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.

And welcome to today's lesson, which is called Interpret and Represent Subtraction Stories, and it comes from the unit, Additive Structures, Addition and Subtraction.

So in today's lesson, we're going to interpret and represent subtraction stories that involve decreasing an amount, and we're going to use the first, then, now structure again to do that.

And by the end of this lesson, you should feel much more confident interpreting and representing those stories and writing equations to match them.

So, let's get started.

So our keywords for today are first, my turn first, your turn.

And then my turn, then your turn.

Now, my turn.

Now, your turn.

And decrease, my turn, decrease, your turn.

Well done.

So in the first part of today's lesson, we're going to represent first, then, now subtraction stories.

In this lesson you will meet Aisha and Alex.

We can represent first, then, now subtraction stories using a tens frame.

In a first, then, now subtraction story, we decrease the whole amount at the start of the story to leave a part of the whole.

First I had five pounds in my purse, there's the five pounds, then I spent two pounds, now I have three pounds left in my purse.

We can represent this as the equation, five minus two is equal to three.

Think about what our counters represent.

The whole group of counters represents the five pounds in my purse at the start of the story, this is the number that was decreased.

The two counters that were taken away represent the two pounds that were spent.

And the three counters remaining represent the three pounds left in my purse at the end of the story.

We can also use a bead string to represent a first, then, now story.

First, there were nine cats on the wall.

Then, four cats jumped off the wall, and there we can see four beads have been taken away.

Now, there are five cats on the wall.

We can write this as the equation, nine minus four is equal to five.

Let's explain how the numbers in the equation are linked to the beads that we used.

The nine represents the nine cats at the start of the story.

It's shown on the bead string as the whole group of nine beads, this is the amount that was decreased.

The four represents the four cats that jumped off the wall.

It is shown on the bead string as the four white beads that were subtracted.

And the five represents the five cats at the end of the story, it is shown on the bead string as the five red beads that are remaining.

Alex and Aisha both represent this story using practical equipment, who is right? First, my piece of string was eight centimetres long.

Then, I cut off five centimetres.

Now, my piece of string is three centimetres long.

So let's see what they do.

So Alex starts with his eight counters, and he subtracts five counters there, doesn't he? To leave three, and Aisha starts off with eight counters, and she subtracts five to leave three.

So they are both right, they both started with eight and then subtracted five to decrease the amount at the start of the story.

The colour of the beads that were subtracted is not important, it is the number of beads, the fact that it was five beads that represent the story, isn't it? So now, let's check your understanding of that.

Which pictures represent this story? And explain how you know.

First, Alex had seven conkers in his bag.

Then, four conkers fell out.

Now, he has three conkers in his bag.

Okay, so let's have a look at the first tens frame.

Okay, let's see that again.

Okay, and now let's look at the bead string.

Okay, and then let's look at that again.

That's right, and now let's look at this at C, the tens frame there.

Okay, and let's look at that again.

Okay, so pause the video now while you think about which picture represents that story.

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

Okay, so A and B were both correct, weren't they? Examples A and B were correct because they started with seven and subtracted four to decrease the amount.

In example C, they started with seven, but they subtracted three, didn't they? So that was incorrect, so well done if you spotted that.

Okay, so when a subtraction equation represents a first, then, now story, the order in which it is written is important.

The amount at the start of the story, the minuend, is the amount that is decreased.

So this must be written first.

So on this case, we can see there's nine counters at the start, so, nine.

The number that is subtracted, the subtrahend, is written after the minus sign.

So minus three, we can see three counters have been subtracted.

The number at the end of the story, the difference, is the part of the hole that is remaining.

So nine minus three is equal to six, and you can see there are six counters remaining.

So now, it is time to check your understanding again.

Represent this story on your tens frame, then write the equation and explain what happened.

First, there were seven pencils in the pot.

Then, I took four pencils from the pot.

Now, there are three pencils in the pot.

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

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

So first, there were seven pencils in the pot.

So you need to write seven in your equation first, don't you? Then I took four pencils from the pot, so you need to take four away and write minus four.

Seven minus four is equal to, we can see there are three pencils in the pot, three counters remaining, so seven minus four is equal to three, well done.

Okay, so we started with seven pencils and subtracted four to decrease the amount of pencils.

Okay, so Aisha represents this first, then, now story as the equation, five minus two is equal to seven.

So let's read the story together.

First, there were seven apples on the tree.

Then I picked five apples from the tree.

Now, there are two apples on the tree.

And there, we can see there's seven counters.

And then we subtract five to represent the five apples that were picked, and there are two remaining.

Aisha has written five minus two is equal to seven.

Is that correct? The minuend at the start of the story must be decreased.

So this needs to be represented first in the equation.

So we can see at the start of our story, there were seven apples, but she has written five at the start of her subtraction equation.

So she needed to write seven, didn't she? That's right, that was her mistake.

So it should have been, seven minus five is equal to two.

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

Represent this story on your tens frame.

Which equation represents a story? First, there were seven stickers in my book.

Then, I used six of the stickers.

Now, there is one sticker left in my book.

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

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

So we can see there were seven and we subtracted six, and there were one remaining.

And so the correct equation was, seven minus six is equal to one.

So, well done if you did that.

So Alex represents a first, then, now subtraction story on his tens frame, here is his 10 frame.

I wonder what number is at the start of his story.

He says, "My counter did not change from the start to the end of my story." And Aisha's saying, "I wonder what number Alex subtracted." Let's tell a first, then, now story to help us find out.

First, there were eight counters on the tens frame, that was the start of his story.

Then, mm counters were subtracted.

Now, there are eight counters on the tens frame.

So what must have been subtracted? That's right, there must have been no counters subtracted, zero, because the number remained the same from the start to the end of the story.

When zero is subtracted from the start of the story, the amount does not decrease.

So all parts of the story look the same.

Let's check your understanding of that.

Aisha represents a first, then, now subtraction story.

The tens frame shows the end of her story.

Which of these numbers will complete her story? Okay, and you can see the story there says, first there were mm counters on the tens frame.

Then, no counters, zero counters were subtracted.

Now, there are six counters on the tens frame.

So you have to decide whether her story started with zero, four, or six.

Pause the video now while you try that.

Okay, and let's see, what did you think? That's right, it should have been six, because there were no counters subtracted and six counters at the end of the story.

So the story must have started with six.

Aisha uses a tens frame to represent a first, then, now subtraction story.

"At the start of my story, there were 10 counters on my tens frame," there they are.

"At the end of my story, there are no counters on my tens frame." And Alex is saying, "I know how many counters you subtracted," I wonder if you do.

We know that when the amount subtracted is equal to the whole amount of the start of the story, there will be zero left.

And so Alex is saying, you must have subtracted 10 counters.

And that's all 10, that's right.

It left zero, none.

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

Fill in the missing numbers to complete the first, then, now story, use a tens frame to help you.

First, there were mm counters on the tens frame.

Then, mm counters were subtracted.

Now, there are no counters on the tens frame.

So pause the video now while you try that.

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

So you could have said, so first there were two counters on the tens frame.

Then, that's right, it would have to be two counters subtracted to leave no counters on the tens frame, wouldn't it? You could have said there were three counters on the tens frame first, then three counters were subtracted.

So there were no counters left on the tens frame.

So as long as the start of your story and the amount subtracted is the same, it would leave zero, wouldn't it? So there, again, four counters on the tens frame.

So that's right, four counters were subtracted.

You could have had any number up to 10, as long as the amount subtracted was equal to the amount at the start of the story, so, well done.

So we can use a bar model to represent first, then, now stories.

First, there were six bananas in the bunch.

And we can see the six counters representing the bananas, can't we? But also, we have a bar of six representing the whole amount.

Then, two bananas were eaten, so part of the six were eaten.

So we draw a bar of two that shows that two was the part that were subtracted.

Now, there are four bananas in the bunch.

And that shows that the part that was remaining from the whole of six, doesn't it? What does each part of the bar model represent? So first there were six bananas in a bunch, then two bananas are eaten, now there are four bananas in the bunch.

The six represents the six bananas in the bunch at the start of the story, doesn't it? The two represents the two bananas that were eaten.

And the four represents the four bananas in the bunch at the end of the story.

So, well done if you noticed that.

Okay, so Aisha represented a first, then, now story on a tens frame.

Okay, we can see the five counters there.

So there must be five at the start of her story.

Let's see which bar model will represent her story.

First, there were five counters.

The bar model must show five as the whole amount, so that's given it a bit of a clue, isn't it? Then, two counters were subtracted.

So the bar model must take two counters from the whole.

So we can see that the correct bar model must be that one there.

Now, there are three counters left in the remaining part.

We can see that there are in that bar model.

Okay, if we have a look at the other bar model, we can see it didn't have five as the whole amount.

And also, there weren't three remaining, were there? So that couldn't have been right, so, well done.

Now it's time to check your understanding again.

Match each bar model to the correct picture.

So I'm going to show you how many are being subtracted in each picture, and then you're going to pause a video and think about which bar model matches which picture.

So let's have a look at the tens frame first, okay? So we can see, look at the tens frame carefully, and then watch what happens.

Okay, so perhaps you could write down the equation to help you remember that.

Let's see it again.

Okay, now let's look at the bead string.

Okay, so here's the bead string here, and let's watch.

Okay, and then let's look at it again.

Okay, so pause the video now while you decide which bar model matches which picture.

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

So if we look at the first bar model, we can see the whole amount is six and two were subtracted.

Okay, so that must match the bead string, okay? And then the second bar model had, first, there were four and then two were subtracted.

So that matched the tens frame.

So, well done you spotted that.

Okay, so let's tell a story of our own that this bar model could represent.

We can write the equation to match, okay? So let's have a look.

Think about the whole amount at the start of the story.

First, there were nine pencils in the pencil case, and we can represent that on our tens frame like that.

Then, my friend borrowed two pencils, so two must be subtracted.

Now, there are seven pencils in my pencil case.

So we can see that there are seven remaining.

So the equation that we would write would be, nine minus two is equal to seven.

So here's the task for the first part of your story, tell a first, then, now story for each bar model shown, and represent it with counters on a tens frame or on a bead string.

Then write the equation that would also represent it, okay? And what do you notice about each pair of bar models? So pause the video now while you try that.

Okay, so let's see how you got on, you may have done this.

So there's our first bar model, and we're going to represent it on the tens frame and tell a story.

First, there were eight pens on the table.

Then, three pens were taken from the table.

Now, there are five pens on the table.

And the equation we would write would be, eight minus three is equal to five.

Okay, then let's look at the second bar model.

First, there were eight pens on the table.

Then, five pens were taken from the table.

Now, there are three pens on the table.

And the equation is, eight minus five is equal to three.

You may have noticed that both stories involve the same numbers, but the amount that was being decreased was different each time, wasn't it? So, well done if you spotted that.

You've worked really hard in the first part of our session today, so that's excellent, well done.

So in the next part of our lesson, we're going to represent subtraction on a number line.

We can represent first, then, now stories on a number line.

First, there were six books on the shelf.

Then, two books fell off the shelf.

Now, there are four books on the shelf.

Which number will be at the start of our story? 'Cause it's a subtraction story, isn't it? So which number will we start with? That's right, six.

We know that six is the amount to be decreased, so we can start our count and count back from six.

We know that two books have to be subtracted, or taken away, 'cause they fell off the shelf.

So how will we represent that? One, two.

Counting back in ones takes a long time, doesn't it? Especially if you had to count back a large number.

So we can count back two together here, can't we? We can put those two jumps into one jump.

And there's minus two.

And then we can see now, there are four books on the shelf.

So four is at the end of our story.

What does each number represent then? Let's have a look.

The six represents the number of books at the start of the story.

The two represents the number of books that were subtracted.

And the four represents the number of books at the end of the story, doesn't it? This number line represents the story below.

How many were subtracted from the number at the start of the story, look carefully.

So we'll read the story together.

First, there were nine pizza slices on the plate.

Then, three pizza slices were eaten.

So now, there are six pizza slices on the plate.

That's right, three pizza slices were eaten.

When a number is subtracted from another number, we know it is called the subtrahend.

Three is the subtrahend.

Is Aisha, right? She's saying, "I can see two lines, I think two has been subtracted." When subtracting on a number line, each space represents one that has been counted.

So you have to count the spaces, not the lines, don't you? You can see one, two, three were subtracted.

So that jump is minus three, three is the subtrahend.

So now, it is time to check your understanding again.

Match each number line to the amount that has been subtracted.

So pause the video now while you look carefully at those number lines and decide.

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

So our first number line here, remember, we have to count the spaces and not the lines.

So we can see there are three spaces, so three is the subtrahend, three was subtracted.

The next number line here, the second one, we can see there are two spaces.

So two is the subtrahend, two was subtracted.

And in the last one, we can see there's just one space, so one is the subtrahend, one was subtracted.

So, well done if you spotted that.

And here's another check.

Which story does this number line represent? So there are two stories, let's listen carefully.

First, Alex had six toys.

Then, he gave three to his friend.

Now, he has two toys.

So the second story is, first, Aisha had six toys.

Then, she gave four to her friend.

Now, she has two toys.

So which story would that number line represent? So think carefully about that, pause the video while you think.

Okay, so what did you think? That's right, so we can see Aisha had six toys.

Both stories started with six, but then we can see that she gave four to her friend, and we can see that there are four spaces there on the number line.

So four was the amount subtracted, four was the subtrahend, well done if you spotted that.

We can write an equation to represent the story shown on a number line, so let's try.

First, the tree was 10 metres tall.

First, we can see 10 on the number line.

This is the number to be decreased, and we write that first in our equation.

Then, three metres were chopped down, they lost three metres off the tree.

So we have to subtract three.

We can see three has been subtracted, this is the subtrahend.

So 10 minus three is our equation so far.

Okay, so now, it is seven metres tall.

Now, we can see that the number at the end of the story is seven.

We know in a subtraction equation, this is called the difference.

10 minus three is equal to seven.

So let's check your understanding of that.

Aisha and Alex both write an equation to represent the story shown on the number line, who is right? So Aisha says, "I think it is seven minus three is equal to four," and Alex says, "I think is just seven minus four is equal to three." Okay, so pause the video while you decide who is right.

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

What did you think? First, we can see seven is the minuend.

This is the number to be decreased, okay? Then we can see that four is the subtrahend.

So we must subtract four, okay? And we knew four was the subtrahend, because there are four spaces.

Okay, now we can see the number at the end of the story is three, this is the difference.

So seven minus four is equal to three, so we can see that Alex was right.

Let's use the number line to complete the story, then write the equation.

First, there were children mm on the bench.

Then, mm children got off the bench.

Now, there are mm children on the bench.

So let's have a look.

First there were eight children on the bench.

Then, two children got off the bench.

Now, there are six children on the bench.

Eight minus two is equal to six, isn't it? Okay, so let's use the number line to tell our own story, and then write an equation.

Okay, so I can see the first number in the story is six, so my story must start with six.

First, I drew six pictures in my book, and I write six first in my equation.

Then, I rubbed out two pictures in my book, so six minus two.

Now, there are four pictures in my book.

Six minus two is equal to four, well done.

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

You will need an number line to represent your story.

"I will listen to the first, then, now stories that are read to me," says Alex.

Then "I will circle the number at the start of the story and show the amount to be subtracted with an arrow." Then "I will circle the number at the end of the story and write the equation," okay? So, for example, first, there were five cats on the wall.

So you would circle five at the start of your story.

Then, two cats jumped off the wall, so you'd subtract two.

Now, there are three cats on the wall, and there.

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

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

You may have done this.

First, there were seven toys in my toy box.

Seven is the start of your story.

Then I took two toys from my toy box, so you have to subtract two.

We have one jump of two there, okay? Now, there are five toys in my toy box, because five is the number at the end of your story.

So, well done, you've worked really hard with our learning today.

And hopefully, you're feeling much more confident now about telling those subtraction stories and writing the equations to represent them.

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

In a first, then, now subtraction story, an amount is decreased by subtracting one part.

This can be represented with practical equipment.

We can write an equation to match these representations.

And when using subtraction to decrease an amount, the amount that is decreased must always be represented first in the equation and in the story.

So, well done, you've worked really hard today, excellent, and I've really enjoyed our lesson.