Lesson video

Hiya.

My name's Ms. Lambow.

Really pleased that you've decided to join me today to do some maths.

Come on, let's get started.

Welcome to today's lesson.

The title of today's lesson is Ordering Negative Numbers, and that is within our unit, Comparing and Ordering Fractions and Decimals, Including Positives and Negatives.

By the end of this lesson, you'll be able to compare negative integers using the greater than or less than symbol.

Quick recap of a keyword or words that we'll be using in today's lesson, and that is the absolute value.

So remember, the absolute value of a number is its distance from zero.

EG, five and negative five are both five away from zero, so they both have an absolute value of five.

Today's lesson, we will split into two separate learning cycles.

In the first of those learning cycles, we will concentrate on a context, so ordering negative numbers in a real-life situation.

And for the second learning cycle, we'll be doing exactly the same thing, but we'll be removing that context.

Let's get started on that first learning cycle.

Here we go.

This is an image of my scratch card, or a scratch card.

Now this is a real-life story, so remember I said that we're going to be looking at things in a context, which means it often has a real-life story behind it.

In 2007, a lottery scratch card was withdrawn from sale.

That sounds a bit odd doesn't it? The Cool Cash games, and that's what they were, the scratch card was called Cool Cash, were released on a Monday, but withdrawn from sale just five days later.

That seems really odd, surely they'd got loads of those printed off, hmm.

The game was withdrawn after some players failed to grasp whether or not they had won.

Here's a story and it was published in the "Manchester Evening News".

One customer contacted Camelot, who run the national lottery, and said, "On one of my cards, it said I had to find temperatures lower than negative eight.

The numbers I uncovered were negative six and negative seven, so I thought I had won, and so did the woman in the shop.

But when she scanned the card, the machine said I hadn't." Another quote from the same lady: "I think Camelot are giving people the wrong impression.

The card doesn't say to look for a colder or warmer temperature, it says look for a higher or lower number.

Six is a lower number than eight.

Imagine how many people have been misled." She was really quite cross because she thought that Camelot, who run the lottery, have been misleading people.

To qualify for a prize, you had to reveal a temperature lower than the figure displayed, and the figure displayed was usually below zero.

So for example, on this lady's scratch card, she revealed negative eight degrees C.

And then she scratched off negative six degrees C and negative seven degrees C.

I'd like you to have a think about why they had not won.

So the lady thought she'd won, but why hadn't she? Hopefully you said something like this.

The greater the absolute value of a negative number, the lower it is, as it is further away from zero.

So negative eight is eight away from zero, negative six is only six away from zero, and negative seven is seven away from zero.

So actually negative six and negative seven are greater than negative eight.

What I'd like you to do now, in a moment, is you're gonna pause the video when I finish speaking and I'd like you to sort the temperatures into whether they are winning temperatures or losing temperatures.

So like I said, pause the video, and when you're ready, come back.

Great work, I'm sure you wouldn't have been fooled by the Cool Cash scratch card.

Let's have a look and make sure you've put those into the right places.

So negative six, negative six is larger than negative eight, so losing temperature.

Negative 10 is smaller, it's further away from zero, so therefore it's smaller.

That goes in the winning temperature.

Negative 8.

5, so I tried to see whether you'd really understood this here by choosing a decimal, and that should go in the winning temperatures, it's slightly further away from zero than negative eight.

Negative three is much closer to zero, so that would be a losing temperature.

And negative 16 is twice as far away, so that must be less than negative eight.

Well done with that.

Here are some places that negative numbers can be seen in everyday life, and I'm sure that you've got your own ideas of where you may have seen negative numbers before.

Let's just have a look at these few that will be using in today's lesson.

Temperature, so we've already mentioned that.

Temperature is a really good one to think about because actually it's something that we come across fairly regularly in our everyday life.

If we think about it, particularly in winter, we know that temperatures go below zero, so we end up with negative temperatures.

Another one might be stories in a building or in a lift.

I know that there is a car park that I go to where I get into the lift and it says minus two and I've parked my car two floors below ground level.

And then sea level, with sea level being zero, so anything in the sea and then above the sea.

Let's have a look at an example then where we are looking at sea level.

