Lesson video

Hello, my name's Mrs. Hopper and I'm really looking forward to working with you in this lesson from our unit on properties of 2D shapes and symmetry.

I'm sure you've met lots of 2D shapes in the past, but we're going to remind ourselves about their names, the properties they have, and maybe introduce a few new ones.

And we're also going to be thinking about symmetry and how we know when a shape or a pattern is symmetrical.

So if you're ready to make a start, let's get going.

So in this lesson, we're going to be investigating symmetry and symmetrical patterns.

And by the end of the lesson, you should be able to find lines of symmetry in real life context and design your own symmetrical patterns.

So let's get into the lesson.

We've got three key words.

Well, a phrase in there as well, haven't we? So let's practise them.

I'll say it first and then you take your turn.

So my turn, symmetrical.

Your turn.

My turn, line of symmetry.

Your turn.

My turn, reflect.

Your turn.

I hope their words and phrases that you are familiar with, but let's just check what they mean because they are really important in our learning today.

So when a shaped pattern or image has two halves that match exactly when folded, it can be described as symmetrical.

And if you were to fold a shape at its line of symmetry, both halves would match exactly.

So in those two pictures, you can see a butterfly and a heart and that dotted line.

And if you imagine that if you folded them along those dotted lines, the two halves would match exactly, and the colours of the dots on the butterfly's wings would match up as well.

And when you reflect a shape, you flip it over a mirror line or line of symmetry without turning it or changing the size.

So it stays the same distance from the mirror line and it looks like an identical shape that's been flipped over that line of symmetry or mirror line.

There are two parts in our lesson today.

In the first part, we're going to explore symmetry in real life contexts.

And in the second part, we're going to be creating our own symmetrical patterns.

So let's make a start on part one.

And we've got Andeep and Izzy helping us in our lesson today.

Andeep and Izzy have been learning about the Olympics.

They come round every four years, don't they? I wonder if you've been watching the Olympics recently.

Andeep says, "I have watched some of the Olympics before.

I liked seeing all the different sports." He says, "Archery was my favourite." Izzy says, "I watched the opening ceremony.

And there were more than 200 flags.

It was so colourful." Andeep says, "You're right, flags are colourful and there are so many different designs." Do you know which flag this one is? Izzy says, "Look at this flag as an example.

What do you notice about it?" Andeep and Izzy look at the national flag of France called the tree colour because it has three colours.

And Andeep says, "I noticed that this flag has three colours." And that's what gives it its name in French.

Izzy says, "I notice that each colour represents one-third of the flag and is a rectangle." So the flag's been divided into three equal parts, and each part is one-third of the whole.

Each part is different colour.

Andeep says, "I notice that this flag is symmetrical." Oh, can you think where the line of symmetry would go? Izzy says, "I noticed that this flag has only one line of symmetry." Did you get that was going to be the line of symmetry? If we folded the flag on that line, then the two parts would match exactly and the colours would match exactly.

Or if we put a mirror there, it would look exactly the same with the mirror there and when the mirror was taken away.

Andeep says, "How do you know there is not another line of symmetry?" It's a rectangle, isn't it, this flag? And rectangles have more than one line of symmetry.

Well, she says, "A rectangle never has diagonal lines of symmetry." That's true.

If you folded along the diagonals, then the two parts do not match exactly.

"How about a vertical line?", says Andeep.

That is a line of symmetry on a rectangle.

Is it a line of symmetry on the French flag though? Ah, Izzy says, "If the colours are not the same on each side, it is not a line of symmetry." If we folded along that line, the shape would match exactly, but the colours wouldn't.

"Okay," says Andeep, "That makes sense." So we are thinking about the pattern and the colours as well as just the shape when we're looking at symmetry in patterns and especially in flags.

Andeep and Izzy want to look at some more flags to see if they have any lines of symmetry.

Did you know this one? This is the national flag of The Netherlands.

It has the same colours in the same order as the France flag.

It's got blue, white, and red.

"Does this mean it will have the same line of symmetry?", says Andeep.

Oh, do you remember the French flag had a line of symmetry and the way we showed it that was horizontal? Does this one have a horizontal line of symmetry? No, this time there is no horizontal line of symmetry, 'cause the colours aren't the same on either side, are they? But Andeep says, "I can see that it has a vertical line of symmetry." That's right.

So this time, we could fold on that vertical line and the two halves would be exactly the same and the colours would match.

"Well done, Andeep," says Izzy, "You are right." Let's check your understanding.

Have a look at the flag of Ireland.

Which is a line of symmetry on this flag? Is it A or B? Pause the video.

Have a think.

And when you're ready for some feedback, press play.

What did you think? Was it A or B? They're both lines of symmetry for a rectangle, but which is a line of symmetry for the flag? That's right.

It's B, isn't it? If you were to fold the flag on its line of symmetry, both halves would match exactly.

If you folded on line A, the halves would not match because the colours are different on either side.

The shape would match, but the colours wouldn't.

Andeep and Izzy continue looking for lines of symmetry in different flags.

Do you know which flag this is? "Here is the national flag of Japan," says Andeep.

"This flag has two lines of symmetry," says Izzy.

Can you see where they're going to be? They're going to be the two lines of symmetry for a rectangle, aren't they? That's right, because the red circle on the flag is right in the middle.

So it's going to be the same whether you fold it horizontally or vertically.

The centre of the circle is the centre of the flag.

Andeep says, "I wonder if there are more flags with two lines of symmetry." Ah, he says, "I think the national flag of Switzerland has two lines of symmetry." That's right.

Again, the shape in the middle, the cross in the middle is right in the middle.

And it is symmetrical as well.

"Yes, you're right.

Well done, Andeep," says Izzy.

Can you think of any more? Oh, Andeep says, "The national flag of Denmark also has a white cross on a red background." Does that mean it's going to have two lines of symmetry as well? Oh, no.

Izzy says, "This only has one line of symmetry because the cross is not in the middle this time." If we folded on the rectangles of the line of symmetry, the shape would match, but the colours wouldn't because the cross is not in the centre.

Andeep says, "I found a flag with no lines of symmetry." Do you know what this flag is? Ah.

"You're right," says Izzy.

"This is the national flag of Greece and it is not symmetrical." Time to check your understanding.

Which of these flags has one line of symmetry? Is it A, the Swedish flag? B, the Nigerian flag? Or C, the flag of Bosnia and Herzegovina? Pause the video, have a go.

And when you're ready for some feedback, press play.

So which flag had one line of symmetry? It was Sweden, wasn't it? We could fold it on a horizontal line of symmetry, but not on a vertical one, because, again, that yellow cross is not in the centre.

What about the Nigerian flag? Well, that flag has two lines of symmetry.

And what about the final one? The Bosnia and Herzegovina flag.

And I apologise if I haven't pronounced that perfectly.

It's a very interesting looking flag, isn't it? I wonder what the history of it is.

Most flags have a history but interesting to research this one.

It doesn't have any lines of symmetry though, does it? We couldn't fold it on either of the lines of symmetry of a rectangle and have the two halves looking exactly the same.

Time for you to do some practise.

Look at lots of different national flags.

How many lines of symmetry can you find in each flag? And how many flags can you find with no lines of symmetry? So Andeep says, "Here are a few flags for you to start with, but you could find more flags of your own to look at too." So pause the video, investigate the symmetry in some different flags, and when you're ready for some feedback, press play.

How did you get on? So for the flags we gave you, the Belgium flag has one line of symmetry.

It's horizontal.

The Lithuania flag has one line of symmetry, but it's vertical because the stripes go in a different direction from the Belgium flag, don't they? The flags of Thailand and Austria have two lines of symmetry because the colours are symmetrical in both directions.

The flag of Guyana has one line of symmetry, all those lovely triangles of colour.

And you'd think that the flag for Czechia has the same lines of symmetry.

It's a similar design to the flag from Guyana, isn't it? But because the top of the flag is white and the bottom is red, and that triangle is only on one side, it actually has no lines of symmetry.

Ah, and Andeep found another one.

He found the national flag of Jamaica, and that has two lines of symmetry.

You can fold it horizontally and vertically, and the two sides will match up and the colours will match.

I hope you enjoyed investigating the flags.

And we're going on into the second part of our lesson.

We're going to be creating our own symmetrical patterns.

Izzy says, "My dad is a graphic designer.

He's been working on some new symmetrical designs for t-shirts." That sounds like fun, doesn't it? Andeep says, "We're really good at finding lines of symmetry.

I bet we could have a go at creating our own symmetrical designs.

So Andeep and Izzy start thinking about how to create a symmetrical design for a t-shirt.

Andeep says, "When something is symmetrical, both sides must match exactly." And Izzy says, "Each part of the pattern must be the same distance from the mirror line." So Andeep and Izzy will use a dotted background to help them to create their symmetrical t-shirt designs.

Andeep says, "We need to choose where we want to have the line of symmetry." Izzy says, "Let's start with a vertical line of symmetry." So there is their line of symmetry or their mirror line.

Now, Andeep and Izzy can start drawing shapes to create their symmetrical t-shirt designs.

What shapes would you draw? I wonder what they're going to draw.

Ah, they've started with a triangle and they've reflected it.

And then another triangle and they've reflected it.

And another one, and they've reflected that one too.

You might have come across a strategy where you think about where the vertex of the shape is and make sure that that vertex is in the same position on the other side of the mirror line.

And that will help you to get your design symmetrical.

And they put a final one in.

So can you see that the vertices of the triangles on the left hand side are the same distance from the mirror line as the vertices of the triangles on the right hand side.

Andeep says, "We've made our first symmetrical design." Izzy says, "I like the colours of this design, but the shapes are all similar." Yes, they're triangles.

