Lesson video

Hi there, my name's Ms. Lambell.

You've made a superb choice deciding to join me today to do some maths.

Let's get going.

Welcome to today's lesson.

The title of today's lesson is Checking and securing understanding of drawing accurate scaled diagrams, and that's in the Unit Bearings.

By the end of this lesson, you'll be able to draw an accurate scale diagram using and choosing an appropriate scale.

Keywords that we will be using in today's lesson are scale factor and degree of accuracy.

A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.

In today's lesson, we won't be necessarily comparing shapes, but we will be comparing real-life distances with distances on diagrams. A degree of accuracy shows how precise a number or measurement is.

So, for example, I may say, "I have measured my height to the nearest centimetre." That would be my degree of accuracy.

Or I may say that I counted the number of buttons in a jar, and that's to the nearest 10.

Or I could choose to say something like, "I have rounded the lottery wins of the millionaire to one significant figure." For today's lesson, I've decided to split it into two separate learning cycles for you.

In the first one, we will concentrate on choosing an appropriate scale.

So, we won't actually be doing any drawing.

We'll be thinking about, is this scale appropriate for what I need to draw? And in the second one, we will then move on to actually drawing our scaled drawings.

And remember, these need to be accurate.

Please make sure you've got your pen, pencil, and ruler ready for this lesson.

It's gonna be really important to have a nice, sharp pencil and a ruler.

Let's get going with that first learning cycle, choosing an appropriate scale.

Alex needs to make a scale drawing of the sketches below.

He decides to use a scale of 1:100.

For which shape is that not a suitable scale? I'd like you to pause the video and consider the scale 1:100.

Can you remember what that means? And if you can, then make a decision, which shape is this not a suitable scale for? And there's one of them.

Three, it would be fine for, but one of them, unfortunately, it would not be an appropriate or suitable scale.

So, pause the video, make your decision with reason, and then come back when you are ready.

Okay, let's see.

It's not suitable for the parallelogram.

Why is it not suitable for the parallelogram? Hm, I wonder.

Well, Alex is asking the same question, "Why is it not suitable for the parallelogram?" And the reason Alex says that is because he say, he's saying, "The dimensions would be eight centimetres and three centimetres, which fit on my page." So, Alex has decided that the dimensions of the parallelogram would be eight centimetres and three centimetres, and he's quite right.

We could draw that neatly with our pencil and our ruler, and it definitely would fit on a page in our book.

Unfortunately, Alex has made a mistake.

Can you see what mistake Alex has made? What he's done is he's read the scale incorrectly.

He's read the scale as 1 centimetre equals 100 metres.

If we look, 800 divided by 100 is 8.

That's where that's come from.

300 divided by 100 is 3.

That's where that's come from.

But what does the scale mean? It doesn't mean 1 centimetre equals 100 metres.

What does it mean? The scale represents 1 centimetre equals 100 centimetres.

Remember, if there are no units, then the units have to be the same for both values in the scale, or might be easier to think of that as 1 centimetre equals 1 metre.

I'd like you to jot down those two scales because I'm gonna ask you to use those in just a moment.

Like I said, I'm gonna ask you now to tell me, please, what would the dimensions of the scaled drawing be? So, using the scale we've just written down, which was 1 centimetre equals 100 centimetres, or 1 centimetre equals 1 metre, what would the dimensions be? It would be eight metres and three metres.

And that is far too big for a scaled drawing.

A check for you to have a go at now.

For which of the following sketches is the scale 1:50 appropriate? This time, I'm asking you to tell me which of these is it appropriate scale for.

Pause a video, make your decision, A, B, or C.

And remember, I want the reasons, please don't just guess.

And then when you are done, come back and we'll check that you've understood why it makes an appropriate scale for some and not for others.

So, pause the video and then I'll be waiting.

Okay, A.

Now, we've got centimetres.

The both of these are in centimetres, so therefore, I can just use my scale.

12 divided by 50 is 0.

24 centimetres, and our rulers can only measure to the nearest millimetre.

The degree of accuracy is millimetres, so therefore, that would be 2.

4 millimetres.

We can't measure with our ruler accurately 2.

4 millimetres.

That's why it would not be an appropriate scale for A.

B, this would be dimensions of 6 and 16.

300 divided by 50 is 6.

800 divided by 50 is 16.

So, this would be fine to draw, wouldn't it? Six centimetres and 16 centimetres.

So, B, it was an appropriate scale for.

And C, it wasn't.

Here, I've got my measurement in metres, but for my scale, I've got no units.

I'm have to make sure that they're both in centimetres.

So, 60 metres in centimetres is 6,000 divided by 50 is 120 centimetres, which is 1.

2 metres.

And again, that's too big.

There's no point in making a scale drawing, which is 1.

2 metres.

So, C, it was not appropriate for.

Aisha, Alex, and Izzy are making a scale drawing of the plan of this block of flats.

Aisha says, "I'm going to use a scale of 1 centimetre equals 3 metres." Alex says, "I'm going to use a scale of 1 centimetre equals 2 metres." And Izzy says, "I'm going to use a scale of 1 centimetre equals 4 metres." I'd like you, please, to decide who has chosen the most appropriate scale.

And as always, I'd like you to give a reason for your decisions.

Pause the video, look at each of the three scales, and decide which is most appropriate and why.

I'll be waiting when you get back.

So, you can pause the video now.

And what did you decide? Let's take a look at them each in turn.

Aisha says, "I am, going to use a scale of 1 centimetre equals 3 metres." What degree of accuracy will they be able to use? So, when they're making these accurate scale drawings, what degree of accuracy will they be able to use? They'll be able to measure to the nearest millimetre.

If we look at our rulers, we've got centimetres, and then that's split into millimetres.

So, that's the nearest thing we could measure to.

So, therefore, we need measurements that are correct to one decimal place when measured in centimetres.

We could draw a line of 2.

4 centimetres.

We couldn't draw a line of 2.

45 centimetres, for example.

Well, at least, not accurately.

Aisha's choice of scale is not appropriate.

Did you decide it wasn't appropriate? Of course, you did.

Why though? 20 divided by 3 does not give an integer result.

20 divided by 3 is 6.

6 recurring.

We can't draw a line with an accurate length of 6.

6 recurring centimetres.

That's why Aisha's scale was not appropriate.

Alex said, "I'm going to use a scale of 1 centimetre equals 2 metres." Alex's choice of scale is appropriate.

Did you decide that? Of course, you did.

But why? That's the most important thing, isn't it? Why was it most appropriate? And the reason is is we take the two dimensions, 20 and divided by 2 because the scale is 1 centimetre equals 2 metres, and 15 divided by 2, we get 10 and 7.

5.

And both 10 centimetres and 7.

5 centimetres are easy lengths to draw with our pencil and ruler.

Now, let's consider Izzy's scale.

I'm going to use a scale of 1 centimetre equals 4 metres.

Izzy's choice of scale is not appropriate, and, of course, that's what you told me.

But why was it? And the reason is 15 divided by 4 is 3.

75.

We cannot draw this length accurately with a ruler.

We can only draw 3.

7 or 3.

8.

So, therefore, it's not appropriate because we cannot accurately draw a line of length 3.

75 centimetres.

Your check for understanding now.

Which is the most appropriate scale to draw an accurate scale drawing of this plan of a house? You've got four options.

1:30, 1:120, 1:180, and 1:250.

The house is 8.

4 metres by 12 metres.

Please pause the video, make your decision with your reasons, and then come back when you're ready.

What did you decide? Well, we're going to take a look at each of them in turn.

For A, we're going to divide by 30.

Notice, I've had to change my 8.

4 metres into centimetres, 840, and my 12 metres into centimetres, 1,200.

That's because my scale is one centimetre to 30 centimetres.

And although those are integers and easy to draw, the drawing would be too big.

It wouldn't fit on a piece of a four paper, would it? If it's got 40 centimetres would be the width of the house.

So, A, unfortunately, is not appropriate.

B, 840 divided by 120 is 7, and 1,200 divided by 120 is 10.

So, that's appropriate.

We could draw a rectangle with dimensions of seven centimetres and 10 centimetres.

C, 840 divided by 180 is 4.

667 to three decimal places, and we can only measure to the nearest millimetre.

So, that is why C is not appropriate.

And then D, 840 divided by 250 is 3.

36.

And again, we can only measure to the nearest millimetre.

That's why that would not be appropriate because we cannot exactly measure a length of a line or draw the length of a line to be 3.

36 centimetres.

So, D was also inappropriate.

When choosing an appropriate scale, the following are useful to consider.

If possible, choose a scale factor, which is a factor of all of the measurements.

If this is not possible, then choose a scale factor that will give dimensions with the greatest degree of accuracy being millimetres.

So, if you are working in centimetres, effectively needs to come out to be to one decimal place, and not rounded to one decimal place, exactly to one decimal place.

Now, you are ready for task A.

The first question in task A, I'm asking you, please, given the scale factor in the first column to identify one from each row that the scale factor is not appropriate for.

Three of the shapes it is appropriate for and one of them it isn't.

And your job is to decide which one.

Remember, you need to show your workings to support your answers.

So, pause the video, have a go at this, and when you come back, we'll move on to question number two.

Well done.

Question two, choose the most appropriate scale for each of the sketches.

So, in the first column, I've given you some sketches of some squares and rectangles.

I've also given you four different scales.

One of those scales is the most appropriate.

Your job is to work out which.

And remember to show you are working to support your answers.

So, pause the video, and I'll be waiting to go through the answers with you when you get back.

Great work on those.

Let's check those answers.

Question number one, for the scale factor 1:2, the shape that it was not appropriate for was shape 3.

The scale factor 1:150, it was not appropriate for shape 1.

1:5,000, it was not appropriate for shape 4.

1:25,000, it was not appropriate for shape 3.

How did you get on? Well done.

Question two, the first shape, it was scale 4, and this, remember, this was the most appropriate.

So, 1:100.

For the second shape, it was scale 1, which was 1:20,000.

The third shape, it was scale 2, which was 1:250.

And then for the final shape, notice here, I'd given you dimensions in metres and kilometres.

So, I'm hoping that didn't trick you up.

Of course, it didn't.

And that was scale 4, which was 1:110,000.

We can now move on then to our second learning cycle for today's lesson, and this is where you're gonna need your pencils and your rulers, drawing accurate scale drawings.

Let's go.

Here is a sketch of the plan of a block of flats we looked at earlier.

Accurately draw the plan of the block of flats on the centimetre squared paper below.

And we're using a scale of 1:200.

We can see the dimensions of the plan are 15 metres and 20 metres.

As we need to find more than one length, the most efficient method is to find the multiplicative relationship between the scaled drawing and real life.

Our scale is 1:200.

Remember, that means every one centimetre on the scaled diagram is 200 centimetres in real life.

To go from the scaled diagram to real life, we multiply by 200.

So, to go from real life to the scaled diagram, what do we do? Yeah, we divide by 200, don't we? Because it's the inverse of multiplied by 200.

Now, we can work out the dimensions of our scaled drawing.

Working in centimetres, we need to divide the real-life distances by 200.

So, remember, we are working in centimetres.

This means that we need to change the dimensions on the sketch into centimetres.

We need to change 15 metres into centimetres and 20 metres into centimetres.

How do you change metres into centimetres? Can you remember how to do that? Of course, you can.

What do we do? We multiply by 100.

20 multiply by 100 is 2,000 centimetres, and 15 multiplied by 100 gives us 1,500 centimetres.

We are now going to find the lengths of our scaled drawing.

2,000 divided by 200 is 10 centimetres.

So, we know the width of the plan is going to be 10 centimetres.

And then 1,500 divided by 200 is 7.

5 centimetres.

So, we know that we need to go up 7.

5 centimetres.

Remember, this was a centimetre square grid.

We know it was a rectangle.

And so we know that the other lines need to be the same length and parallel to the opposite sides.

This is the plan of the block of flats.

A different scale here, we've got 1:150.

We need to make an accurate drawing of this sketch of a garden.

All of the vertices are right angles.

The scale is 1:150.

