﻿Hi, I'm Miss Kidd-Rossiter, and I'm going to be taking the lesson today on representing ratio. We're going to do it mainly in the context of shape, and it's a really exciting topic. So I hope you really going to enjoy it. Before we get started, can you make sure that you're in a nice quiet space, you're free from all distractions and that you've got something to write with and something to write on. If you're able to, it'd be really great if you have a ruler for this lesson as well. If you need to pause the video here to get anything that you need, then please do, if not, let's get going. So today let's try this activity. Then Antoni, Binh, Cala and Xavier are drawing rectangles. Antoni says the side lengths of my rectangles are in the ratio 5:2. Binh says the side lengths of my rectangles are in the ratio 6:2. Cala says the shorter sides of my rectangles are 1/3 of the length of the longer sides. And Xavier says the longer side of my rectangles are 2 1/3 times the length of the shorter sides. You've got to draw an example rectangle for each student. If you've drawn one, can you draw another, can you draw another, can you draw another? And then how could you compare the rectangles that they've drawn? Pause the video now and have a go at this task. Excellent work. Which side did you draw first for each of these? Did you draw the longer side or the shorter side first? Can you draw one starting the other way round? So if you started with the longer side, this time can you start with the shorter side. Pause the video now and have a go at that. Excellent. We're going to go through this in the connect part of the lesson. So let's go. So we're going to compare Antoni and Binh first of all. So can you tell me a rectangle that you drew for Antoni? Excellent. So there are loads of different ones here, so I'm just going to give you one example. So Antoni could have drawn his rectangle and he could have had the longer side is 10 centimetres and the shorter side is four centimetres. Do you agree that that's in the ratio 5:2? So let's just double check. Longer to shorter, 10:4. Does that simplify to 5:2, tell me now? Excellent, it does, doesn't it? So that was one example that we could have had. What faction of the longer side is the shorter side here? So we've got our longer side, which is 10 centimetres, and if we draw our shorter side underneath it, which is four centimetres, what fraction of the 10 centimetres is the four centimetres? Tell me now. Excellent. It's 4/10, isn't it? Or can we simplify that? Excellent, 2/5. Can we see a relationship here between the fraction and the ratio? Could we write the longer side as a fraction of the shorter side? Tell me now. Yes we could. What would that fraction be? Tell me now. Excellent. So the longer side as a fraction as the shorter side would be 10/4, which simplifies to 5/2, or if you prefer to write it as a decimal 2.5. So the longer side is 2 1/2 times the shorter side. Is there a relationship here with the ratio? What about Binh's rectangle then? So her side lengths are in the ratio 6:2. So again, there's loads of different rectangles that you could have drawn. Here's one that I've drawn and they're going to have, you should have drawn yours with a ruler because they would be much neater than mine. So I'm going to say that Binh has done hers 18 centimetres here to six centimetres here. Is that in the ratio 6:2? Let's just double check. So longer side to shorter side, 6:2. Do we have the same constant of proportionality to get from two to six and from six to 18? What would it be? Tell me now. Excellent. It's three, isn't it? So therefore, yes, these are in the same ratio. So what fraction of the longer side is the shorter side here? So if we've got 18 and we've got our six centimetres, what fraction is that? Tell me now. Excellent, the shorter side is 6/18 of the longer side, isn't it? Which simplifies to 1/3, brilliant. How does a third relate to the ratio 6:2? Think about that for me. What about the other one then? So, what fraction of the shorter side is the longer side? Well it would be 18/6, which is three. So the longer side is three times the length of the short side. Again, can we see a relationship with the ratio here? Moving on then to Binh and to Cala. So we've already looked at one of Binh's and we said that hers was 18 and six centimetres. And we said that the shorter side is 1/3 of the longer side. And we also said that the longest side is three times the shorter side. So what does that mean about Binh's statement and Cala's statement? Tell me now. Excellent. They could be describing the same rectangle, couldn't they? Let us do another example just to check for Cala. So we've got a longer side and let's call this one 300 metres. Cala's shorter side would be 1/3 of this, wouldn't it? So it'd be 100 metres. So that would be an example of Cala's. Is that in the ratio 6:2? So it could, I have the same constant of proportionality here to get from six to two, to 300 to 100. Yes I could, what would it be? Tell me now. Excellent. It would be a multiply by 50, wouldn't it? Is there a simpler ratio here than 6:2 that we could write? Tell me now. Excellent. It's 3:1, isn't it? So all of the rectangles for both Binh and for Cala are in the ratio longer side to shorter side 3:1. Finally, then we've got Xavier. Xavier's is a bit of a tricky one I think to think about. So let's have a go at drawing one. What did you come up with here? I'm going to draw my shorter side as being 12 millimetres. What would that mean my longer side is? So 2 1/3 times 12. So let's think about that as 12 times two is 24 millimetres. 12 millimetres remember I should include my units. And 12 millimetres times 1/3 is the same as saying, what is a 1/3 of 12, which is four millimetres. So all together 2 1/3 times 12 is 28 millimetres. So Xavier's rectangle could look like that. There's also lots of other options again it could look like. So let's have a look then of the ratio of our longest side to our shorter side here. So the longest side is 28 millimetres and the short side is 12. Can I simplify this ratio? What would it be? Excellent. I could simplify it, 7:3. What fraction of the shorter side is my longer side? We already know that, don't we? We know it's 2 1/3 times. So let us think about what fraction of the longer side is the shorter side? So can you tell me now? Excellent, it'd be 12 millimetres out of 28 millimetres, wouldn't it? And what does that simplify to? Excellent, 3/7. So the shorter side is 3/7 of the longer side. Really good work. You are now going to apply everything that you've learned to the independent task. So pause the video here, navigate to the independent task. And when you're ready to go through some answers, resume the video. Good luck. Excellent work on the independent task, well done everyone. So let's go through these then. So side lengths of a triangle are in the ratio 3:5:2. What fraction of the perimeter is the longest side? So the longest side has to be the part that's represented by the biggest part of the ratios. It has to be represented by the five. So it has to be five out of something. And how many parts of our ratio do we have in total? Excellent, 10. So that means that the fraction of the perimeter that is the longest side is a half or 5/10. Side lengths of a triangle are in the same ratio. What fraction of the longest side is the shortest side? Well, we know that the shortest side must be represented by the two. So it has to be two out of five. Excellent. And the sidelines of the triangle still in the same ratio. What fraction of the shortest side is the longest side? So again, this will be the opposite way around, 5/2. Good work. Here are your answers for question four, pause the video if you need to check them. And here comes your answers for question five. Pause the video now if you need to check them. Now, just be careful here, because you might have been caught out a little bit because we were told that the side lengths were in the ratio 4:3. So if we had 4:3 and the longer side was eight, then the constant of proportionality here is two. So our shortest side would be six, which I bet most of you got six metres. But then remember that the perimeter is the whole distance around the outside of the shape. So if this is eight metres and this is six metres, then this is also six metres and eight metres. So you would need to do eight metres add six metres, add eight metres add six metres, which gives us our 28 metres or the other way you could have done was two times the eight metres add the six metres, okay? So just be careful there. Pause the video if you need to check these answers. So moving onto the explore task now then. So Yasmin and Zaki each draw a triangle with an angle of 30 degrees. Can they draw triangles that meet the following conditions, so that their side lengths are in the same ratio, but are not identical? So could they both draw right angled triangles? Could they both draw triangles that have the same area? And could they both draw triangles that have the same perimeter. Pause the video now and have a go at this task. Excellent work that absolutely loads here. So I'm sure you've had a good go at it. There are lots of different ways to approach this, but one way might be to draw a right angled triangle here and then make sure that this is 30 degrees either angle. This is my 90 degrees. And then we will say that this is six centimetres and this is three centimetres. So the ratio here would be 1:2, wouldn't it? Could we draw another triangle that's maybe a bigger or smaller. You would use a ruler. Where this is still a right angle. This is still 30 degrees. And these are still in the same ratio. I'll leave you to think about that. So you could have put anything here. We could have got that this is 4.5 centimetres, which would mean that this is what? Excellent, it would be nine centimetres. Good work. So keep going with this activity. I hope you can draw absolutely loads of great triangles. Because we've gone like the rectangles and triangles today, if you'd like to share your work with Oak National, then please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. That's the end of today's lesson. So I hope you've enjoyed it. And I really have enjoyed teaching you. Don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon. Bye.

