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