Lesson video

Hello, my name is 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 are going to be thinking about completing different types of symmetrical patterns.

I wonder if you've come across that word before.

Symmetrical.

Well, we're going to be learning lots about it today.

So let's make a start.

Here are our keywords and phrases for this lesson.

We've got symmetrical, line of symmetry, and mirror line.

So I'll take my turn and then it'll be your turn.

Let's give them a practise.

My turn, symmetrical, your turn.

My turn, line of symmetry, your turn.

My turn, mirror line, your turn.

Excellent.

Let's have a look at what those words mean.

Some of them might be new or we might not have used them for a long time.

So let's check, 'cause they're going to be really important in our lesson.

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

So can you see that butterfly? We might meet that butterfly again.

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

So symmetrical means when two things are exactly the same on one side to the other, and they're exactly the same because if you placed a mirror on that line of symmetry, then they would look exactly the same in real life and the bit in the mirror as well.

And the mirror line is another term to describe the line of symmetry.

So let's make a start on this lesson.

There are two parts.

In the first part, we're going to be completing simple symmetrical patterns.

And in the second part, we're going to look at some more complex symmetrical patterns, perhaps a little bit more complicated, maybe more parts to them.

So let's get into part one.

And we've got Lucas and Sam helping us in our lesson today.

Sam and Lucas are exploring patterns and shapes in an art lesson.

When a shape can be folded in half and both sides are the same, the line where you folded is called the line of symmetry.

So can you see what they've done? They've folded a sheet of paper in half.

They've cut out a shape from sort of the folded paper.

And then when they open it out, both sides are exactly the same.

And the fold is like the line of symmetry or the mirror line that we learned about in our keywords.

The line of symmetry is also known as the mirror line, because if you place a mirror on the line of symmetry, the image you see in the mirror matches the other half of the shape.

We haven't got a proper mirror on this slide, but let's have a look and imagine what that would be like.

You might have some mirrors that you could do this with in your classroom.

So if those are the mirrors that we've just placed on those lines of symmetry on that mirror line, the reflection we see would look exactly the same as the half of the shape we can see for real.

So let's just look at that again.

Whole shape, no mirror.

And then with the mirror, the shape looks exactly the same, but part of it we are seeing is a reflection in the mirror.

Sam can use a line of symmetry to make a butterfly painting.

So she's cut out a butterfly.

I wonder if she folded the paper first to make the two halves of the butterfly exactly the same.

So there we go.

If we folded the butterfly in half, that would be our line of symmetry.

If we put a mirror there, we'd see exactly the same butterfly as we can see when we can see both halves of it.

Sam says, "I will only paint one half of the butterfly." So she's putting some paint dots on one half of her butterfly.

Now she says, "I can fold my butterfly following the line of symmetry and press it down." So there we go.

She's folded it.

She's going to give it a good press down.

And she says, "When I unfold it, the paint will be on both sides.

What do you think it will look like?" Hmm.

What do you think? Should we see? Ah, look at that.

So she's unfolded it, and what do you notice? The pattern on one side is a reflection of the other side.

That means that when it is folded, the two halves will match.

So can you see when it was folded, those two blue dots at the very top are in exactly the same place.

The two green dots would be in exactly the same place, and so on for all the other dots of colour.

When a shape or image has a line of symmetry like Sam's butterfly, it can be described as symmetrical.

So this butterfly is symmetrical.

It has a mirror line or a line of symmetry down the middle.

Meaning that both sides are exactly the same when seen in a mirror.

Right, well, Sam and Lucas want to investigate this further.

So they want to create their own symmetrical patterns, but they're going to use a grid this time.

So Lucas says, "I will shade one of the squares blue." So he's done that.

And can you see that we've got that line down the middle? And Sam says, "I know the dotted line is the line of symmetry or the mirror line." So which other square should be shaded blue to make this pattern symmetrical? We can't fold it over.

It's not paint this time.

So which other square should be shaded so that the pattern is symmetrical? Sam says, "I can visualise this in half on the mirror line." So she's imagining it folded over.

And where would that blue square be now? Ah, it would be there, wouldn't it, where the arrow says.

Lucas says, "I can see I need to shade this square to make the pattern symmetrical." "The squares we have shaded are both touching the mirror line," says Sam.

Can you that where the mirror line is in the middle? They're both touching that mirror line.

Sam and Lucas can continue shading squares to create a symmetrical pattern.

Lucas says, "If I shade the square that is furthest away from the mirror line on my side.

." There we go.

He's put it in pale green.

Sam says, "Then I need to shade the square that is furthest from the mirror line on my side." So there we go.

Can you see? That's now symmetrical.

If you folded those over, the blue square would be on the blue square and the green square would be on the green square.

And if we put a mirror on that line, then the reflection would look exactly the same as the part we could see.

Sam says, "If I shade the square that is one square away from the mirror line on my side.

." She's shaded it in a pink colour.

Lucas says, "Then I need to shade the square that is one square away from the mirror line on my side." There it is.

And you can see that their patterns are exactly the same on either side.

When you folded them over, they would line up perfectly.

And if we put a mirror on the line of symmetry down the middle on the dotted line, then the reflection would look the same as the bit that we covered up with the mirror.

Time to check your understanding.

How could you make this pattern symmetrical by shading more squares? Pause the video, have a go, and when you're ready for the answers and some feedback, press play.

How did you get on? So you might have started by looking at the squares closest to the mirror line.

They both need to be shaded the same colour for the pattern to be symmetrical.

So we'd need to shade that one in that sort of pinky peachy colour.

Where did you go next? Ah, then you could look at the squares that are one square away from the mirror line.

And both of those need to be shaded the same colour.

So they both need to be that purpley colour.

And finally, we're going to look at the squares that are furthest from the mirror line and shade both of those the same colour.

So those are both a yellowy colour.

So if you put a mirror down the dotted line, the picture wouldn't change.

What you saw in the mirror would be exactly what you'd covered up with the mirror.

So it is symmetrical.

Lucas and Sam will try drawing shapes on their grid to create a symmetrical pattern.

So we're gonna move away from colours and think about shapes.

Lucas says, "I will draw a circle, triangle, and a pentagon." And Sam says, "I will also draw a circle, a triangle, and a pentagon." Is that a symmetrical pattern? What do you think? "On my side," Sam says, "The circle is closest to the mirror line." But Lucas says, "On my side, the pentagon is closest to the mirror line.

That means it's not a symmetrical pattern." Ah, Sam has repeated Lucas' pattern instead of drawing the reflection of it.

She's going to try again to create the symmetrical pattern.

Can you think what she's going to have to do? Now Lucas and Sam can look at the position of each shape and explain how they know that this pattern is symmetrical.

Lucas says, "Now the two shapes closest to the mirror line are both pentagons." Sam says, "Each triangle is one square away and each circle is two squares away from the mirror line." So now they know that that pattern is symmetrical.

If you imagine folding the paper on the mirror line, then you would see that all the shapes would be on top of each other.

The circles would be on top of each other, the triangles, and the pentagons.

So it is a symmetrical pattern.

Time to check your understanding again.

Which patterns are symmetrical, A, B, C, or D? Have a look.

Pause the video, and when you're ready for some feedback, press play.

So which did you think was symmetrical? Well, A is symmetrical, B is not symmetrical, C is not symmetrical, and D is symmetrical.

A and D are symmetrical patterns, because when you start from the mirror line, each pair in the grid is the same.

So you can see that in A, the hexagons are closest to the mirror line, the triangles are one square away, and the squares are two squares away.

And in D, even though we've got empty squares, two squares away from the mirror line, we've got our trapeziums are on either side of the mirror line and our circles are one square away.

And there, we can see the arrows showing us.

In B, we've repeated and not reflected the pattern, so it's not symmetrical.

If we folded along the mirror line, then the hexagon and the square would be on top of each other, and that's not what we want.

The triangles are in the right place, but the hexagon and the square would need to be swapped.

And C has two triangles on one side and only one triangle on the other side.

So it can't be symmetrical.

We haven't even got the right number of shapes on each side of the mirror line.

So we need to draw another triangle one square away on the right-hand side.

Time for you to do some practise.

How many different symmetrical patterns can you create on these grids using only circles and squares? And in question two, explore creating symmetrical patterns with a partner.

You could draw on one half and ask them to complete the pattern, then they could design a pattern on one half for you to complete.

And Sam says, "When you complete the pattern, remember to look carefully at what is closest to the mirror line." It's often easiest to work that way and then work further out.