I draw a rectangle and the side lengths are in the ratio 5:7. What fraction of the perimeter are the longer sides?

I have a bag of pink and brown cubes. 5/11 of the cubes are pink. What is the ratio of pink cubes:brown cubes?

A triangle has side lengths in the ratio 5 : 5 : 3. What type of triangle is it?

A triangle has side lengths in the ratio 5 : 5 : 3. What fraction of the perimeter is the shortest side?

A rectangle has side lengths in the ratio 4:3. How long would the longer side of this rectangle be, if the shorter side is 24m?

Representing Ratio Quiz

In this lesson, we will learn about different representations of ratio, including the relationship between fractions and ratio. These are mostly seen in the context of shape.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Representing ratio

Ratio review (9.7a)

Geometry

THEME

UNIT

Ratio and proportion in geometry

Dividing into a ratio

Ratio problems

Fill in the gap: The _____________ of proportionality of ADE to ABC is 1.5.

Fill in the gap: The ratio of 𝐴𝐸: 𝐴𝐶 = 6: 9 = 2:___

A line segment ABC is split in the ratio AB to BC as 3 : 5. What fraction of the line segment is AB?

The angles in a triangle are in the ratio 3 : 4 : 5. What type of triangle is it?

The ratio of Adam’s height to Tony’s height is 7 : 9. Adam is 154 cm tall. How tall is Tony?

A box contains caramel and toffee chocolates. 3/10 of the chocolates are caramel. What is the ratio of caramel to toffee chocolates in the box?

At a bake sale 25% of the cupcakes on sale are chocolate.  3/5 of the cupcakes are vanilla and the rest are peanut butter. What is the ratio of chocolate:vanilla:peanut butter?

The ratio of roses to violets is 3 : 4.  The ratio of violets to daisies is 6 : 5. What is the ratio of roses to violets to daisies, in its simplest form?

Lesson overview:Representing ratio

Core Content

Ratio review (9.7a):