A shape is enlarged by an integer scale factor more than 1. What does not change from the object to the image?

A square is enlarged by a scale factor of 3. The object had side length 4cm, what is side length of the image?

A regular pentagon has been enlarged by scale factor 5. The side length of the image is 35mm, what is the side length of the object?

Enlargement by an integer scale factor quiz

﻿Hi, my name is Miss Kidd-Rossiter and I'm a maths teacher from Hull. I'm going to be taking you through today's lesson on enlargements by a non-integer scale factor. It's a really great topic and I'm really looking forward to teaching it to you. Before we get started, can you please make sure that you're distraction free, and if you can be, you're in a nice quiet space where you can really concentrate. If you need to get anything, or you need to move yourself to a quiet room, then pause the video now to do that. If not, let's get started! So for today's try this activity, you need to have a look at the shapes that are on the grid on your screen. Can you decide which ones are enlargements of each other? If you need a couple of hints, there's some on the next slide, but if not pause the video now and have a go at this task. If you did need a couple of hints, there's two questions now on the screen that should help you out. A reminder that a non-integer is a non-whole number, so that might be key to this activity. Pause the screen now and have a go at this task. Hopefully, you've managed to find some enlargements there. Probably the easiest one to find was that A was an enlargement of C, with a scale factor of 2. And I'm just going to mention one more, but there were several more that you could have found. B is an enlargement of A, because 2 multiplied by 1.5 gives me 3, and 4 multiplied by 1.5 gives me 6. So that means that B is an enlargement of A, with a scale factor of 1.5. We're moving on to the connect part of the lesson now. So you have got two students on your screen, Bin and Xavier, who have given us different statements about the enlargements on the screen. Pause the video now, read the statements and decide who you think is correct and why. Well done for that, so let's have a look. We know that our rectangles have these dimensions, so you should have figured that out. Let's say that the blue rectangle here is our object and the pink rectangle here is our image. So that means we have to decide what is our scale factor of enlargement to go from the blue rectangle, to the pink rectangle. So what do I multiply 4 by to get 10? So 4 times something gives me 10, and you should know that the inverse operation of multiplication is division, so to find out our question mark, we can do 10 divided by 4, which gives us 2.5. Now remember, that for it to be an enlargement, both sides, all sides have to have been multiplied by the same scale factor. So we need to just check our other side as well. So 6 times something has to give me 15, and again using our inverse operation, that tells us that our question mark has to be 15 divided by 6, which is also 2.5. So, Bin's statement, where the scale factor of enlargement is 2.5, is correct, if we use the blue rectangle as the object and the pink rectangle as the image. What about if we do it the other way round? So we use the blue rectangle as the image, and the pink rectangle as the object. So we've still got our dimensions the same. This time, we have to think, I have to times 10 by something to get 4, and we continue to use our inverse operations. So, something is equal to 4 divided by 10, and we know from simplifying four tenths, that that gives us two fifths, but as we said on the last one, we have to double check that all our lengths have been multiplied by the same scale factor, otherwise it's not an enlargement, so 15 multiplied by something gives us 6, we'll use our inverse operations again, so 6 divided by 15 is equal to our scale factor, and again we can simplify six fifteenth to two fifths. So Xavier is also correct, but this time if we use the pink rectangle as the object, and the blue rectangle as the image. We're now going to apply today's learning to an independent task, so pause the video now, navigate to the worksheet when you've completed it, come back and we'll go through some answers. Really well done on that independent task, some quite tricky questions on there, so you've done really well to make it through. We're going to go through some of the answers now. For the first question, you were asked to identify which shapes were enlargements of each other, and then identify the scale factors. Now there's loads of answers here, so I'm not going to be giving you all of them, but I will go through some. I found it easiest to write them into a table, but it doesn't matter how you've done it, I'm sure all your answers are brilliant. So here's my table, so, the first one that I decided was an object was J, and I realised that H was an enlargement of J, with a scale factor of a half. I also knew that F was an enlargement of J, with a scale factor of three quarters. Now remember if you wrote these as decimals as well, that's absolutely fine. I also knew that J was an enlargement of H, and this time the scale factor was 2. Another one is that J is an enlargement of F, and this scale factor was four thirds, or if you wrote it as a decimal, 1.3 recurring. And the final one that I'm going to give you is that H is an enlargement of G, with a scale factor of one third, or if you wrote it as a decimal, 0.3 recurring. But as I said, there are lots of different ones on there, so I've not captured them all there, you might have got some different ones, but the only one which shouldn't have been included in any of your enlargements was E, because E is not an enlargement of any of the other shapes on the grid. Question 2 then, said identify the triangles that are not enlargements of the triangles marked X. Give reasons for your answers. So B is not an enlargement of X, C is not an enlargement of X, A is an enlargement of X, because X has a base of 4 squares, and a height of 4 squares, so the scale factor here is a half, from X to A. Let's just double check D, D has a base of 8 squares, and a height of 8 squares, so D is an enlargement of X. So why is B not an enlargement of X? Well, our base has stayed the same, so that would be a scale factor of 1, but our height has increased to 8, so that means the scale factor there would be 2, and we know that for an enlargement to work, it has to be enlarged by the same scale factor. Here, for C, the base is 8, but the height is only 3 So where the base has been enlarged by scale factor 2, the height has not been enlarged by the same scale factor, so it is not an enlargement. And for Question 3, it's quite tricky for me to go through your working out, but I'm sure you've all done a really good job of this. Just double check. Scale factor of 2, your left hand side should now be 4 squares. Scale factor of 1.5, your left hand side should now be 3 squares. Scale factor of a half, your left hand side should now be 1 square. And a scale factor of 1, your shape should be exactly the same. So really well done on that, we're now going to move onto the explore task. So pause the video, read the activity and then have a go at it. When you're ready to have a little bit of discussion, resume the video. Okay, brilliant work on that, again quite a tricky activity, so good work if you did it. There were lots of pairs here that you could have found. What you should have noticed is that when you enlarged a shape by a scale factor of a half, then enlarged the new shape by a scale factor of 2, you went back to the original shape. And that was the same here, when you enlarged by a scale factor of two thirds, and then enlarged the new shape by a scale factor of 1.5, you should have gone back to the original shape. So another example you could have found was a quarter and 4, would do the same thing. Or another one, would be four thirds and three quarters. Now, a bit of a key word for you here, all these pairs are reciprocals of one another. Really good work on this if you got some more answers, there are loads more, I can't possibly cover them all, but I'm sure you've done a really really great job. That's it for today's lesson, so thank you very much for all your hard work. I hope you've learned loads. I'm looking forward to hopefully seeing you again in the future. Bye!

Which of these statements best describes a 'non-integer'?

A square has side length 12cm. It is enlarged by scale factor 2/5. What is the side length of the image?

A regular hexagon is enlarged by a scale factor of 3.5. The image side length is 31.5m. What is the side length of the object?

Enlargement by a non-integer scale factor quiz

In this lesson, we will learn how to enlarge shapes by a non-integer scale factor. It would be helpful if you could have squared paper and a ruler for this lesson.

Maths

Y9 Maths

Key Stage 3

Year 9

Miss

Enlargement by a non-integer scale factor

Similarity and enlargement

Ratio and proportion

THEME

UNIT

Enlargement by an integer scale factor

Enlargement from a given point

Enlargement by a negative scale factor

Describing enlargements

Similar triangles

Nested triangles

Area of similar shapes

Fill in the gap: if the scale factor of an enlargement is __________ 1, then the image is smaller than the object

Which of these is an incomplete description of an enlargement?

A shape has been enlarged and the image has a larger area and is in a different orientation to the object. Which of the following options could describe this enlargement?

Fill in the gap: if one shape is an enlargement of another, then these shapes are called ________ shapes.

What is the scale factor of enlargement from ABC to LMN?

Are PQR and SPR similar?

The two rectangles below are similar. What is the scale factor of enlargement if the object is on the left and the image on the right?

Fill in the gap: to find the area scale factor, you must ______ the scale factor of enlargement.

Which of the following options best describes an enlargement of scale factor -1?

Which of the below images show a correct enlargement of scale factor -2, about the given point?

Lesson overview:Enlargement by a non-integer scale factor

Core Content

Similarity and enlargement: