Lesson video

Hello, my name is Mr. Tilstone and it's my great pleasure to be working with you today on what might be a new concept to you and that is negative numbers.

So, if you are ready, let's begin.

The outcome of today's lesson is I can represent a change story using addition and subtraction symbols.

Our keywords, which we are going to do in a my turn, your turn style are as follows.

So, my turn positive change.

My turn, negative change.

My turn, negative number.

Shall we see what those words and phrases mean? If an overall amount has increased, we can describe it as a positive change.

If it has decreased, we can describe it as a negative change and we're going to see lots of different examples in lots of different contexts in today's lesson of positive and negative changes.

And this is really important, any number less than zero is a negative number, a very important piece of information that we're going to revisit again and again.

Our lesson today is split into two cycles.

The first is going to be know that a change can be positive or negative, and the second is going to be represent a change using a negative number.

So, let's begin with cycle one, shall we? Know that a change can be positive or negative.

In this lesson, you're going to meet these two characters.

You might have met them before.

We're gonna have Sofia and Jun to help us out today.

So, Jun and Sofia are playing a game.

They have an unknown number of marbles in the bag.

So, you can see the bag there.

There's some marbles inside of it.

I don't know how many marbles there are in that bag.

You dunno either and Jun doesn't know and Sofia doesn't know, it's unknown.

Jun says, "I will say a number "and add that number of marbles to the bag." So, he's going to add some marbles to the bag.

Sofia says, "I will say a number "and take out that number of marbles from the bag." She's going to take out some marbles.

Let's see what they do.

So first of all then, Jun says, "Three.

"I will put in three marbles." He's going to add three marbles to the bag and Sofia says, "Two, I will take out two marbles." Let's see what happens.

Here's the three marbles in the bag.

Here's the two marbles taken outta the bag.

My question is this, has there been a change to the number of marbles in the bag? Have I think about that? Yes or no? Has there been a change? Well, there are now more marbles in the bag than there were at the beginning.

Sofia says, "I took out fewer marbles than you put in." She only took two out, but he put three in.

So, there's been a positive change.

There are more marbles now in the bag than there were at the start.

That's a positive change.

Again, I'm gonna go again.

So, Jun this time, just like before, let's put three marbles in and Sofia's going to take four marbles out.

Let's have a look at that.

Three in, four out.

Same question.

Has there been a change to the number of marbles in the bag? Yes or no? What do you think? Has there been a change? Yes, yes, there has been a change.

Are there more marbles in the bag now than there were at the store or are there fewer? Have a little think about that.

More marbles now or fewer marbles? Fewer.

There are fewer marbles in the bag now than they were before they played this round.

One more marble was taken out than was put in.

So, therefore there has been a negative change.

So, that's our key word in action, negative change.

Let's do a little check for understanding, shall we? Okay, describe the change.

Is it a positive change or is it a negative change? So, let's have a look at what's going on this time.

So, this time Jun's put four marbles into the bag and Sofia's taken seven marbles out.

Have a think about that and pause the video.

Well, let's have a think.

Four marbles have been added to the bag and seven marbles have been taken out, that makes that a negative change.

There are fewer marbles in the bag than there were at the start.

Let's do some practise.

So, Task A, number one is complete the table.

So, we've got a table, let's have a look at it.

On the left hand column we've got the number of marbles added to the bag.

And in the middle column we've got the number of marbles taken outta the bag.

What you've got to do is decide, has that been a positive change or a negative change? For number two, we're gonna look at a different context this time.

So, this time it's piggy banks.

So, Jun has some one pound coins in his piggy bank.

He adds some one pound coins to the piggy bank and takes some one pound coins out.

Complete the table.

So, let's have a look.

So, in the left hand column we've got the number of one pound coins added to the piggy bank, in the middle column, the number of one pound coins taken outta the piggy bank.

And you've got to decide once again, is that a positive change or is that a negative change? For number three, we've got a different context.

Again, this time it's about buses.

So, there were some people on a bus, the bus stopped and nine people got on, at the next stop, four people got off.

