Lesson video

Hello, my name is Mrs. Buckmire.

And today I'll be teaching you about enlargements and area.

So make sure you have something to write with, something to write on.

It'll be excellent if you have a pencil and rubber because we'll be doing some drawing.

And a straight edge like ruler as well, but don't worry if not.

Remember, pause whenever you need to, and also when I ask you to please and rewind if you need some extra help.

If you want to hear it again, sometimes it is useful.

Let's begin.

Okay, what I want you to do first is calculate the area of the following shapes.

So I hope that there are ones you recognise and any you can't do then maybe just have a little guess on what you think you'd have to do.

And then listen carefully when I go through the feedback.

Pause the video and have a go now.

Okay, so the first one is a triangle.

How do you find the area of a triangle? Good, it's base times perpendicular height divided by two, make sure you divide it by two.

Did you remember that? Good job.

So you should have gotten 9 cm².

And so the next triangle is the same thing.

Nine times six is 54.

54 divided by two, what did you get? 27 cm² So you guys can see either half or six times nine is the same as six times nine divided by two.

Okay, let's go to a rectangle.

Length times width, 60 cm².

Oh, what's this shape called? Good.

It's a kite and find the area of a kite.

Excellent.

So you could actually see that if I move this triangle around there, so it becomes like this.

And if I move this one, I'm drawing badly, there, It becomes like that.

So our overall shape becomes a rectangle.

So it's actually six times 12.

72 cm².

Well done.

If you've got that.

And this one now, this is a rectilinear shape, I split it into two rectangles, so maybe I'll put a line there.

So then I've got 13 times two here.

And what would this missing length be? What did you get? Yeah, eight, take away two.

So six centimetres.

So then six times three, which is 18.

26 plus 18.

26 plus 20 is 46, take away two.

Is it 44? Yes, 44 cm² Well done if you've got those correct.

Pause the video and maybe, copy down any ones that you got wrong and maybe write yourself a note on what you need to remember.

So maybe for triangles, remember to divide by two For a kite, you can just multiply six and 12, for the rectilinear shape, split it into rectangles wherever you need to do to remind yourself and for next time.

Okay, so I want to know what is the same, What is different about the patterns that Antoni has created.

There are three patterns there in the top row, the second row and third row.

And maybe, and one bit of a challenge.

Can I make a similar pattern for this rhombus and maybe do a little sketch and actually a similar pattern for the rhombus.

Pause the video and have a go.

Okay, you paused it, had a go? So what did you say was the same? Yes.

So for all of them, they start off with one shape, then there's four, and then there's nine.

Okay.

What else do you notice? Oh, you're already thinking about scale factors.

So the length, so you could think about how this one is a scale factor of one, this one, now this length is two and this length is double as well.

So actually this one's a scale factor of two and here we have a scale factor of three.

So that's our scale factor.

And then actually, note that the area also increases.

So one, and then it's four for everyone.

And then it's nine shapes for everyone.

And, shall we write that down, So it was one shape, four shapes, nine shapes.

Anything else? What was different? Yeah, with the top row and the bottom row, it looks like, Well, actually, no, with the bottom row it looks like the squares haven't really changed orientation at all.

Looking the same, they could have changed maybe, they're all you know, rotational symmetry, but it looks like yeah, they've all been kept the same.

But with these middle ones, for the top and bottom one actually, there's some orientation change.

They all stay the same.

That's interesting.

They are different shapes.

Yes.

The first one is a triangle.

What's the second? What shapes are those? Trapeziums. They are made out of trapezia or trapeziums And the last one square, they are different shapes.

Did you say anything else? Excellent.

Okay, interesting.

Right? Let's think then, can I make similar shapes out of a rhombus? Have you had a go? Oh wait, something else, The word tessellate, great word, I almost forgot to write that word down.

Let's write that down.

This word, did anyone use it? Tessellate.

What does that mean? Good.

There's no gaps between them actually.

That's really, really important cause as long as the shape tesselates, then actually, there's a special relationship between that and how the area increases compared to the scale factor.

Maybe you're already looking into that.

So maybe you're already saying, oh, is there any relationship between these numbers? Well done if you are.

Let's move on and think about Antoni's rhombus pattern.

Okay, so, we start off with one and then how many in the next pattern? Good.

Four.

And how many in the next one? Nine, really well done.

If you created a pattern that looks like this, good work, give yourself a big tick.

So Xavier says when you enlarge a shape by scale factor of three, the area gets three times greater.

Hmm, do you agree? Pause the video and have a think.

If you agree, why do you agree? If you don't agree, why don't you agree? Defend your answer.

Okay, so did you agree? You did not agree.

Why not? Excellent.

You can see in this diagram that well first, this area is one triangle.

And then we have four triangles, and then we have nine triangles, and it's this one where the scale factor is three because each side length has been increased by three times.

So three lots there, three lots there.

So nine triangles.

Same here, we start with one, parallel and rhombus.

And then we have nine rhombuses.

So these numbers relate to the areas.

Remember with area, we can use informal, and we can actually do it by shaped space.

So it goes one to nine.

So the area doesn't get three times greater.

How much greater, How many times greater does it become? Yes, when a scale factor- when a shape is being enlarged by scale factor of three, the area gets nine times greater.

Well done if you predicted that.

I wonder what would happen if the scale factor was four? Hmm, how much big would the area get? That's for you to think about.

You're ready for your independent tasks.

This looks familiar.

It looks a bit like we tried this because it has the same shapes.

But what I want you to do is draw sketches.

So actually don't use a ruler to measure your side, but just draw a sketch on the shapes, labelling actually what the dimensions would be, after they've been enlarged by scale factor of seven.

So, how do you- And then I want you to find the area of them and tell me how the enlargement affects the area, okay.

So first you're doing a sketch of what would the lengths be if we enlarged the shapes by a scale factor of seven, and then you'll find the area, and maybe you don't have to find all of them, maybe then you can actually say, how the enlargement affects the area.

Okay, Pause and have a go.

Okay, so I put on the lengths first, if you want to you want to pause and just check those, but I'll talk about them while I go through.

So the area- So we know A of a triangle, what was it? Good, 441 cm² The area of the rectangle, the new area is? And so the triangle is 1323 cm² 2940 cm², 3528 cm² and 2156 cm².

Okay? It's hard.

I can't really see any relationship between these, but maybe when you were working it out, you thought of something.

So maybe I can see actually.

How do we go from nine to 441? Need a calculator for that.

441.

Actually, let's do a little - We never do this.

Let's do a little bus stop.

Yeah, nine gets into four zero times, nine goes into 44.

And five, oh, it's not five.

It's four.

Mrs Buckmire is doing bad, live modelling of this.

A is 36 and 36 and 81, uh, 49.

Okay, what about here? Is it 49? Maybe you could do 27 times 49.

Maybe pause and have a little check.

What does that equal? Use whatever method you use multiplying.

Good, it does equal this.

Hmm, maybe check the other 60 times 49 well I can do 60 times 50 is 3000 and then take away 60, it is 2940.

Oh it looks like all of them to get from the original area to the new area we times by 49 Yes, the new area is 49 times original area.

Well done if you got that, even better if before answering you predicted and you didn't actually even have to write in the calculation You just you just knew.

I wonder how you knew.

Okay, so we're going to explore a bit more.

Now.

I love this site.

This is mathsbot, a free website, you can google mathsbot tangrams, and you'll come to this page that I'm showing on the screen here.

And what Rosie has done is created a- oh, Yasmin sorry, is created a polygon using pattern tiles and then enlarged it by a scale factor of two.

Okay, I'm even going to show you her doing it.

I'll show you live.

Let's go like this.

Now you can see her creating it, okay.

And you can do this as well.

So you can either do this question using Yasmin's shape, or you can actually just make your own.

So you can use mathsbot but make your own shape, and then enlarge it by a scale factor of two.

Okay.

Because I want to see what the enlarged shape looks like.

That's what I'm most interested in.

And then I want to see, how did the enlargement affect the area? Okay.

So either, using Yasmin's enlarge that shape by a scale factor of two.

And when you do it, can you actually draw in all the individual shapes as if it was made up of this smaller shape each time.

And then can you describe how the enlargement affected the area? Okay, so you can either do it using this shape, you either create your own shape on mathsbot and do it or even if you are lucky enough to be in school maybe and have tiles or you want to draw your own table bigger you can do that.

It's all about just exploring it so you know what, be as creative as you like.

You know, your imagination is the limit, you create the shape yourself.

Okay? Let's see.

Okay, I'll give you some support on the next slide.

Okay, so just some support.

Here it is enlarged, Okay, so this gives you kind of the outline, if that helps, and you can pause and think about how the shapes would fit in.

Although just to help you out, here it is, for just the squares.

So what I've done is I've made their length no longer one it's now going to be two.

And this height here, no longer one is now two.

So that's what we need to do for all of the other ones.

And then I think, oh, how did the enlargement affect the area? How do I know? So do pause and have a go.

Okay, right.

another little video of Yasmin doing it here.

You can see she is enlarging it by a scale factor of two.

And so what do you notice about this? Yeah, she's had to copy them so there's four of each one.

What else did you notice? Did you see how actually sometimes you have to rotate, even here so you have to rotate certain shapes.

For parallelograms she didn't have to but for the triangles she did.

That's interesting, but they do tessellate at the end, so there's no gaps at the end.

Nice.

So what did you comment about the area? Yeah, you needed four extra of each one to mean the area's four times greater.

Interesting, so that enlargement of two makes their area four times greater.

Cool.

Well, really, really well done if you had a go at that.

And excellent work if you have had a go, either tried this, you got involved with doing independent tasks, And then the explore and well if you just had a go like maybe you did it on mathsbot, maybe you drew your own picture.

I would love to see it.

So if you would like to share your work on Instagram, Facebook or Twitter, you need to ask your parent or carer to share your work there, and you should tag @OakNational #learnwithOak.

I'd love to see your work, anything that you're proud about, from transformations or from any of this work, I'd love to see it.

Have a lovely day.

Make sure you do the exit quiz.

Thank you for your hard work.

Bye.