﻿Hi I'm Miss Kidd-Rossiter, and I'm going to be taking your lesson today on dividing into a ratio. It's going to build on the work that we've already done laying the groundwork for dividing into ratio. Before we get started, please make sure you're in a nice quiet area and that you've got no distractions. You're also going to need something to write with and something to write on. If you can a ruler would be really helpful for today's lesson, 'cause you're going to be drawing lots of nice diagrams. If you need to pause the video here to get anything, then please do. If not, let's get going. So for today's Try this activity, you've got to share 100 pounds between three charities so that each charity gets an exact whole amount of pounds. When you've done that, you need to express the sharing as a ratio and then figure out what fraction of the £100 is donated to each charity. So pause the video here and have a go at this activity. Excellent work well done. There's absolutely loads of combinations here of money that you could have given away. So I can't possibly go through all of them, but let's go through one example together. I'm going to give Charity A, the first charity £30. I'm going to give Charity B £50, and I'm going to give Charity C £20. Let's just double check that that adds up to my £100. So 30 add 50 is 80 add more 20 is a hundred pounds. So that's correct. So I'm just going to write it a bit bigger, 30 pounds to 50 pounds to 20 pounds. How else could I write this ratio? Could I simplify it? Tell me now. Excellent, I could couldn't I? It would be 3:5:2. So that's my ratio in its simplest form. What fraction then of the 100 pounds does Charity A get? So Charity A will get 30 pounds out of the 100 pounds, which we can simplify to three tenths. What about Charity B then? So Charity B will get 50 pounds out of the 100 pounds, which simplifies to five tenths, doesn't it? Or we can simplify it further to a half, so Charity B is getting half the money and then Charity C is getting 20 pounds out of the 100 pounds, which we know simplifies to two tenths or one fifth. So Charity C is getting one fifth of the money. Can we see how the two tents, the five tenths and the three tenths might relate to this ratio here? Pause the video now and think about that. Excellent. I can see that Charity A is three parts of the ratio out of a total of 10, B is five parts out of a total of 10 and C is two parts out of a total of 10. Excellent work, well done. Let's have a look at the connect part of today's lesson then. So we can represent dividing 60 pounds between charities in the ratio, one to three to six using a bar model. So this is building on the work that we've already done on using bar models. You can see there that I've drawn my one part of the ratio here at the top. I've drawn my three parts here and I've drawn my six parts here. As we've mentioned previously, it's really important that all the pieces of this bar model are the same exact size. So they're the same width and they're the same height because each individual part of my ratio is worth the same amount. We are then asked, what is the donation to each charity and what fraction of the total is donated to each charity. So let's have a go at this together. So we've got 60 pounds and we're sharing it in the ratio 1:3:6. So how many parts of my ratio do I have in total? Tell me now. Excellent. We have 10 don't we? So to find what one part is, we'll do 60 pounds divided by our 10 parts. And that tells us that one part of the ratio must be worth six pounds. So I can write that in here, each part has got to be worth six pounds. So if each part is worth six pounds, how much is each charity getting? Pause the video now and work that out. Excellent! So let's look at the first charity then. So we'll call that Charity A, the one that's getting one part of the ratio. So how much does Charity A get? Tell me now. Excellent. Six pounds. How much does Charity B get, tell me now. Excellent. 18 pounds because we do six pounds, times three don't we? 'Cause we've got three parts. And then Charity C, how much does Charity C get? Tell me now. Excellent. 36 pounds because we've got the six pounds and we've got six parts, haven't we? Brilliant. So what fraction of the total is donated to each charity then? So Charity A is getting six pounds out of 60, which we know is one tenth. So that's how much Charity A is getting. I need remember to put in my units, don't I? Charity B is getting 18 pounds out to 60 pounds, which we know simplifies to three tenths and Charity C is getting 36 pounds out of 60 pounds, which we know simplifies to six tenths. And again, we could simplify that further to three fifths. What you're going to do now is pause the video and have a go at creating your own bar models to represent dividing 60 pounds between three charities in the ratios that are on the screen. Then you've also got the question, what fraction of the largest share is the smallest share. So pause the video here and have a go at this activity. Excellent work, well done. We're going to go through these quite quickly because I don't want to just be doing the same thing over and over again. So the first one then, we've got our 60 pounds and we're dividing it between six parts in total so that gives us the one part is 10 pounds. So that means that Charity A is getting 10 pounds, Charity B is getting 20 pounds and Charity C is getting 30 pounds. So let's do this last one together. What fraction of the largest share is the smallest share? So what is our smallest share first of all? Tell me now. Excellent, it's 10 pounds and what is our largest share? Tell me now. Excellent. It's 30 pounds isn't it? So 10 pounds out of 30 pounds, we simplify to one third. Excellent. Second one then. So this time we're dividing our 60 pounds into 12 equal parts. So that means that each one part is worth five pounds and that means then that Charity A will get 15 pounds, Charity B will get 20 pounds and Charity C will get 25 pounds. So fraction then, the smallest share is 15 pounds out of the largest share, which is 25 pounds. And we can simplify that down to three fifths. Excellent. The third one then, we're going to look at together. So we're sharing in the ratio N:N:N. Now we don't know what this number is. This N could represent any number, it could represent one. So we could draw each part the same size there. Remember you're doing it with a ruler and it will be much neater than mine. So we're saying that this part here is N. Could be that N is representing two, in which case it would be like this. Could be that N is representing four. N could be any number here but what's important is that each bar that you draw is the same size. So Charity A, Charity B and Charity C are getting an equal share of the 60 pounds. And again, yours would be much neater than mine it would be drawn with a ruler and would be exactly the same size. So if we've got that, these are 60 pounds, but we've got our 60 pounds divided by three because each share is equal so we're dividing it into the three charities equally, which tells us that each share will be 20 pounds. So each charity, Charity A, and Charity B and Charity C will each receive 20 pounds. So what fraction of the largest share is the smallest share where they're all the same. So 20 divided by 20 gives us one. You're now going to apply what you've learned to the independent tasks so pause the video here, navigate to the independent task and give it your best go. When you're ready, resume the video. Good luck. Excellent work on that independent task, I hope you gave it a really good go. I'm going to put the answers on the screen now and some of them we'll talk through. So pause the video at any point to mark your work. Here's the first set of questions. Those are all the answers. So please pause the video here and check what you've done. If you wrote anything different for what you notice, that's absolutely fine. You could have worded it completely differently to me and I'm sure it's still a great explanation. Match the descriptions of the sharing then. So the ones that are coloured the same are matched together. So that's this one here and this one here and then this one, this one and this one. We're moving on to the explore activity now, Antoni and Binh are each sharing the same amount of money between two charities. Antoni is sharing his money in the ratio 1:3, Binh is sharing her money in the ratio 1:5. Antoni then says, "Together we're sharing in the ratio 2:8." Do you agree with Antony? And if you do or don't, can you explain your reasoning using a bar model? So pause the video here and have a go at this task. Antoni said he'll share his money in the ratio 1:3, so we could represent that using this bar model, couldn't we? And Binh said she's sharing her money in the ratio 1:5. So we could represent using this bar model. Do we agree that together, we're sharing in the ratio 2:8? Pause the video now and tell me what you think. Excellent. Even though we have two red parts and eight blue parts there, we can't say that it's the ratio 2:8 because we can quite clearly see that each of Binh's parts is much smaller than each of Antoni's parts. And we know that in a ratio, all the parts have got to be the same size. That's it for today's lesson so thank you so much for all your hard work on dividing into a ratio. I hope you've enjoyed it as much as I have. Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned and I hope to see you again soon for some more maths. Bye.

In this lesson, we will divide a quantity into a ratio of the form a : b : c and compare the relative sizes of the parts to each other and to the whole.

Maths

Y7 Maths

Key Stage 3

Year 7

Miss

Dividing into a ratio II

Ratio

Ratio and proportion

THEME

UNIT

Groups

In the same ratio

Equivalent ratios

The rule of four

Ratio and proportion in geometry I

Ratio and proportion in geometry II

Dividing into a ratio I

Fill in the gap: We can describe the ____________ between two or more quantities by comparing them with each other.

I make groups of grey and white counters in the ratio 3:4. How many white counters are there in five groups?

Fill in the gap: 2 litres of red paint and 5 litres of white paint are in the same_______ as 5 litres of red paint and 12.5 litres of white paint.

Fill in the missing number: I mix 4 litres of yellow paint with 10 litres of red paint. The ratio of yellow to red is …. : 5.

The ratio of the top bar is 1 : 5 : 2. What is the equivalent ratio shown on the bottom bar?

Light green paint is mixed with green : white as         2: 5. What ratio would be needed for 12 units of green?

Lots of the same groups of yellow and red counters are put in a bag. Fill in the missing value in the ratio table.

State the ratio between the side lengths AB and BC.

Fill in the gap: We can divide a line segment into a given ________ by considering the coordinates of its endpoints.

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

Amit and Bernie share 100 sweets in the ratio 2:3. How many sweets will Amit get?

Yellow paint and blue paint are mixed in the ratio 2:3 to make 1 litre of green paint. How much yellow paint is needed?

Lesson overview:Dividing into a ratio II

Core Content

Pupils Will Learn

Ratio: