Lesson video

Hi, I'm Miss Kidd-Rossiter, and I'm going to be taking you through the first of two lessons on ratio and proportion in geometry.

I really enjoy it, so I hope you are going to too.

Before we get started, can you make sure that you're in a nice, quiet area if possible, and that you're free from all distractions.

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

If not, let's get going.

So, for today's try this activity, you've got two trees on your screen.

Tree A is 1.

8 metres tall, and its shadow is 2.

3 metres long.

And tree B is 7.

2 metres tall, and it's your job to figure out how long you think its shadow will be.

Pause the video here and have a go at this activity.

When you're ready, resume the video.

Excellent! I hope you've had a really good go at that activity.

How did you do it? I hope that you've written down some nice notes there.

One way that I thought about it, was organising my thoughts into a table.

So, you can see, on the left hand side I've got the tree and the shadow, and then I've got tree A and tree B going on the top.

So for the tree, for A I know that it's 1.

8 metres tall, and the tree for B I know is 7.

2 metres tall.

And for A, I'm told that the height, the length of the shadow is 2.

3 metres.

So, I know from my work on the rule of four, that I have a relationship going across my table, and I also have a relationship going down my table.

So, what would I multiply 1.

8 by to get 7.

2? Tell me now.

Excellent.

It's four, isn't it? That means I would also need to multiply 2.

3 by four to get the length of my shadow for B, which gives me 9.

2 metres.

You could have also have figured it out by working out the constant here, where you had to multiply by 23 over 18, and that would have given you the same answer.

So your final answer should have been a nice sentence that was written where you said, I think the shadow will be 9.

2 metres long.

So, for today's connect activity, you've got Anthony, Ben, and Carla on your screen, and they're talking about some triangles, and whether they're enlargements of other triangles.

Your job is to pause the video, read the statements, and decide who you agree with and why.

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

Good luck! Excellent.

Let's talk about these one at a time, then.

So, Anthony first of all, he says the triangle with side lengths six centimetres, eight centimetres, and 10 centimetres, is an enlargement of the triangle with side lengths four centimetres, five centimetres, and three centimetres.

Do you agree with him or not? Tell me now.

Excellent.

I agree too, well done.

I agree because, I can see that I multiply three centimetres by two and I get a side of six centimetres, don't I? I can also multiply four centimetres by two, and get a side length of eight centimetres.

And I can multiply five centimetres by two, and get a side length of 10 centimetres.

Now, this is important, because I can multiply each side length by the same thing.

So I can multiply each side length by two, and get the new triangle.

The jumbled up word, it doesn't matter here, it's just whether one triangle is an enlargement of the other.

And it is, and we know that this number here is what we call our scale factor.

So, it's a scale factor of two, or, linking it to work that we've already done, we could call it our constant of proportionality.

Pause the video here and make a note of those two terms, cause they're really key.

We're going to talk about them more going forward.

What about Britney's statement then? So, she says the triangle with side lengths eight centimetres, eight centimetres, and six centimetres, is an enlargement of the triangle with side lengths five centimetres, five centimetres, and three centimetres.

So, if they are an enlargement of each other, we should be able to times all of the lengths by the same scale factor and get the new triangle.

So, five times something will give me eight centimetres.

Five centimetres, sorry, I should have said that to be careful with my units.

So five centimetres times something gives me eight centimetres, and we know using our inverse operations, that to get our something, we would do eight centimetres divided by five centimetres.

So that means we can leave it as a fraction, there is eight over five, or we can change it into a decimal, 1.

6.

So, five centimetres times 1.

6 gives me eight centimetres.

That will be the same for the other side length.

That is five centimetres.

Let's now check for our third side length.

So, three centimetres times 1.

6.

What does that give you? Pause the video now and tell me.

Excellent, it gives me 4.

8 centimetres, doesn't it? So, this cannot be an enlargement of the other triangle, because they've said that their triangle has a side length of six centimetres, and if we were enlarging by a scale factor of 1.

6, then our third length would have to be 4.

8 centimetres.

So, we disagree with Ben.

Finally then Carla.

Carla has a triangle with side lengths four centimetres, five centimetres, and six centimetres, and she says that that is an enlargement of the triangle with side lengths, eight centimetres, 10 centimetres and 12 centimetres.

What did you think? Tell me now.

Excellent, I agree as well.

So, we thought, eight and we're multiplying it by something to get four centimetres.

And again, I've been silly there and I've missed out my centimetres here.

Remember to include them.

So, question mark.

My something has to be equal to four divided by eight, which simplifies to a half or 0.

5.

You can use the fraction or the decimal, it doesn't matter.

So let's check now that that works for our other ones.

So 10 centimetres times my scale factor of 0.

5 is five centimetres.

So that one's worked, hasn't it? And let's check our final one, then.

12 centimetres multiplied by our scale factor of 0.

5 gives us six centimetres, so that one has also worked.

notice that we still call it an enlargement, even though our shape is getting smaller.

And that's absolutely fine.

So, we've got our scale factor here, which is also our constant of proportionality.

So, remember those two words, cause they're really key.

Right, you're now going to apply your learning to the independent task.

So, pause the video here, have a go at the independent task, and when you're ready, resume the video.

Good luck! Your first question then on the independent task, was this one.

Here are the answers.

We've got our constant of proportionality there.

Remember, if you went back the other way, so if you went from this one to this one, and you said that the constant of proportionality was a half, that's absolutely fine as well.

So, well done for that.

For question two, I'm going to give you the answers in three parts.

So if you need to, at any point, pause the video, check your work, and then resume the video.

So part a, here are all the coordinates.

Part b, here are all the ratios.

And for some of these, you could have simplified them.

So for part two here, if you wrote it as three to two, that's absolutely fine.

But for part three, if you wrote it as one to three, that's absolutely fine.

For part four, if you wrote it as one to two, that's great.

And for part six, if you wrote it as one to two, that's fine as well.

For part five, I found this one quite tricky, and I had to actually get my ruler out and measure it.

So, I saw that from A to C was that length.

And then I could see how many more of those lengths it took to go from A to G.

So, one, two, three.

So that's why my ratio there is one to three.

For part C then, find the constant of proportionality between the triangles.

So, let's do this one together.

So for part i, what was the constant of proportionality? Tell me what you got now.

So we're going from ABC to ADE.

So, we've got two here, and four here.

So I would say that our constant of proportionality is two.

For part two, we're going from ABC to AFG.

So this bigger one here, which gives this length here is six, isn't it? So that means that our constant of proportionality is three.

And then from ADE to AFG.

So ADE to AFG, our constant of proportionality here is 1.

5.

Moving on to the explore task now then.

Zaki is considering the enlargement of triangles.

He makes the statement below.

Is his statement always true, sometimes true or never true? Pause the video here, read the statement, think about it, and then when you're ready to, resume the video.

So, what did you think? I think this is sometimes true, because we can find a way to make it an enlargement by adding five centimetres, but it would have to be a special type of triangle.

But also sometimes it could be false, because remember, when we're making an enlargement, we want the constant of proportionality.

So, we want to be multiplying by the same thing each time.

So thinking about that, that I've just told you, if you want to, pause the video there and have another go at this task.

That's it for today's lesson.

Thank you so much for all your hard work.

I hope you've learned a lot about geometry in proportion.

Please navigate to the quiz so you can show me what you've learned.

Have a good day! Bye!.