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.

In this lesson, we're going to be reflecting polygons in a line of symmetry, including when there are no sides parallel to the line of symmetry.

Do you remember what parallel means? It means when two lines are exactly the same distance apart.

So in this case, our lines are not going to be parallel to the line of symmetry at all times.

So let's have a look and see what that means.

We've got some keywords and phrases in our lesson today.

We've got line of symmetry, mirror line, reflect and reflection.

So let's practise saying those before we look at what they mean.

Are you ready? I'll take my turn, then it'll be yours.

My turn, line of symmetry, your turn.

My turn, mirror line, your turn.

My turn, reflect, your turn.

My turn, reflection, your turn.

Excellent, I'm sure there are words that you have used already perhaps, so let's have a look and remind ourselves what they mean, 'cause they're going to be really useful to us in our lesson today.

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

So the line of symmetry on that heart is shown with a little dotted line.

And if you can imagine folding the heart on the dotted line, the two sides of the heart would match exactly.

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

If we placed a mirror on that dotted line on the heart, what we saw in the mirror would look exactly the same as what we saw when we took the mirror away.

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

So you take your shape and you flip it over onto the other side of the mirror line.

And the reflection of a shape is the mirror image of that shape.

And you can see in that picture we've got two rectangles.

One is a mirror image of the other.

They're the same distance away from the mirror line as well.

So there are two parts to our lesson today.

In the first part, we're going to be reflecting simple polygons in a line of symmetry, and in the second part we're going to be reflecting complex polygons in a line of symmetry.

So let's make a start on part one.

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

Aisha and Sam are going to play a reflection game.

Aisha says, "I will draw a shape on one side of the grid, and you need to reflect it in the line of symmetry or the mirror line." Sam says," I know what reflect means.

I need to draw what I would see in a mirror if it was placed on the line of symmetry." Are you gonna play along with Sam? See if you can put the shapes in the right place as well.

So here's our grid.

Aisha draws her first shape for Sam to reflect, and she's going to reflect it in that dotted line, the mirror line or the line of symmetry.

So there's the shape that Aisha's drawn.

Sam says, "I can see that this rectangle is one square away from the line of symmetry.

So I need to draw my rectangle one square away on the other side." So there's Sam's rectangle, and if we put a mirror on that line of symmetry, what we saw in the mirror would be exactly the same as what we'd see if we took the mirror away.

"Well done, Sam," says Aisha, she's got it right.

Aisha draws another shape for Sam to reflect.

Sam says, "The rectangle is one square away from the mirror line again.

I will make sure that the top and the bottom of the rectangle line up." So she's drawn at the same distance away from the mirror line and the top and the bottom line up.

Is she right though? Have you spotted something? Aisha says, "Not quite, Sam, try again." Sam's had another look.

"Oh yes, I see it now," she says, "Your rectangle is two squares wide, but mine is three squares wide." So the shape you reflect must be exactly the same size as the starting shape.

"I can correct that easily," she says.

I hope she drew in pencil.

So there we go, she's changed her shape, and now her shape is the same distance from the mirror line, the top and the bottom line up, and it's the same width, it's two squares wide.

"Great work, Sam," says Aisha.

Here's another one.

So what have we got to remember when we are reflecting this shape? Can you remember all the things that Sam was thinking about? She says, "I will make sure that I look at the length and the width of your rectangle this time to make sure mine is the same size." So she can see that it's one, two, three, four, five long and three wide.

There we go, five long and three wide.

Can you spot something? "So close, Sam," says Aisha, "Just one mistake." What's Sam forgotten? "Oh," she says, "I forgot to check how far it was away from the mirror line." This time it was two squares away or two dots away and she'd only put one.

"I can have another go now I've spotted my mistake," she says.

What's she going to have to do? That's right, she's moved her shape one square further away from the mirror line.

"Excellent reflecting, Sam," says Aisha.

Time to check your understanding.

Which image shows a reflection, is it A, B, or C? Pause the video, have a think, and when you're ready for some feedback, press play.

Which one was it? That's right, it was B, wasn't it? In A, the two shapes aren't the same distance from the mirror line, and in C, the two shapes aren't the same size, are they? Aisha and Sam will continue to play their reflection game.

"This time I'm going to make it a bit more difficult," says Aisha, "I might move the mirror line to a different position." And Sam says, "Maybe you could draw some different shapes this time too?" They were all rectangles before, weren't they? Oh, can you see now? We've gone from having a vertical mirror line to having a horizontal mirror line.

I wonder what shape Aisha's going to draw.

Here it is.

Ooh, that's a sort of rotated L shape, isn't it? It's also a hexagon.

Sam says, "I can see that the longest side of this hexagon is closest to the mirror line.

So I need to draw the longest side of my hexagon closest to the mirror line too." So there we go, is it the same distance apart from the mirror line? It is.

Is her shape the same size? Well, it is, the narrow bit is one square wide and the long bit is two squares wide.

And the sort of L bit that sticks up is one wide as well.

"Well done, Sam," says Aisha, "You've got it right." So she thought about making sure that the shapes were the same length this time, the dimensions were the same.

Aisha draws another shape for Sam to reflect.

She says, "This time the hexagon is one square away from the mirror line again.

I will draw my hexagon one square away from the mirror line like yours." Is that right? Aisha says, "Not quite, Sam, try again." What mistake has Sam made? Well, she says, "The side closest to the mirror line on your shape is only one square long, but mine is two squares long." Ah, oh, she says, "I forgot to flip my shape over the mirror line.

I can fix it." Imagine if a mirror was on that mirror line, what would the shape look like in the reflection? That's right, now she's flipped that shape.

So closest to the mirror line is that short side, and furthest away from the mirror line is the long side, but the shapes are in the same position relative to the mirror line and they're the same size.

"Great work, Sam," says Aisha.

Here's another one.

Well, it's another L shape.

Slightly different length this time.

And have you spotted how far away it is from the mirror line? Where would you draw it? Sam says, "I will make sure that I flip my hexagon over the mirror line this time." There we go, she says, "I flipped it over the mirror line." Is that right? "So close, Sam, just one mistake." What's the mistake Sam's made this time? "Oh," she says, "I forgot to check how far away it was from the mirror line." Oh, it's two away and she's only put hers one away.

"I can have another go," she says, "Now I've spotted my mistake." And she's moved it so it's the same distance away from the mirror line.

"Excellent reflecting, Sam," says Aisha, and well done, Sam, for realising what you've done wrong and being able to make your corrections.

Time to check your understanding.

Which image shows a reflection, is it A, B, or C? Check carefully.

Has it been flipped? Is it the same size? Is it the same distance away from the mirror line? Pause the video, have a look.

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

Which one was it this time? That's right, it was C, wasn't it? A hasn't been flipped, and B is a different distance away from the mirror line.

So C has been flipped and it's the same size and it's the same distance away from the mirror line.

Well done if you spotted that.

Time for you to do some practise now.

In question one, you are going to reflect each polygon in its line of symmetry.

So you're going to draw the reflection, and the line we've put there is that line of symmetry or we can call it the mirror line as well.

And in question two, you're going to play the reflection game with a partner.

Take turns to draw the starting shape or the reflection in the line of symmetry.

Have a go at each one, be the person drawing the first shape and then make sure you get to turn at being the person drawing the reflection as well.

Have a go at those two questions and when you're ready for some feedback, press play.

How did you get on? So these are the reflections you should have drawn for each one.

You had to remember that the shape was flipped, you had to remember that it was the same distance away from the mirror line and that the shapes were the same size.

And if you had a mirror to hand, you could put a mirror onto that line of symmetry or that mirror line and check that what you saw when the mirror was there was exactly the same as what you saw when the mirror was taken away.

And I don't know what shapes you might have drawn in question two when you were having a go at playing the reflection game, but here are some that we drew.

And can you see as well? Just make sure they're all the same distance from the mirror line, the shapes are all the same size, and the shapes have been flipped.

I hope you enjoyed reflecting your shapes in the mirror lines.

And onto part two of our lesson.

We're going to be reflecting complex polygons in a line of symmetry.

Ah, do you remember at the beginning we talked about things not being parallel to the mirror line? I think this is where we're going to look at this.

So Aisha and Sam are continuing their reflection game.

Sam says, "I think this shape might be harder to reflect because the sides are not parallel or perpendicular to the line of symmetry." So our line of symmetry is a vertical line of symmetry.

So if the sides were parallel, they would be in that same line, the same distance apart.

If they were perpendicular, then they would make a right angle with our line of symmetry.

So this time they're not parallel or perpendicular.

So we're gonna have to think about another way of getting our shapes in the right place when we reflect them.

Sam says, "I will reflect one vertex at a time to help me complete the reflection correctly." So she's going to think about where the vertices of the shape are and see if she can plot those on the other side of the mirror line to help her.

So she's starting with that top vertex.

How far away is it from the mirror line? One, two, three dots away.

So it's going to be on that same line, and it's going to be one, two, three dots away on the other side.

So that's where that top vertex is.

What about this next one? Well, it's one dot away from the mirror line, so she can plot the pink cross there.

What about this one, the one furthest away from the mirror line? How many dots away is it? One, two, three, four, five, six dots away.

So along that same line, we're going to have to go one, two, three, four, five, six dots in the other direction and put our red cross.

And then we've got our bottom vertex.

And that's one, two, three, four dots away.

So we're going to go one, two, three, four dots away on the other side.

Let's take all those numbers away.

"Now," says Sam, "I can join the vertices to complete the reflection." So there we go, she's reflected that shape accurately.

She's flipped the shape, the shape is the same size and the vertices are the same distance away from the mirror line or that line of symmetry.

Well done, Sam, that's a really good strategy to use.

"Great work, Sam," says Aisha as well.

Aisha draws another shape for Sam to reflect.

This time we've got a triangle.

And again she says, "I will reflect one vertex at a time to help me to complete the reflection correctly." So that top vertex is one, two, three dots away.

So she's going to put a dot three dots away on the other side or across.

The one that's furthest away is one, two, three, four, five, six away again, right on the edge of our grid.

So she's going to put a cross there.

And the last one is one, two, three, four dots away.

So she's going to put a cross four dots away on the other side of the line of symmetry.

Now she says, "I can join the vertices to complete the reflection." "Excellent reflecting, Sam," says Aisha, that's really good.

It's a really good strategy to use.

We can be sure that our shape has been flipped, that the vertices are the same distance away from the mirror line, and that the shape is the same size.

When things were parallel and perpendicular to the mirror line or the line of symmetry, we didn't have to think so much about the vertices, but when we haven't got those lines that are parallel or perpendicular, so no horizontal and vertical lines, it's really useful to think about the vertices in our shape.

Here's another one.

Can you predict what it's going to look like? Well, we have got one side that is parallel to the mirror line this time, to the line of symmetry.

So we've got one that will help us a little bit more, but again, she's going to reflect one vertex at a time.

So this one is one dot away, so we're going one dot away.

The next vertex is one row of dots down, isn't it? And it's one, two, three, four, five dots away.

And then the one at the bottom we can see is directly underneath the green one, one dot away again.

And now she can join the vertices to complete the reflection.

"Excellent reflecting, Sam," says Aisha.

That strategy's worked again.

Time to check your understanding.

You've got a statement here, is it true or false? This shape has been correctly reflected in the line of symmetry.

Decide if it's true or false and explain why.

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

What did you think? It was false, wasn't it? It hasn't been correctly reflected.

When you reflect one vertex at a time, you can see that one of the vertices is in the wrong position on the grid.

The vertex that's highest up is in the wrong place, isn't it? It's three dots away from the mirror line in the original and it's only two dots away in the reflection.

So this one is correct, this one's correct, this one's correct.

Ah, but that one should be one square further out or one dot further out.

Now it's correct, isn't it? Well done if you've got that right.

And time for you to do some more practise.

This time, you've got some polygons to reflect in the line of symmetry that are not parallel, perpendicular or not all of them.

So you need to think about marking one vertex at a time and then joining them with straight sides.

So I hope you've got a ruler at hand to help you.

And in question two again, you're going to play that reflection game with a partner.

Take turns to draw the starting shape or the reflection in the line of symmetry.

And Sam says, "Could you include a triangle, a pentagon, and a polygon with no right angles in your game?" See if you can include examples of those shapes as well.

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

How did you get on? So these are the reflections that you should have drawn for each polygon.

Did you make sure to put each vertex in the right place on the other side of the mirror line so that you made sure that your shape was flipped, the same size and the same distance away? And I dunno what shapes you played with the reflection game, but we tried to have a go at the shapes that Sam suggested.

So we've got a triangle, we've got a pentagon there, it's an irregular pentagon, in the middle of the top, we've got a hexagon on the right hand side at the top, another triangle, another pentagon and another pentagon to finish with as well.

So we've got lots of pentagons, one hexagon and two triangles.

And in some of those shapes there were no right angles.

So our triangles didn't have right angles on this occasion, our bottom right pentagon didn't, and the hexagon at the top didn't either.

I hope you had fun playing that game.

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

We've been reflecting polygons in a line of symmetry.

So what have we been thinking about? Well, we've learned that when you reflect a shape, it will be the same distance from the line of symmetry on both sides, and that you can reflect a shape by counting the position of each vertex, and making a mark, and then joining the marks with straight lines.

And you could also do that by using a ruler to measure.

I hope you've enjoyed reflecting polygons in lines of symmetry and I hope I get to work with you again soon, bye-bye.