So pause the video, have a go at those two tasks, and when you're ready for some feedback, press play.

How did you get on? So in question one, we were just using circles and squares, so you may have created different patterns, but here are some that we created.

And can you see that if we check, moving out from the mirror line, we can see that our patterns are symmetrical and not just repeats.

And again, question two, lots of different possibilities.

You might have used colours, you might have used shapes.

But did you remember to look carefully at what was closest to the mirror line to help make sure your pattern was symmetrical? I hope you did, and I hope you had fun creating symmetrical patterns.

And on into the second part of our lesson, we're going to have a look at some more complex symmetrical patterns, perhaps a bit more complicated.

Ooh.

Now Lucas and Sam can explore creating symmetrical patterns on larger grids.

So we haven't just got strips here, we've got larger grids, but you can still see that we've marked in that line of symmetry, that mirror line down the middle with a dotted line.

Sam says, "I will draw some shapes on one side of the grid." So there we go.

She's drawn some shapes.

Can you picture, can you imagine what the reflection is going to look like to make that symmetrical? And Lucas says, "I will complete the pattern one row at a time and I will look at how close each shape is to the mirror line." Good thinking, Lucas.

That's a really good strategy that he's going to use.

So he's seen that there is a square next to the mirror line.

So he's put a square next to the mirror line.

What would be next in that row? That's right, there'd be a circle one square away from the mirror line.

And then how to complete that row? That's right.

A square.

Two squares away from the mirror line.

Has he put the square in the right place? He has, hasn't he? The square isn't touching the mirror line.

It's one square away.

And what about the bottom one? Well, to make it symmetrical, that's got to be underneath the circle, hasn't it? Another way to think about where those extra squares would go, would be to look at where they are in relation to the circle.

So if Lucas puts his one above and one below the circle, that's another way to check that he's got them in the right places and made the pattern symmetrical.

Lucas says, "This time I will draw some of the shapes on one side of the grid." So he's drawn some shapes.

What do you notice this time? Sam says, "I notice that the squares make a T shape that is one square away from the mirror line." Can you see? It's a sort of T shape on its side.

But there's nothing touching the mirror line this time.

So she's got to be really careful about where she puts her squares.

There we go.

One square away from the mirror line and she's made a T shape.

Is that right? Lucas says, "On my T shape, the part with only one square is further away from the mirror line than the part with three squares." Is that true for Sam's? It isn't, is it? Sam says, "My part with one square is closer to the mirror line.

I think I made a mistake, but I know how to correct it." Can you imagine what she's going to do? Can you picture what it's going to look like? That's right, isn't it? Yes.

She needed to have the part with one square furthest from the mirror line and the part with three squares one square away from the mirror line.

I think she'd done that repeating idea, hadn't she? Let's have a look.

Let's go back to what her original one was.

She'd repeated the pattern, hadn't she? She needed to reflect the pattern to create a symmetrical pattern.

Well done for correcting it, Sam.

Time to check your understanding.

How could you complete this pattern to make it symmetrical? Pause the video, have a go, think about the mirror line, and when you're ready for some feedback, press play.

How did you get on? So the symmetrical pattern should look like this once it's complete.

I wonder where you started.

You might have started with the square at the bottom because it's closest to the mirror line.

You might have focused on drawing all the circles first and then added in the squares.

Or you might've noticed the straight line of shapes down the middle and drawn those first.

I think I'd have done a combination of the first idea and the second.

I think I'd have put the square in at the bottom first and then realised there was a circle next to it.

And then looked to see that from the circle up, I've got two squares, a circle, and another square.

And then that last circle is next to the sort of middle of the row, isn't it? So I think I might have worked along and then up, and then out to the final circle.

I'm not sure.

How did you do it? I wonder if you could talk to someone.

How did you see that pattern to make it symmetrical? So they're going to carry on exploring these patterns on a larger grid, but can you see what's happened this time? This time we've got a horizontal mirror line.

Our mirror lines have been vertical lines before, haven't they? So this time with our horizontal mirror line, we're going to make sure that we think about reflecting the top and the bottom of our patterns.

So let's have a look and see what Sam and Lucas are going to come up with.

Sam's going to draw some shapes on the grid on one half, and she's going to challenge you and Lucas to complete the pattern to make sure that it is symmetrical.

Wow.

She's drawn a lot of shapes for us to think about.

Lucas says, "I'm going to start with the shapes that are closest to the mirror line." I think that's a good idea.

So he's put his circles in and then his squares.

And he can check, he's got the right number of circles and squares.

He's got two circles and four squares, which is what Sam had.

And they are right next to the mirror line and next to each other.

And then he can see that the other squares follow on out from the circles so he can add in those final two squares.

Is he correct? I think he is.

Well done, Lucas.

I hope you saw that as the pattern to make it symmetrical as well.

Sam says, "I think we could take turns to shade in squares to create another symmetrical pattern." "Great idea," says Lucas, "I'll go first." Go on then, Lucas.

So he's shaded a square.

Where's Sam going to shade a square? That's right.

It's above the one that Lucas has shaded and it's one square away from the mirror line just like Lucas' is.

If you imagine folding that paper, those two squares would be on top of each other.

Lucas has shaded another one.

What do you notice this time? It's right next to the mirror line, isn't it? Easy one to shade in for Sam.

Oh, how can we think about where this square is? Well, you might have said it's three squares away from the mirror line, or you might have seen how it joined on to the square that was already a square away.

So it's joined on at one of its vertices, one of its corners, isn't it? And another one.

That one's not touching any of the other squares either, is it? But it's one square away from the mirror line and it's also one square away from one of the other squares in our pattern.

Lucas says, "We could start using another colour.

Would you like to go first this time, Sam? That's very generous of you, Lucas.

"Thank you, Lucas," says Sam, "I will use blue." Oh, so she's put a blue next to the square that's furthest away from the mirror line.

Well done, Lucas.

That's the right place to put it.

And she's put another one.

This one's next to the mirror line, isn't it? And can you see? It touches those two squares that are already there.

Well done, Lucas.

That's the right place.

And one more there, which kind of fits into those other squares.

Excellent.

And they've created a symmetrical pattern using two colours.

I think that's a really lovely idea, isn't it? Taking it in turns and making sure that the square that you shade reflects the square that your partner shaded.

Well done, Sam and Lucas, great teamwork.

Time to check your understanding.

Lucas has shaded these squares.

Which squares should Sam shade so that the pattern is symmetrical? Pause the video, have a go, have a think.

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

Which squares did you think? Remember, it can be helpful to start with the parts of the pattern that are closest to the mirror line.

So we could put those two squares in first.

Now the other ones, where are they sitting? That one is one square away from the mirror line, but it just touches the one that we've already drawn.

And that square was sort of in the next column from the two that are together, but two squares away from the mirror line.

So have we done it successfully? We have.

Well done.

Time for you to do some practise now.

How many different symmetrical patterns can you create by drawing three circles and two squares? That's all you can use.

Three circles and two squares.

And we've got some grids with a mirror line that is vertical and some grids with a mirror line that is horizontal.

Make sure you know which one you are using.

And in question two, explore creating symmetrical patterns with a partner.

You can draw on one half and then ask them to complete the pattern, and then they could design a pattern on one half for you to complete.

Or you might do the one square, one square game that Sam and Lucas played.

Pause the video, have a go at creating symmetrical patterns, and when you're ready for some feedback, press play.

How did you get on? Hope you enjoyed that.

Lots of different possibilities, but these are some of the symmetrical patterns you could create by drawing three circles and two squares.

I wonder if you drew any of those.

Did you remember to change when it went from the vertical mirror line to the horizontal mirror line? I hope that didn't catch you out.

And again, in question two, so many different possibilities, different colours, different places you could have shaded, but here are two symmetrical patterns.

One with a horizontal mirror line and one with a vertical one.

I hope you enjoyed your symmetrical pattern creation tasks.

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

We've been completing a symmetrical pattern.

So what have we learned about today? We've learned that a pattern is symmetrical when one half is a reflection of the other half.

The line of symmetry is also known as the mirror line, because when you place a mirror on the line of symmetry, the image you see in the mirror is the same as the other half of the symmetrical pattern, shape, or image.

And when completing a symmetrical pattern, it can be helpful to look carefully at how close each part of the pattern is to the mirror line.

Thank you for all your hard work.

I hope you've enjoyed working with symmetry in this lesson, and I hope I get to work with you again soon.

Bye-bye.