Show your understanding on today's lesson by completing the quiz

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

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:___

Fill in the gap: The ratio of 𝐴𝐸: 𝐸𝐶 = ___: 1

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

Ratio and proportion in geometry II

﻿Hi, I'm Miss Kidd-Rossiter And this is the first lesson of two on dividing into a ratio. I love this topic. It's one of my absolute favourites to teach. So I'm really happy that you're here to learn with me. Before we get started would you please check that you're in a nice quiet place if you're able to be. You've got absolutely no distractions, and that you got something to write with and something to write on. A ruler might help you in today's lesson if you've got one. So please grab one if you can. Pause the video now if you need to sort anything out, if not, let's get going. Today's try this activity then. Antoni and Binh have fundraised 60 pounds to donate to charities. How do they split the money so that, first one, one donation is four pounds more than the other donation? Second one, one donation is four times as much as the other donation? Third one, one donation is one third of the total. And fourth one, one donation is one third of the other donation. So there's some questions there for you to think about. If you can find the monetary answers, think about how you might write these as ratios. So pause the video now and have a go at this activity. Excellent, well done there. Some really tricky things in there, so I hope you managed okay. Here are the monetary answers. So here are the answers there. How could we have written the first donation as a ratio then? So we could have written it as 28 to 32. Can we simplify that a too? Tell me now. Good, we could have simplified it to 14 to 16, couldn't we? Could we simplify it any further? Excellent, we could have simplified it as seven to eight, couldn't we? What about the second one then? We've got 12 and 48 pounds. So we could have written it as 12 to 48, but before we even got to that, we might have been able to write it as another ratio. So one donation is four times as much as the other. If our original donation is one, and the second donation is four times that, so it would have to be in a ratio of one to four. What about the third one then? One donation is one third of the total. So that means we will have three parts in all. One is one part of it. And the other is two parts. 'Cause that makes one third of the total and that is two thirds of the total. And then the final one, one donation is a third of the other donation. So that would be in the ratio one to three, because if we were to draw that as a quick diagram, we can see that that one part is third of the total diagram. Excellent work well done. So moving on to the connect part of the lesson now, and we're going to look at representing dividing into a ratio using a method called the bar model. So we're going to represent dividing 60 pounds in the ratio, one to five using one of these bar models. So first of all, I'm going to draw my one part of my ratio, and I'm going to represent it as one rectangle like that. And I'm going to draw the five parts of my ratio underneath the one part. And you should notice that each part of my ratio is exactly the same size because we know that to be true about a ratio, don't we? Each part is exactly the same size. So each one part there is the same height and the same width. And we know that this full bar model represents 60 pounds. So how many parts do I have in total here? Tell the screen now. Excellent I have six parts, don't I? So I have 60 pounds, which is represented by six parts. So I could say that one part, is the 60 pounds divided into six parts. So what's 60 pounds divided into six parts? Tell me now. Excellent, it's 10 pounds, isn't it? So I know that one part of my ratio is 10 pounds. So each of these one parts represents 10 pounds of my total. So what is one part of the ratio representing then? Tell me now. Excellent, it's 10 pounds. And what is the five parts of my ratio representing? Tell me now. Excellent, 50 pounds. So my final ratio is 10 pounds to 50 pounds. What fraction of the total is my one part? Tell me now. Excellent, it's 10 pounds out of 60 pounds, which we could simplify to one sixth, couldn't we? What fraction of my five parts is my one part? Tell me now. Excellent, we could say it's 10 pounds out of 50 pounds, which simplifies to one fifth. Excellent work, well done. You're going to have a go, some on your own now. So I've left mine on there to help you. I'd like you to pause the video and have a go at drawing your own bar models to represent dividing 60 pounds in the ratio one to four. And then in the ratio, two to eight. Each time work out the fraction of the whole 60 pounds that each charity receives. So pause the video now and have a go at this activity. Excellent work, let's look at the first one together. So your diagram should have looked something like this, where you've got one part and then four parts representing the 60 pounds. This time one part is 60 pounds divided by five parts in total, which means that one part must be 12. So each part here must be 12 pounds. What fraction did you get then? What fraction did the first charity receive of the total 60 pounds? Tell me now. Excellent, so charity one gets 12 pounds out of 60 pounds, which we can simplify to one fifth. And charity to gets how much? Tell me now. Excellent, 48 pounds out of 60 pounds, which we can simplify to four fifths. Well done, good work. What about then the second one? So this is what your diagram should have looked like two parts to eight parts. And that's representing our 60 pounds. So this time we can work out one part by doing 60 pounds divided by 10 parts. So that tells us that each part is six pounds. I'm not going to write them in all of them this time, but you know what they are. So six pounds is each part here. So what fraction does charity one receive? So charity one will receive six pounds, and another six pounds so 12 pounds in total, out of 60 pounds which simplifies to one fifth. And charity two, receives 48 pounds because we've got six pounds times eight there out of 60 pounds, which simplifies to four fifths. Do we notice something there, we had the same thing here, didn't