Fill in the gaps: If the proportion between the ____________ is constant, then the ratios are __________________.

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

Squash and water are mixed in the following ratios to make a drink. Which drinks will taste the same?   A) 4:10   B) 3:8    C) 9:24    D) 15:25

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

Light green paint is mixed with green : white as         2: 5. Write the ratio for the white paint needed for 1 unit of green.

Equivalent ratios quiz

﻿Hi, my name is Ms. Kidd-Rossiter. And I'm going to be taking you through today's lesson on the rule of four, which is a really exciting part of this ratio topic. So I hope you're really going to enjoy it. Before we get started, can you please make sure that you've got no distractions, you're in a nice quiet place if you're able to be, you've got something to write with and something to write on. If you need to pause the video now to get anything ready, then please do. If not, let's get going. So for today's try this activity, you've got some times tables grids on your screen. It's your job to, first of all, complete these, for some of them, there might be more than one solution. So have a look out for that and see if you can find a second or third solution. Then I want you to consider what multiplicative relationships can you see between the rows. So that's going down the table and what multiplicative relationships can you see between the columns? So that's going across the table. So pause the video now and have a go at this task. You'll see now, that I've put the answers on the screen. For the two where we've got asterisk in the top corner, that's because that is just one of several possible solutions. So you could have found something different there. And the last one, I didn't fill in any answers 'cause there was so many different possibilities that I couldn't possibly capture all of your wonderful thoughts. Did you notice any multiplicative relationships either going across or going down? If you did, keep those thoughts in your head 'cause we're going to explore that in the connect activity. As I said, today's connect activity is going to add to what we did in the try this. So we've got a greengrocer and they're making bags of red and green apples. There are the same amount of red apples in each bag and at the same amount of green apples in each bag. She then puts some bags into a box and gives them to schools. Pause the video now and see if you can figure out what are the missing numbers in that table. Did you get it? It is 180, isn't it? So can we see any relationships here? How would I get from two to 60? If I've got two apples in each bag and 60 apples in each box, then I'm multiplying by 30 going across here, aren't I? So that means I must have 30 bags in each box. And this is my constant of proportionality. Let's now work for six and 180, let's just double check. Six multiplied by 30 is 180. So yes it does. What about then going down, could I have worked out 180 in a different way? If I've got two green apples and six red apples in a bag, how do I get from two to six? Pause the video now. Tell me what you got. Excellent! We multiply by three, don't we? So we've got a constant here as well. Is that the same for the number in the box? Let's just double check. 60 multiplied by three is 180. So that's correct. So I can see that I've got a multiplicative relationship going across my table and a different multiplicative relationship going down my table. Let's think about that in another example. Here, we've got green apples, three in a bag and red apples, five in a bag. And we're told that there's 27 green apples in the box. What goes in the missing section here? Tell me now. Excellent. It's 45 red apples. How did you get that? Did you use the constant of proportionality going across the table, which is nine, or did you use the constant going down the table, which is 1.6 recurring or five over three. Which way did you do it? Let's go through one more example together. This time, we've got six red apples in a bag and 33 in the box. What could go in these sections here? What did you choose? There are several different solutions to this, so well done, whatever you said. We're going to move on now to the independent tasks. So pause the video here, navigate to the independent task. And then when you're ready to go through some answers, resume the video. Well done for having a go at that independent task. I hope you applied your knowledge of the rule of four and the different multiplicative relationships that we have within these tables. I'm going to go through some of the answers. Some will just appear on the screen and you can pause the video to mark them. Others I will talk through in full. So for these tables, here are your answers. Pause the video now to check. Which one did you find easiest to work out? Can you read me your explanation now? Well done! Question two then, two bottles of drinks tastes the same. Fill in the grid. What's the ratio of squash to water, and how much bigger is bottle two? So let's fill in the grid first. So let's identify both of our multiplicative relationships. So going across from 60 to 45, what have we multiplied by? Good. We've multiplied by 0.75 here, haven't we? Or you could have said 3/4, which is the equivalent fraction, well done. And what about going down? This one might have been slightly easier to work out. What's our multiplicative relationship here? Excellent. We're multiplying both three, aren't we? To go from 20 to 60. So what number multiplied by three gave me 45? Tell the screen now. Excellent. 15 Centilitres. Don't forget your units. What is the ratio of squash to water? So we have two different ratios, don't we? We have 20:15 or we have 60:45. And we know that these are equivalent ratios. So either of those is correct. Or if you did, you could have found another equivalent ratio to simplify it down, as 4:3. Well done if you said any of those. How much bigger is bottle two? Well, we worked that out here when we worked out this constant. So our bottle two is three times bigger than bottle one. And you would have written that in a full sentence. Cause I know that you'll get by . Question three then. Jenner says the missing number is 35. Ed said the missing number is 19. Who do you agree with? Tell me now. Well, I agree with Jenner. Did you send Jenner too? I think the missing number is 35. Because if we look at our multiplicative relationship going across and we're multiplying by five, aren't we? So that means seven times five is 35. What mistake has Ed made? He's thought about it as an additive relationship, hasn't he? He said three, add 12 is 15. And so he's also added 12 onto seven to get 19, but we know it's a multiplicative relationship, not an additive relationship. Well done. So for today's explore task then, we're going to be pretending to make some muffins. We've got, flour to sugar to milk, and for it to be delicious, they need to be in the ratio five to three to two. Which of the mixes that are on the right-hand side of your screen will make delicious muffins? And then, if we've got two kilogrammes of flour and one kilogramme of sugar, and we want to make as many muffins as we can, how much milk will we need? Pause the video now and have a go at this task. Let's talk about some of the solutions here then. So which of these, first of all can make delicious muffins. Did you figure them out? Which ones are in the same ratio as five to three to two? So the top one is, this one is, and this one is, the other two are not in the same ratio, so they will not make delicious muffins. Did you find any multiplicative relationships? There are absolutely loads. So I'm just going to pull out too. So if you see here, going from 400 grammes of flour to 1.6 kilogrammes of flour, I've multiplied by four there, haven't I? So there's one multiplicative relationship. And here's another one going across the table, going from 960 grammes to 640 millilitres, we know that 640 is 2/3 of 960. So that multiplicative relationship is being, is multiplied 2/3. Here's the answer to the last question. I hope you got that. I'm not going to talk through it 'cause we're running out of time. I hope you really enjoyed that task. And if you didn't find any multiplicative relationships, pause the video now and try and find some more. That's it for today's lesson. So thank you so much for all your hard work. I hope you've learned loads about the rule of four and the different multiplicative relationships we can have in tables. I hope to see you again soon for another ratio lesson, but don't forget to take the quiz on today's lesson so you can show me what you've learned. Have a good day. Bye.

Have a go at this quiz to check your understanding

Fill in the gap: If two quantities are in the same ratio then there are _______ relationships I can use to find a missing value.

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

Yellow and red counters are in the ratio 2 : 3. What fraction of the counters are yellow?

The rule of four quiz

In this lesson, we will identify multiplicative relationships between 'times tables' and use patterns to solve problems in direct proportion contexts.

Maths

Y7 Maths

Key Stage 3

Year 7

Miss

The rule of four

Ratio

Ratio and proportion

THEME

UNIT

Groups

In the same ratio

Equivalent ratios

Ratio and proportion in geometry I

Ratio and proportion in geometry II

Dividing into a ratio 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.

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:The rule of four

Core Content

Ratio: