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 using folding to investigate lines of symmetry in 2D shapes.

Hopefully, you've been thinking about symmetry recently.

And you know what? 2D shapes are two dimensional shapes.

They are flat shapes.

Let's have a look at what's going to be in our lesson.

We've got a keyword and a key phrase as well.

So our keyword is kite and our phrase is line of symmetry.

Let's practise saying those, and then we'll have a look at what they mean.

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

My turn, kite.

Your turn.

My turn, line of symmetry.

Your turn.

Excellent.

I wonder if you've come across a kite before.

You might have flown a kite in a park or on the beach while you're out for a walk.

It's not that sort of kite we're looking at, but you'll probably see why the kites that we fly are called kites when we look at the shape.

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

So, a kite is a quadrilateral with two pairs of adjacent, equal sides, or let's just think about what that means.

A quadrilateral is a shape with four sides, and adjacent means next door to each other.

So we can see that at the top of our kite, these two sides at the top are the same length, and these two sides at the bottom are also the same length.

So adjacent means next to each other.

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

And you can see that with the dotted line on this heart.

And that's gonna be really important to us in our lesson today.

And there are two parts in our lesson.

In the first part, we're going to be investigating the symmetrical properties of a kite.

And in the second part, we're going to be looking at the symmetrical properties of polygons.

So let's start exploring kites.

And we've got Sofia and ep helping in our lesson today.

ep is drawing and making different quadrilaterals.

Remember, quadrilaterals are four-sided shapes.

He says, "I know that these are all rectangles, and the first two shapes are also squares." Squares are special rectangles where they have four rectangles, but all four sides are the same length.

He says, "I know that these are trapeziums because they have one pair of parallel sides." Remember, parallel sides are the sides of the same distance apart all the time.

So one has a set of vertical parallel sides and the other one has a set of horizontal parallel sides.

And he says, "This shape is a parallelogram because it has two pairs of parallel sides." It's opposite sides are parallel to each other like the sides in rectangles and squares.

"That means," he says, "that the first three shapes I drew are also parallelograms because they have two sets of parallel sides as well." "And this," he says, "is a rhombus.

It's a type of parallelogram that has four equal sides," like a square that's been squashed.

He says, "I can draw these shapes, but I'm not sure what they're called." Can you think from what we've just looked at in our keywords? Sofia can help Andeep to name his quadrilaterals.

She says, "These are called kites.

I can draw more kites like this." Can you see that some of those kites might look like the sort of kite that you might see somebody flying in the park or on the beach on an ice breezy day? A kite has two pairs of sides that are equal in length, but these pairs are adjacent or next to each other rather than opposite each other as you would find in a rectangle.

So there are four sides and two of the pairs are the same length, but those pairs are next to each other.

They're adjacent.

So there we can see labelled a pair of adjacent, equal sides, same length, and the other pair of adjacent, equal sides.

And there you can see on our other kites, one pair of adjacent, equal sides and the other pair of adjacent, equal sides.

Time to check your understanding.

These are all quadrilaterals, but which shapes are also kites? And Sam's reminding you that kites have two pairs of adjacent, equal sides.

So pause the video, have a go.

And when you've identified all the kites, press play.

How did you get on? Well, this shape is a kite.

It has two pairs of adjacent, equal sides.

And there they are.

This one, the same.

This one's not a kite, is it? In fact, I don't think it's got any sides of the same length.

So it's just an irregular quadrilateral.

This side is a kite, two pairs of adjacent, equal sides.

This one isn't.

It's a parallelogram, isn't it? So it has opposite pairs of equal sides.

This one is a kite.

This one isn't a kite.

And this one is a kite.

This one is a parallelogram.

So it has opposite pairs of equal sides, not adjacent, equal sides.

I hope you found all five kites that were hidden on that slide.

Sofia and Andeep can investigate lines of symmetry by folding.

When you fold a shape on its line of symmetry, the two halves will match up exactly.