Sea level is zero, as we can see on the diagram.

Anything above sea level will be a something number, and anything below sea level will be a something number.

What I'd like you to do is to just have a think, what words do you think are missing in those two sentences? Great work.

If you think about it like a thermometer with zero, anything above zero is a positive temperature.

That means then that anything below sea level will be a negative number.

We're gonna write now the following in order from highest to lowest, so from the highest to the lowest, and these are the things that we are going to order.

We've got fish at negative three metres, octopus at negative 1800 metres, a kite at 150 metres, a seagull at 200 metres, and a shark at negative 1200 metres.

I'd like to pause the video and have a go at this before we go through it together.

So I want you to list them from which is the highest to which is the lowest.

Pause the video, have a go, and come back.

Super, so this is the order and I'm sure you will have got this right.

The seagull would be the highest in the sky, it is 200 metres above sea level.

Then the kite is a little bit lower than that, well not a little bit, it's 50 metres lower than that.

And then the fish we're now going down into sea level, we're into those negative numbers, so the fish is three metres below sea level, the shark is 1200 metres below sea level, and the octopus is the last one, which is negative 1800 metres below sea level.

Well done if you put those in the right order.

I'm sure you did.

Gonna have another go now then at you doing something independently.

You're gonna list the temperatures in order from warmest to coldest, and you're going to decide which of my answers is correct.

So is A in the correct order, remember we're going from coldest to warmest, is it B, or is it C? Pause the video.

When you've got an answer, come back.

See you soon.

Super, let's have a look then.

So remember if we we're doing for coldest to warmest, we want the one that's furthest away from zero, so the one with the largest absolute value.

And that is B.

A, they are in the correct order, but unfortunately I've ordered them from warmest to coldest.

And we can see the question actually asked us to do from coldest to warmest.

Now you're ready to have a go at some independent tasks.

So there are three questions within this task A.

What I'll do is I'll go through each question in turn.

The first one is just the same as you just did in that check for understanding.

I'd like you to write the following temperatures, coldest to warmest, pause the video, and come back and check your answers with me in a moment.

Now we can move on to question number two.

Wow, there's a lot of information here, isn't there? Don't worry.

We'll go through it all together first.

A quiz has 10 questions.

Dunno about you, but I love a quiz.

Points are given as follows: two points for each correct answer, minus one for each missed answer, and minus three for an incorrect answer.

We've got some of our Oak characters here, our Oak Academy students.

We've got Lucas, Laura, Jacob, and Sofia, and they're all giving us information about how they scored in the quiz.

So what you are going to do is you're going to work out their score and rank them from lowest to highest.

So let's just read through what they've got.

Lucas: "I got three correct, three missed questions, and four incorrect." Laura: "I got five correct, one missed question, and four incorrect." Jacob: "I got four correct and six incorrect." And Sofia got three correct, five missed questions, and two incorrect.

So you need to work out their total score and then rank them from lowest to highest.

Pause the video now.

Good luck, come back when you're ready.

Now remember I said there are three questions within task A, within this learning cycle.

So let's have a look now at question three.

Now I really, really like this question.

A hotel has 10 floors below reception, which is on the ground floor, which we're going to call floor zero.

There are bedrooms only on floors minus two, minus four, minus six, and minus seven.

On the other floors are the following.

There's a staff room, a gym, restaurant, a maintenance office, a basement, and a swimming pool.

What I'd like you to do is to use the clues to work out what is on each of the floors.

So your clues are, the swimming pool is two floors below the gym.

The staff room is between the basement and the maintenance office.

The restaurant is higher up than the gym.

The maintenance office is seven floors below the restaurant.

Right, so a lot of information there, but don't worry, you've got all of the skills that you need to be able to solve this problem.

So take your time, maybe draw out the table and write down the floors and then fill in the information that you know is definitely right and then you should be able to work out the rest.

Good luck with this.

Like I said, it is a challenging problem, but you'll be fine.

Come back when you're ready.

Pause the video now.

Wow, brilliant, well done.

I hope you enjoyed that one.

Now we're ready to go through the answers to those three questions.

So let's have a look.

One A, we should have, I'm not gonna read out the degrees C for all of them, I'll just read out the temperatures.

We should have negative 10, negative eight, negative five, negative four, negative two.

B, negative 27, negative 24, negative 22, negative 18, and negative 16.

C, negative 48, negative 43, negative 34, negative 32, and negative 23.

And D, negative 110, negative 104, negative 100, negative 96, and negative 88.

Well done if you got all of those right.

Now let's have a quick look at question number two.

So we can see now what each of the students scored.

Lucas scored negative nine, Laura scored negative three, Jake scored negative 10, and Sofia scored negative five.

So in order from the lowest to the highest score, we should have Jacob with negative 10, followed by Lucas with negative nine, Sofia with negative five, and Laura with negative three.

So well done Laura, you won the quiz.

Now that challenge, that was question three.

You should have, on floor zero was reception.

On minus one was the restaurant, minus two were the bedrooms, minus three, gym, minus four was more bedrooms, minus five, pool, minus six and minus seven were more bedrooms, minus eight was the office, minus nine was the staff room, and then minus 10 was the basement.

How did you get on with that? There's a bit of logic and a bit of number problem solving there.

Well done if you got those right.

We're now going to move on to our second learning cycle.

We're gonna be doing exactly the same as we just have, but we'll be removing that context.

So instead of thinking about things above and below sea level, or temperature, or the stories in a building, we will be just looking at the negative numbers alone.

Remember I did say earlier, sometimes it is useful, though, to think about them as temperatures.

It can also be useful to consider negative integers on a number line.

Here's my number line.

Absolute values increase as we move from zero to the left, and as we move from the zero to the right, the absolute values increase.

Which is greater, negative 46 or negative 50? The absolute value of negative 46 is 46 and the absolute value of negative 50 is 50.

The integer, remember, with the highest absolute value, is the least, because they are both negative, but negative 50 is further away from zero.

So negative 46 is greater.

And we can use our symbol there, remember I said that's what we were going to be looking at during today's lesson, that was our learning outcome.

I'd like you to do the same thing here now.

I'm sure you're ready to do this so remember, we're thinking about absolute values.

The greater the absolute value, the smaller the number.

I'd like you to pause the video and decide which symbols need to go between these three pairs of numbers.

Good luck.

Come back when you're ready.

Great work.

Now let's have a look.

We should have negative 185 is less than negative 158, negative 6875 is less than negative 6785, and negative 35,024 is greater than negative 35,042.

Well done if you got those right.

Here's a statement that Aisha and Jun are looking at.

The integer with the greatest absolute value is the smallest.

And Aisha says, "Is this always true?" "No, it's not always true." Can you think of an example when the statement is not true? Hopefully you managed to come up with a situation when this is not true.

So for example, if you were comparing seven and negative two, the absolute value of seven is seven, and the absolute value of negative two is two.

Seven has a higher absolute value, but negative two is less than seven, as we're comparing a negative integer with a positive integer.

The statement is only true if you are comparing just negative integers.

So it's really important to remember that this only is true if we're only comparing negative integers.

We're now going to have a look at some number lines.

So on this number line, we can see that I've placed a zero and I've placed negative three.

Negative three is three below zero, so we can see here from the number line that each of the spaces represents one.

What number is the A pointing to? Negative seven, well done.

What about B? That's right, negative one.

Let's have a look at this one.

So I've placed on my number line negative 10 and zero.

This time I've moved five places to get to negative 10.

That means that five parts represents 10.

So we need to take the 10 and divide it by the five parts so that we can work out what one part is representing.

So each part this time represents two.

So we need to remember each part this time is representing two, not one.

What number is the arrow pointing to? Yep, you're right.

Negative 12.

Each was representing two, this is one space below negative 10, so it's negative 12.

What about B? A little bit more challenging maybe, but you can do it.

Well this is negative four, we've gone two spaces below zero, so that's negative six.

What's halfway between negative four and negative six? And that's negative five.

Well done if you got that one right.

Let's have a go at some of those now, then.

What I'd like you to do is to work out in each of these what number the arrow is pointing to.

Remember you will need to check what the number, what the scale on the number line is representing.

Pause the video.