So think about that.

Nine people got on, four people got off.

Overall, is this positive change or is it a negative change? And then between April and May, the grass in Sofia's garden grew seven centimetres.

At the beginning of June, Sofia cut the grass by nine centimetres.

Is this a positive change or a negative change? And there's a little drawing there to help you to understand that.

Pause the video.

Good luck with this task and we'll see you soon for some answers.

Welcome back.

How did you find that task? Well, let's have a look.

So, for number one then five marbles added to the bag and three taken out.

That's overall a positive change.

If four marbles were added to the bag and seven taken out, that's a negative change.

There are fewer in there and specifically three fewer.

If two marbles are added to the bag and nine taken out, that makes that a negative change.

Again, seven negative to be precise, seven fewer.

And then if eight marbles are added to the bag and four taken out, that's a positive change overall, four more than they were at the start.

If one is added to the bag and no marbles are taken out this time, that's a positive change.

A slight positive change.

There's one more in the bag than they were at the start.

And then if no marbles were added to the bag, but one taken outta the bag, that's a negative change.

And specifically there's one fewer marble than there was at the start.

So number two, Jun has some one pound coin in his piggy bank.

He adds one pound coins to the piggy bank and takes some one pound coins out, complete the table.

So, if he adds five one pound coins and takes three out, that's a positive change overall.

There are more there at the end then at the start.

If three are added and four are taken out, that's a negative change.

There's one, one pound coin fewer.

If eight are added and five taken out, that's a positive change.

There are three more than there were at the start.

If two are added, an eight taken out, that's a negative change, specifically six pounds less than there was at the start.

And then if three pounds are added and eight pounds are taken away, that's a negative change.

Five pounds less to be specific.

Okay, this bus problem then.

So overall, if nine people got on and four people got off, that makes that a positive change overall.

There were gonna be five more people on that bus than there were at the start of the problem.

And then between April and May, the grass in Sofia's garden and grew seven centimetres.

So, you could see that on the drawing, you could see that May's taller than April and at the beginning of June, Sofia cut the grass by nine centimetres.

So, you can see that there's been a cut to the grass.

Is it a positive change or a negative change overall? It's a negative change.

Shall we do cycle two? Okay, let's go.

This is represent a change using a negative number.

Let's return to that game.

So, we'll return to the first example that we saw as well or to an earlier example rather.

So, Jun put three marbles in the bag and Sofia took four marbles outta the bag, if you remember, meaning there was a negative change, there's a negative difference of one, because there is now one fewer marble.

So, that's how we can describe that negative change, that negative difference of one.

Now here's how we could use an equation to express that.

We could say, three subtract four equals and listen for this part, negative one.

That's how we're going to say that.

So, that's how we write it and that's how we're going to say it.

Negative one.

So, let's say that again.

Three subtract four equals negative one.

So, as Jun is reminding us, we read that symbol there as negative one.

You might hear people saying minus one and that is not incorrect.

That's perfectly fine, but we're going to use the language negative one.

And Sofia's right, that is a negative number.

So, there's been another negative change this time.

What would the equation be this time? Let's have a think.

So, Jun's put five marbles in.

Sofia's taken eight marbles out.

How would that look? There's a negative difference of three, because there are now three fewer marbles than there were at the start.

We could express that as follows.

Now there's all sorts of language to describe that symbol.

We could say takeaway, subtract, minus, but let's go for, so that's five subtract eight equals.

This is the important part.

You remember how we say it? Negative three.

We read it as negative three.

It is once again a negative number.

Let's think about what each part of that equation represents then.

So, the five represents the number of marbles added to the bag.

Got that? The eight represents the number of marbles, taken outta the bag, have a thing what the negative three represents.

The negative three represents the change in the number of marbles.

I'd like to read that again, but I'd like you to read along with me if you will.

Are you ready? The five represents the number of marbles added to the bag.

The eight represents the number of marbles, taken out of the bag.

The negative three represents the change in the number of marbles.

So, let's check if you understood that part.

Jun and Sofia have played the game again and written the following equation.

Use the stem sentence to say what each of the numbers represents.

So, we've four, subtract six equals negative two.

So, the four represents the hmm, the six represents the hmm, the negative two represents the hmm.

So, if you've got a partner next to you, talk about this together, see if you can agree, pause a video and have a go.

Let's see.

So, the four represents the number of marbles added to the bag.

The six represents the number of marbles taken outta the bag and the negative two represents the change in the number of marbles.

Very well done if you got that right.

I think you are ready for some more independent practise.

Let's have a look.

So, you've got that table again, but with a slight change.

So, we've got the number of marbles added to the bag in the left column as before.

We've got the number of marbles taken outta the bag in the middle column as before.

But this time the right hand column says equation.

So, that's where you're going to represent that as an equation.

So, one's been done for you.

Let's have a look.

So, if four marbles are added to the bag and seven marbles taken outta the bag, that gives us the equation.

Four, subtract seven equals negative three.

See if you can complete the rest of them.

Now some will be negative and some will be positive.

For task two, again, you'll see this table that you've seen before but with a change.

So in the left hand column, it's the number of one pound coins added to the piggy bank in the middle column, the number of one pound coins taken outta the piggy bank.

But the change this time is you've got to write that as an equation.

And once again, some will be a positive difference and some will be a negative difference.

And for task three, bus stop and four people got on.

And the next stop, nine people got off, write an equation to show the change in the number of people.

So, we're looking for an equation, just like in task one and two.

And the same for number four then, so between April and May, the grass in Sofia's garden grew six centimetres.

At the beginning of June, Sofia cut the grass by eight centimetres.

Write an equation to show this change.

Pause the video.

Good luck with that and I'll see you shortly for some answers.

Welcome back.

Let's have a look how we got on with that then.

So, the first one was done for you.

Let's have a look at the next one.

If five marbles were added to the bag and three were taken out, the equation becomes five, subtract three equals negative two.

If two marbles are added to the bag and nine taken out.

This time, it's a negative change.

So, that's two subtract nine equals negative seven.

If eight marbles are added to the bag and four are taken out, that's gonna give us a positive change.

That's eight subtract four equals four.

If one marble is added to the bag but zero taken out, that gives us the equation, one subtract zero equals one, a small positive change.

And if zero marbles are added to the bag but one is taken out, that gives us the equation zero, subtract one equals negative one and that is a negative change.

And for task two, complete the table.

So, if five one pound coins were added and three were taken out, that gives us the equation.

Five takeaway three equals two, a positive change.

If three were added and four taken out, that gives us the equation.

Three, subtract four equals negative one.

So, it's a negative change.

If eight were added and five taken out, that gives us the equation eight, subtract five equals three, a positive change.

If two were added and eight taken out, that gives us the equation two.

Subtract eight equals negative six and negative change.

And if three were added, an eight taken out, that gives us the equation three.

Subtract eight equals negative five.

Very well done if you got those right.

For task three, the equation is as follows.

So, if four people got on and nine got off, that becomes four.

Subtract nine equals negative five, given their is a negative change to the number of people on the bus.

Well we've come to the end of the lesson.

So, our lesson today has been represented, change story using addition and subtraction symbols.

So, to summarise some of the key ideas there, change can be positive or negative and we've seen lots of context where it can be positive or negative.

We've seen the marble game that Jun and Sofia were playing.

We've seen grass growing and being cut.

We've seen buses with people getting on and off.

We've seen piggy banks.

When more of an item is removed than is added, you say there has been a negative change.

Equations can be used to illustrate change where the answer is a negative number, this represents a negative change.

So, let's have a look at an example here.

So, we've got Jun and Sofia playing the game.

Jun's adding three marbles and Sofia's taking four away.

And that gives us the equation three.

Subtract four equals negative one.

And just a reminder, we read that as negative one.

You've been amazing today.

I've thoroughly enjoyed talking about negative numbers and negative changes with you.

Hopefully I'll see you again soon, but a big well done on your achievements today.

Take care and goodbye.