And in fact, when they're reflected, they've created kites, haven't they? This time, Andeep and Izzy will try to create a different symmetrical design with different shapes.

They changed the mirror line.

It's now horizontal, isn't it? So they've reflected a right angle isosceles triangle, and they've created a square.

Now, they've reflected another triangle, and this time, they've made a bigger triangle.

This time, it's an isosceles triangle if you include the mirror line.

And so they've created a rhombus, or we could call that shape a kite because it does have two pairs of adjacent equal sides.

It just so happens that all the sides are the same length.

So we can also call it a rhombus.

And there's another triangle, a scalene triangle.

Ah.

And this time, we've created one of those kites where the final vertex sort of goes in rather than pointing out in the other direction.

So an inverted kite, sometimes known as a delta or an arrowhead.

And they put a similar sort of kite on one edge of their square and reflected it.

And then what shapes that? It's an irregular pentagon, isn't it? And an irregular Pentagon.

What an interesting design they've created.

"Now, we have lots of different shapes and colours in our design," says Andeep.

Ah, and Izzy's used a mirror to show that it's symmetrical.

Can she see she's put the mirror there.

We take the mirror away, put the mirror back, and nothing changes.

So our design is symmetrical.

Andeep says, "I wonder if we could create a design that has two lines of symmetry." What would they need to do? Have a look and a think before they share their ideas.

Izzy says, "Well, let's add a vertical line of symmetry and change the design." So what is symmetrical and what isn't symmetrical? Well, their big square is symmetrical still, isn't it? And their big pink rhombus in the middle is symmetrical too, but they're gonna have to change some other things, aren't they? So they're going to change their design.

So it has two lines of symmetry.

Andeep says, "We need to change either the blue triangle or the green kite." Can you see the ones that are inside the red square? So he's changed the kite into a blue triangle.

So now that is reflected, and that part of the pattern has two lines of symmetry.

But you've still got a problem, haven't we? Oh, or he could change it the other way.

This time, he changed the triangles into kites.

Izzy says, "We also need to change the purple shapes in the corners." So we either need four pentagons or four kites.

Andeep says, "This is my favourite design.

I will choose this one for my t-shirt." "I agree," says Izzy.

"Let's draw it carefully onto our t-shirt." Oh, look at that.

They found the middle of the front of the t-shirt, didn't they? And managed to get their design on the middle, so that it looks symmetrical and it's centred on the t-shirt.

"It looks great," says Izzy.

I agree, I think that looks really lovely.

I wouldn't mind a t-shirt like that.

Time to check your understanding.

Which pattern has two lines of symmetry? Imagine putting a vertical and a horizontal mirror line onto these patterns.

Which one has two lines of symmetry? Pause the video, have a think.

And when you're ready for some feedback, press play.

Which one was it? A, B, or C? It was B, wasn't it? We can put those two mirror lines or lines of symmetry in and we can see that if we folded or put a mirror on either of those lines, then the shapes would match exactly.

And if the mirror was there, the pattern would look exactly the same with or without the mirror.

What about the other two shapes? Well, they both have one line of symmetry, don't they? Can you see it's those pink bits on those shapes that mean that we can't have two lines of symmetry.

But on B, the pink bit is in the middle of the shape, and therefore, it will reflect in both lines of symmetry.

Time for you to do some practise.

You're going to explore using different shapes and colours on the grids to design your own symmetrical patterns.

Can you see that in one grid, you've got a vertical line of symmetry.

In the middle grid, you've got a horizontal line of symmetry.

And for the final grid, you've got two lines of symmetry.

So you're going to create a pattern with two lines of symmetry.

So have a go at exploring patterns with one and two lines of symmetry.

And when you're ready for some feedback, press play.

How did you get on? Did you have fun? Of course, there are lots and lots of different things you could have done, different colours you could have used, different shapes you could have used, but you might've created symmetrical designs like these.

So you might've used strategies like counting the dots to plot the vertices on the other side of the mirror line.

Or you might've decided to draw shapes where the mirror line dissected them, cut them in half.

And that was easy.

You could draw the whole shape all at once then.

So I hope you were successful in creating some designs.

And maybe you could go on and put your design on a t-shirt if you really like it.

And we've come to the end of our lesson.

We've been investigating symmetry and symmetrical patterns.

What have we learned about today? Well, we've learned that there are lots of real life examples where you can find lines of symmetry.

For example, in flags.

Lots of designers create symmetrical designs on items such as tiles, wallpaper, and clothing.

Maybe you could have a look at some of your t-shirts.

Are they symmetrical? What about the patterns in tiles and maybe wallpaper in your house? Are they symmetrical as well? And we know that when a pattern is symmetrical, you can fold along its line of symmetry and the two halves will match exactly both in the shape and in the colours.

I hope you've enjoyed exploring symmetrical shapes and symmetrical patterns.

Thank you for all your hard work and your mathematical thinking.

And I hope I get to work with you again soon.

Buh-bye.