So Andeep asks, "Do kites have a line of symmetry?" What do you think? Sofia says, "Let's investigate." Good thinking, Sofia.

So here is a kite.

It's got two pairs of sides next door to each other that are equal.

Andeep says, "If we fold the kite this way," ah, both halves match up exactly." Can you see he's folded his kite down that vertical line in the middle? He says, "This is a line of symmetry." Sofia says, "If we fold the kite this way, ah, the parts do not match up.

So that is not a line of symmetry." This kite has one line of symmetry.

What about this one? Can you imagine how we're going to fold it? Andeep says, "If we fold the kite this way, both halves match up exactly.

This is a line of symmetry." And we've marked it with that dotted line again.

Sofia says, "If we fold the kite this way, oh, the parts do not match.

So that's not a line of symmetry." So this kite also has one line of symmetry.

What about this kite? It's not sitting on a horizontal or vertical line, is it? How could we fold it to show a line of symmetry? Andeep's found a way.

Well, can you picture where the line's going to be? That's right.

He's folded from the vertex between one pair of equal sides to the vertex between the other pair of equal sides, and both halves match up exactly.

So that is a line of symmetry.

But if we join the other two vertices and fold along that line, the parts do not match.

So that's not a line of symmetry.

So this kite also has one line of symmetry.

Time to check your understanding.

Sofia has tried to draw a line of symmetry on each kite, but she's made some mistakes.

Can you spot the mistakes? How could you help Sofia to find the lines of symmetry? Pause the video, have a think, and when you're ready for some feedback, press play.

How did you get on? So that was a line of symmetry, that was a line of symmetry, and that was a line of symmetry.

But what about the other shapes? They weren't, were they? If you folded along those lines, the two halves would not match.

You could remind Sofia that a line of symmetry should divide a shape into two parts that are the same.

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

If you folded on each of the lines that Sofia drew, some of the parts would not match, but we can correct them.

So there's a line of symmetry, there's a line of symmetry and there's a line of symmetry.

The lines of symmetry divide the shape into two parts that are exactly the same.

So all the kites that Sofia and Andeep have investigated have one line of symmetry.

So Andeep says, "Do you think a kite will always just have one line of symmetry?" Sofia says, "Maybe.

Let's check if there are any other kites we haven't investigated yet." So a kite always has two pairs of adjacent, equal sides.

And we can see our sides there marked in two different colours.

The two sides of the same colour are the same length.

Andeep says, "What if both pairs of adjacent, equal sides were the same length?" So let's see if we can change that kite.

Ah, there we are.

So we've still got adjacent pairs of sides that are the same length, but now all our sides are the same length.

What shape's that? Ah, Sofia says, "This kite is also a rhombus." So when a kite has two pairs of adjacent, equal sides that are the same length as each other, it can be described as both a kite and a rhombus.

So this kite, which is also a rhombus, has two lines of symmetry.

Sofia says, "I wonder if there are any other special cases like this." So there's our rule.

A kite always has two pairs of adjacent, equal sides.

Andeep says, "What if both pairs of adjacent, equal size were the same length and all four angles were right angles?" Can you picture what shape we're going to get? That's right.

Sofia says, "This kite is also a square because it has four equal sides and four right angles." "So this kite has two lines of symmetry as well," says Andeep.

Is he right? "No," says Sofia, "a square actually has four lines of symmetry." We could fold or put a mirror on lines that go halfway along each side to the other side.

So a square actually has four lines of symmetry.

Time to check your understanding.

So true or false, a kite can only have one line of symmetry.

Is it true? Is it false? And why? Pause the video and have a think.

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

What did you think? It's false, isn't it? When a kite is also a thrombus or a square, it will have more than one line of symmetry.

If a kite has two pairs of adjacent, equal sides, but those pairs of sides are not the same length as each other, then it will just have one line of symmetry.

But it's not always true.

Time for you to do some practise.

Cut out these kites and try to find the lines of symmetry by folding them.