we? This was one fifth and this was four fifths. Why is that the case? Pause the video now and tell me. Excellent, one to four and two to eight are equivalent ratios, well done. Pause the video now and navigate to the independent tasks to show me what you've learned, when you're ready to go through some answers, resume the video, good luck. Well done on that independent task. There are some quite tricky questions in there. I'm going to go through some of the answers and some of the answers I'm just going to put on the screen. So if you need to pause the video at any point to check your work then please do let us go. So first question here are all the answers. And when you were asked to explain something you noticed there might've been other things that you wrote, but there are a couple of examples there on the screen of things that you could have come up with. So pause the video now and check your work. Question two then. Every week Amit, Bernie and Charlie saved some pocket money in the ratio, one to four to five. So you can see on your screen that I've already drawn the bar model there, where the top is Amit, the second is Bernie, and the third is Charlie. How much do they each need to save per week for them to have collectively saved a hundred pounds after five weeks? So this is quite a tricky question I think. So let us first of all divide a hundred pounds into the ratio one to four to five. 'Cause then we can see how much money they need to have saved each. So how many parts do I have in total? Tell me now, excellent 10. So I'm doing a hundred pounds divided by 10 to find out what one part is and that will be 10 pounds, won't it? So that means Amit has got 10 pounds, Bernie has got four lots of 10 pounds. So how much has he got in total? Tell me now, excellent 40. And Charlie will have had to say five lots of 10 pounds, which is how much? Tell me now, excellent 50 pounds. So that's how much they need to save each in order to have a hundred pounds after five weeks. But that's how much they need to save in five weeks. And the question asked us, how much do I need to save per week? So if Amit needs to save 10 pounds in five weeks, how much does he need to save each week? Tell me now. Excellent, he needs to say two pounds per week. Remember you will write these answers in lovely, full sentences I haven't got the room to do it on the board but you will. Bernie then he has got 40 pounds that he needs to save in five weeks. So how much is that per week? Tell me now. Excellent, eight pounds. And Charlie has got to save the most. He's got to say 50 pounds in five weeks. So how much does he need to save per week? Tell me now. Excellent, he needs to save 10 pounds, well done. How be then if Bernie saves three pounds per week, how much will they have saved collectively, after eight weeks? Now this is quite tricky this one. We're told the Bernie's full parts represent three pounds. So he has three pounds represented by four parts. So how can we work out what one part of the ratio is? Tell me now. Excellent, we'll do three pounds divided by four, which tells us that one part has to be 75P. Now we know that each part of this ratio is exactly the same size. So that means that every single one of the parts in this ratio has to be worth 75P. How many parts of the ratio do we have in total? Tell me now. Excellent, we have 10, don't we? If we did 10 lots of our 75P, then we'll work out how much they save all together in a week, which would be seven pounds 50. But we were asked how much have they saved after eight weeks? So we need to multiply that figure seven pounds 50 by eight, and we get our answer of 60 pounds. And you would have written a nice sentence to say, they will have collectively saved 60 pounds after eight weeks, well done. Here are the answers to question three. So just check those for me. And finally, we're moving on to the explore task then. So how many different rectangles can you draw with integer values for the length and the width and an area of 64 centimetre squared? What is the ratio of width to length for each rectangle? And then write the ratios in the form one to N, where N is a whole number. So pause the video now and have a go at this task. You need a little bit of support, that's absolutely fine. I've drawn a table there that helps me to collect my thoughts on this task, so that might help you as well. If I'm looking for an area of 64 centimetre squared, then I know I'm looking for factor pairs of 64, because I was told that it was an integer, which is a whole number, length and width, okay? So I'm looking for factor pairs of 64. So I've given you some of them there, and you've got to tell me, what would I multiply one by to get an area of 64. And you can do the same for each one. And then you need to tell me what the ratio would be. So pause the video now and have a go at this activity. Excellent work, well done everyone. So here are your answers. There are lots of answers there. So hopefully you managed to get some of them if not all of them. Don't forget that even though it is a square, we can still count it because a square is a regular rectangle. Excellent work everyone I'm really impressed I hope you got some of those. That's the end of 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've enjoyed teaching it to you. Please don't forget to go and take the end of lesson quiz so you can show me everything that you've learned, and hopefully I'll see you again the next time. Thank you, bye.

Amit and Bernie share 100 sweets in the ratio 2:3. What fraction of the sweets will Amit have?

Amit and Bernie share 100 sweets in the ratio 2:3. What fraction of the sweets will Bernie have?

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

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

In a group of 72 children, the ratio of boys to girls is 5:4. How many girls are in the group?

Dividing into a ratio I quiz

In this lesson, we will divide a quantity into a ratio of the form a : b 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 I

Ratio

Ratio and proportion

THEME

UNIT

Groups

In the same ratio

Equivalent ratios

The rule of four

Ratio and proportion in geometry I

Dividing into a ratio II

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.

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 I

Core Content

Ratio: