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 looking at reflecting shaded squares and polygons in a diagonal line of symmetry.

You might have been exploring symmetry in vertical and horizontal lines of symmetry or mirror lines, And today, we're going to look at diagonal lines, ones that aren't vertical or horizontal.

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

We've got lots of key words in our lesson today and a couple of phrases, so we've got line of symmetry, mirror line, reflect and reflection.

They may be words we are familiar with but let's just give them a practise and then look at what they mean.

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

So my turn line of symmetry.

Your turn.

My turn, mirror line.

Your turn.

My turn, reflect.

Your turn.

My turn, reflection.

Your turn.

Well done.

Let's check the meanings of those words, they are going to be really useful to us today.

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

And can you see on the heart, there's a dotted line, if you folded that heart on the dotted line, the line of symmetry, both the halves would match exactly.

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

Sometimes we check symmetry by putting a mirror on that line of symmetry or that mirror line to check that when the mirror is there, the shape looks exactly the same as when we take the mirror away.

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

And the reflection of a shape is called the mirror image of the shape, it's been flipped over that mirror line, it's the same shape, it's the same size, it's the same distance from the line of symmetry, but it's been flipped over.

Look out for those words as you go through today's lesson.

So there are two parts to our lesson today, we're going to reflect shaded squares in a diagonal mirror line, and we're going to reflect polygons in a diagonal line of symmetry.

So let's make a start on part one.

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

Jacob and Sofia are going to play a reflection game.

Jacob says, "I will shade a square on a grid.

"You need to reflect it in the line of symmetry "or the mirror line." Sofia 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." So Jacob shades his first square for Sofia to reflect.

Ha, Sofia's got a strategy.

She says, "Your square is the fourth square "from the line of symmetry.

"I will shade the fourth square from the line of symmetry "on this side." So she's counted those squares and she's shaded in her square.

"Well done, Sofia," says Jacob, she's put it in the right place.

Ooh, Jacob shades two squares on a new grid with a horizontal line of symmetry.

What would your strategy be here? What would you be looking at? Well, Sofia says, "The first square is one square away "from touching the line of symmetry." So she's drawn it in.

The second square is two squares away from touching the line of symmetry but it's in that same sort of column, isn't it? So there we are.

And Jacob says, "Well done, Sofia, this is a bit easy for you." And Sofia says, "I have practised reflecting "in horizontal and vertical lines of symmetry before." So she's good at this, she's been practising.

Jacob says, "Maybe I could try using a diagonal line of symmetry "to make this game more difficult." Let's have a look.

Sofia says, "I'm up for the challenge." Ooh, so Jacob tries a new grid with a diagonal line of symmetry.

Can you see that it's cutting the squares in half? So it's a little bit more challenging to count this time.

Let's see what Sofia's going to do.

She says, "One vertex of your square "is touching the line of symmetry.

"That means one vertex of my square "should be touching the line of symmetry too." I think she's got it right, hasn't she? "Spot on," says Jacob.

Jacob shades another square for Sofia to reflect.

Can you think where it's going to go? Sofia says, "Your second square "is next to the first square you shaded." She's right, it is.

"So I will shade the square "next to the first square I shaded." Is she right? Jacob says, "I'm not sure that's correct." I wonder how we could check.

Can you think of a checking strategy? Oh, Sofia says, "I could place a mirror on the line of symmetry, "if my reflection is correct, "the shaded squares I see in the mirror will be the same "as the squares that you shaded." So she's going to put a mirror along that line of symmetry or mirror line.

Oh, did you see what happened? That's what Jacob drew and then Sofia drew and that's what we see in the mirror.

Jacob says, "The image in the mirror "does not match the squares I shaded." Now that Sofia has used the mirror to check, she can try again to reflect Jacob's shaded square.

Can you think where it needs to go? She says, "I know that this square should not be shaded, "so which one should be?" She says, "I know that the square I shade "needs to be next to the first square I shaded." So can you see there's really only one possibility because it can't be touching the mirror line and it's got to be joined by a whole side to the square that she's shaded already.

So she says, "It must be this one." "Good thinking, Sofia, you are right." And this time if we put a mirror along the line of symmetry, we would see exactly the same image with the mirror there and with the mirror removed.

Sofia says, "I've noticed that the first reflection "is one square across and one square down." So can you see those arrows showing that the square's gone one square across and one square down.

And the second reflection is two squares across and two squares down.

And there are the arrows to show it as well.

I wonder if that's a strategy we can use.

Jacob says, "Good thinking, Sofia, you are right." Jacob shades another square for Sofia to reflect.

Can you think where this one's going to go before Sofia has a go? You might want to pause and have a think.

Sofia says, "Your shaded square is five squares across "from the line of symmetry.

"That means I need to count five squares across "and five squares down to shade the reflection." So that square is five squares in a row across, and when we flip it, it will be five squares down on the other side of the mirror line.

So there it is.

"Great reflecting, Sofia." That's a really good strategy, isn't it? That's one to remember from when you are doing your tasks.

Oh, indeed, you can check using it now.

So which image shows a reflection? Think about Sofia's strategy for counting the squares along and down or up and across.

And decide which one of these images shows a reflection.

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

Which one did you think it was? It was C, wasn't it? Three squares across and three squares down.

And if we look on the other ones; A was three squares across and three squares down, and so was B, but they were put in different places.