And in question two, how many different kites can you draw? Can you mark the lines of symmetry on each kite? And Sofia's reminding you a kite should have two pairs of equal, adjacent sides, adjacent meaning next door to each other.

Pause the video, have a go at questions one and two.

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

How did you get on? So you could use folding to find these lines of symmetry.

So, most of them had one line of symmetry, but one of them was a rhombus, wasn't it? The two pairs of adjacent sides were actually equal to each other as well.

So that had two lines of symmetry.

I wonder what kites you drew for question two.

Here are some that we drew.

And we've marked on the lines of symmetry with the dotted lines.

Can you see, we found the kite that's also a square? So it has got two pairs of adjacent, equal sides, but all the sides are the same length and all the angles are right angles.

So that makes it also a square.

And a square has four lines of symmetry.

I hope you enjoyed exploring kites and their lines of symmetry.

And on into the second part of our lesson, this time we're going to be investigating the symmetrical properties of polygons, not just kites.

Andeep and Sofia have investigated the lines of symmetry that can be found in a kite.

Andeep says, "I wonder what we could find out about lines of symmetry if we look at other shapes?" Sofia says, "Let's investigate!" Ooh, look at all those shapes.

Andeep and Sofia know the names of these shapes.

Do you know the names of these shapes as well? You might want to pause here and have a little think before we name the shapes.

So what have we got? We've got an isosceles triangle.

It's also got a right angle.

So it's a right-angled isosceles triangle.

What's next? A rectangle, an equilateral triangle, 'cause all the sides are the same length.

What about the next one? It's got one pair of parallel sides, so it is a.

Well done, it's a trapezium, yes.

What about the next one? It's a pentagon.

Is it a regular pentagon? It isn't, is it? It's an irregular pentagon.

The next one, all four sides are the same length.

It's a square.

The next one, we've got six sides.

They're all the same length.

It's a hexagon, and it's a regular hexagon.

Next one is a circle.

And our last one, two pairs of parallel sides, it's a parallelogram.

So let's investigate the symmetrical properties of these shapes.

If you fold a shape on a line of symmetry, both parts will match exactly.

So this is a line of symmetry.

This is not a line of symmetry.

If we folded on that horizontal, dotted line, then the two parts would not match exactly.

"Could you fold on one of the diagonals to find a line of symmetry?" says Andeep.

So diagonals are where we join opposite vertices.

So there we go, there's a diagonal.

If you folded along this line, will the sides match? Or this one? No, they wouldn't, would they? Sofia says, "Neither of these lines is a line of symmetry." So this trapezium has one line of symmetry.

What about this? It was an isosceles triangle, wasn't it, with a right angle.

So, the vertical line down is not a line of symmetry.

If we folded there, the two sides would not match.

And the horizontal line isn't either.

So, has it got no lines of symmetry? Andeep says, "I wonder if it would help to rotate the shape to turn it around." Ah, now we've rotated the shape.

What can you see? Sofia says, "Now I can see this triangle has one line of symmetry." If we folded along that line, the two halves would match.

And Andeep says, "Now I can draw the line of symmetry on the triangle in its original position." Let's rotate it back again.

There we go.

And the line of symmetry goes there.

It goes from our one angle that's different to the middle of our one side that's different.

Remember, isosceles triangles have two equal sides and two equal angles.

And our line of symmetry joins the unequal angle to the middle of the unequal side.

But Sofia says, "This also shows that a line of symmetry does not always have to be horizontal or vertical." Remember, horizontal is straight across the flat line and vertical is a straight up and down line.

So lines of symmetry don't have to be just horizontal or vertical.

Time to check your understanding.

Which shape has a line of symmetry drawn correctly? Is it A, B, or C? Pause the video, have a think.

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

What did you think? It was A, wasn't it? Lines of symmetry don't have to be horizontal or vertical.

You could show a line of symmetry on shape B and C by drawing the lines here instead.

So there it is on B.

And on C, we've got those two.

I wonder if there are others for shape C as well.

Those are lines of symmetry though, on shape C.

Andeep and Sofia continue to explore lines of symmetry in different shapes.

So, "This is a line of symmetry," says Andeep, and, "This is a line of symmetry," says Sofia.

"Could you fold all of the diagonals to find the line of symmetry?" says Andeep.

Yes, this is a square, isn't it? So the diagonals are both lines of symmetry in a square because all four sides are the same length.

If we folded the shape along any of those lines, the two halves would match exactly.

So this square has four lines of symmetry.

What about the rectangle? This is a line of symmetry, and this is a line of symmetry.

If we folded along any of those lines, the shapes would match exactly.

Could you fold along one of the diagonals to find a line of symmetry? Would that work? Or that one? No, they're not lines of symmetry.

If you imagine folding your rectangle, you might be able to try this with a piece of paper.

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

So this rectangle has two lines of symmetry.

Just to check your understanding.

True or false? This is a line of symmetry.

What do you think and why? Pause the video, have a go, and when you're ready for some feedback, press play.

What did you think? It's false, isn't it? If you folded the shape on this line, the two parts would not match exactly.

You could use your own paper rectangle to explore this.

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

In question one, you're going to sort the shapes into the table.

Are there any shapes that cannot go into the table? And why do you think this is? And for question two, you're going to draw some more shapes of your own in each part of the table.

So there's an example of a shape that is not a quadrilateral.

It doesn't have four sides.

Pause the video, have a go at questions one and two.

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

How did you get on? Let's have a look at question one.

We were sorting the shapes into the table.

So the table asked us to sort into shapes that were quadrilaterals in the top row, not quadrilaterals in the bottom row.

And then in the first column, they had to have one line of symmetry.

And in the second column, they had to have more than one line of symmetry.

Let's look at D.

D is a trapezium, so it is a quadrilateral.

So it goes in the top row.

How many lines of symmetry does it have? Well, that trapezium has one line of symmetry, so it must go in the top left-hand box.

What about shape E? E is a square and it is a quadrilateral, and it has more than one line of symmetry.

So that is where the square goes.

And B, shape B went in there as well.

It's a rectangle, has more than one line of symmetry, and is a quadrilateral.

What about C? Ah, C is not a quadrilateral, it's a triangle.

But it's an isosceles triangle, so it has one line of symmetry.

What about A? A is a circle.

It's certainly not a quadrilateral, but it definitely has more than one line of symmetry.

And we can say the same for shapes G and H.

What about the ones that didn't fit into the table? Well, F and I didn't.

F was the irregular pentagon and I is the parallelogram, and they can't be placed in the table because they have no lines of symmetry.

One is a quadrilateral and one is not a quadrilateral, but neither of them have a line of symmetry.

They don't fit into our table.

And here are some shapes that you could have added.

So we've added a couple of quadrilaterals with one line of symmetry.

Do you notice what shapes they are? They're kites, aren't they? This shape is also a kite.

It has two pairs of adjacent, equal sides.

Sometimes people call this a delta, and sometimes you call it an inverted kite.

We added a rhombus into the quadrilateral with more than one line of symmetry.

We added a triangle and a pentagon into the not-a-quadrilateral, but they did have one line of symmetry.

And we added an octagon into the bottom right-hand box of our table because it's not a quadrilateral, but it has more than one line of symmetry.

I hope you enjoyed investigating all those shapes.

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

We've been investigating lines of symmetry in 2D shapes by folding.

What have we learned about today? Well, we've learned that when you fold a shape on a line of symmetry, the two halves will match exactly.

And it's helpful to try folding a shape in different ways when you're looking for lines of symmetry.

A line of symmetry is not always horizontal or vertical.

That's something to watch out for.

And some quadrilaterals, such as a parallelogram, have no lines of symmetry.

Others, such as some kites have one line of symmetry, and others such as a rectangle can have more than one line of symmetry.

I hope you've enjoyed exploring symmetry in 2D shapes and that you've been able to do some folding as part of your lesson.

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

Bye-bye.