Lesson video

Hello.

My name is Mrs. Buckmire.

And today I'll be teaching you about enlargements.

So make sure you have a pen and paper.

If you have a pencil and a ruler or straight edge and a rubber that could be helpful, but you don't need it.

And remember, pause the video when I ask you to, but also whenever you need to, and you can always rewind the video and listen again to help yourself out.

Let's start.

Okay, try this feedback.

I want to know what is the same, what is different about the shape S and the shape T? Pause the video and have a think.

Okay, what did you come up with? It's always the same.

Yes, they're both the same shape.

They both have right angles in them.

They're both Ls really.

What's different? T is a lot bigger than S, true.

The top of T has a length of two while this one is one.

This length is two, while this length is four, this one is one, while this one is two What are you noticing? Excellent, all the side lengths are what? All the side lengths of T are double the side lengths of S.

Maybe you said, what is different? All the side lengths of S are half the side lengths of T.

Well done.

So we could say S is an enlargement of T by scale factor a half.

So that's because all of S's side lengths are half of T side lengths.

We could say T is an enlargement of S by scale factor of two.

So what we're noticing is enlargement doesn't just mean getting bigger.

It can mean getting smaller as well.

So for S is an enlargement of T, it's just a half.

So it's between that number is between zero and one.

So it's like a fraction of the other shape.

So imagine S following an enlargement of scale factor three, one, half, zero.

What would it look like? Pause the video and even draw it.

If you don't feel too confident, you can kind of just imagine and maybe say in words, what you think is going to happen, even better if you do both.

Pause and have a think.

Okay, so this was a scale factor of one.

It's exactly the same.

What happens when you scale factor three? It was three times bigger.

Scale factor half? Oh was half the size.

And scale factor two.

Now it hasn't lined up best here.

So I'm just going to quickly write on to this one, with the length of two, this one with a length of three, and this part was one half.

I could also go around and put in the other lengths as well.

So for example, this one would have been six.

That length from there all the way down to here, this one, three, should have been three.

This one, three.

This one, what did you get? Good, it was six and all the way to the top, should have been nine.

Okay, so check your ones carefully.

Okay, so is B an enlargement of A? How could you change one of the dimensions of A or B so that it is if it's not? Okay, let's check this out.

So I would compare the longest side.

So six and 12.

Well, B is double, that B's longest length is double the longest length of A.

The shortest length of B is not double length A.

So no, it is not an enlargement, cause they're not in the same proportion.

Cause to get from six to 12, that's a double to get from four to six, we can't double it.

So we could change six couldn't we? We could change it to eight and then it works out, right? Yes, it does.

Cause then actually go from here to here is times two.

So now going from there to there times two.

Hmm, could you change the other one? Could you change, keep six, and change 12? So how do we get from four to six, ah, times? What is it? 1.

5, so to get from six to what we want this number to be, we have to times by 1.

5, so one and a half, half of six is three, so six plus three, nine, so nine centimetres.

Now they're in proportion.

So this B let's call it B1 has a scale factor of two compared to A, and this one has a scale factor of three over two or 1.

5.

So what we can see, a shape is an enlargement of another if all sides have been multiplied by the same scale factor.

That's really important.

Maybe add that to your notes as something that you want to remember from today's lesson.

Okay, so is B an enlargement of A? I'm going to give you some quick fire questions.

I want you to tell me is B an enlargement of A? Tell me, is it? Yes, it is.

What's the scale factor? Fantastic, it is five.

So two times five gets the 10, three times five gets the 15.

Is this one? Is B an enlargement of A? Tell me.

No, it is not.

Could you change the lengths so that it is? Yeah, which one? You could change both of them.

So you could change 10 so that we get 12 centimetres.

Maybe that's the one you first thought of, counting by two, or to get from six to 10, what do you have to times by? That one's harder.

You can actually times by 10, over six.

So here I would get 40 over six, but well done if you've got, I'd expect you to get this answer.

So that's what.

Let's do another one.

Okay, is it an enlargement? No, it is not.

Could you change it so that it is? So, oh, wait a second.

Is it, it is an enlargement look, cause here to here, we times by 2.

5 or two and a half and here to here two and a half times six.

So two times six is 12.

Half of six is three.

Add it on, it gets 15.

Oh, Maliah.

It is an enlargement well done, if you weren't bored.

Yes, it is enlargement.

The scale factor is five over two, or two and a half.

Good job.

Okay.

This student used a six by four rectangle and a 12 by eight rectangle, to enlarge A by scale factor of two.

Hmm, let's look at this closely.

So what I noticed that they've done is they've gone from the middle here of that six by four.

And they've also done the same here.

So between the 12 by eight, it's actually in the middle, and then they've gone to the, this one goes four up to get to this point and here they've gone two, four, six, eight up to get to here.

Yeah, so it's doubled.

So actually what can we really use for when there's curve? Because actually you're looking at key points.

So looking at actually kind of what we can find about, I just compared this height, this 11, even between these two parts.

Yes.

And then you could maybe compare again between this point and this point.

So that one's two and this one between this point and this point is four.

Anything else? Good, so this length here is currently four there.

And this one's two.

What else do you notice? Fantastic, so I wonder how the perimeters compare.

Excellent, so if each length has been doubled and perimeter is length all the way around the outside of the edges, then yeah, the perimeter will double too.

So perimeter increases by the same, by the same scale factor.

So actually the perimeter will be times by two.

Also I noticed that set, each one of these, it kind of become a two by two here.

That's interesting, isn't it? Because if you see that, like by this one here, it just touches like just the one corner there.

And then here is of that four.

So it's kind of, yeah, it's been enlarged like that.

So it's become a two by two.

Awesome.

All right, let's get you practising.

Okay, so I want you to sketch each of the following shapes on square paper, then enlarge by scale factor three.

Now you do not need to use some square paper if you don't have it, you can actually adjust kind of writing the key dimensions.

So like if I didn't have square paper and I was drawing this triangle here, like I know that it's square paper, but I'd draw the triangle, and then I'd say, Oh, this length is currently two, this length is currently four.

And maybe one of these lengths or this length is currently two as well.

And then when I draw the diagram, then I think, okay, how does it compare? Okay.

So what's going to happen now when I enlarge it by scale factor of three? Pause the video and just have a go.

Okay, so I've done this without square paper.

So we already said this was two, this was four, and this was two.

So the length from here to here, if it's scale factor three, sorry.

Yes, enlarged by scale factor three is now going to be six.

And this length, how was the height of it going to be, compared to the six perpendicular height is going to be from two.

It's also going to be six and the length of course.

So from one side, all the way to the other, rather than four, times it by three, it's going to be 12.

So it should have got six, six and 12 by what about here? So we've got, this is three.

This is one.

And we've got lows for back here.

This is one, this is two, that's two, that goes down by one.

And this is two.

And this is one.

It's in a similar fashion scale factor of three.

You could say, oh, this bit is going to be nine.

This is going to be three.

You should be checking yours as we're going along.

This bit, so it was originally one, now it is three, good.

This bit six.

And the height from here to there is going to be two.

Distance here, two times three is six.

This one's going to be six and this one's going to be three.

Well done, if you got that, excellent.

Okay, so here now with this one is may, maybe a bit hard is why we do that.

I would choose the centre and then say, so here is one by two.

So if it's enlarged more three, this should be a three by six.

And then the same in all the other quarters of our oval, Oh, this one's hard.

So this looks like it's like 1.

5 ish.

The length of course looks like it's 2.

5.

So I would say it was like 2.

5 times three.

So 2.

5 plus 2.

5 is five, plus 2.

5 is 7.

5, and then going downwards.

It was 1.

5 times it by three, 1.

5 plus 1.

5 is three, plus 1.

5 is 4.

5.

So then I would kind of just then just have a little go at drawing it or, hey.

I don't think this is bad.

There you go, like that.

Was, I never got anything that resembles it.

Okay, so for your explore, you can see the circles C1, C2, C3, and C4.

They're shown below.

What I want you to do is select two of the circles and describe the enlargements connecting them.

Then I want you to compare the lengths of the parts along the arc, A to B, B to C, C to D and A to D.

What I mean by that is maybe compare, how does A to B compare to B to C? How does A to B compare to A to D? You just explore it, whatever way you like, maybe try and come up with four or five different kind of, maybe four statements connecting different ones.

Okay.

Just pause and have a go.

Okay, there are so many different things you can do here.

So when I'm selecting two of the circles, so I'm describing the enlargement.

So I can say, for example, that C1 and C2 have enlargement of scale factor one.

Cause they're actually the same.

They both have the exact same radius of one centimetre.

And what else could we say? What's major between C3 and C1? Good.

C3 is an enlargement of scale factor two of C1 because their radius is two times bigger.

What about C4? That was a hard one.

What is the radius of C4? Do you know? So this length is one, that's also one.

So that's one plus one, plus two to get to the centre.

So it was four so well done if you got that.

So C4 is a scale factor of four of C1.

So if that's the case, was C1 an enlargement of C4? Good, C1 is a scale factor of a quarter of C4.

Well done if you've got any of those.

So the scale factor affects all the lengths equally.

So in the same proportion, that's, what's really key there.

Okay, so now I want to compare the lengths of the paths along the arcs.

So, and C to D well, C to D is equal to A to B.

That's one thing you can say.

Where's my pen? Here we go C to D equals A to B.

What else can we say? We can say B to C, so BC can I say is equal to two lots of AB.

And we can also say AD equals four lots of AB.

Excellent, well done if you've got anything like that.

Really, really good job today, everyone.

If you did the try this, you had a go at the connect and the independent task and explore as well.

You just listened in and make good notes.

You should be very proud of yourself.

Hopefully you've learned a bit about enlargement.

What's the one thing you need to remember from today? Excellent, so how does the scale factor affect the perimeter? Interesting, the scale factor affects the lengths, which in turn, affects the perimeter.

Well done.

So I would love for you to do the exit quiz, as I think that'd be really helpful for your learning and hopefully I'll see you in another lesson.

Have a lovely day.

Bye.