Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson.

The lesson comes from our unit on multiples of 1,000.

So we're gonna be looking at those bigger numbers.

How are they put together, how are they composed, where do we find them in real life, and how can we learn about them so that we can work with them when we're solving problems. So if you're ready to make a start, let's get going.

So in this lesson, we're going to be reading scales of graphs and measures using knowledge of the composition of 10,000 and 100,000.

So we're going to be looking at how divisions of those numbers can help us to interpret data and to read divisions on scales.

We've got two keywords in our lesson today.

We've got multiple and gridlines.

So I'll take my turn and then it'll be your turn.

My turn, multiple, your turn.

My turn, gridlines, your turn.

They may well be words you are familiar with, but let's just check what they mean 'cause they're going to be useful to us in our lesson today.

So a multiple is the result of multiplying a number by an integer, not a fraction.

So that's multiplying by a whole number.

And a gridline is a horizontal or vertical line that helps organise data on a graph or chart.

We've got two parts to our lesson today.

In the first part, we're going to be estimating values.

And in the second part, we're going to be drawing graphs.

And we've got Sam and Jun helping us in our lesson today.

So let's start by looking at a graph.

The graph shows the number of electric cars sold in each year.

So how many cars were sold in each year? Sam says, "This graph cannot tell us the exact number of electric cars sold in each year as the scale does not go up in ones." And that's something really important.

You need to look at the scale to think how accurate you can be with your estimates and with your judgments on what each bar is worth.

We can see that each major gridline goes up in multiples of 100,000.

Those are the ones that are currently marked on the scale.

And each minor gridline, so the ones in between, goes up in multiples of 25,000.

We can see that there are four equal divisions between zero and 100,000, and then 100,000 and 200,000 and so on.

And we know that 100,000 divided by four is equal to 25,000.

So each of those smaller gridlines marks 25,000.

So we can estimate the number of cars sold each year now.

So Sam's going to talk us through her estimate for 2018.

She says, "This is just below the 25,000 gridline, so my estimate is 20,000 cars." So now she's looking at 2019 and she says, "This looks halfway between 25,000 and 50,000, so let's say 37,500." And 37,500 is exactly halfway between 20,000 and 50,000.

What do you think for 2020? Sam says, "This looks like it is just above 100,000, so I'm going to estimate 110,000." What about 2021? Sam says, "And this is just under 200,000, so I think it's about 185,000." Have you noticed that only one of her estimates has a 500 in it? And that's because she was thinking about a midpoint and she knew the value of the midpoint had a 500 in it.

Otherwise, she's estimating sort of to the nearest thousand.

So for 2022, she says, "This is nearly 275,000, so I'll estimate 265,000." What about 2023? And she says, "This is between 300,000 and 325,000, so I'll go for 315,000." They seem like pretty sensible estimates to me.

Do you agree? So Sam's recorded her estimates and the actual values in a table.

Can you look and see which estimate was the most accurate? Well, Sam says, "I was only 350 away from this one." So her estimate was 37,500 and the actual was 37,850.

Do you remember that was the one where she used the fact that she was about halfway between two known values? "But I was only 313 away from this one," she says.

Yes, her estimate was 315,000 and the actual was just over 314 1/2 thousand, I'm estimating as well now and rounding.

How could we have made these estimates even more accurate? Well, Sam says, "If the graph had more gridlines, we could have been even more accurate." She says, "Let's make a graph with 10 minor gridlines between each major gridline." Ooh, lots of gridlines there.

So what are we counting in now? Well, if we've got 10 minor gridlines, then we must be counting in steps of 10,000 this time.

Sam says, "Now you can see 2018 is under 20,000, so an estimate of 17,000 would've been more accurate." And in 2021, this is about on the 190,000 gridline.

So let's have a look would those have been better.

So she's going to change her estimate for 2018 from 20,000 to 17,000, and she's going to change her estimate for 2021 from 185,000 to 190,000.

So now she says, "Our estimates are even closer.

The extra gridlines meant we could be more accurate." Time to check your understanding.

So tick the situations when it would be best to overestimate.

Sometimes we want to know that we've got more than enough to do something.

Sometimes it's all right to estimate just under the amount.

So have a look at A, B, C, and D and tick the situations where you think it would be best to overestimate a value.

Pause the video, have a think, and we'll come back and talk about our answers.

What did you reckon? Well, we reckoned A and D would be times when it would be good to overestimate.

So the size of shoes when you buy them, you don't want shoes that are too small.

If your shoes are a little bit too big, that's better than being a little bit too small.

And D, the amount of rain that might fall on one day.

Well, if you are trying to collect the rain water or perhaps, oh my goodness, you might have a leak and you are wanting to put something underneath to catch any drips, you want to make sure that you've got a container that's bigger than you need so that it doesn't overflow.

So B, how much money you owe somebody.

Well, you want that to be right, don't you? But if you overestimate, then you might try to pay them too much, which isn't needed, is it? If you're a little bit under, they'll tell you what else you owe.

And how many bags you can fit in a car boot.

You certainly don't want to overestimate that because then you might have things you can't fit in your car.

So better to be on the cautious side, on the safe side when you are estimating something like that.

And another check.

This graph shows the predicted number of cars to be sold in the next year.

So how many cars were predicted to be sold? Pause the video, look at the graph, and see what you think your estimate would be.

So what was your estimate? Sam reckons, "They've predicted that about 510,000 cars will be sold." We know that those minor gridlines are counting up in 10,000.

So it's just one gridline above 500,000, so 510,000.

Time for you to do some practise now.

You are going to estimate the values from each bar graph, and there are four of them, and then complete a table.

And then think about the values in your table.

So the graphs show the time spent gaming in one year for Alex, Sofia, and Andeep, but you'll notice that the graphs change each time.

Here are A and B.

Here are C and D.

So you're going to make an estimate from each graph, and then you're going to record your estimates in this table.

And then for question two, you're going to compare your first and last estimates and the actual number of minutes spent gaming for each child which we've given you in this table.

How accurate were your estimates and did yours improve each time? Pause the video, have a go, and we'll get together for some feedback.

So how did you get on? Sam says, "Here are my estimates." So you can see how her estimates, some of them changed quite a lot, some of them didn't change very much.

So her estimate for Alex changed in graph C to 52,000 and stayed the same for graph D.

For Sofia, her estimate changed each time.

It dropped quite a lot between A and B, then went back up a bit for C, and came down a little bit for D.

And for Andeep, her estimate just went down a little bit, but then didn't change between graphs C and D.

I wonder what yours look like.

How much did you change yours between? Did you notice that the gridlines allowed you to be more accurate as you went on? And in part two we asked you to compare your first and last estimates and the actual number of minutes spent gaming.

How accurate were your estimates and did yours improve each time? Sam says, "I think my estimates were more accurate when there were more gridlines on the y-axis." I think that's probably true, and I wonder if you found that out as well.

Okay, and on into part two of our lesson, this time we're going to be drawing graphs.

So this table shows the changes in the price of a house over a five-year period.

How could this be represented in a graph? You might want to have a think about that before we carry on and model how we can turn this into a graph.

Sam says, "Because the values all begin with 200,000, I think it would be best to go up in gridlines of 100,000." Do you agree with Sam? Jun says, "We will also need minor gridlines too though so we can be more precise." Yes, they all do start with the 200,000, but then we've got some 5,000s in there as well.

And we want to be accurate so that we can see the difference between 230,000 and 225,000.

Jun says, "Look at the numbers carefully, what do we think would be best for the minor gridlines?" And Sam says, "They're all multiples of five, so we could go up in lots of 5,000." That sounds sensible, doesn't it? Then we can be really accurate with the size of our bars.

"Let's try," says Jun.

"Firstly," he says, "We need to draw a straight line for the x-axis where we will say each year." So the x-axis, if you remember, is the horizontal axis in a graph.

Sam says, "There are five years, so we will need five equally spaced bars." And in a bar chart that we're going to draw, the bars shouldn't touch each other.

There should be a gap between them.

So Jun says, "We have five years to mark on, so I will need a line that has five equal parts." Sam says, "You could mark five lots of two centimetres." So this isn't a scale obviously, but here is a ruler marked in centimetres.

So Jun's going to draw his lines.

Two centimetres, four centimetres, six centimetres, eight centimetres, 10 centimetres.

So his x-axis is 10 centimetres long and he's divided it into five equal parts of two centimetres.

And Sam says, "We need to label the x-axis too so we can show what it represents.

We can call it 'years.

'" Jun says, "Now, this is a bar graph, so each label will be placed between each marker." So we've got year one, year two, year three, year four, and year five in between each of the marks.

And that's where our bars will sit.

Jun says, "Now, we need to draw the y-axis.

It's perpendicular to the x-axis." So the y-axis is a vertical axis and it needs to join the x-axis, the horizontal axis, with a right angle.

So that makes them perpendicular, two lines that meet at the right angle.

And he says, "This y-axis will show the house prices." Sam says, "Let's mark on the major gridlines first with two centimetres for every 100,000." So let's have a look.

Two centimetres.

Four centimetres.

Six centimetres.

And Jun says, "Let's label each major interval now." Starting at zero, we were going up in 100,000s, weren't we? So 100,000, 200,000, 300,000.

Sam says, "And now we can include the minor intervals." What did they say they were going to count in? They were going to try and count in 5,000s, weren't they? Wow, that's a lot of individual lines, isn't it? How many 5,000s are there in 100,000? Well, two 5,000s equal to 10,000, and there are 10 10,000s.

So there must be 20 divisions.

Each interval goes up in multiples of 5,000.

We can't write them all in there.

We haven't got space to write all those numbers.

So that's what we need to know by looking at the graph and looking at the scale, we need to understand what those minor gridlines are showing us.

Oh, and Jun says, "Don't forget to label the axis.

We can call it 'house price.

'" There we are.

Now we can draw on each bar.

There needs to be a space between each one.

So there was our table showing us the house price each year.

So there is the line for 230,000.

So we can draw our bar up to that line.

For year two, it was 260,000.

There's our bar.

For year three, 225,000, there's our bar.

For year four, it was 240,000.

There's our bar.

And for year five it was 235,000, if you remember.

So our bar's just a little bit lower.

So there are our bars.

Are we finished? Whoa.

Jun says, "No.

And finally, a graph title!" The change in house price over a five year period.

Time to check your understanding Titles should be written on a bar graph for? And we've got four options there, A, B, C, and D.

Which ones do you think need to be on a bar graph? Pause the video, have a think, and we'll come back and share our answers.

What do you think? Well, we need a title for the graph.

We need to know what the x-axis represents, we need to know what the y-axis represents, but we don't always need to know each individual bar.

It's really useful to label each individual bar if you are looking at a graph and trying to answer questions about it.

But when we are just presenting information in a graph, we don't need to label each individual bar.

Another check.

It's better to draw a y-axis with: A, B, or C.

Have a think, and we'll come back and share our answers.

What did you think? You might have thought more intervals.

We know that's been good for when we've been estimating, but actually it really depends on the numbers in the data.

If we've only got numbers that are looking at numbers to the nearest 50,000, say, we don't need to have 10,000s marked on there.

It was useful in the graph we've just drawn to have 5,000s because that was the level of accuracy we needed.

So always look at the numbers you're representing and that will help you to decide how to divide up your y-axis.

Or if your bars are going horizontally, it might be your x-axis.

Time for you to do some practise.

Two questions.

For question one, you are going to use the following data to draw your own bar graph.

And we've got some data there around festivals and ticket sales.

And then for question two, you are going to compare your graph to other pupils.

Maybe you could compare with a friend.

Which do you think is the most accurate, and how could you improve your bar graphs? Pause the video, have a go, and we'll come back and discuss what you've done.

How did you get on? This is what our graph look like.

So we decided to have a scale that went up to 300,000 because our highest number was just over 200,000.

And again, we marked our scale in divisions of 5,000.

So there were quite a lot of divisions there, but it helped us to be accurate.

When you compared, did you find that you'd use different numbers of divisions? Was it more accurate to use more divisions or fewer divisions? Maybe your graph didn't go up quite as high as 300,000.

Perhaps you stopped it at 250,000, perhaps.

And if you stopped it at 250,000, you might have been able to make your division slightly bigger in the size of graph that you drew.

Anyway, I hope you enjoyed having a go at drawing a bar graph, and then comparing the scales that you'd chosen and how that affected the accuracy of your graph.

Now we've come to the end of our lesson.

We've been reading the scales of graphs and measures using knowledge of the composition of 10,000 and 100,000.

What have we learned about? Well, to read graphs accurately, it's important to identify the value of the intervals marked by the gridlines.

That is really important when you're reading a graph.

It's easier to estimate precise numbers on a bar graph when there are more gridlines to mark the intervals.

And you can apply your understanding of the common partitions of 10,000 and 100,000 to help you identify the value of gridlines.

I hope you've enjoyed learning a bit more about reading scales and about those common partitions of 10,000 and 100,000.

This work can be really useful not only in your maths, but perhaps also in science, and maybe in geography if you're doing some surveys.

Anyway, thank you very much again for all your hard work and your thinking, and I hope I get to work with you again soon.

Bye-bye.