Lesson video

Hi, I'm Ms. Kidd-Rossiter and I'm going to be taking you through today's lesson on enlargement by a negative scale factor.

Really great topic, continuing on from all the work that we've done so far on enlargements.

If you can, make sure that you're in a nice, quiet space where you can concentrate and that you're free from distractions.

If you need to, pause the video now so you can get yourself sorted.

If not, let's get going.

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

On your screen, you can see three shapes.

You've got centre of enlargement, shape A, and shape B, and shape C.

It's your job now to pause the video and have a think about what's the same and what's different.

If you're struggling a little bit with this activity, you might want to think about the size of the shapes, and the orientation.

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

Hopefully you had a really good go at that try this activity and you managed to come up with some similarities and differences.

We're now going to build on the work that we did on enlargements from a given point.

On the right-hand side of your screen, you can see that we've got shape A, which is our object and shape B, which is our image.

What was the scale factor of enlargement from, if shape A is the object and shape B is the image, tell the screen now, what's the scale factor? Brilliant.

You should have said that it was three.

What are the two ways that we could have worked that out? Pause the video now and think about that.

Brilliant.

The first way is that we could have compared the length of the side.

So we can see that this one here is two squares wide, and this one here is six squares wide, and we could have done the same for the height of the triangle.

The other way that we could have looked at it is from the given point.

So from our given centre here, P, to this vertex is one arrow, and from the same vertex to this top left corner of B it's three arrows, so that we can see that that is a scale factor three, enlargement.

What about then A and C? So this time A is our object, and C is our image.

Pause the screen now, and have a think about what you think has gone on here.

Okay.

Hopefully you realise that it's still an enlargement.

We've still enlarged our shape.

This has gone from two squares and we've got six squares here.

It can't be an enlargement of scale factor three, because if it was an enlargement of scale factor three, it would have given us this image here.

You can see, that instead of going in the same direction, our rail lines have gone in the opposite direction.

When we enlarge in the opposite direction, this is by a negative scale factor.

So we're enlarging shape A by a negative scale factor.

Our negative scale factor for this enlargement is -3.

So you can see, that from P to this vertex was one arrow, in the opposite direction, we've done it three arrows, one, two, three, and that's given us the corresponding vertex.

Let's look at a second corner.

We can see this one arrow here has taken us to this vertex.

So we're going to stretch by -3 in the opposite direction, one, two, three, to give us this vertex.

And then finally, we've got this bottom vertex here.

When we enlarged by a scale factor of -3, we stretched by three in the opposite direction, one, two, three, and that vertex now becomes the top.

So key things to know about negative enlargements are that they change the orientation of the shape.

If the scale factor is equal to -1, then the size of the shape stays the same, but the orientation changes.

If the scale factor is less than -1, then the size of the shape will increase and the orientation will change.

And if the scale factor is less than zero, but more than -1, then the size of the shape will change and it will become smaller, and the orientation will change.

You're now going to have a go at applying what we've learned to the independent task.

So pause the video, navigate to the independent task and then resume the video when you're ready to go through some answers.

Well done at having a go at that independent task.

We're going to go through some of the answers now.

So the first thing you were asked to do was to copy down the diagram to the left and then enlarge the shape by all the scale factors given on your screen.

We're going to go through the first one and the final one in detail, and I'm going to show you the answers to the others.

So for the first one, enlarge by a scale factor of -1 from 6,4.

Now a scale factor, -1 should be telling me that it's going to stay the same size, but then orientation is going to change.

So the first thing I'm going to do is I'm going to plot my centre, which is 6,4.

So you can see that on the graph there.

Then the next thing I would do is drawing my write lines.

So through the centre and through each vertex of the pentagon.

Then I can see, I can measure from the centre, to each vertex.

And I know I have to go the same distance in the opposite direction for my image.

And you'd repeat that for each vertex.

And then you would see that this is the shape that you end up with.

So really good work if you've got that, if not check your work, maybe listen back to my explanation and give it another go.

If you need to pause the video now and have another go at this task.

There, this will take a moment.

Here's my centre, here's my enlargement.

For part C, see, here's my centre, here's my enlargement.

For part D, here's my centre, and here's my enlargement.

And for part E, we're going to do the same thing, plot the centre, which in this case is 5,3.

So it's actually on the pentagon.

And now we're going to draw in our rate lines.

So here they are.

And we do the same thing, we measure from the centre to each vertex.

And this time it's a scale factor of -2.

So we do it in the opposite direction, multiplied by two.

So from here to this vertex was one square.

So it will go two squares in the opposite direction.

And then we repeat that for each vertex to give us our final answer of this pentagon.

So that is your final answer.

I hope you got that one.

If not go back and check your work and maybe re-listen to my explanation.

For the second task, you were asked to draw the axis, like the ones on the screen, and then enlarge A with the centre P and scale factor -2, which should have given you this shape here, scale factor -1.

5, which should have given you this shape here.

Finally, scale factor -0.

5, which should have given you this enlargement here.

Well done on that task.

It was quite tricky.

So really good for persevering.

We're going to finish off today's lesson with this explore task.

Zaki is saying that he's going to complete an enlargement on the shape on your screen.

He says that the image will have a greater area, and the same orientation as the object.

I would like you to write similar statements, for each of the scale factors that are given here in the boxes.

Pause the video now and have a go at that task.

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

For the first one we had with a scale factor of -1.

Hopefully you wrote your answers in full sentences.

I'm just going to go through the key points.

So scale factor of one would have the same area and the same orientation.

So you should have written a sentence that says the image will have the same area and the same orientation as the object.

For a scale factor between zero and one.

So greater than zero and less than one, it will have a smaller area and the same orientation.

So your sentence should have said, the image will have a smaller area and the same orientation as the object.

For a scale factor, which is equal to -1, you should have realised that it had the same area, but a different orientation.

So your sentence should have read, the image will have the same area and a different orientation to the object.

For scale factor greater than one the image will have a greater area, and the same orientation as the object.

So this is actually what Zaki was talking about.

So when you found some examples, you could have had any number that was greater than one With a scale factor, which is greater than -1, but less than zero, the image will have a smaller area and a different orientation to the object.

And finally, for a scale factor, less than -1, the image will have a greater area and a different orientation to the object.

So really well done with those.

I hope that you had a really good go at that activity.

And if not, you've listened to my explanation.

I know that you will have drawn some really great enlargements today, so if you'd like to, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak.

That's it for today's lesson.

I hope you've learned loads, really hope to see you again soon.

Bye.