Lesson video

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

I'm really looking forward to today's lesson.

I know you're going to work really hard and we'll do really well.

So let's get started.

So welcome to today's lesson.

And it's called "Furthering Understanding of Subtraction as Decreasing an Amount," and it comes from the unit Additive Structures, Addition and Subtraction.

In today's lesson, we're going to be looking at 'First, then, now' subtraction stories, and we're going to be comparing it to other addition and subtraction stories.

Okay, so by the end of today's lesson, you should have a much deeper understanding of 'First, then, now' subtraction stories and how they are linked to other types of stories.

So let's get started.

Okay, so our keywords for today are subtraction.

My turn, subtraction.

Your turn.

And decrease.

My turn, decrease.

Your turn.

And addition.

My turn, addition.

Your turn.

And increase.

My turn, increase.

Your turn.

Excellent, well done.

Okay, so in our lesson today, the first part of our lesson, we are going to compare a decrease in amount to partitioning.

Okay, two different ways of subtracting.

And in our lesson today, we will meet Aisha and we'll also meet Alex.

They'll be helping us with our learning.

Okay, so can you help Alex and Aisha solve the problem? Let's see what it is.

First, Alex and Aisha have five bananas.

Then they eat two bananas and throw them away.

How many bananas do they have now? And we can see the bananas have been thrown away there, haven't they? "I know how to find out," says Aisha.

"Some bananas have been thrown away.

I will use subtraction." She knew that when you take away, it's the same as subtracting.

When one part is taken away from the whole group, the amount in the whole group is decreased.

It is a subtraction story.

We can represent this as 5 - 2 = 3.

What does each number in the equation represent? The five represents the five bananas in the whole group at the start of the story, doesn't it? The two represents the two bananas that were thrown away.

These bananas were subtracted.

And there they are, subtraction.

The three represents the three bananas left at the part remaining.

What happens if we do not throw the bananas away? A different type of story, so we can tell a different story.

There are five bananas in the whole group.

Two of them have been eaten.

How many have not been eaten? "I wonder what type of story this is," says Aisha.

When one part of the whole amount is partitioned from the whole group, this is also subtraction.

It's a different type of subtraction.

And there we can see those two have been partitioned from the group.

And we can represent this also as an equation.

5 - 2 = 3.

What's the same in each story? The whole group at the start of each story is the same, isn't it? They both started with five bananas.

There so in our equation, the five is the same.

The part of the whole that was subtracted is the same.

We can see they both subtracted two.

In one story two were thrown away.

And in the other story, two were partitioned from the whole group.

The part of the group remaining is also the same, isn't it? The three in the equation, that's right.

The three bananas that are left.

This means the equation to represent them is the same.

And we can see that there, can't we? What's different in each story? In the first story, the bananas have been thrown away.

We cannot see them in the whole group anymore, can we? The minus signs shows they've been taken away or subtracted.

In the second story, the bananas can still be seen as part of the whole group.

The minus sign shows they have been partitioned or subtracted.

Act out this story using counters to represent the hot and cold drinks.

There we can see them there.

So there were four drinks on the table.

Those four counters represent the four drinks.

The three cold drinks were taken.

How many drinks were left on the table? Write an equation to represent this story.

And we would write 4 - 3 = 1.

To show that the drinks were taken, we removed three counters.

Now we cannot see them in the whole group.

Perhaps you could think about what the numbers in the equation represent from the story.

Now, here is a different subtraction story to act out.

Use double-sided counters to represent the drinks.

There were four drinks on the table.

Three of them were cold drinks.

And there, so we turned over over three counters to represent those cold drinks.

How many drinks were not cold? Write an equation to represent this story.

So this time instead of decreasing an amount, it's as a partitioning subtraction story, isn't it? 4 - 3 = 1.

And again, perhaps you could think about what those numerals in the equation represent.

To show that the drinks were not hot, we turned over three counters.

We can still see them in the whole group.

So now it's time to check your understanding.

Represent this story with counters, then write the equation to represent it.

There were seven cakes at a party.

The chocolate cakes were eaten.

How many cakes were left at the party? So pause the video now while you try that.

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

So we can represent our cakes with counters.

So that represents the whole group of seven cakes.

And then we can see that two counters were subtracted.

They represent the cakes that were eaten.

They were taken away, weren't they? And the equation will be 7 - 2 = 5.

In this story, the chocolate cakes were eaten, so they were taken away or subtracted from the whole group.

Now we cannot see them in the whole group.

So here's another check now.

Represent this story with double sided counters.

Then write the equation to represent it.

So it's a different subtraction story this time.

There were seven cakes at a party.

Two were chocolate cakes.

How many were not chocolate cakes? So pause the video now while you try that.

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

So we needed seven counters.

Didn't we? To represent the whole group of seven cakes.

And then, we know that two were chocolate cakes, so we needed to turn over two counters to represent the two that had been partitioned from the group.

And then, we can see that the red counters represent the cakes that were not chocolate cakes, the remaining part of the group.

So the equation we would write would be 7 - 2 = 5.

Well done.

In this story, the chocolate cakes were one part of the group, so we partitioned or subtracted them.

We can still see them in the whole group.

Okay, so let's use the stem sentences here to complete this 'First, then, now' subtraction story.

First, there were eight hats in the shop.

Then, oh, so Alex has given us a clue.

He's saying one part of the whole group has been taken away.

The two stripy hats were sold.

Now, there are six hats in the shop.

And our equation to represent that would be 8 - 2 = 6.

Perhaps you could think about what the numerals in that equation represent from the story.

So now let's use the stem sentences to complete this partitioning subtraction story.

There were eight hats altogether in the shop.

Mm at them were mm.

How many of them were not mm? So Alex is giving us a clue there.

He says, "I need to partition one part of the whole group." And it's our story, so we can decide which part we're going to partition, can't we? So let's have a look.

There were eight hats altogether in the shop.

I think I'll say two of them were stripy.

So we partitioned the two stripy hats, haven't we? How many of them then were not stripy? So I chose to partition the stripy hats.

And the equation to represent that would be 8 - 2 = 6.

Okay, so time for another check now.

Use the stem sentences to complete this 'First, then, now' subtraction story and write the equation.

First, there were five toys in the toy shop.

Then, mm? Now, there are, mm? Okay, look carefully at the picture to help you.

Okay, and pause a video while you try that.

Let's see how we got on.

So first there were five toys in the toy shop.

We can see them in the picture at the start of the story, can't we? Then what happened? So Alex is saying, "Which part of the whole group has been taken away?" That's right.

Then the three knights were sold, weren't they? And now, there are two toys left in the shop.

The two unicorns are remaining from the whole group, aren't they? So well done if you spotted that.

What's the equation that would represent that? That's right.

5 - 3 = 2.

So well done.

So we've got another check here.

This time it's a different type of subtraction story.

Now use the stem sentences to complete this partitioning subtraction story.

Okay, so the story is there were five toys altogether in the toy shop.

And then, mm of them were mm.

How many of them were not mm? So Alex is giving us a clue there.

"Which part of the whole group will you partition?" So you can decide, can't you, what your story's going to be.

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

Okay, and let's see what you did.

So there were five toys altogether in the toy shop, okay? Three of them were knights.

So you could have chosen to partition the knights, couldn't you? How many of them were not knights? And we can see.

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

You will need some double-sided counters.

And here's Aisha, and she's telling us what to do.

Okay, so she's doing this task as well.

She says, "I will tell a 'First, then, now' story about each picture and represent it with counters using the stem sentences to help me.

Then, I will tell a partitioning story about the same picture.

Each time, I will write an equation to represent it." Okay, so you will have some pictures and some stem sentences.

Here they are, okay.

And the stem sentences for the decreasing amount, an amount subtraction story is here.

First, there were mm, then mm, now mm.

Okay, you also have some stem sentences for the partitioning subtraction story.

And they are, there were mm altogether.

Mm of them were mm.

How many were not mm? So you use those stem sentences to describe the pictures, okay? So pause the video now while you have a try at that.

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

You may have done this.

Okay, so we're describing the balloons picture here, aren't we? So let's tell our decreasing in amount subtraction story, first, okay.