When you've got your three answers, come back and check in and see how you got on.

Super.

Let's have a look then.

A, we should have negative four, so we could check whether it was going up in ones.

It was, so therefore it's negative four.

B is negative 12, so this time we can see that each part was worth two.

This is six parts below zero, so negative 12.

And then C, you should have negative seven.

Again, the number line was representing, each part was representing two.

And so if we go down we can see that it's between negative six and negative eight, which is negative seven.

I'm sure you've got those right, well done.

Let's move on.

Aisha and Jun are trying to write these integers in ascending order.

Okay, ascending order.

Which way round does that mean we need to be writing them? Is that smallest or largest or largest to smallest? Now I always remember that descend means going down, D and down.

So ascend must mean going up.

So this really just means we are going from the smallest to the largest.

Jun's list is here, negative 14, negative 10, negative seven, negative eight, negative three.

Aisha says, "I think one of them is in the wrong place." Just have a think.

Do you you agree with Aisha? "You're right, Aisha," so Jun has spotted that actually Aisha is right, "I've got the negative seven and the negative eight the wrong way around." Did you also identify that was where the mistake was? Well done if you did.

Now we can have another check for understanding.

Which of the following are in ascending order? So these are in ascending order.

Pause the video and when you've decided whether it's A, B, C, or D, then you can come back and we can check your answer, good luck.

Super work.

Let's have a look then.

It was actually D.

In A, the negative 59 was in the wrong place.

In B, the negative 24 is in the wrong place.

And in C, they are in descending order.

So remember, we needed to work out which was in ascending, so that's going from the smallest up to the largest, brilliant.

Task B, then.

Remember this is really just the same as the temperature task that we did in task A.

I've just removed the degrees C.

If you prefer to think of them with those degrees C on the end, then you can, but remember we're just thinking about absolute values.

The larger the absolute value, the smaller the number is, and here we're only looking at negatives, so that is always going to be true.

Pause the video, come back when you've got your answers to those five lists.

All done? And then question number two.

I'd like you to put the following order, sorry, I'd like you to put the following integers into the grid.

So the numbers need to go from least to greatest from left to right and least to greatest from top to bottom.

You can use each number once and once only.

It's a little bit more challenging.

Just have a think about it before you get started.

Maybe if you've got a mini whiteboard, you could do this on there so you could rub them out.

If not, I would suggest using a pencil and paper so that you can rub out numbers if you need to move them around.

Like I said, challenging, yes.

Are you ready? Definitely.

Good luck, off you go.

Great work, so there's a lot to do there, wasn't there, putting all of those numbers into that grid.

Here are our answers then.

A, negative nine, negative eight, negative six, negative five, negative three.

B, negative 28, negative 25, negative 19, negative 18, negative 13.

C, negative 99, negative 91, negative 89, negative 88, negative 19.

D, negative 312, negative 265, negative 256, negative 119, and negative 112.

And then E, lots of six, threes, twos, and ones in this one, all in various orders, so let's check these carefully.

Negative 6321, negative 6312, negative 6231, negative 6213, negative 6132, and negative 6123.

Well done if you've got those right, especially that last one.

And here is the order in which the numbers should be.

Now I'm not going to read all of these out, so what I'm gonna suggest you do is pause the video, check your answers, and then when you're ready, you can come back, and then we'll do a summary of what we've learned in today's lesson.

Super, let's summarise then what we've done during today's lesson.

So I have mentioned it quite a few times today and that's because I think it's super important, that it can be useful to think of temperature when dealing with negative numbers.

Because we think about it, we know which is colder, we know that negative 10 is colder than negative five, so therefore negative 10 must be smaller than negative five.

So for example, negative seven is colder than negative two.

So we can write it with that inequality symbol, so we can write negative seven is less than negative two.

And also we looked at the fact that we can use a number line and that can be useful when we're ordering or comparing negative integers, remembering that as we move left from zero, the absolute values increase, and as we move right from zero, those absolute values increase.

You've done superbly well during today's lesson and I've really enjoyed it.

I hope you join me again soon.

We'll be moving on and looking at some other things with negative numbers very, very soon.

Thank you.

Goodbye.