# Lesson Video: Symmetrical Shape Patterns Mathematics

In this video, we will learn how to recognise symmetric patterns of shapes and find the missing shape in a symmetrical pattern.

13:02

### Video Transcript

Symmetrical Shape Patterns

In this video, we’re going to learn how to recognize patterns of shapes that are symmetrical and also to find the missing shapes in a symmetrical pattern.

We use the word symmetrical to describe a shape or an object that’s the same on both sides. If we draw a line right through the middle of a symmetrical shape, it’ll look the same both sides of the line. For example, if we draw a line all the way through the center of this shape here, we can see that it’s a bit like a reflection. Both sides of the shape are exactly the same. The shape is symmetrical.

Now, in this video, we’re not thinking about shapes on their own, but we’re thinking about the patterns that they make. Here’s a shaped pattern. Often, when we look at patterns, we look at them from left to right, and we look for a repeating part. But we can see in this pattern, there isn’t a repeating part. Red square, green square, blue circle, pink circle, pink circle again, blue circle, green square, and then red square. We can’t say this is a repeating pattern, but it is another type of pattern. What do you notice about these shapes?

Well, whether we start on the left and go towards the right or start on the right and go towards the left, it’s the same series of shapes: red square, green square, blue circle, pink circle. In fact, by doing this, we can see where the center point of our pattern is. If we draw a line right down the center of our pattern, we can see that it’s symmetrical. It’s the same on both sides. We can match the shapes the same order from the middle: two pink circles, two blue circles, and so on. Any pattern that’s the same on both sides of the center is a symmetrical pattern.

Here is an interesting pattern for two reasons. First of all, it doesn’t have two shapes that are exactly the same next to each other in the middle. With our last pattern, we could draw a line of symmetry in between the two middle shapes. But where would you draw your line of symmetry in this pattern? We can see that the middle shape is this square here. It’s just one square on its own. So, the line of symmetry or the middle point of our pattern is right down the center of that square. Can you see how the shapes are the same on both sides of the line now? Well, almost all of them because we’ve got a missing shape.

How can we complete the pattern? Well, we could start from the middle or from either end and look at each shape in turn. Let’s start at both ends and we’ll move our fingers each time. To begin with, we’ve got some pink triangles and then we’ve got our missing shape. But we can see on the left-hand side we have a blue circle. The missing shape must be a blue circle because if we carry on, we can see that the pattern continues to be symmetrical: two red triangles, two green circles, and two equal halves of an orange square.

Do you think you can recognize some symmetrical patterns now? Let’s try answering some questions where we have to identify the patterns and also fill in some missing shapes.

This pattern is symmetrical. What shape is missing?

If we’re given a repeating shape pattern, we often look at it from left to right, and we notice part of the pattern that keeps repeating itself. But if we look at this pattern from left to right, we can’t see any parts that are repeated again and again. That’s because this isn’t a repeating pattern. Instead, we’re told that this pattern is symmetrical. What does it mean for something to be symmetrical?

We know that for something to be symmetrical, we can draw a line through the middle of it and it will be the same on both sides. Now, for a pattern to be symmetrical, it must also be the same on both sides. But where’s the middle of our pattern? Where could we draw a line where the pattern is the same on both sides? Can you see where we could draw our line? This wouldn’t be right, would it? On one side of the line, we’d have a green rectangle and on the other side, a yellow square. This isn’t a line of symmetry.

This looks more like it. On both sides of the line, we can see a yellow square. And as we move outwards, the pattern changes in exactly the same way. We then have two green rectangles. Now, we can see on the right-hand side of our pattern, there’s a missing shape. But we can use our knowledge of symmetry and how the pattern changes to work out what this missing shape is.

Can you see what it’s going to be? After the green rectangles come the blue triangles, only we haven’t got a blue triangle on the right-hand side, have we? But as soon as we sketch it on, we can see that our pattern now looks symmetrical. We found the center line of our pattern, and we made sure that it looked the same on both sides of this line. Our missing shape is a blue triangle.

Emma is making a symmetrical pattern. She has drawn her mirror line. What is the missing part of her pattern?