First, there were three balloons at the party.

We can see them there.

Then we could say one balloon blew away.

There we go.

You may have crossed it out in your picture or covered it up.

Now there are two balloons at the party.

And we would represent that with the equation 3 - 1 = 2.

Okay, so now let's start again and tell our partitioning subtraction story.

So there were three balloons altogether.

One of them was spotty.

And we partitioned the spotty one, didn't we? How many were not spotty? Or you may have chosen to partition the not spotty ones off instead, it's up to you, isn't it? Okay, and the equation to represent what we did there when we partitioned the spotty balloon was 3 - 1 = 2.

So well done, if you've got that, excellent work.

You've worked really hard in the first part of our lesson.

Okay, so now in the next part of our lesson, we're going to compare a decrease in amount to an increase in amount.

Alex tells a 'First, then, now' story.

Act out the story he tells, okay.

And we can use the pictures to help us.

First, there are three children standing on the mat.

Then, two more children come to stand on the mat.

Now, there are five children standing on the mat.

I wonder if this is an addition story or a subtraction story.

In an addition story, the number of the at the start of the story increases, okay? It becomes greater the amount, doesn't it? In a subtraction story, the number at the start of the story decreases.

Okay, the amount becomes less.

The number three was increased in this story, wasn't it? So it is an addition story, okay.

We can see that the amount became greater.

So now it's time to check your understanding.

Let's represent this new story on a tens frame to find out if it is an addition story or a subtraction story, okay.

So think about which part of the story will help us to find out.

First, my sunflower was three centimetres tall.

Then, it grew another three centimetres.

Now, it's six centimetres tall.

Okay, so pause the video now while you think about whether that is an addition or a subtraction story.

And what did you think? Aisha's there.

She's saying the number three was increased, the quantity, the amount became greater.

So it must be an addition story.

Here are the parts of the story they're presented in a slightly different way, aren't they? Which part of the story will tell you if it is an addition or a subtraction? Aisha says, "I will look at the then part of the story to see if an amount has been added or subtracted." And Alex says, "I will look at the numbers at the start and end of the story." Has the number at the start of the story increased or decreased? So let's explore this idea a little bit further using a number line.

First, my sunflower was three centimetres tall.

Then, it grew another three centimetres.

Now, it is six centimetres tall.

Which part of the number line tells us that it is an addition story? We can look to see if the number at the start of the story has increased or decreased, can't we? We can see three was increased there.

Okay, we can look to see if a number has been added or subtracted.

We can see that three were added.

So we know it is an addition story.

We can represent our story with an equation.

First, my sunflower was three centimetres tall.

Then, it grew another three centimetres.

So we increase the amount by adding three.

Now, it is six centimetres tall.

So, 3 + 3 = 6.

Here is a different story.

Let's represent this story to find out if it is an addition story.

Which part of the story should we look at to find out? First, I had eight pounds.

Then, I spent six pounds.

Now, I have two pounds left.

Have some been added or subtracted? Has the number at the start of the story increased or decreased? Alex noticed the part of the story that said, "Then, I spent six pounds." If you spend money, you take it away.

I think it's subtraction because some were subtracted.

But Aisha's saying that she looked at the start and end of the story.

"First, I had at eight pounds.

Now, I have two pounds." So she can see the number at the start of the story was decreased.

So she knows its subtraction.

She found out a different way, didn't she? Let's write an equation to represent the story.

8 - 6 = 2.

And you may think about what those numerals represent in the story.

Okay, so let's represent this story on a number line then.

First, I had eight pounds.

Then, I spent six pounds.

Now, I have two pounds left.

Which part of the number line tells us that it is a subtraction story? Then, I spent six pounds.

So it's the subtraction of six.

We can see we subtracted six there, can't we? Okay, so now it's time to check your understanding again.

Okay, so match each number line to show whether it represents an addition or a subtraction story.

Okay, so think about which part you will look at to help you with that.

Pause the video while you decide.

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

Okay, so let's look at this first number line.

And we can see we started with seven, didn't we, our story with seven.

And then, we subtracted two to reach five.

