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 composing symmetrical shapes from two identical shapes.

So identical means exactly the same.

So we're going to be using two shapes the same to see if we can create symmetrical shapes.

Let's have a look at what's in this lesson.

We've got three key words, well, two in a phrase, symmetrical, line of symmetry and identical.

So let's just rehearse those words and then look at what they mean.

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

Are you ready? My turn, symmetrical.

Your turn.

My turn, line of symmetry.

Your turn.

My turn, identical.

Your turn.

Well done.

Do you know what all those words mean? Let's check their definitions 'cause they're gonna be really useful to us in our lesson today.

When a shape, pattern or image has two halves that match exactly when folded, it can be described as symmetrical and we've got a butterfly there.

You might have seen how this is created.

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

And we often show the line of symmetry with a dotted line like we have on the butterfly and on that heart shape.

And two shapes that are exactly the same can be described as identical.

So look out for those words as we go through our lesson today.

There are two parts to our lesson.

In the first part, we're going to be exploring symmetry using two identical triangles.

And in the second part we're going to use two identical quadrilaterals.

So let's make a start on part one.

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

Izzy and Alex have been making cards for their friends.

That's a nice idea.

Can you see that they've used that trick of folding the paper in half, cutting out a shape, and then when you open it out, it is symmetrical because you cut the two halves at the same time.

So we've made a heart and a star.

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

And you can see it there marked with a dotted line on those two shapes.

And Alex says, we created these symmetrical shapes by folding and cutting.

Izzy says, "I wonder if there are other ways of creating symmetrical shapes." So Alex and Izzy want to create their own symmetrical shapes.

Alex says, "If both sides of a symmetrical shape are the same, maybe we could use two shapes to help us." "Good idea" says Izzy, We should make sure that the two shapes are identical.

They're exactly the same, otherwise it won't be symmetrical, will it? They've got two triangles there, two isosceles triangles, two sides the same and one side different, two angles the same, and one angle different.

Time to check your understanding.

What shapes do you think Izzy and Alex could create by joining these two identical triangles? And Izzy says, "You could cut out some triangles of your own to explore this." Pause the video, have a go.

When you're ready for some feedback, press play.

How did you get on? Here are some that we created.

Did you create those shapes? Did you manage to create your shapes by lining up a whole side against another whole side? So Izzy and Alex want to create their own symmetrical shapes.

Were all of those shapes that we created symmetrical.

Let's have a think.

Alex says we could join the isosceles triangles like this to create a quadrilateral.

There we go.

We have created a quadrilateral.

"Is this shape symmetrical?" Says Izzy, what do you think? Can you think where you would draw a mirror line or where you could put a mirror so that the shape you saw in the mirror was exactly the same as the shape you saw without the mirror? They do both think this shape is symmetrical.

And they can explain why.

Alex says, "If I folded this shape in half, both parts would match up exactly." Let's see.

That's right.

So he's folded the right part over the left part and they match exactly.

So there is his line that he folded.

So his line of symmetry or his mirror line.

And Izzy says, "If I place a mirror here, I can see that the image in the mirror matches the shape." And we haven't got a real mirror, but we can show what it would look like.

So with our mirror, the reflection would be exactly the same as the shape we could see.

So their shape is symmetrical and they found two ways to show that they're going to join them to make a different shape.

Ah, what do you think they're going to find about this shape? Alex says, "I know that this shape is called a thrombus." Do you know what a rhombus is? It's a shape where all four sides of the same length, but there are two pairs of equal angles.

Sometimes I like to think of a rhombus as a square that's been squashed.

If we straightened that shape up and gave it four right angles, it would be a square.

'cause all the sides are the same length, but because we've squashed it, it's now a rhombus.

Izzy says, "Let's check if it's symmetrical." What two things did they do last time to show that the other shape was symmetrical? They folded and they used a mirror.

Can you think where they'd fold and where they'd put the mirror this time? Okay, Alex says, "If I fold this shape on the line I've drawn." So that's the line where the two triangles meet.

Both parts would match up exactly.

Let's see, there we go.

Folded looks just like one of the shapes, doesn't it? Because they are absolutely on top of each other.

So there's our dotted line, our mirror line, and Izzy says, "If I place a mirror on your line, I can see that the image in the mirror matches the shape." So there we go.

It's not a real mirror, but I'm sure if you had a mirror you'd be able to see that as well.

So again, they've shown that this shape is symmetrical and they've shown it in two different ways.

But Izzy and Alex have found two lines of symmetry on this rhombus.

Alex says, "I've noticed that I could also fold this shape on this line and both parts would match up exactly.

"Your right," says Izzy, "I can place my mirror there too to show that this is a line of symmetry." So that's her mirror.

So that's a line of symmetry.

And if Alex did his folding again the two halves of the shape would be exactly the same.

So this rhombus has two lines of symmetry.

Izzy and Alex can join their isosceles triangles in a different way.

So that was that third shape that you made.

If we join them like this, we make a parallelogram.

You remember parallelograms have two pairs of parallel sides.

"But is this shape symmetrical?" Says Izzy, what do you think? Alex says, "If I fold this shape in half, the parts do not match up exactly." Oh, they don't do they? We can see that.

And Izzy says, "If I place the mirror here, I can see that the image in the mirror does not match the shape.

Well, it's the same, but it's not in the same orientation as the original one.

So we've actually created the shape we've been looking at first, but it's not the same as our original shape.

So this shape is not symmetrical even though it's made of two identical triangles.

Something to watch out for.

Sometimes shapes look like the sorts of shapes we see all the time and we think that they will be symmetrical.

But it's worth thinking really carefully.

If I fold it, will the two halves match up? And if I put a mirror line there, will it look the same? Time to check your understanding.

So there are some descriptions and some shapes.

Can you match the shapes to their descriptions? Pause the video, have a go.

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

How did you get on? So let's look at that top description.

This shape is made from two identical triangles.

It has one line of symmetry.

So remember it's only got one line of symmetry and it's made from two identical triangles.

So that matches with that bottom shape, the one we've looked at already.

So the second description says this shape is made from two identical triangles.

It has two lines of symmetry.

Well that was the one we looked at this way where we joined up our triangles on their shortest side.

So it has two lines of symmetry.

Can you picture where those lines of symmetry are? You might remember them from when we looked at the shape in the first part of this lesson.

The third description says this shape is made from two identical triangles.

It has no lines of symmetry.

That's right.

That was parallelogram that we'd just been exploring.

And the final description says this shape is not made from two identical triangles.

I think it does have a line of symmetry, but it isn't made from two identical triangles.

Time for you to use in practise using two identically Isosceles triangles create a shape to match each description.

So a shape with no lines of symmetry, a shape with one line of symmetry and a shape with more than one line of symmetry.

And in question two, using two identical scale or equilateral triangles, can you create shapes to match each description? Remember scale triangles were ones where all the sides of different lengths and all the angles are different.

And equilateral triangles are ones where all sides are the same length and all the angles are the same.

And again, can you create shapes with no lines of symmetry, one line of symmetry and more than one line of symmetry.

And what do you notice about the shapes that you've created? Pause the video, have a go.

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

How did you get on? So in question one, you might have created shapes like these when you used two identical isosceles triangles.

So that was our parallelogram with no lines of symmetry.

That was our quadrilateral with one line of symmetry.

And that was our rhombus that had two lines of symmetry.

Ah, that's an interesting one, isn't it? It's another isosceles triangle, a different one that has no lines of symmetry, that has one line of symmetry.

And those two create a square.

And that also has more than one line of symmetry.

What about when you use the equilateral triangles? Ah, it's not possible to make a shape that belongs in either of these columns using two identical equilateral triangles.

There's only one shape you can make and it has more than one line of symmetry.

Ah, did you spot that? That's really interesting, isn't it? Equilateral triangles have all their sides the same length.

So there's really only one way you can join them together and it makes a shape that's a rhombus and it has more than one line of symmetry.

What about the scale triangles? Lots of different possibilities here.

'cause you can make an awful lot of different triangles.

So no lines of symmetry.

One line of symmetry.

More than one line of symmetry.

Our scale triangle had a right angle, so it was a right angled scale triangle.

And there's another possibility.

No lines of symmetry, it's a parallelogram, again.

Also interesting shapes there.

Or you might come across the names of these shapes in a lesson at some point.

And it's not always possible to create a shape that has more than one line of symmetry from two identical scaly triangles.

When they have a right angle, then it is, but it isn't always if they are not right angle scaly triangles.

I hope you've enjoyed exploring shapes with triangles.

Time to go into the second part of our lesson.

This time we're going to explore symmetry using two identical quadrilaterals.

Alex and Izzy have explored the different symmetrical shapes that can be created with two identical triangles.

Alex says, "I wonder what we could create with two identical quadrilaterals." Izzy says, "What quadrilaterals could we use?" So they know the names of these quadrilaterals.

Do you know the names of these as well? You might want to pause before we share them.

So a square, a rectangle.

And remember, a square is a special sort of rectangle because it has four rectangles.

A parallelogram, two pairs of parallel sides, a trapezium which has one pair of parallel sides.

And this one, we've been looking at this one in part one of our lesson is a rhombus.

That's right, four sides the same length and two pairs of opposite angles that are equal.

Alex says, "I would like to start with the trapezium." So time for you to have an explore.

What shapes could Alex and Izzy create by joining these two identical trapeziums? At least two vertices of each shape should be touching.

So that means we are lining them up along the lines.

And Izzy says, "You could cut out some trapezium of your own to explore this." Pause the video, have a go.

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

How did you get on? So you could have made this shape, this shape, this shape or this shape.

Under what you called those shapes? Could you name them all? Let's see how we can use those to think about symmetry.

Alex and Izzy will explore whether the shapes they make from two identical quadrilaterals are symmetrical.

So they're going to use those trapeziums again.

So this is one shape they've created.

Alex says we could join the trapeziums like this to create a hexagon.

It's a very irregular hexagon, isn't it? But is it symmetrical? That's Izzy's question.

Izzy and Alex both think that this shape is symmetrical and they can explain why.

Alex says, "If I folded this shape in half, both parts would match up exactly." So he is going to fold along that mirror line, that line of symmetry that he's put in.

And they do.

They match up exactly.

And as he says, "If place a mirror here, I can see that the image in the mirror matches the shape." So they've shown in two ways that this shape does have a line of symmetry.

They're going to join them in a different way to make a new shape.

Ah, what about this one? "It's another hexagon," says Alex.

Is this shape symmetrical? What do you think? They think it is symmetrical and they've put in a dotted line to show the line of symmetry.

Alex says, "If I folded this shape in half, both parts would match up exactly.

Let's see.

That's right, they do.

And what's is he going to do? That's right.

She says if I place a mirror here, I can see that the image in the mirror matches the shape.

Well done, Izzy.

So again, they've shown in two ways that this shape has a line of symmetry.

Oh, but Alex has noticed that he could also fold the shape on this line and both parts would match up.

"Your right," says Izzy "and I can place my mirror there too to show that there is a line of symmetry." There's her mirror.

So Izzy and Alex have found two lines of symmetry on this hexagon.

They're going to join it in another way to make a new shape.

Haha, this one.

What do you notice about this? Ah, what sort of shape have they made this time? We've explored one of these before.

Alex says, "I know this shape is called a parallelogram." "Let's check if it's symmetrical," says Izzy.

Do you think it will be? We looked at a parallelogram before, didn't we? Alex says, "If I fold this shape on either of these lines, the parts do not match up exactly." So those are not lines of symmetry.

And Izzy says, "If I placed a mirror on either of these lines, the image in the mirror would not match the shape." So those are not lines of symmetry.

This parallelogram is not symmetrical, even though it is made from two identical trapeziums. Time to check your understanding.

Again, can you match the descriptions to the shapes? Pause the video.

Have a go.

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

How did you get on? So the top description says this shape is made from two identical trapeziums. It has one line of symmetry.

That's right.

It was that shape, wasn't it? That hexagon, irregular hexagon.

The next one says, this shape is made from two identical trapeziums. It has two lines of symmetry.

Which one was that? That's right.

It was the other hexagon, wasn't it? And that had two lines of symmetry.

The way we've got the shape oriented, one is vertical and one is horizontal.

The third description says this shape is made from two identical trapeziums. It has no lines of symmetry.

It was that parallelogram, wasn't it? Parallelograms that are not rectangle squares, don't have line of symmetry.

It's worth remembering that and realising that you can show that and demonstrate it in different ways.

And the bottom description says, this shape is not made from two identical trapeziums. Well, there we go.

It is made from two trapeziums, but they're not identical.

One's a lot smaller than the other, isn't it? That shape does have a line of symmetry.

The way we've drawn it, it would have a line of symmetry that was horizontal.

And time for you to do some practise.

So for question one, using two identical quadrilaterals, create a shape to match each description.

What happens when you use squares, rectangles, parallelograms, or rhombuses? And remember that at least two vertices of the shape should be touching.

So we're joining those shapes up along a side that matches.

And in question two, read each sentence carefully and decide if it is always true, sometimes true or never true.

And draw some shapes that help you to explain why.

Pause the video, have a go at your tasks.

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

How did you get on? So in question one, you were using identical quadrilateral.

So let's have a look with a square.

Ah, we can't make a shape with no lines of symmetry by joining two squares together.

And we can't even make a shape with one line of symmetry only joining two squares together.

But we can make a shape with more than one line of symmetry.

But that's the only shape we can make.

What about our rectangle that isn't a square? No lines of symmetry.

We can't make a shape with just one line of symmetry by joining two rectangles together.

But we can make two different shapes with more than one line of symmetry.

What about parallelograms? We know they don't have a line of symmetry, do they? So we can join two together and make a bigger parallelogram.

And it still won't have any lines of symmetry.

But we can join them together to make a shape that has one line of symmetry.

But we can't join them together to make shapes with more than one line of symmetry, not with this sort of parallelogram.

And what about the rhombus? Well, two rhombuses can join together to make another parallelogram with unequal sides.

And that will have no lines of symmetry.

We can join the two thrombus together to make a shape with one line of symmetry.

And we can't join them together to make a shape with more than one line of symmetry.

I hope you discovered all of that as well.

And for question two, you are reading each sentence carefully and deciding if it is always true, sometimes true or never true.

So joining two identical trapeziums will create a symmetrical shape.

Well, that is sometimes true.

The parallelogram though was not symmetrical.

Joining two identical rectangles will create a symmetrical shape.

Again, it's sometimes true.

When you join the same length sides together, all the shapes made from two identical rectangles are symmetrical.

If you join a shorter side to a longer side, it's possible to create a shape with no lines of symmetry.

It's about joining two identical parallelograms to create a symmetrical shape.

Well, this is sometimes true, but the larger parallelogram shape is not symmetrical.

Joining two identical squares will create a symmetrical shape.

Yes, this is always true.

All shapes made from two identical squares are symmetrical.

There's only one way we can join them because squares have all sides the same length.

And joining two identical rhombus will create a symmetrical shape.

Sometimes, remember that parallelogram shape is not symmetrical.

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

You've worked really hard.

Well done.

We've been exploring symmetry by joining two identical shapes.

What have we learned about? Well, we've learned that a shape is symmetrical when one half is a reflection of the other half.

This means that when you fold a shape on a line of symmetry, the two halves will match exactly.

And you can join two identical shapes together to create a new shape.

Sometimes the new shape will be symmetrical, but it is possible to create a shape with no lines of symmetry.

And we've got some examples here.

I hope you've enjoyed exploring identical shapes and joining them together and looking at the symmetry of the shape you've created.

And I hope I get to work with you in another lesson soon.

Bye-Bye.