I have 5 yellow counters and 7 green counters. What fraction of the counters are green?

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?

5 litres of red paint and 8 litres of yellow paint are mixed to make orange. Which of these would give the same shade of paint?

Squash and water are mixed in the ratio 2:5. Which other drink will taste the same?

Purple paint is made by mixing blue paint and red paint in the ratio 4:3. How much blue paint is needed to mix with 24L of red paint?

Representing Ratio Quiz

﻿Hi, my name is Miss Kidd-Rossiter, and I'm going to be taking you through today's lesson on enlargement. Before we get started, make sure you've got no distractions. And if you're able to, you're in a nice quiet place, so you can fully concentrate on the work that we're going to do. Really excited to get started. If you need to pause the video now, then please do. If not, let's get going. We're starting today's lesson with a try this. Jasmin and Zaki are drawing enlargements of the triangle shown. All the triangles they draw, have integer side lengths. Jasmin says, "My new triangle has perimeter 33 centimetres." Zaki says, "The shorter side on my new triangle is six centimetres." Your job is to figure out what are the lengths of the triangles that they've drawn, and how many triangles with integer side lengths, can you draw that have a perimeter less than a hundred centimetres. Pause the video now and have a go at this task. If you're struggling, let me give you a couple of hints. The lines on this triangle tell us that their shape is isosceles, it's an isosceles triangle. That means that these two sides have the same length. So they're both four centimetres. The other thing you might be struggling with, is this word, integer. Integer just means whole number. So not a fraction, not a decimal, an integer is a whole number. So pause the video now and have another go if you were struggling. Brilliant work guys, I'm really impressed. Let's move on and have a think about these together. Let's look at Jasmin's statement first. She says, "My new triangle has perimeter 33 centimetres." What's the perimeter of the triangle that was given to you? Tell the screen now. Great, it was 11 centimetres. So I'm just using this p to represent perimeter today. So the perimeter was 11 centimetres. On Jasmin's triangle then, she's got a perimeter of 33 centimetres. What do you think we might have to multiply the side lengths by to get a perimeter of 33 centimetres? Tell the screen now. Excellent, if you said three, let's try it. So four centimetres times three is 12 centimetres. So we know that both of our equal sides are 12 centimetres, and three times three is nine centimetres. Let's check that that gives us a perimeter of 33 centimetres. 12 add 12 is 24, add nine is 33. So that's correct. This is the triangle that Jasmin was thinking of. Let's see what's similar. So the first shape, the one that was on the screen to begin with, had side lengths in a ratio, four to three. What is the ratio of side lengths in Jasmin's triangle? Tell the screen now. Brilliant, it's 12 to nine. Can you notice anything about these ratios? Zaki said that the shorter side on his new triangle is six centimetres. So let's have a go at drawing that. The shortest side, is it the base, or is it the pair of equal sides? Tell the screen now. Excellent, it's the base. So we know that the base of Zaki's triangle is six centimetres. What have I multiplied three by to get six centimetres? Tell the screen now. Excellent, two. So that means that I need to multiply the four centimetres by two as well, to get eight centimetres. As we did on the previous slide, we said that the ratio for the original shape was four to three. What's the ratio of side lengths in Zaki's shape? Tell the screen now. Excellent, eight to six. Do you notice anything about these ratios? Did you manage to answer the last question? I'm going to tell you that the answer is nine different triangles. If you didn't manage to find them all, maybe you want to pause the video now and have another go at that task. With the connect part of the lesson, you'll see the triangle from the try this on your screen. We already discussed that the side lengths, are in the ratio four to three, where four is the longer side, and three is the shorter side. I'm going to show you how I could represent this as a diagram. So each centimetre here is represented by a box, for the longer side. And for the shorter side, each centimetre is represented by the same size box. Here we can see quite clearly, that the shorter side is three quarters of the length of the longer side. Now let's think about the perimeter. What would the perimeter of this shape be? Tell the screen. Excellent, 11 centimetres. So what fraction of the perimeter is my shorter side? Tell the screen now. Excellent, it's three elevenths of the perimeter. We could write this in the ratio, eight to three, because the shorter side has three elevenths share of the perimeter. Now let's have a look at an enlargement of this triangle, and see whether we get the same thing. So what ratio are our sides in this time? Tell the screen now. Excellent, eight to six. And eight to six is an equivalent ratio of four to three. So if we write our four to three, and eight to six, we can find a constant of proportionality that we multiply both parts of our ratio by to get the new ratio. So what do I multiply four by to get eight? It's two. And what do I multiply three by to get six? It's also two. So our constant of proportionality for these ratios is two, and that's also the same as our scale factor of enlargement. Let's see what fraction of the longer side is the short side here. So it's six eighths of the longer side, and we know that six eights simplifies to three quarters. So again, we've got the same fraction as we had in the original shape. What about the perimeter of this one? What will it be? Tell the screen now. It's 22 centimetres, well done. What fraction of the perimeter is our shortest side? Tell the screen now. Excellent, it's six twentieth seconds. What do we know about this fraction? Excellent, it simplifies to three over 11. Again, we can see that our shorter side takes the same share of the perimeter. So what would our ratio be this time? It would be 16 to six, and we know that this is an equivalent