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 that are dissected by the line of symmetry and explore the new shapes that are created when a polygon is reflected.

So dissected means they've been cut in half by the line of symmetry.

So let's get into our lessons, see what we're learning about.

We've got some key words and phrases here.

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

They may well be words and phrases you're familiar with, but let's practise them anyway and then we'll find out what they mean.

So are you ready? I'll take my turn, then it'll be your turn.

My turn line of symmetry.

Your turn.

My turn mirror line.

Your turn.

My turn, reflect.

Your turn.

My turn, reflection.

Your turn.

Excellent.

As I said, you may well be familiar with those words, but let's just remind ourselves of what they mean 'cause they're going to be really important in our lesson today.

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

And we can see a line of symmetry there on that heart shape shown by the dotted line.

And another term for that line of symmetry is a mirror line.

If we were to place a mirror on that dotted line, then the image we saw in the mirror would be exactly the same as the one we saw if 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 and the reflection of a shape is the mirror image of a shape.

Let's have a look at how those words are gonna help us today.

There are two parts to our lesson.

So in the first part of our lesson we're going to reflect polygons dissected by the mirror line.

So cut in half.

And in the second part we're going to explore polygons dissected by the mirror line.

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.

I wonder if you've played something similar recently.

Aisha says, "I will shade a shape on the grid and you need to reflect it in the line of symmetry or the mirror line." And Sam says, "I know that reflect means I need to draw what I would see in a mirror if it was placed on the line of symmetry." Good thinking, Sam.

So Aisha shades her first shape for Sam to reflect.

She says, "I can see a vertical line of four squares touching the line of symmetry." So she's going to repeat that because that's what would happen if she flipped the shape over the mirror line.

She says, "At the top, I can see that the second square away from the line of symmetry is shaded." So she's going to shade that one as well.

"Well done Sam," says Aisha, she's successfully reflected the shape.

Aisha shades another shape for Sam to reflect.

Oh, she's drawing on the other side of the paper this time, hasn't she? Sam says, "I can see a row of three squares at the top and three squares at the bottom." So she's going to shade the three at the top and the three at the bottom.

What else can she see? She says, "I can see two squares, one above the other that are two squares away from the line of symmetry." And they join together the lines that she's drawn already.

And there they are.

"Great reflecting Sam," says Aisha.

She's successfully reflected Aisha's shape, hasn't she? Drawn the mirror image of it in that line of symmetry or that mirror line.

Oh, Aisha shades another shape for Sam to reflect.

Can you see what's changed here? This pattern looks trickier.

She says, "I'll reflect one column at a time." So we've now got the horizontal mirror line, haven't we? So she's going to do a column at a time.

So that first column has three squares shaded.

So she's shaded three squares.

The next one has two, then one, then two.

In these last two columns, I noticed that the shaded squares are not touching the line of symmetry.

Well spotted Sam.

So she's left one square and then shaded her two squares and now she's got to leave two squares and then shade her final square.

"Great reflecting Sam," says Aisha again.

She thought through that really carefully and systematically, didn't she? Aisha shades another shape for Sam to reflect.

We've gone back to a vertical mirror line.

Line of symmetry this time, haven't we? Can you see we've got a half square as well.

Sam says, "I can see a larger square made up of three rows of three smaller squares." Oh yes, that's right.

With the extra bit on the top.

So she's going to reflect that part of the shape.

That square.

On the top corner that is furthest away from the line of symmetry I can see half a square shaded.

Oh, is that right? "You are so close," says Aisha, "Just one error." Can you see the error that Sam's made? "Oh," she says, "I've shaded the wrong half of the square at the top." She sort of moved it across rather than reflected it.

"On your side," she says, "There is a vertex, which is three squares away from the mirror line." Haha, that's right.

There it is.

But her vertex wasn't in the right place.

"I need to shade it like this," she says.

That's it.

Now we've got a reflection, a mirror image of the shape that Aisha shaded.

You corrected your mistakes Aisha.

Great job.

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.

How did you get on? It was A, wasn't it? In the other shapes the position of these vertices helps us to see that these do not show a reflection.

Here's what the reflections should look like.

I hope you spotted those.

Aisha says, "I wonder if we could play the same game but drawing shapes on dotted paper this time." Sam says, "As long as there is a mirror line, I will still be able to draw the reflection of your shape.

Let's try it." So Aisha draws her first shape for Sam to reflect.

She says, "I can see that these vertices are both one square away from the line of symmetry.

I need to mark my vertices one square away on the other side of the line of symmetry." There they are.

So now she can complete the shape and it's one larger rectangle.

"Great work Sam," says Aisha.

Aisha draws another shape for Sam to reflect.

Can you think what this is going to look like when we've completed the reflection? What shape are we going to have? Sam says, "I can see that this vertex is five squares away from the line of symmetry.

I can mark and then join the vertices." That's the only one she needs, isn't it? Because she's going to join the top down to that vertex and carry on the line across the bottom.

What shape have we got? We've got a bigger triangle, haven't we? Aisha says, "You are spot on.

Well done Sam." I think Sam's really got this idea of marking the vertices on off to a fine art, hasn't she? I think we can all learn from Sam.

It's a really good strategy to use.

Aisha draws another shape for Sam to reflect.

Can you see that we've changed the mirror line now it's horizontal, not vertical.

She says, "I can see that this vertex on Aisha's shape is one square away from the line of symmetry." So she's drawn it on her side and this vertex is two squares away from the line of symmetry.

So she's plotted it on her side and now she can join them up.

So what shape have we got this time? Got a pentagon, haven't we? "Brilliant work," says Aisha.

Time to check your understanding, which image shows a reflection.

Think carefully.

Are the shapes flipped or the same size? And are all the vertices the same distance away from the mirror line or the line of symmetry? Pause the video, have a go.

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

What did you think? Well it wasn't A, was it because that vertex is in the wrong place and it wasn't B was it either.

Again the vertex was in the wrong place.

But C was correct.

All the vertices were in the correct places reflected across the line of symmetry or the mirror line.

And we can see they all line up.

They're all in the right places.

If you reflect each of these vertices, you can see that these images do not show a reflection.

Here are the reflections correctly.

There we go.

So now all of them are correct.

Time for you to do some practise.

So in question one, you're going to shade the squares to show the reflection of each polygon in the line of symmetry.

And in question two, you're going to draw the reflection to complete each polygon, mark the vertices one at a time, then connect them with straight lines.

What shapes are you going to make? Pause the video.

Have a go at those two questions.

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

How did you get on? So these are the squares you should have shaded to complete each reflection.

Are you ready? So two, one two, three down touching the mirror line and then another two across.

So here you might have gone a row at a time or you might have gone a column at a time.

And there are the next two and then we have another four to look at as well.

So you might have gone a column at a time here 'cause our mirror line was horizontal, making sure that everything is the same distance from the mirror line.

And then in this one you might have started closest to the mirror line and worked out.

I think that's what I would've done.

And then double check that I'd met up properly with my final ones, which were right in that bottom left hand corner of the grid.

For the next one, I'm not sure, I might have worked out from the mirror line perhaps.

And for the last one I think I'd have looked at that first column that I could do that was connected to the mirror line and then worked out from there.

And being really careful with that half square, making sure I had the correct half of the square shaded in.

Well done if you've got all those right.

And then here we were focusing on the vertices.

So these are the reflections you should have drawn for each polygon.

So looking at the position of those vertices, we can complete the shapes.

So we've shown it for the first one and for the rest you would've plotted the vertices and we'd have got along that top row, a rectangle, a trapezium, a triangle, and another trapezium.

And on the bottom row, a kite, an irregular hexagon, an octagon irregular again, because the two vertical lines are longer than the others.

And then an irregular one, two, three, four an irregular octagon as well.

I hope you enjoy playing around and finding those reflections.

And on into the second part of our lesson, we are going to explore polygons dissected by the mirror line again.

So Aisha and Sam look back at the shapes they drew.

Aisha says, "First I drew a rectangle with one side touching the mirror line." Sam says, "Then I drew the reflection and the shape we made was another rectangle." Aisha says, "On our second turn I drew a triangle with one side touching the mirror line." And Sam says, "Then I drew the reflection and the shape we made was another triangle.

" "On our third turn," Aisha says, "I drew a quadrilateral with one side touching the mirror line." "Then I drew the reflection and the shape we made was a pentagon." Ah, so before we had a rectangle and a bigger rectangle and then a triangle and a different triangle.

This time we drew a quadrilateral and we ended up with a pentagon.

Aisha says, "I wonder when you reflect a triangle that has a side that touches the mirror line, will you always create another triangle," she says.

Good question.

"Let's investigate," says Sam, "I will draw another right angled triangle," says Aisha.

When I draw the reflection, we create another triangle.

This triangle isn't a right angled triangle though, is it? But it will be an isosceles triangle because the reflection means that two of the sides will be the same length.

"Let's try starting with an isosceles triangle with no right angle," says Aisha.

"Oh," says Sam, "When I draw the reflection, we create a rhombus." So how did that happen? Well, we had an isosceles triangle and the sides that we reflected were the two sides that were the same length.

So now we've created a shape with all four sides of the same length, but two opposite pairs of equal angle.

And those are the properties of a rhombus.

"Let's try a scale triangle with no right angle," says Aisha.

Also, Sam, when I draw the reflection, we create a kite or we can't have a rhombus this time because the sides weren't the same length to start with.

So now we've created a shape with adjacent pairs of equal sides, next door sides that are equal or two pairs of them.

And that's a property of a kite.

Gosh, that's a lot of investigating.

Aisha says, "We found out that when you reflect a triangle that has a side that touches the mirror line, you can create many different shapes." Sam says, "We've created a triangle, a rhombus and a kite.

I wonder if there are any other shapes you could create." Let's just pause and check our understanding.

We've got a true or false.