So that must be a subtraction.

And then, the next number line, the second one, we started with five and we added two to reach seven.

So that must have been an addition.

So well done.

Now we've got a check here.

So this time match each number line to show whether the number at the start of the story has been increased or decreased.

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

Okay, so what did you think? So let's have a look at the first number line here.

7 + 3 = 10.

So we can see that seven has been increased in size, hasn't it? Okay, the quantity, the amount became greater.

Okay, and then this one below here we can see that the start of our story is 10, and we subtract three to reach seven.

So that has been decreased because a number 10 was the amount was decreased in size, it became less.

So well done.

Okay, so Aisha tells a 'First, then, now' story.

What mistake has been made? First, I had four pennies in my pocket.

Then, three pennies fell out.

Now, I have seven pennies in my pocket.

Let's represent it on a tens frame to find the mistake.

So first, I had four pennies in my pocket.

Then, three pennies fell out.

The first number was decreased, wasn't it? The number at the end of the story should be less than at the start of the story.

So we couldn't have had seven pennies left at the end of the story, could we? In this subtraction story, the number at the start could not increase, could it? Okay, so now time to check your understanding again.

Which of the following stories cannot be correct? Explain how you know.

Okay, so first, my tower was five bricks tall.

Then, I added another four bricks.

Now, there is one brick in my tower, okay? And the next story is first, my tower was five bricks tall.

Then, I added another four bricks.

Now, there are nine bricks in my tower.

So pause the video now while you think about that.

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

So that first story could not have been correct, could it? This could not be correct because when more bricks were added to the group, the number at the start should increase, shouldn't it? Okay, so well done if you notice that.

Now, let's look at each equation to decide which one matches the story.

So we've got 6 + 3 = 9.

And we've got 9 - 3 = 6.

Okay, and let's have a look at the story.

First, there were nine cups in the cupboard.

Then, three cups smashed.

Now, there are six cups in the cupboard.

Aisha is telling us in the 'then' part of the story, some cups were subtracted.

The number at the start of the story decreased.

So it must be 9 - 3 = 6.

So well done if you spotted that.

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

Alex wrote an equation to represent this story.

Which equation did he write? Explain how you know.

Okay, so there are two equations.

4 + 3 = 7.

7 - 3 = 4.

Okay, and here's the story.

First, there were four pencils in the packet.

Then, I put in three more pencils.

Now, I have seven pencils in my packet.

So pause the video now while you decide which equation represents that story.

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

Okay, so we can see that 4 + 3 = 7.

Okay, because there were four pencils in the packet at the start of the story, and then three were added.

4 + 3 = 7 at the end of the story.

Three pencils were added to the group, so the number at the start of the story increased.

So now here's your task for the second part of today's lesson.

Tell a 'First, then, now' story for each of these equations.

Then represent it with counters on a 'First, then, now' board.

Okay, and you can see the equations are arranged in pairs, aren't they, in twos.

So what do you notice about each pair of equations? What's the same and what's different? So pause the video now while you try it.

So, let's see how you got on with this.

Then you may have done this.

So, we can look at the first equation.

Okay, and we can see that at the start of the equation, there are five.

So five, and then we added one.

Didn't we? 5 + 1 = 6 at the end of the story.

Okay, and then the next equation, the one beneath it, we have six at the start of the story.

And this time, we are decreasing the amount.

So we say 6 - 1.

We subtract one.

6 - 1 = 5.

Did you notice in each pair of equations the same number is added and subtracted, isn't it? The number at the end of the addition equation is the same as the number at the start of the subtraction equation, isn't it? The number at the start of the subtraction equation is also the same as the number at the end of the addition equation.

Okay, so well done.

You've worked really hard in today's lesson.

Excellent work.

So let's look at what we found out today then.

We can subtract by partitioning, or we can subtract by decreasing an amount.

Two different ways of subtracting.

Both types of subtraction stories are represented by the same equation.

In an addition story, the amount at the start of the story is increased.

And in a subtraction story, the amount at the start of the story is decreased.

Okay, so lots of new learning today.

Okay, so well done.

Excellent work today.

I really enjoyed today's lesson.