Lesson video

Hi, my name's Miss Kidd-Rossiter and I'm going to be taking you through this lesson today on areas of similar shapes.

We're going to be building on all the work we've done so far on enlargements and similarity.

Before we get started, can you make sure that you're free from distractions, you've turned off all notifications, and if you're able, you're in a nice quiet place, so you can concentrate.

If you need to pause the video now to get hold of anything or to find yourself quiet place, then please do.

But if not, let's get going.

So we're starting today's lesson with the try this.

You've got a shape on your screen, and I'd like you to enlarge it by the scale factors that are given to you on the left hand side, when you've done those enlargements, can you notice what happens to the area? Pause the video now and have a go at this task.

So I hope you've had a go at that , try this activity.

What was the area of the shape on your screen? Tell the screen now please.

Excellent, three squares.

When we enlarged our shape by scale factor of two.

You should have got the shape that's on the screen now.

What's the area of this shape? Tell the screen now.

Excellent, it's 12 units squared or 12 squares.

What about when you enlarge your shape by scale factor three? What did you get for the area then? Excellent, you should have got 27 units squared or 27 squares.

And what about when you enlarged shaped by scale factor 2.

5? What did you get then? What was the area? Tell the screen now.

Excellent, you should have got 18.

75 squares, 18 and three quarters or 18.

75 units squared.

So what's happened to the area? You could have said it's got greater, that's true.

Can we notice the relationship between the scale factor of enlargement and what the area increases by? That's what we're going to look at now in the connect.

So moving on to the connect activity now, I want you to pause the screen and have a go at answering the first question on the slide.

So what's the scale factor of enlargement going from A to B? If A, is the object, B the image, pause the video now and figure that out.

Excellent, tell the screen, please.

What is the scale factor of enlargement? Brilliant, it's two.

So the scale of factor of enlargement is two.

I could write my widths of my rectangles in the ratio, 10 to 20, where is A to B.

And I could write the heights of my rectangles in the ratio, five to 10.

What do we notice about these two ratios? Excellent, they're equivalent.

What's the simplest form of this ratio one to two? Excellent, so we can see that this is where we get the scale factor from.

The every one centimetre on shape A we have two centimetres on shape B, right.

Pause the video now, please, and work out the area of each shape A and B.

What's the area of shape A? Tell screen now please.

Excellent, 50 centimetres squared.

And what's the area of shape B? Tell the screen now please.

Excellent, 200 centimetres squared.

Therefore, we were to write the areas of A to B in a ratio, what would it be? 50 to 200.

Is that what you thought? Could you simplify this ratio for me? Tell the screen now.

Excellent, it's one, four.

So we can see that when we're enlarging the area, we have to enlarge by scale factor of four.

What's the relationship between two and four.

Can you think about that for me? We're going to move onto the next slide and see if you can spot a pattern.

So again, we've got two similar shapes here, pause the video and find the scale factor of enlargement for me please going from A to B.

What's the scale factor of enlargement? Tell the screen now.

Excellent, it's three this time.

So we're going to write in a ratio again, A to B our lengths.

So the base of the triangles in the ratio, four to 12 and the height of the triangle is in the ratio three to nine.

Are these equivalent ratios? Tell the screen.

Yes, they are well done.

What's this ratio in its simplest form? Tell the screen now.

Excellent, one to three.

So again, this relates to our scale factor because for every one centimetre on A we've got three centimetres on B.

Pause the video now and work out the areas of these two triangles.

What's the area of shape A? Tell the screen now.

Excellent, six centimetres squared.

What's the area of shape B? Tell the scream now.

Excellent, 54 centimetres squared.

So for the areas, what would our ratio be of A to B? So area of a is six centimetres squared and the area of B is 54 centimetres squared.

Can we simplify this ratio? What did you get? Tell the screen.

Excellent, one to nine.

So when we're enlarging a shape by a scale factor of three to find the corresponding area, we would have to multiply by nine.

Can you find a relationship between nine and three? Good, hopefully you've thought about this one and the last example, and you've realised that the area scale factor is the scale factor of enlargement squared because three times three is nine.

And in the last example, two times two is four.

So pause the video now and make note of this.

The area scale factor is the scale factor of enlargement squared.

Pause the video now and note that down.

Well done, that's really key.

So make sure you've got that written down.

We're now going to move on and you're going to apply your learning to the independent tasks.

So pause the video now, when you're ready to go through it, come back and we'll go through it together.

Okay, let's go through something else.

To this independent task well done for giving it a go.

Calculate the length of BC.

Well, we can see that the scale factor of enlargement from ABCD to EFGH is two, isn't it? Eight multiply by two gives us 16.

So what multiplied by two gives us eight? Correct, four centimetres.

So you all should have got that one.

That's excellent, well done.

Calculate the area of both rectangles.

So we know that this rectangle here has an area of 32 centimetres squared, and we know that this rectangle here has an area of 128 centimetres squared, well done.

What's the scale factor between the areas of ABCD and EFGH? So we can write it in a ratio 32 to 128.

And then when we simplify this ratio, we get one to four.

So that tells us that the scale factor of enlargement for our areas is four.

Triangle ABC is similar to triangle DEF which is similar to triangle, GHI.

So that all three of those are similar.

What scale factor is AC multiplied by to give DF? So what do we multiply three by to get 4.

5? We could have worked that out and our answer is 1.

5.

What is the scale factor that the area of ABC is multiplied by to give the area of DEF? Well, we know that the area scale factor is the scale factor of enlargement squared.

So 1.

5 squared gives us 2.

25.

So that is our answer for part B that's our scale factor of enlargement.

So what is the area of DEF? Well, we know that the area of ABC is eight.

So we can multiply that by 2.

25 and what does that give us, tell the screen now, 18 centimetres squared, well done.

And then finally we need to work out the area of GHI.

So, first of all, let's work out the scale factor of enlargement of three to 1.

5.

What is the scale factor of enlargement there? Tells the screen.

Excellent, it's a half.

So our enlargement scale factor is a half or 0.

5.

So that means that our area scale factor will be a half squared.

So what's a half squared.

Can you tell me good? It's a quarter or 0.

25.

So we've got to multiply eight by 0.

25 to get our area and eight multiplied by 0.

25 is just two centimetres squared.

So that's our area there.

Right, we're moving onto the explore task now.

So you've got two shapes on your screen.

Are those shapes similar? What's the relationship between the area of these shapes? Could you use nine copies of the shape? Could you use 16 copies of the shape? And can you draw your own shapes? Pause the video now and have a go at this activity.

What did you find out? Are the shapes similar? What do you think? Yes, these two shapes are similar, well done.

What's the relationship between the area.

We've worked that out going through today's task.

So you should have used that to help you find out whether you can use nine copies of the shape and whether you can use 16 copies of the shape.

Not going to tell you the answers to those.

I'm going to leave you to puzzle on them.

That's the end of today's lesson.

So thank you so much for all your hard work on that.

If you've drawn some great enlargements or some great copies of shapes in that explore tab, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

Thank you so much for all your hard work today.

I hope to see you again soon, bye.