ratio to eight to three, and it has the same constant of proportionality. What you're going to do now, is you're going to navigate to the independent task and you're going to apply what you've learned. When you're ready, check back in and we'll go through some of the answers. Well done for having a go over that independent task. Let's go through some of the answers now. So the ratio between the side lengths, AB and EF is four to 20, or you could have simplified that down to one to five. The constant of proportionality. Well, first of all, let's write our ratios alongside on ABCD is four to two. And on EFGH, is 20 to question mark. We don't know what that length is yet. What do I multiply four by to get 20? Well, I multiplied by five. So my constant of proportionality is five. Now I found my constant of proportionality. I can use it for part C to help me find FG. So FG is two multiplied by five, which is 10 centimetres. Don't forget your units. So I'm not going to go through this question in full, cause there's quite a lot of ratios that you have to find, but I will tell you whether the pairs of triangles are enlargements or not, and the constant of proportionality. So for A, are these triangles, enlargements of each other? Tell the screen now. Yes, they are, well done. So these ones are enlargements of each other and our constant of proportionality is four. So well done if you've got that, and well done for writing down the ratios too. Part B then. Are these pairs of triangles enlargements of each other? Tell the screen now. No, they're not, excellent. Because two pairs of sides have been enlarged by a scale factor of a half, but the final pair of side has not. If I was enlarging 10 centimetres by a scale factor of a half, it should give me five centimetres, not 5.5 centimetres. Part C then. Are these triangles enlargements of one another? Tell the screen now. Yes, excellent, well done they are. And our constant of proportionality here is 1.5. Or if you wrote it as a fraction three over two. And finally part D. Are these two triangles enlargements of each other. Tell the screen now. No, they're not. Well done. Two pairs of sides have been enlarged by a scale factor of 2.5, but the last side hasn't. If it had been, then it should be 8.75 centimetres, not nine centimetres. For this pair of pentagons, one is an enlargement of the other, state the ratio between the side lengths of the bases of the pentagons. So we know that that's four to 10, or you could have simplified that and written it as an equivalent ratio, two to five. Well done if you did that. Part B, state the constant of proportionality. So first of all, we need to write our ratio of our side lengths. So for our small pentagon, we've got the ratio four to 3.5 to x, and we can do the same with the larger pentagon, which is 10 to y to eight. So we need to find our constant of proportionality. So what do I multiply four by to get 10? What do I multiply four by to get 10. Tell the screen now. Excellent, 2.5. So our constant of proportionality is 2.5. So that's our answer to part B. Now let's use that to find our missing lengths. So 3.5 multiplied by 2.5 gives us y, which is 8.75 millimetres. Don't forget your units. And then this one's a little bit trickier because we're not multiplying this time, we're going to divide. So x times 2.5 gave me eight, so I can figure out what x is by doing eight divided by 2.5. What's the answer to that, tell the screen now. Excellent, it is 3.2 millimetres. So we're moving onto the explore task now. Zaki is using sticks to form shapes. He has lots of sets of the sticks that are shown on the right hand side of your screen. So he's got loads of those sticks. He's made a set of triangles that are enlargements of each other, so you can see them on your screen. What are the missing dimensions? Could he make another enlargement? And what other sets of shapes could he make? Pause the screen now, and have a go at this task. Well done for having a go at that task. It was quite tricky in places. What did you find then? What were the missing dimensions on this one, first of all? Excellent, four centimetres, well done. Because you could realise that the constant of proportionality between this smaller triangle and this larger triangle here was two. What about this larger triangle then. What's the base going to be here? Excellent, it's 4.5 centimetres, well done. Could he make any other enlargements? Tell me now the other enlargements that you made. One that I made, was one that looks like this. So I said that these were eight centimetres, my equal sides. What does that mean that my base is? Excellent, six centimetres. There were also lots of other sets of shapes that he could make. Well done for having to go at this explore task. I hope you can keep going with it for a bit, cause there's lots in there. So don't feel like you have to stop. That's it for today's lesson. I hope you've learned loads on enlargements. I've really, really enjoyed teaching you. If you've drawn lots of lovely enlargements and you'd like to share them with me, and please share your work with Oak National. If you'd like to, ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. Don't forget to do the quiz for today's lesson, and hopefully I'll see you again in the future. Bye.

Fill in the gap: the diagram shows a triangle that has been _________ by a scale factor of 3.5.

Fill in the gap: the ratio between the side lengths AB and BC is 2 : ____.

Fill in the gaps: The _______ between the side length DE and EF is also 2 : ___.

Fill in the gap: The constant of _________ between the two triangles is 3.5.

What is the length of DE?

Enlargements quiz

In this lesson, we will learn how ratio relates to enlargements of shapes.

Maths

Y8 Maths

Key Stage 3

Year 8

Miss

Enlargement

Ratio (8.6a)

Ratio and proportion

THEME

UNIT

Representing ratio

Double number lines

The rule of four

If a double number line starts with 4 on the top and 3 on the bottom, what will be the first number that appears both above and below the lines?

On a double number line, 4 is above the line and 4.8 is below the line. What is the constant of proportionality?

What is the constant of proportionality for this number line?

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?

Lesson overview:Enlargement

Core Content

Ratio (8.6a):