The multiplicative relationship between the scale drawing and real life is multiplied by 150.

So, to go from real life to the scaled drawing, we are going to, yeah, divide by 150.

Next, remember, we need to make sure that we are working in centimetres.

We're going to multiply all of our numbers in our dimensions by 100.

So, we get 1,200 centimetres, 570 centimetres, 420 centimetres, and 900 centimetres.

We now need to divide all of the dimensions of the garden by 150.

And we can see that clearly from our scale.

That gives me eight centimetres, 3.

8 centimetres, 2.

8 centimetres, and six centimetres.

We're now going to draw this, and this is the centimetre square grid.

So, I start with my eight centimetres.

and then six centimetres.

My next line is 2.

8.

So, I am going to need my ruler here.

So, I'm going to get my ruler, and I'm going to mark where 2.

8 is.

And then going across from here, it's 3.

8 centimetres.

So, I'm going to mark where that is.

I can then draw in those two lines.

And I know that all of my vertices are right angles.

So, I know that this line going up needs to be parallel to the eight centimetre line and goes as high as the eight centimetre line, and then I can complete my garden.

What is the length of that side? It's six centimetres.

Subtract 3.

8 centimetres, which is 2.

2 centimetres.

What we're gonna do now is we're gonna check that line on our diagram is 2.

2 centimetres, and it is.

It's 2.

2 centimetres.

I love it when I can check my answers, and we can do that so many different places in maths, which is one of the reasons why I love maths so much.

Now, you are ready to have a go at task B for me, please.

You are gonna draw the following rectangle and right angle triangle using the scale given.

So, for the first one, you're gonna use the scale 1:5.

And for part B, you're gonna use a scale of 1:400.

I'd like you, please, draw these neatly, accurately.

So, use your pencil and your ruler, make sure that your line, if it's supposed to be 10 centimetres long, it's 10 centimetres long, not 9.

9 or 10.

1.

When you are done, come back, and then we'll move on to question two.

Great.

Question two, you are gonna draw an accurate drawing of this sketch of the garden.

You're going to firstly though need to choose an appropriate scale.

So, one of those scales is appropriate.

So, think about how we check the appropriateness of a scale.

And then, when you've chosen the correct scale, you can then, please, accurately draw the garden.

Pause a video, and then come back, and I will reveal the final two questions for today's lesson.

And finally then, question number three.

This time, I'm asking you to choose your own appropriate scale.

So, I've not given you a scale.

Please choose your own.

Think about what makes a scale appropriate.

When you are done with drawing these, please, rejoin me, and then we'll go through the answers.

Well done.

Question number one, you should have a rectangle, and your rectangle should have dimensions of five centimetres and 16 centimetres.

And for part B, your triangle should have a height of 1.

2 centimetres and a width of 5.

8 centimetres.

Question two, the most appropriate scale was 1:400, so that was C.

And then you can see there, the measurements that you should have.

Please pause the video and check those.

I'm not gonna read them out 'cause we might get confused where we are.

And I really do hope that you measured your line at the top and checked that it was 2.

3 centimetres.

And then, finally, question three.

These are just some examples.

You may have chosen a totally different scale.

So, I chose for A, a scale of 1:12, which gave me a rectangle with dimensions of three centimetres and five centimetres.

And then for B, I chose a scale of 1:80, and that gave me a height of three centimetres and a base of 13.

5 centimetres.

Like I said, those are just some examples.

You may have something different.

Let's summarise our learning from today's lesson then.

When choosing an appropriate scale, the following are useful to consider.

If possible, choose a scale factor, which is a factor of all measurements.

If this is not possible, choose a scale factor that will give dimensions with the greatest degree of accuracy being millimetres.

To convert between measurements in real life and on scaled diagrams or maps, we find the multiplicative relationship between the values in the ratio.

So, for example, if our scale is 1:150, then to go from the scaled diagram to the real life, I multiply by 150.

But to go back from real life to my scaled diagram, I divide by 150.

Well done with today's learning.

I've enjoyed working alongside you.

Hopefully, I'll see you again really soon to do some more maths.

But until then, please, do take care of yourself.

Goodbye.