When you reflect a rectangle that has a side that touches the mirror line, it will always create a larger rectangle.

Do you think that's true or false? And why? Have a think.

You might want to go back and look at some of the pictures you've drawn, some of the images you've reflected.

See if you think that's true or false.

And if you can explain why.

Pause the video, have a go.

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

What do you reckon? Well, it's true, isn't it? Look at these examples to see how a rectangle that has a side that touches the mirror line will always create a larger rectangle when it's reflected, those lines will always be continued.

And the fourth side that we add in will always be parallel to the mirror line and parallel to the other side that's been reflected.

So yes, we'll always create a larger rectangle.

Aisha says, "We've reflected one polygon in a line of symmetry.

I wonder if we could reflect a pattern involving different polygons," she says.

And Sam says, "Maybe some of those polygons could be dissected or cut in half by the mirror line like we've been looking at already." Let's have a look.

Ooh, look at that pattern.

So Aisha's drawn this for Sam to reflect.

What do you notice about it? Sam says, "I can see triangles that have been dissected by the mirror line cut in half." She says, "I'll draw the reflection of these triangles first." So she might think about plotting the position of the vertex and joining them up.

And then she create those two triangles.

Now what else can she see? She says, "The other polygons in this pattern are not dissected by the mirror line.

I can reflect each polygon by counting how far away it is from the mirror line." Or she might have thought about the vertices as well.

So that square was a whole square away from the mirror line that is a square as well.

But one of its vertices was touching that vertex, the outer vertex of the other square.

And then she can also complete the other square because it had one vertex touching that square and one vertex touching the triangle.

So there we go.

She's successfully reflected the shape.

And it's time for you to do some practise.

You are going to explore the different shapes that you can make when you reflect a triangle that has a side that touches the mirror line.

We found lots of different shapes.

Can you find any more? And in question two, you're going to draw as many examples as you can on squared paper to show why each statement may be true or false.

And you've got three statements there to investigate.

And in question three, you're going to reflect this pattern in the line of symmetry.

And then can you design your own symmetrical pattern using different polygons? Pause the video, have a go at those three questions.

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

How did you get on? So here are some of the shapes that you can make when you reflect a triangle that has a side that is touching the line of symmetry.

What shapes have we created? Well, we've got some kites there, haven't we? The first two on the left hand side are kites, and the second one in on the bottom is a kite as well.

Sometimes kites have two sides that make a point inwards pointing towards the other vertex.

They look a bit like an arrowhead.

Some people call them a delta and they can be called an inverted kite.

We can also create another triangle.

We can create a square and we can create a rhombus.

And rhombus is a parallelogram as well.

So we can create different quadrilaterals and larger triangles.

Question two, you are investigating the three statements.

So the first one said, if I reflect a shape that is touching the mirror line, the number of sides always doubles.

Hmm, that's false.

Let's have a look at a couple.

So this shape had four sides before the reflection.

It was a trapezium and the whole shape after we reflected it.

If we think about the outside of the shape has six sides.

This shape had three sides before we reflected it.

It was a triangle with one side touching the mirror line.

The overall shape that we've created still has three sides.

So the number of sides does not always double when you reflect a shape with one side touching the mirror line.

The second statement said, if I draw a shape with three sides then reflected, I could end up with a square.

Well, this can be true if you choose the right triangle to start with.

It has to be a right angled isosceles triangle so that the sides that we reflect are the two sides that are the same length.

And the angle reflected is a right angle.

And the third statement said, I can draw a quadrilateral that makes a hexagon when I reflect it.

And this can be true.

And the example we've got here is a trapezium.

And when we reflected it, it became a hexagon.

In question three, you were reflecting the pattern that we'd given you and then designing your own symmetrical pattern.

So here we could see a triangle that had been cut in half or dissected by the mirror line and another one there.

And then we've got a square that sits next to the triangle.

We've got a square sitting on the end.

You might even have seen a longer rectangle in the middle there as well.

And then that final square, we might have wanted to plot a couple of vertices here.

And if we'd done that, we'd have correctly positioned it here in the reflection.

Well done if you got that right, there was lots to think about there wasn't there.

And you could have designed your own symmetrical patterns using polygons.

And it might have been something like this.

And the reflection of our rectangle, our triangle to create a square.

It was a right angled isosceles triangle, another right angled triangle on the side of what is now a square, and then our two smaller squares as well.

I hope you enjoyed exploring symmetry with different polygons.

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

We've been reflecting polygons that are dissected by the line of symmetry cut in half.

What have we learned about today? We've learned that when you reflect a shape, each vertex will be the same distance from the line of symmetry.

And that's a really useful strategy to remember to help you when you are reflecting shapes, you can reflect a shape by counting the position of each vertex, making a mark, and then joining the marks with straight lines.

And when you reflect a polygon that has a side touching the mirror line, you can sometimes create a new shape.

I hope you've enjoyed exploring more symmetry today.

Thank you for your hard work and I hope I get to work with you again soon.

Bye-bye.