now let's draw a bar model for Jun's equation, five minus two is equal to three.

So this time we start with the minuend and the whole amount and we subtract two to get the other part of three.

So well done.

What do you notice about those two bar models? That's right, they're the same because the picture we are describing each time is the same.

It's just whether it's been combined to make the whole or whether the whole has been partitioned to find one part.

So now it's time to check your understanding, match the questions to addition or subtraction.

So we'll read the story and decide if it's addition or subtraction.

So here's the first one.

There are six counters altogether.

Four are red.

How many are not red? So pause a video now while you think about whether that's addition or subtraction.

Okay, so what do we think? There are six counts altogether, four are red.

How many are not red? We are partitioning the whole group.

So it is subtraction.

Now let's have a look at the other one.

There are four red counters and two white counters.

How many are there all together? So pause the video now while you think about that.

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

So this time we are combining the two parts to make the whole.

So it will be addition.

Well done, excellent.

Okay, so now let's tell an addition story for this picture.

And there's Izzy.

She's saying should I start with the parts or the whole? In an addition, we are putting the parts together.

We will describe the parts first, there are three cups with juice and three cups without juice.

How many cups are there all together? So we're combining the two parts in addition, aren't we? And there we can see we've put them together to make the whole.

Now let's tell a subtraction story for this picture.

Should I start with the parts or the whole asks Izzy again, in subtraction we are taking apart one part from the whole.

So we'll describe the whole first, there are six cups in the whole group.

There are three cups without juice.

How many cups are there with juice? And there we can see, we partition the whole group to find the other part.

So now it's time to check your understanding, tell an addition story for this picture, then write the equation.

Remember to describe the picture to help you think about what you're going to start describing first.

Pause the video while you do that now.

Let's see how you got on.

So you could have said there are four cakes with cherries and three cakes without cherries.

How many cakes are there all together? So you described the two parts and then we'd have to put them together, combine them to find the whole.

And the equation would've been four plus three is equal to a seven.

And because we know we can combine the add-ins in any order, you may have also described it the other way round and said three plus four equals seven.

Now here's the second part of your check.

Tell a subtraction story for this picture and write the equation.

Remember to describe the pictures to help you.

So pause the video while you do that now.

Okay, and let's think about the story you told together.

So you could have said there are seven cakes, four have cherries.

How many cakes do not have cherries? And that would've been represented as seven, minus four is equal to three.

Or you could have said there are seven cakes.

Three do not have cherries.

How many cakes do have cherries? And that would've been seven minus three is equal to four.

So you could have decided to subtract either part, couldn't you? So well done, excellent.

So now your task for the second part of today's lesson is to look at this picture and use the groups of objects in the pictures to tell some addition stories, each time write the equation and use counters to represent it on a bar model or a part, part hole model if you prefer.

Okay, and then when you've done that, tell a subtraction story for the same group of objects representing that in the same way.

So for example, you might look at the balloons and tell an addition story for them and then a subtraction story for them.

Okay, so pause the video now while you do that, Let's see how you got on.

Okay, so you may have done this.

We'll just choose one example.

So I'll choose the balloon example.

There are six balloons that are blown up and two that have burst.

How many balloons are there all together? So that's my addition story.

And there we can say, see if the counters there, six counters representing the six blown up balloons and two counters representing the two burst balloons.

And when we combine them to make the whole, we can see that there are eight balloons altogether, six plus two is equal to eight.

Then my subtraction story would be there are eight balloons, two have burst, how many have not burst? And then you would subtract the two, partition the two, and see that there were six balloons remaining.

Eight minus two is equal to six.

So well done, excellent.

You've worked really hard in today's lesson and found out lots about subtraction and also about addition.

So well done, so let's think about what you've learned in today's lesson.

In problems when you know the hole on one part of the hole, you can use subtraction to find the missing part.

This can be represented with a subtraction equation in problems when you know the parts you can use addition to combine them to find the hole.

And this can be represented with an addition equation.

So well done, excellent work in today's lesson.

Worked really hard and I've really enjoyed it.