Lesson video

Hi, I'm Miss Kidd-Rossiter, and I'm a maths teacher in Hull.

Today, we're going to be starting the first lesson of a really exciting unit on similarity and enlargement.

Today's lesson focuses on enlarging by an integer scale factor.

Before we get started, can you just double check that you've got a nice quiet space to work if possible, and that you're free of any distractions.

when you're ready to go, resume the video.

Okay, so we're starting today's lesson with a try this.

In a moment, three rectangles will come onto your screen.

Your job is to have a go at finding out some things that are the same and some things that are different.

So pause the video now and have a go at answering this question.

If you're struggling a little bit with this activity, it might help you to think about the angles in the shapes.

So I can see in A, that I've got a right angle here.

Is that the same in B and C, or is it different? What about the other angles? It also might help you to have a think about the side lengths.

So for example, on A here, I can see that this side is two, whereas on B and on C, my bottom side length is four.

What about the height of the rectangle? I can see the on A and B that's clearly the same.

What height is it? What height is rectangle C? what's the same and what's different? Hopefully you've had a really good go at that try this activity.

We're now going to move on to the connect part of the lesson, where we're going to look at what is an enlargement and then enlarging some shapes of our own.

So first of all, I'm going to tell you that shape C is an enlargement of shape A.

And shape B is not an enlargement of shape A.

Pause the video now and have a think about why.

Okay, so hopefully you had a think about the side lengths of each of the rectangles, and also the angles of each of the rectangles.

If you didn't, pause the video now and have a go at that.

Okay, great.

So first of all, let's think about the angles.

We can see that each of our shapes has four right angles, one in each corner.

So this at the moment doesn't distinguish B from C at all.

Then we have to have a look at the side lengths, and this is where it becomes clear to me, Why C is an enlargement of A and why B is not.

I can quite clearly see that I've multiplied each of my side lengths of A by the same thing to get my side lengths of C.

So I've multiplied two by two to get four.

And I've multiplied six by two to get 12.

This number that we multiply by is called the scale factor.

So from A to C our scale factor is two.

We can also see that this is why B is not an enlargement.

Although we've multiplied two by two to get four, we haven't multiplied six by two to get 12.

So that leads us to this definition.

One shape is an enlargement of another if the same scale factor can be used to multiply the lengths of each side of the original shape to give the lengths of each corresponding side of the enlarged shape.

And the angles of both shapes are the same.

We've got this original shape here, which we're going to call the object, and we're going to enlarge that to create an image.

We're going to enlarge this shape by scale factor three.

So at the moment, the top of my shape is one square wide.

I'm going to multiply that by my scale factor of three.

And that tells me that my top of my image will be three squares wide.

At the moment, the left hand side of my object is two squares high.

So that means that the height of my image will be six squares high.

I'm doing this on a screen.

When you're doing this, you will use a ruler to make sure you're really accurate.

The base of my object is two squares wide.

So that means that the base of my image will be six squares wide because I multiply two by my scale factor of three and get six.

I can then finish off my shape in the same way.

Again, you would use a ruler.

So this now is my image.

So that's important language that we use, our original shape is our object.

And the enlarged shape is our image.

Here's another shape, is this image an enlargement of this object? Pause the video now and tell me why or why not.

Hopefully you realise that this image is not an enlargement of this object because we've not multiplied each side by the same scale factor to get the image.

Here, we've gone from one to two squares.

So our scale factor would have been two.

And here, we've gone from one to three squares.

So our scale factor would have been three.

So this image is not an enlargement of this object.

We're now going to practise what you've learned so far in the independent task.

So close the video and navigate to the worksheet.

When you've finished, resumed the video to continue with the lesson.

Well done on that independent task, we're now going to go through the answers.

So when A is the object and B is the image, our scale factor is two.

When A is the object and C is the image, our scale factor is four.

When A is the object and D is the image, our scale factor is the three.

And when B is the object and C is the image, our scale factor is two.

You can see here that for question two, I've already done the answers for you.

So pause the video now and mark those.

Let's discuss question three.

So what do we notice about the perimeters of the shapes in question two? So you can see that in red, I've already done the perimeters for you.

And what you should have noticed is that the perimeters are also increased by the same scale factor as the lengths of the sides.

Finally, explain why Z is not an enlargement of Y.

Well, you can notice here that the height of Y is three squares and the height of Z is six squares.

So, so far it's looking like it could be an enlargement 'cause I've multiplied three by two to get six.

And then the width of my rectangle is two for Y and it's three for Z.

So if I was to multiply by the same scale factor that I've multiplied by here, then the width of my rectangle should be four not three.

So that's why it's not an enlargement of Y.

Okay, the final part of today's lesson is the explore task.

Pause the video now, read the screen and have a go at the activity.

When you're ready to discuss it, resume the video.

Well done, that was a really tricky task, so fantastic effort for persevering with it.

The first thing I did was I worked out the area of my purple pentagon, which was nine units squared.

Then I thought about how I could record the areas of my other shapes.

So I decided to draw a table.

When the scale factor of enlargement was two, I found that the area of my purple pentagon was 36 units squared.

When the scale factor of enlargement was three, I found that the area of my purple pentagon was 81 units squared.

And when the scale factor of enlargement was four, I found the area of the purple pentagon to be 144 units squared.

Now, the next thing I did was think about what do I multiply nine by to get 36? So that answer obviously is four.

So if I multiply by two, I get 18, and then I have to multiply by two again.

What about for the scale factor of three? What do I multiply nine by to get 81? Well, the answer is nine, so I could do nine times three times three.

What about when the scale factor was four? What do I multiply nine by to get 144? Well, the answer is 16, so that would be nine times four times four.

How else could I write two times two or three times three, or four times four? What about when I'm enlarging by a scale factor of n? What would I need to multiply nine by to get the correct area here? So, pause the video now and have a think about that.

Well done if you realised that another way of writing two times two would be to write two squared and the same for three times three, we could write that as three squared.

And then you could have realised that to get the correct area here, I would have to multiply nine by n by n.

And that would give me an area of 9n squared.

This was tricky, so don't worry too much about it if you didn't understand.

We're going to come back to this later in the unit.

That brings us to the end of today's lesson.

So thank you so much for all your hard work.

I hope you've enjoyed it.

And I know that you will have all learned lots.

Hope to see you again soon, bye.