Lesson video

Hi there.

My name is Mr. Tilstone and it's really nice to be working with you today on a negative numbers lesson.

So if you are ready, let's begin.

The outcome of today's lesson is I can interpret sets of negative and positive values in a range of contexts.

We've got two keywords today.

So my turn, your turn.

Ready? So my turn, temperature, your turn.

And my turn, elevation.

Your turn.

Let's find out what those words mean.

You might have encountered at least one of them before I think.

So temperature, probably the more common of those two words is how hot or cold something is.

And elevation can be used to describe an object's height above sea level.

Our lesson today has two cycles, negative and positive temperatures and interpreting negative numbers in a variety of other contexts.

But let's begin with negative and positive temperatures.

Are you ready? In this lesson, you're going to meet Andeep.

You might have seen Andeep before.

He's going to be lending his a hand.

Andeep says this, I read that the temperature in Antarctica is negative 30 degrees in January and negative 43 degrees in February.

So it's hotter there in February.

Is Andeep correct? Let's have a little think about that.

Hmm, I don't think he is correct, but why might he think this? Let's explore, let's investigate.

So negative 30 degrees Celsius is 30 degrees less than or colder than zero.

And we can see that on this number line, negative 43 degrees is 43 degrees less than or colder than zero.

And we could see that on the number line that would appear somewhere between those two marked intervals.

For negative temperatures the further the number is from zero, the colder it is, Andeep has not considered the meaning of that negative symbol.

So it wasn't quite right there.

So negative 43 is colder than negative 30.

30 degrees is 30 degrees greater than or warmer than zero degrees.

43 degrees is 43 degrees greater than or warmer than zero degrees.

We can see that on the number line in between those marked intervals.

For positive temperatures the further the number is from zero, the warmer it is.

So if the temperature in Australia in January is 43 degrees and sometimes it does get to that, it's really hot, isn't it? And in July it's 30 degrees, it's hotter in January.

The further to the left on a horizontal number line, the temperature is the colder it is.

So here we've got a horizontal number line and the further to the left, the colder.

So here we've got minus 40 degrees, minus 40 degrees Celsius you might say as well.

Here we've got a value in between two mark intervals.

Halfway between.

That's negative 15 degrees celsius.

So negative 40 degrees is colder than negative 15 degrees.

The further to the right, the temperature is the warmer it is.

So negative 15 degrees is warmer than negative 40 degrees because it's further to the right.

Let's have a check.

So use the number line to help you put the following temperatures in order from coldest to warmest.

So we've got negative 32, 25, zero, one and negative 19.

They're mixed up at the minute.

Can you put them in order from coldest to warmest? Pause the video and have a go.

Let's see how you got on.

So from coldest to warmest, it goes negative 32 degrees Celsius and then negative 19 degrees Celsius and then zero.

Then onto our positive ones we go one and 25.

And here's where they would appear on that number line.

So negative 32 would appear in between those two marked intervals, but close to negative 30, negative 19 would appear in between negative 20 and negative 10, but much close to negative 20.

Just like nineteens quite close to 20.

Zero degrees, that's quite straightforward.

That's exactly where that, remember that's not positive or negative.

One degree, just a little bit further to the right than zero degrees and then 25 degrees we're going between those two marked intervals.

Halfway in between in fact.

Okay, let's have a look at some negative and positive temperatures.

So we've got a table here.

We're going to reveal bits of information one bit at a time.

So we've got the temperatures in the North Pole and the temperatures in Sydney in Australia.

Okay, so in January we can see that the minimum temperature it gets to is negative 40 degrees Celsius and the maximum temperature it gets to is negative 12 degrees Celsius in January.

Now in Sydney by contrast, it's 19 degrees.

That's the minimum temperature it gets to and 26 degrees is the maximum temperature it gets to.

So in January at the North Pole, the coldest temperature is negative 40 degrees, which is 40 degrees colder than zero.

The warmest temperature is still a negative value.

It's negative 12 degrees, which is 12 degrees colder than zero.

So they're both negative, but negative 12 is warmer.

In January in Sydney the coldest temperature is 19 degrees, which was 19 degrees warmer than zero.

The warmest temperature is also a positive value.

They're both positive values is 26 degrees, which is 26 degrees warmer than zero.

So where do these temperatures fit on this number line? So we've got a number line, it's got marked intervals that are going in multiples of 10.

Remember values can and do and will exist in between those intervals.

So let's have a look.

So negative 40, that's a marked interval that goes just there.

Negative 12 is in between negative 20 and negative 10, but close to negative 10.

So it goes there.

19 is in between 10 and 20, but close to 20 and 26 is just over halfway between 20 and 30.

So it would appear just there.

Where is the temperature difference greater in January.

So is it greater in the North Pole? Is a difference greater that is or is a difference greater in Sydney? I can see that looking at the number line, have a think about that.

The temperature difference is greatest at the North Pole.

The gap between the minimum and maximum temperatures is greater than in Sydney.

The gap's quite small in Sydney compared it's not such a big range of temperatures, quite a big range in the North Pole in January.

Let's have a check.

So we've got some different places this time.

We've got Antarctica and Manchester, we've got January and February and there's a temperature.

So in January and and the Antarctica, the minimum is negative 30 degrees.

The maximum is negative 26 degrees.

And in Manchester two and eight and in February in the Antarctica minimum negative 43, maximum negative 38 and again two and eight.

So no change between the months there.

So complete the sentences.

We've got a stem sentence here in February in Antarctica, the coldest temperature is degrees, which is degrees colder than zero.

The warmest temperature is degrees Celsius, which is degrees colder than zero.

Work with a partner if you can see if you can agree on the missing gaps there and pause the video.

I'll see you soon.

Okay, did you manage to fill in those gaps? Let's have a look.

In February and Antarctica, the coldest temperature is negative 43 degrees, which is 43 degrees colder than zero.

The warmest temperature is negative 38 degrees, which is 38 degrees colder than zero.

And well, and if you've got those, let's do another check.

Is the minimum temperature in Antarctica colder in January or February? And we've given you a little bit of a clue there by putting those temperatures in purple.

So how do you know? So have a think about that and pause the video.

The minimum temperature is colder in February.

It's 43 degrees colder than zero.

In January it's 30 degrees colder than zero.

So it's warm, it's still very, very cold, don't get me wrong, but it's a little warmer than negative 43 degrees.

And on the number line, here's where they would appear.

So negative 43 would appear in between negative 40 and negative 50, but close to negative 40 and negative 30 would appear exactly on that marked interval just there.

Let's have another check, which is called in February, Antarctica or Manchester.

And again, I've colour coded those to help you out, pause here.

Okay, well the answer to that is the temperatures in Antarctica in February are all negative, but in Manchester they're all positive.

So Antarctica's got to be colder.

And here's where those values would appear.

So negative 43 would be just here, negative 38, just here in between negative 40 negative 30 two would be just there and eight would be just here.

So you can see both of those Manchester temperatures are positive.

Both of the Antarctica temperatures are negative.

Look at the maximum temperatures in Antarctica in January, February and March.

So they're the temperatures in purple, they're the maximum temperatures in those three months.

Are they getting warmer or colder? So it's going negative 26, negative 38, negative 50.

Is that getting warmer or is that getting colder? Pause the video.

Well the answer is they're negative and they're getting further and further away from zero.

So therefore they're getting colder.

So the distance between zero and the temperature is increasing each time.

So it's getting colder.

Let's see, those are the number line.

So here's negative 26 in between negative 20, negative 30, here's negative 38, just a little bit to the right of negative 40.

And in between negative 40, negative 30 and negative 50.

That's a bit easier because that's one of the marked intervals.

There we go.

Another check.

Look at the maximum temperatures in Manchester in February, March and April.

Are they getting warmer or colder? Pause the video.

Well, let's see.

The temperatures are all positive and they're getting further and further from zero.

So they're getting warmer.

Let's see those on the number line.

Here's eight, here's 11, here's 14.

They're getting warmer, they're getting further from zero Time for some independent work I think.

Do you feel like you're ready for it? I think you are.

Okay, so task number one, decide whether each statement is true or false and explain your answer each time.

So on Sunday the temperature was negative three degrees Celsius and on Saturday the temperature was negative four degrees Celsius.

So Sunday was colder than Saturday.

True or false.

And explain at noon at the temperature was negative five degrees Celsius.

One hour later the temperature is negative two degrees Celsius, the temperature went up.

True or false, explain.

And for number two, explain why negative 63 degrees Celsius is colder than negative 55 degrees.

So it's colder.

Can you explain why it's colder? How come? So we've got some questions.

So for the North Pole and Sydney, what's the coldest minimum temperature in degrees Celsius.

And again for the North Pole and Sydney, which is the month with the lowest minimum temperature and for the North Pole and Sydney, which is the highest maximum temperature.

So we're looking for a number there.

And then finally, which is the month with the highest maximum temperature.

So all of that information can be found on that table.

Still using that table B which month in the North Pole has the warmer maximum temperature? November or December.

Explain your answer.

C, describe the change in temperatures in the North Pole from October to December.

D, describe the change in temperatures in Sydney from October to December.

And E, which month in the North Pole has the smallest difference between maximum and minimum temperatures? You might want to think about the temperatures on a number line to help.

Pause the video.

Good luck with that and I will see you very shortly for some feedback.

Let's have a look how you got on.

So one A, that's false and you might have put something like negative three is only three degrees below zero, but negative four is four degrees below zero.

But the important part is that's false.

And for B that is true and you might have put something like negative two is closer to zero and is therefore the warmer of those two negative temperatures.

And then for two you might have put something like negative 63 is 63 degrees colder than zero, but negative 55 is only 55 degrees colder than zero.

I say only that would still be freezing, that would still be really cold.

And then for three A, the coldest minimum temperature in the North Pole is negative 13 and is Sydney at 14.

The month of the coldest minimum temperature North Pole, December, Sydney, October, the warmest maximum temperature North Pole negative three degrees, Sydney 25 degrees.

And then the month of the warmest maximum temperature North Pole, October, Sydney, December.