We’re told that Emma has made a symmetrical pattern and we can see a picture of it. Let’s remind ourselves what the words symmetrical pattern mean. When something symmetrical, it’s the same on both sides. That’s why the idea of a mirror is really useful when we’re thinking about symmetry. A mirror reflects what’s in front of it, and it looks the same on both sides. We’re told in the question that Emma has drawn her mirror line. Can you see where it is? Here it is, let’s label it in a bright color so it stands out for us.

Now, this mirror line is important. It’s in the very center of Emma’s pattern. And because Emma’s pattern is symmetrical on either side of the mirror line, the shapes are the same. Up close, next to the mirror line at the top, we have two yellow squares, and the next two shapes along are the same. We have two blue triangles. Now, although Emma is making a symmetrical pattern, she hasn’t quite finished it yet. There’s a part to her pattern that’s missing, and we’re asked, what is the missing part of her pattern? We need to think of the shapes that belong in this space.

Now, you may think it’s got something to do with these two shapes that are at the bottom, the pink circle and the blue triangle. And you know what? You’d be right. Now, it would be very easy to look at these shapes and to think, “Well, it must be the same on both sides.” The answer’s got to be a pink circle and a blue triangle. Well, if you think the answer is this, you’re almost there, but the answer is not quite right. And we can see why if we put these shapes into position. Can you spot the mistake? If we start from the mirror line, just like before, and we compare the shapes on either side, we start with a blue triangle on one side, but the shape on the other side doesn’t match. It’s not the same, and neither do the next two shapes along.

Can you see what we need to do to make the pattern symmetrical? You’ve got the right shapes, but they’re not in the right order. The nearest shape to the mirror line needs to be a blue triangle and then the pink circle. Can you see how the shapes match now? The pattern is the same on both sides of the mirror line. It’s symmetrical. The missing part of Emma’s pattern is a blue triangle followed by a pink circle.

Liam is making a symmetrical pattern. He has drawn his mirror line. What shape should he put in position A? Which position should he put the green diamond in?

In this problem, we’re told that Liam is making a symmetrical pattern. We’re also told that he’s drawn his mirror line. And you know, a mirror line is a clue as to what makes a pattern symmetrical. We know that symmetrical patterns are the same on either side of a mirror line. Just like a mirror reflect our face back at us, we could say that the mirror line reflects the shapes. If we start with the top-row shapes to begin with and we put our finger on the mirror line, whether we move it to the left or to the right, we’ll see the same shape.

Liam’s put a yellow square on either side of his mirror line. He’s made his pattern symmetrical. Can you see he’s done the same with the bottom two shapes he’s chosen too? He’s chosen a blue triangle on either side of his mirror line at the bottom. Now, at the moment, we can see four missing shapes, A, B, C, and D. It’s almost as if Liam hasn’t quite finished his symmetrical pattern, has he? Let’s help him complete some more of his pattern by answering these two questions.

Firstly, we’re asked, what shape should he put in position A? If we look at position A, we can see that it’s the next shape along to the yellow square on the top row. Can you see what we need to use to help us? We need to look back across the mirror line and see which shape is next door to the yellow square on the other side. It’s a blue triangle, isn’t it? And if we put a blue triangle in there to check, it looks right. This shape is the same on both sides of the mirror line. It’s the second shape along.

In the second question, we’re given a shape and we’re asked which position Liam should put it in. We’ve only got positions B, C, and D left. Which position should Liam put the green diamond in? The first thing we can do is to find the green diamond in Liam’s pattern. Can you see it up here on the top row? Now, for Liam’s pattern to be exactly the same on both sides of his mirror line, can you see where he needs to place the green diamond? At the moment, it’s on the top row, furthest away on the left. So, the other green diamond should also be on the top row, furthest away on the other side of the mirror line. This is position B.

We know that Liam’s pattern is symmetrical because it’s the same on either side of his mirror line. To keep his pattern symmetrical, we know that the shape that he needs to put in position A needs to be a blue triangle, and he also needs to put the green diamond in position B.

So, what have we learned in this video? We’ve learned how to recognize patterns of shapes that are symmetrical. We’ve also learned how to find the missing shapes in a symmetrical pattern.