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 will do really well, so let's get started and welcome to today's lesson, which is called Interpret and Represent Addition Stories, and it comes from the unit, Additive Structures: Addition and Subtraction.

So in our lesson today, we are going to be interpreting and representing addition stories that involve increasing an amount, and we're going to use the first, then, now structure to do that.

And by the end of today's lesson, you should feel much more confident with telling your own first, then, now stories and also with writing equations to match them.

So let's get started.

Our keywords today, the words that will be important for our learning are, first, my turn, first, your turn.

And then my turn, and then your turn.

And now, my turn, now, your turn.

And increase, my turn, increase, your turn.

Well done, that was excellent.

So in the first part of today's story, we are going to represent first, then, now addition stories.

And there we are, that's what we're going to be doing.

And in our lesson today, you will meet Aisha and also Alex, they're going to be helping us with our learning, we'll see them throughout our lesson today.

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

In a first, then, now addition story, we increase the amount at the start of the story to make the whole.

First, I had three pounds in my purse, that's the start of the story.

Then, I saved another two pounds.

Now, I have that's right, five pounds in my purse.

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

Let's think about what our counters represent.

The three blue counters represent, that's right, the three pounds in my purse at the start of the story, this is the amount that was increased.

The two red counters represent the two pounds that were added, and the whole group of five counters represent the five pounds at the end of the story.

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

And there's some beads, look.

First, there were five cats on the wall, then four more cats sat on the wall, now, there are nine cats on the wall.

We can write this as the equation, I wonder what we'll write.

That's right, five plus four is equal to nine.

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

The five represents the five cats at the start of the story, this is the amount that was increased.

It got larger, didn't it? A greater amount, it was increased.

The four, that's right, represents the four cats that were added and the nine represents the nine cats at the end of the story.

Alex and Aisha both represent a story using practical equipment, look and see.

Alex has used a tens frame and Aisha's used a bead string.

Who is right? Let's have a look at the story.

First, Aisha was three years old.

Then, five more years passed, now, she is eight years old.

Hmm, so you can see they both represented that story.

Who is right? That's right, they're both right, they both started with three, that was the number to be increased, wasn't it? And then added five to increase the amount at the start of the story.

The colour of the beads that are added are not important.

It is the number of beads or counters that represent the story, so the five more years passed, we had to have five counters or beads, but it didn't matter what colour they were, did it? Okay, so now it's time to check your understanding.

Which pictures represent this story? And then you've got to explain how you know.

First, Alex was three years old, then four more years passed by, now he is seven years old.

So which of those pictures is going to represent that story? Let's have a look.

So we've got there, we have that, and then the bead string, and there we go.

So pause the video now while you have a think about that.

So what did you think? That's right, both A and B represented that story because they both started with three, three beads and three counters.

And then they added four, didn't they? Example C, they started with four and added three, didn't they? They did it the other way round.

So they increased the number four.

Okay, well done with that, excellent.

When an addition equation is written to represent a first, then, now story, the order in which this is written is important.

The number representing the first part of the story is the amount that must be increased.

So this must be written first.

So there we can see six, the number that is added, the addend is written after the plus sign.

So six was the number to be increased, the first number in the story, and then we had plus three, that's the number that is added.

And there's our plus, our three that's been added.

The number at the end of the story, the sum, is the total amount altogether.

And in this case, you can see six plus three is equal to nine.

So time to check your understanding again.

Represent this story on a tens frame.

Then write the equation and explain what happened.

So let's have a look at the story.

First, I had five beads on my bracelet, then I added another three beads.

Now I have eight beads on my bracelet.

So pause the video now while you represent that story and write the equation.

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

So first I had five beads on my bracelet.

So first of all, you needed five counters to represent those five beads, didn't you? Then I added another three beads.

So there's three counters to represent those three beads.

And now we can see altogether we have eight beads, eight counters, so eight beads on my bracelet.

I wonder what the equation would look like.

What did you write? That's right, five plus three is equal to eight, excellent.

We started with five beads and added three to increase the amount of beads.

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

Let's have a look at the story.

First, my fence was five metres long.

Then I built another two metres of fence, now my fence is seven metres long.

What is her mistake, I wonder, what did she do there that wasn't quite right? So let's have a look at the story.

First, my fence was five metres long.

So we need five counters to represent that five metres.

And then I built another two metres of fence.

So we need two counters to represent the other two metres of fence.

It is the amount at the start of the story that must be increased, so this must be represented first in the equation.

And what Aisha did is she represented the two first in her equation, didn't she? And then added five, and that is not what happened in our story.

Well done if you spotted that.

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

So represent this story on your tens frame and then think about which of those equations would represent that story.

So first there was one sticker in my book.

Then I added six more stickers.

Now there are seven stickers in my book.

So pause the video now while you represent that and then select the correct equation.

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

Okay, so let's have a look at how we would represent that story.

First, there was one sticker in my book.

So we would need one counter, wouldn't we, to represent the one sticker? Then I added six more stickers and they represent the six more stickers.

Now there are seven stickers in my book.

So which equation did you select? That's right, one plus six is equal to seven.

Excellent, well done.

This tens frame shows the start of a first, then, now story.

At the end of the story, the tens frame looks exactly the same, that's strange, isn't it? Alex says, "I think a mistake has been made.

In a first, then, now addition story, the number, the start of the story must increase." And Aisha is saying, "Not always." Ooh, what do we think? Let's tell a first, then, now story to see what was added.

First, there were four counters on the tens frame, we can see them, can't we? Then hmm, counters were added.

Now there are four counters on the tens frame, still four.

What did you think? Well done, that's right, there were zero counters, no counters were added.

So the amount at the start of the story did not increase, did it? There must have been no counters added.

When zero is added to the start of a story, the amount does not increase.

So all parts of the story look the same, don't they? Well done.

So now let's check your understanding of that.

Tell your own first, then, now addition story, where zero is added and represented on a tens frame.

Use the stem sentences to help you tell the story.

So first, there were, mmm counters on the tens frame, then zero counters, no counters, were added.

Now there are mmm counters on the tens frame.

So pause the video while you try that yourself.

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

So there are lots of different ways you could have completed that story, but let's have a look.

You may have done this.

You could have said first there were seven counters on the tens frame, then zero, no counters were added, so now there are still seven counters on the tens frame.

That's right.

You could have picked any number up to 10, couldn't you? To represent on the tens frame.

When zero is added, the number will stay the same from the start to the end of the story.

Excellent, well done with that.

Alex and Aisha are playing, guess my number.

Alex is trying to guess the number at the start of Aisha's story.

"This time, the amount I added was the same as the amount at the end of the story," says Aisha.

"I know what the number at the start of your story is," says Alex.

"The number at the start of your story must be zero." Did you think that? We know that if the whole amount at the end of the story is equal to the part that was added, the story must start with zero.

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

Look at the first, then, now story, how many counters must have been added to the tens frame? Okay, so let's read it together.

First, there were zero counters, no counters on the tens frame, then mmm counters were added.

Now there are nine counters on the tens frame.

So have a think about that and pause the video while you try.

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

So first there were no counters and at the end of the story there were nine counters.

So how many counters must have been added? That's right, there must have been nine counters added.

Excellent.

What would the answer be if the story had ended with eight counters, I wonder? Pause the video while you have a think about that.

Okay, and what did you think? That's right, eight counters would've been added to the tens frame if there'd been eight at the start of the story.

Because when the story starts with zero, the amount added must be equal to the amount at the end of the story.

Well done, excellent if you spotted that.

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

First, there were four books on the shelf, so we can see a bar of four.

Then, two more books were added to the shelf, so we can see two more counters, and we put on another bar of two this time.

Now, there are six books on the shelf and we can see a bar representing six there, can't we? What does each part of the bar model represent? The four represents the four books on the shelf at the start of the story.

That's right, the two represents the two books that were added to the shelf.

So they were put onto the four.

And the six represents the six books on the shelf at the end of the story.

That's the whole amount when you add the two to the four, isn't it? Aisha represents a first, then, now story on a tens frame.

I wonder what her story is.

So let's have a look, we can see three counters on the tens frame and then two more added.

So let's see which bar model will represent her story.

First, there were three counters, the bar model must show three squares first.

So which one is that going to be? Then, two counters were added.

So the bar model must show two more squares.

Did you spot it? So we know it must have been that bar model because the order in which you add in a first, then, now story is important, isn't it? So now time to check your understanding of that.

So you're going to match each picture to the bar model that represents it.

So there's a bead string and you can see how many beads were on at first and it also shows you how many were added.

So pause the video now while you decide which bar model represents that bead string.

Okay, and did you spot it? That's right, you can see that first there were four beads on the bead string, then two beads were added, now, there are six beads on the bead string.

So it must have been the bar model with the four at the start of the story.

Now, let's have a look at this tens frame.

That's right, we can see that there were two counters at the start of the story.

First, there were two counters, then, two more counters were added, so it must have been that bar model there.

And finally have a look at this tens frame and match that to the correct bar model.

Okay, and let's see what you think.

So, it must have been that one.

We know that there were two counters at the start of the story and four counters were added.

Well done, excellent.

Now Alex uses the bar model to tell the story.

What is his mistake? Okay, so let's have a look at what he did.

First, there were four children on the bench, then he said five more children came along, now, there are nine children on the bench.

Can you spot what the mistake was there? That's right, he didn't start with the first number, he must start with the first number and increase the amount.

So he should have started with five, that's right.

First there were five children on the bench and then four more children came along.

It's because the order in which we add is important, isn't it? In a first, then, now story, and the equation to represent that is five plus four is equal to nine.

Let's tell a story of our own that this bar model could represent and we can write the equation to match.

So I think, hmm, our story has to start with, that's right, seven, I think I'll say first there were seven pencils in the pencil case, and I can represent that with seven counters on a tens frame.

Then, my friend gave me two more pencils.

Now there are, that's right, nine pencils in my pencil case.

And the equation would be seven plus two is equal to nine.

That's right.

Okay, so your task for the first part of today's lesson is to 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 represent it, so you can see some bar models there.

And you've got to think about what you notice about each pair of bar models.

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

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

So you may have done this.

First, there were five pens on the table and you could use five counters to represent the five pens.

And then three more pens were put on the table.

So now there are eight pens on the table and you would represent that with the equation that said five plus three is equal to eight.

And then the second bar model, this time, you're starting with three instead of five.

First, there were three pens on the table, then five more pens will put on the table, now, there are eight pens on the table and the equation to represent that would be the other way around, three plus five is equal to eight.

Okay, and then what did you notice about that pair of bar models? You may have noticed that both stories involved the same numbers, but the amount that was being increased, the amount at the start of the story, was different each time, wasn't it? So well done if you spotted that, excellent.

The second part of today's lesson is when we're going to be looking at representing addition on a number line.

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

First, there were four books on the shelf, then, two more books were added to the shelf, now, there are six books on the shelf.

Which number should we start counting from, do you think? That's right, we know that four is the amount to be increased, so we can start counting from four.

We know that two more books were added, so how will we show that? That's right, one, two.

Counting on in ones could take a long time, I think I will count on two here.

So you can do your count of two in one step, can't you? And we know that's plus two, and then now there are six books on the shelf.

So six is the amount, the whole amount at the end of the story.

What does each number represent? The four represents a number of books at the start of the story, doesn't it? The two represents a number of books that were added and the six represents the number of books at the end of the story, that's right, well done.

This number line represents the story below, how many were added to the number at the start of the story? So let's have a look at the story.

First, Alex climbed six steps.

Then, he climbed three more steps.

Now, he has climbed nine steps.

Okay, so how many were added to the number at the start of the story? That's right, it was three, 'cause the story says then he climbed three more steps.

So that's the amount that was added and we show it by jumping one step on the number line.

Can you see, we've jumped our three in one step, haven't we there? That's right.

When a number is added to another number, we know it is called an addend.

Three is the addend.

Now here's Aisha and she's saying, "I can see two lines, I think two has been added." Is Aisha, right? When adding on a number line, each space represents that one has been counted.

So you must count the spaces not the lines.

So we can see there that one, two, three spaces.

So that's three numbers, so we should have plus three.

It wasn't two, was it? Three is the addend.

So now it's time to check your understanding again, match each number line to the amount that has been added.

So you can see that there's an arrow on each number line, but it doesn't tell us what that arrow represents, it doesn't tell us how many have been added.

So you've got to look carefully to work that out.

So pause the video now while you try that.

And how did we get on? Let's have a look at this first number line.

We can see that two is the amount at the start of the story and then we jump on.

Now remember we have to count the spaces and not the lines, don't we? So one, two, three.

So it will be three is the addend there, that's right, three were added.

And then let's look at this next number line.

So we can see that if we count the spaces, there are two spaces, so this time two is the addend.

And then if we look at that final number line, we can see that there's just one space.

So one is the addend, one has been added.

So well done if you spotted that.

Okay, so here's another check for you to do.

So let's have a look at our number line and it says which story does this number line represent? So let's look at the stories.

First, Alex climbed two steps.

Then, he climbed three more steps.

Now, he has climbed six steps.

That's the first story.

The second story.

First, Aisha climbs two steps.

Then, she climbed four more steps.

Now, she has climbed six steps.

So you've got to think which story does that number line represent? Pause your video now while you have a think about that.

Which one did you think? Let's have a look.

That's right, it was that story, 'cause we can see that we started with two, didn't we? And then if we look at the spaces, there are four spaces.

So that means that we have added four, so one, two, three, four.

You can see we count the spaces.

And so we can see that she climbed four more steps.

Well done if you spotted that.

So we can write an equation to represent the story shown on the number line.

So let's do it together.

First, Aisha's sunflower was seven centimetres tall.

So in our equation we write seven.

Then, it grew three centimetres more.

So we can see that we have added three.

So we say seven plus three.

Now, it is 10 centimetres tall.

So seven plus three is equal to the whole amount of 10, isn't it? First, we can see seven on the number line, that was the number at the start of the story, this is the amount to be increased.

Then, we can see that three have been added.

This is the addend.

And you can see that in the equation and on the number line.

Now, we can see that the number at the end of the story is 10.

And we know this is called the sum in an equation, don't we? Seven plus three is equal to 10.

So time to check your understanding of that then.

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 four plus three is equal to seven." And Alex says, "I think it is three plus four is equal to seven." So who do you think is right? Pause the video now while you have a think about that.

And who did you think was right? Let's have a look.

That's right, it was Alex.

First, we can see three on the number line, this is the amount to be increased.

And we can write it in the equation there, can't we? Then, we can see that four has been added, this is the addend.

So three plus four, it's important that it's got the number that is at the start of the story, at the start of our equation, isn't it? And then now we can see the number at the end of the story is seven, this is the sum.

So three plus four is equal to seven.

Alex was right, wasn't he? Well done.

Okay, so let's use the number line to complete the story then write the equation.

So first, there were mmm children on the bench, then mmm more children came along.

Now there are mmm children on the bench.

So first, there were how many children at the start of the story? That's right, there was six children on the bench.

Then, how many children were added? That's right, so it must be then two more children came along.

We can see a step of two with the arrow there, can't we? Now there are, that's right, eight children on the bench.

So excellent.

Six plus two is equal to eight.

So let's use the number line to tell our own story and then write an equation.

So we've got, first, we can see it has to be something with four.

So I'm going to choose, I think, four pictures.

First, I drew four pictures in my book and I represent that first in the equation, don't I? Then I drew two more pictures in my book.

So it would be four plus two.

Now there are, that's right, six pictures in my book.

So my equation here is four plus two is equal to six, and I used the numbers on the number line to tell my story, didn't I? So here's your task for the second part of today's lesson, and Alex is telling us what to do here.

So you will need a number line to represent the story.

So have a number line ready.

I will listen to the first, then, now stories that are read to me, so you'll hear some stories.

And then I will circle the number at the start of the story on my number line, and show the amount to be added with an arrow.

One jump to show what has been added.

And then I will circle the number at the end of the story to show the now part of the story and write the equation to represent it.

So let's have a look at an example.

For example, first, there were three cats on the wall.

So you would circle three.

Then, two more cats jumped on the wall.

So you would look at two spaces and then we will jump in one step, won't we? Plus two represents the two more cats, now there are five cats on the wall, and that's five at the end of the story.

So pause the video now while you listen to the stories and have a try at that yourself.

So let's see how you got on.

You may have done this.

First, there were five toys in my toy box.

So you would circle a number five, that's right.

Then I put two more toys in my toy box.

So you would do one jump of two.

Now there are seven toys in my toy box.

And seven is the number at the end of the story.

So well done.

You've worked really hard in today's lesson and hopefully you feel really confident now about writing equations to represent first, then, now addition stories and representing them on number lines and telling the stories yourself.

So well done.

So let's see what we've learned in today's lesson then.

In a first, then, now story, an amount is increased to make the whole, this can be represented with practical equipment such as a bar model or a number line.

We can write an equation to match these representations, can't we? And when using addition to increasing amount, the amount that it has increased must always be represented first.

So well done, you've worked really hard in today's lesson and I've really enjoyed working with you.