For B it's November.

And you might have put something like November is two degrees close to zero.

You might have put something else as well.

For C, it could include it's getting steadily colder, something like that.

For D you might have put something like it gets steadily.

And then for E, October is the month the smallest difference.

Cycle B is interpret negative numbers in a variety of other contexts.

So we've seen temperature.

Let's look at some other contexts.

Are you ready? So this is our first new context.

So we've got some water here and we've got a sea level.

Okay, so this is sea level.

A zero could be used to denote that elevation.

You might have seen that quite recently.

It is neither positive nor negative.

As with all zeros, not positive, not negative.

The bird is above sea level at a positive elevation.

It is 20 metres above sea level and we can see that 'cause it's in line with a marked interval.

Okay, we've got a fish.

Hmm, what's the elevation of the fish? Let's have a look.

That's negative 10.

So our number line is going up and down in tens.

The fish is below sea level at a negative elevation.

It is 10 metres below sea level or negative 10 metres we could say.

Got another fish here.

Okay, so that's further down, that's that's further below sea level, that's deeper down.

That's at negative 60 metres.

The fish is further below sea level, it is 60 metres below sea level or negative 60 metres.

Let's have a check.

So Andeep's mother is a diver.

Ooh, is she deeper when she is at negative 10 metres or when she is at negative 50 metres.

Talk to your partner, see if you can agree and see if you can explain why.

Pause the video.

Well here we are.

Here's Andeep's mother.

That's where she is, when she's at negative 10 metres and that's where she is when she's at negative 50 metres.

So she's deeper at negative 50 metres.

What words could complete the generalisations here? So when an object is above sea level that mm, the number is from zero, the the object.

And when an object is below sea level, the the number is from zero.

The the object.

Pause a video, can you fill in the blanks? Let's see.

So you might have some different answers here, but you might have got these ones.

When an object is above sea level, the further the number is from zero, the higher the object.

When an object is below sea level, the further the number is from zero, the deeper the object.

And again, you might have used some alternative words.

Time for another practise task.

So task B, number one, add the following labels to the drawing.

So A, so you could have put an A somewhere on this drawing a bird at 15 metres above sea level.

B, sunken treasure 60 metres below sea level.

C, a shark 20 metres higher than the treasure is.

So you need to figure out the treasure first before doing that.

D, an octopus 10 metres below sea level we've got sea level there gonna be 10 metres below.

E, a clownfish the same distance below the sea level as a bird is above it.

Hmm, and a dolphin deeper than the clownfish but higher than the shark.

Number two, decide whether each statement is true or false and explain your response each time.

So a whale was at negative 70 metres, then swam to negative 40 metres, the whale went down.

Is that true or false explain ? In a car part level negative two is above level negative five true or false? Explain.

I was on level negative three of the car part, I had to go down the stairs to get to level negative two.

True or false? Explain.

And finally number three, put the following numbers in a descending order.

Descending.

So we've got 17 negative 8.

53, 0.

03, negative 25 and zero.

And finally look at the fourth and fifth numbers on that list.

On your ordered list, please write some numbers that will go in between them.

Pause the video, have a go at that and I'll see you soon and I'll let you know how you got on.

That's B number one.

A.

A bird at 15 metres above sea level would be just here halfway between 10 and 20 between those intervals.

So the intervals are going up and down in tens.

So we can work out that 60 metres below sea level or negative 60 will be just there where B is.

C, 20 metres higher than the treasure.

That's two intervals above it, just there.

And D, 10 metres below sea level we know sea levels at zero.

So 10 metres below is the interval below and E will be just here, same distance below the sea level as bird is above it.

So if the bird is 15 metres above, then the clownfish is 15 metres below and the dolphins anywhere deeper than the clownfish but higher than the shark.

So it could be anywhere along that line.

Number two, decide whether each statement is true or false.

So for a, if a whale was at negative 70 metres then swam to negative 40 metres, did it go down? No, that is false.

It went up because negative 40 is closer to zero or to sea level than negative 70 is.

B, in a car park level negative two is above level negative five.

That is true, it is closer to the ground floor and C, I was on level negative three of the car park.

I had to go down the stairs to get to level negative two.

That's false because negative three is further away from the ground level, so you'd actually have to go up the stairs.

Number three, put the following numbers in descending order.

So that's going down.

That is 17, three, 0.

03, zero, negative 8.

5, and negative 25.

Your fourth and fifth numbers on that list are zero and negative 8.

5.

And we're looking for some numbers that were going between those.

Well, there are infinite possibilities really, but we're looking for anything that's a negative number and anything greater than negative 8.

5.

So for example, a whole number might be negative six and a decimal number that you might put in might be something like, for example, negative 6.

25, anything like that up.

We've just about come to the end of our lesson now.

So our lesson today has been interpreting sets of negative and positive numbers in a range of different contexts.

So negative numbers exist in a variety of real life scenarios, but whatever the context is, the further the negative value is from the zero line, the lower the value is, the further the positive value is from the zero point, the higher the value is.

I've really enjoyed working with you today and I hope to work with you again soon.

But until then, take care and goodbye.