Lesson video

Hi there, I'm Mr. Tilstone, and it's my great pleasure to be working with you today on a lesson all about negative numbers.

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

The outcome for today's lesson is I can use knowledge of positive and negative numbers to interpret graphs.

And our keywords for today, we'll do this my turn, your turn, are you ready? So my turn axis.

My turn axes.

Now it looks like it's spelled axes, doesn't it, but it's axes.

The X and Y lines that cross at right angles to make a graph or grid are called axes, which is the plural of axis, so you can see on this graph here, we've got an X axis and a Y axis, so we've got axes.

Our lesson today is split into two cycles.

The first being negative data values on bar graphs, and the second being negative data values on line graphs.

So if you're ready, we'll start with our first cycle, which is negative data values on bar graphs.

So let's have a look, we've got a bar graph here.

Just like coordinate grids, bar charts have an X axis and a Y axis, so we can see we've got an X axis, in this case it's the months.

And we can see we've got a Y axis, in this case it's temperature.

To determine the value of each bar, draw or follow a straight horizontal line to the Y axis.

So we've done that look, so we're looking at the temperature here in May.

So we've done a horizontal line from the top of the May bar over to the Y axis taking us to the temperature in May.

So, what was the maximum temperature in May? And what are the unmarked intervals showing? The marked intervals are in tens, so we can see that look, so it's going zero, 10, 20, and then the other way, negative 10, negative 20, negative 30.

So we've got some marked intervals, we've got some unmarked ones as well.

So five divisions between the marked intervals, meaning each one is worth two.

And we'll do a little count to check that, so if you start with zero log, we'd go zero, two, four six, eight, 10.

Yes, that fits.

So therefore the maximum temperature in May was 16 degrees celsius, so if we look at the 10 log and we're counting in two as it goes 10, 12, 14, 16.

Okay, what was the minimum temperature in November? So let's find the November temperature, now, you might notice on this bar chart there's two different colours, for the bars.

We've got a dark colour and a light colour.

And the light color's showing the minimum.

So if we find November, the November bars, we've got two November bars, maximum and minimum.

This one's asking us for the minimum.

So we're going to draw that horizontal line across from that, now remember it's going in twos.

So what do you think the temperature might be? Let's have a look.

So the scales march in steps of two.

The minimum temperature in November was negative 22 degrees celsius.

And remember we are counting in twos, so if you said negative 21 there, you're not considering the value of the unmarked intervals.

So be careful.

Why is there only one bar for September, and only one bar for October? Are there missing bars, is there missing information, or, in fact, do we have all the information that we need there? Actually, yes we do.

The minimum temperature in September is zero degrees, and the maximum temperature in October is also zero degrees.

Let's do a check for understanding, shall we, what was the maximum temperature in February? And we've done a little circle around February just to help you out, see, to focus your attention.

And what was the minimum temperature in August, so maximum for February, minimum for August.

Pause the video and have a go.

How did you get on with that? The maximum temperature in February was negative 12 degrees.

So we can see that look, so look at the maximum temperature, that's a darker bar.

Draw a horizontal line across from that, and that is negative 12.

And the minimum temperature in August was six degrees.

So find August, find the August bar, and go across from that and it takes us two, four, six degrees.

So well done if you got those, you are on track.

Okay, in what month was the highest maximum temperature, so let's look at the dark bars, and focus on that one.

And then in what month was the lowest minimum temperature, so highest maximum, highest dark bar, and then lowest minimum.

So lowest light bar.

Well the highest maximum temperature was in July, that's the one that's got the tallest bar.

So it's in July, and we can see, it's in between two of the unmarked intervals.

So the lowest minimum temperature was in January, and once again, it's in between the unmarked intervals.

The highest maximum temperature is between two divisions or two intervals, so it must be 23 degrees.

Yes, because it's halfway between 22 and 24, so it must be 23.

So remember, values do exist in between the intervals.

And what was the lowest minimum temperature, well, that's in between two as well, isn't it, so let's have a look.

The lowest minimum temperature is between two divisions or intervals, so it must be negative 29.

Yes, it's in between negative 28, which is unmarked, and negative 30, which is marked.

Halfway between 28 and 30 is 29, so halfway between negative 29, 28 and negative 30 is negative 29.

Let's do a check.

What was the lowest maximum temperature and what was the highest maximum temperature? Pause the video and have a go, good luck.

Okay, how did you get on with that, let's have a look.

The lowest maximum temperature is between two divisions, so it must be negative 19 degrees celsius.

And the highest minimum temperature is between two divisions, so it must be nine degrees celsius.

So here on this chart, our odd numbers are in between the marked and unmarked intervals.

What was the difference, that's a different question, isn't it, what was the difference between the maximum and minimum temperatures in April? Now you might have had some recent experience working out difference between positive and negative values.

So let's have a look at that.

You can use the Y axis as a number line, and add the distances either side of zero.

So here, look, we've got our first value, which is, let's have a look, two, four, six, that's seven.

And the minimum value is two, four, six, eight.

So we've got seven is a distance between zero and the positive value and eight is a distance between zero and a negative value.

Eight plus seven equals 15.

The difference in temperature is therefore 15 degrees celsius.

Time for some practise.

Here we've got a graph, a bar graph, and it shows the maximum and minimum monthly temperatures for Elephant Island in the Antarctic.

Question 1A, which months have a temperature difference of more than four degrees celsius? B, which months have a temperature difference of two degrees celsius? C, what is the greatest difference between the maximum and minimum temperatures in one month? And D, what do you notice about the temperatures on Elephant Island? And number two, we've got a different graph.

This shows the maximum and minimum monthly temperatures for Calgary in Canada, it's another bar graph, but it looks a bit different.

Question 2A, which months have a temperature difference, which bridges zero degrees celsius? B, which months have a temperature difference of more than 12 degrees celsius? C, what is the difference between the highest maximum and the lowest minimum temperatures? And D, what would be the best months to book a skiing holiday? So good luck with that, make sure you've got all the possibilities where it asks for more than one possibility, and I'll see you shortly.

Welcome back.

How did you get on with that? Let's have some feedback, shall we? Question 1A, the months that have a temperature difference of more than four degrees celsius, are June, July and August.

And B, the months that have a temperature difference of exactly two degrees celsius, that's January, February, March, October, November and December.

The difference is exactly two degrees And see the greatest difference between the maximum and minimum temperatures in one month is in June and July.

The difference between those two months is six degrees celsius.

And what do you notice about the temperatures on Elephant Island? It's colder in what we call the summer months.

It's in the southern hemisphere.

Question 2A, the months that have a temperature difference which bridges zero degrees celsius, so it goes across zero degrees, that is January, March, April, and November, they are all the possibilities, make sure you've got all of those please.

And B, the months that have a temperature difference of more than 12 degrees celsius, that's January, April, July and August.

And see the difference between the highest maximum and lowest minimum temperatures.

The highest maximum temperature is 23 degrees celsius, and the lowest minimum temperature is negative 14 degrees celsius.

And the difference between those, if we add those distances from zero together, we get 37 degrees celsius, well done if you got that.

And finally, for this round of questions, the best months to book a skiing holiday.

Well, for skiing it needs to be cold for the snow to be on the slopes.

And November, December, January, and February are a very cold sequence of months, so they would be their best time to book that skiing holiday.

Very well done if you got those questions right.

Are you ready for cycle two? That's negative data values on line graphs, we've looked at bar graphs so far, let's move on to line graphs.

Have you encountered those before? Let's have a look.

This graph charts the outside temperature across part of a winter's day.

What's the same and what's the different compared to the previous graphs? Have a look, have a think.

Can you see anything that it's got in common with the graphs that we've just been looking at? What about anything that's different? Okay, let's investigate.

Well, it is the same, in so much as it shows both positive and negative value, so you can see that, so look at the Y axis, it's got positive values above zero and it's got negative values below zero, just like before.

It includes data about temperature, that's the theme of this graph, it's a temperature graph, just like before.

But it's got some differences too, it's different as it's a line graph, there are no bars on this graph.

The X axis has a different unit, it's time, a different unit of time, in fact, so this is measuring time within a day.

The Y axis intervals are different as well.

So the Y axis is going up in ones this time, and there are no unmarked intervals.

The line shows whether the temperature is increasing, decreasing, or staying the same from hour to hour.

Between 6:00 and 7:00 a.

m, there is an increase in the temperature, shown by the line going upwards, so let's have a look at that line between six and seven.

It's a diagonal line, and it's pointing upwards, so that's showing an increase.

The temperature increases by three degrees.

So it goes from a negative value to a different negative value, from negative five to negative two.

And that's a three degree difference.

Between 1400, that's 2:00 p.

m.

, and 1500, that's 3:00 p.

m.

, there is a decrease in temperature, it's going down a decrease.

Shown by the line going downwards, so can you see that's a different kind of line between those two, it's a downwards line, so it's a decrease.

Here we go.

So we've seen a time when it's increased in temperature, and a time when it's decreased in temperature so far.

There's another kind of line as well, can you spot it? In that case though, the temperature decreases by one degree celsius.

So it goes from positive seven to positive six, that's a one degree difference.

Have a look at this one though.

Between 11 and 12.

That flat horizontal line between 11 and 12 shows that there was no change in the temperature.

So at 11 o'clock it was four degrees, and at 12 o'clock it was still four degrees.

And we can show that by the flat horizontal line.

It remains at four degrees celsius.

Time for a check.

Describe the change in temperature between eight o'clock in the morning and nine o'clock in the morning.

Pause the video, have a go.

Let's see what you got for that.

There is a one degree increase in temperature between 8:00 a.

m.

and 9:00 a.

m.

, a one degree.

It went from negative one to zero, a difference of one.

And the diagonal line pointing upwards shows that increase.

So the lowest temperature on this graph that we can see is negative five degrees celsius, so here it is, look.

So at 6:00 a.

m.

, it was negative five degrees celsius.

The highest temperature is seven degrees celsius.

To calculate the difference between between lowest and highest temperatures, the distances from zero can be added together.

So just like earlier on in the lesson.

So think about the the differences or distances from the negative value to zero, and from the positive value to zero.

So from zero to the highest at seven degrees celsius, and from zero to the lowest at negative five degrees celsius, so, we've got two distances, a five and a seven.

Five and seven or seven plus five equals 12, so the difference is 12 degrees celsius.

The Y axis is the same as a number line.

That's essentially what it is, it's a vertical positive and negative number line.

Let's have a check.

Calculate the difference in temperature between the start and the end of the day, so you can see that the start of the day is six in the morning, see what the temperature is there.

We talked about that earlier on.

And the end of the day is 1600 or 4:00 p.

m.

So see if you can read that graph and calculate the difference in temperature.

Pause the video and have a go at that.

Let's see.

Here's the start of the day.

Negative five degrees celsius.

Here's the end of the day.

So we're going to draw the line, vertical line up to the the line, on the graph.

And then a horizontal line across from it, a straight horizontal line.

And that takes us to five degrees.

So we've got negative five and five.

The difference between negative five and zero is five, and the difference between zero and five is also five.

And then what do we do to those two numbers? We add them together.

Five add five equals 10.

So the difference between the start and the end of the day is 10 degrees celsius.

So we've extended the X axes on the graph, and it's got some new times on some later times.

By 1700, the temperature had dropped to one degree celsius, and by 1800 it had dropped to negative two degrees celsius.

These values can be plotted on the graph, and that's what we're going to do now.

So the first thing that you would do, with your ruler, you would go across, using a horizontal line, you'd go from the one degree, so that's a temperature that we know it is at 1700, over to the 1700 line.

Now, you don't need to draw a line, in fact, please don't draw a line.

Sust use your ruler so that you know where to go.

But what you do need to do is put a dot there.

So put the dot where it meets.

And then you can take your ruler away.

And then we're going to do the same thing for the negative two.

So use your ruler, to make a horizontal line, and then plot that with a dot.

So it's negative two degrees at 1800.

Take your ruler away.

And then what you do need to do is draw lines to join the dots.

So there's one, and there's two, and we plotted those values onto our chart.

Let's do a check for understanding, shall we, so what was the change in temperature between 1600 and 1800? Pause the video and have a go.

Let's see.

Well, here's our 1600 temperature, we put a little circle around that just to highlight that, and there's our 1800 temperature.

And you could use your ruler to draw a horizontal line for the Y axis, but the temperature at 1600 is five degrees, and the temperature at 1800 is negative two degrees.

And the difference between those, if we add those two distances to zero is seven, five plus two is seven.

Very well done if you got that, you are definitely on track in today's lesson.

The graph here shows the average outside temperature in the last six months of the year, so it's a slightly different graph.

So we've got our X axis that's showing the months.

And the Y axis, once again, showing temperature.

Now, you might notice this time it's a little bit different because we have got some marked intervals but also some unmarked intervals.

So our marked intervals are going in twos.

And our unmarked intervals are going in ones.

So you can see some missing information, but we can work it out.

So in between two and four, for example, that's going to be three.

Just like before, this graph's got both positive and negative values on it.

Just like before, you can see some increases, when the line's pointing upwards, and some decreases when it's pointing downwards.

Okay, so your task, is describe the change in temperature between September and October.

That's A.

B, what was the lowest temperature? C, what was the highest temperature? D, what was the difference between the lowest and highest temperatures? And E, in December, the average temperature was negative two degrees.

Plot that on the graph.

So pause the video, and have a go.

Good luck and I'll see you very shortly.

Welcome back, that was your final task for today, let's give you some feedback.

So for A, the change in temperature between September and October, your responses might be, it decreases, by five degrees celsius from four degrees, to negative one degree, so something like that.

B, the lowest temperature was negative three degrees.

C, the highest temperature was 13 degrees.

The difference between the lowest and highest temperatures was 16 degrees, and the average temperature was negative two degrees celsius.

Plot that on the graph.

Here it is.

So well done if you got that, so you can see that's a slight increase from November to December.

We've come to the end of our lesson, so today we've been looking at graphs that contain both positive and negative numbers.

Negative numbers can exist on graphs, they can be found on the X axis and or the Y axis.

When calculating differences between positive and negative values on graphs, use the axis as a number line to add together the two distances from zero.

That's the end of the lesson, you've been absolutely amazing, it's been a real pleasure working with you and I hope to see you again soon.

Take care and goodbye.