So the arrows mark where those shaded squares should be to make those into reflections as well.

Sofia says, "I would like to shade some squares "for you to reflect this time." She says, "I'm also going to move the line of symmetry." I wonder where she's going to move it to.

Jacob says, "Let's take turns to shade and then reflect." We will build up a symmetrical pattern on our grid.

Ah, so this time our diagonal mirror line or line of symmetry is going the other way.

Sofia shades a square for Jacob to reflect.

He says, "Your shaded square is the fourth square away "from the line of symmetry." Ah, he's gone down to find his four squares, hasn't he? He says, "That means I need to count four squares down "and four squares across to shade the reflection." There it is.

"You are spot on, says Sofia, "well done." He says, "I've noticed I could also count the squares "the other way round." Is that how you saw it? Is how I saw it, I think.

I could count four squares across and then four squares down to shade the reflection.

So the square obviously is in the same place, we've just thought about it in a slightly different way.

"That's another way to reflect my square, "good thinking," says Sofia.

Now Jacob shades a square for Sofia to reflect.

She says, "Your shaded square is the second square down "from the line of symmetry.

"That means I need to count two squares up "and two squares across to shade the reflection." That's right.

You could also look at it as being half a square away from the mirror line, so half a square away from the mirror line on the other side.

That's a different way of looking at it.

"Excellent reflecting," says Jacob.

Jacob and Sofia continue to shade and reflect squares to build up their symmetrical pattern.

Have a look as we go through this sequence and I'll pause between the original square and the reflection for you to predict.

So where do you think that one's going to go? It's touching the mirror line, isn't it? So there we go, the vertex is touching on the other side of the mirror line.

So let's look at the next one.

So we could count the squares up and across, but look, it's touching one of the squares that's already there, isn't it? So can we find the reflection of the square that was already there and then join it by a vertex? We could look to do that as well, couldn't we? Or we could count how many squares away it is on the diagonal from the mirror line, so it's one, and then it gets to the square that's on the mirror line, so we leave one square and then draw it, so it's going to go there.

Lots of different ways that we could think about how to reflect these squares across the line of symmetry.

And there's another one, how could you think about that one? Well, it sort of makes three in a row, doesn't it? So we need to add one to make three in a row but it's also one, two, three, four down to the bottom corner and four across.

And one more going in there, where's that one going in? Well, we could look at the grid itself, it's one in from the corner, isn't it? It also makes a little L shape.

So it's going to make a sort of inverted L shape on the other side.

And Sofia says, "I can place a mirror on the line of symmetry "to check that our pattern is symmetrical." So when she puts the mirror there, we shouldn't see any change to the pattern.

And we don't, do we? Jacob and Sofia know that their pattern is symmetrical because the image they can see in the mirror matches the they have shaded on their grid.

Time to check your understanding, which image shows a reflection? Try to count the position of each shaded square first and then check by using a mirror.

So pause the video, have a go, and when you are ready for some feedback, press play.

How did you get on? Which one shows a reflection? It's A this time, isn't it? Did you count the squares to the mirror line across and down or up and across? And did you check with a mirror? So what would B and C look like if they showed a reflection? Let's change the images.

Ah, there we go, now you can imagine putting a mirror on that line of symmetry and the image would be the same whether the mirror was there or the mirror was taken away.

Time for you to do some practise.

For question one, you're going to reflect the shaded squares in the line of symmetry.

And for question two, you're going to shade more squares on each side of the line of symmetry to make a symmetrical pattern.

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 these are the squares you should have shaded to complete the reflection.

So our first square, our second square, and our third square.

And you might have counted one, two, three squares across to reach the mirror line and three squares down.

And then we can see that all those squares are going to be in a line, and there are the completed patterns.

So did you count across remembering Sofia's strategy? It worked really well, didn't it? I hope it helped you to complete those symmetrical patterns.

And you could have shaded these squares to make a symmetrical pattern, can you see, we've outlined them in some purple there on the first one and then on the second one and then on the third one, and we've now created three symmetrical patterns.

Jacob said, "I shaded other squares too "but I made sure that I always reflected the square I shaded "in the line of symmetry." He says, "Did you try this as well?" Let's have a look at a couple of his.

Ah, so he did the blue ones that are two squares up and two squares across from the mirror line.

And this one here, which is one, two, three, four, five squares across and five squares up, or five squares across and five squares down whichever way you looked at it.

I hope you had fun making those symmetrical patterns.

So on into the second part of our lesson and we're going to reflect polygons in a diagonal line of symmetry.

Sofia says, "I wonder if we could play the same game "but by drawing shapes on dotted paper this time." Jacob 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 Jacob draws a shape for Sofia to reflect first.

Can you predict where the reflection is going to be? Sofia says, "This vertex is three squares across "from the mirror line or three dots.

"I need to reflect this vertex "and then join the points with straight lines." So she's plotted the position of the vertex on the grid, and now using a ruler, she can complete the shape.

There we go, what have they made? Jacob says, "You reflected my shape perfectly, "we have created a square." Jacob draws another shape for severe to reflect.

She says, "I need to reflect each vertex again." So she's counted three dots across, three dots down.

Here, she's counted two dots across and two dots down.

And for the final one, she's going to count four dots across and four dots down.

So now she's got her three vertices and she can join them up.

She says, "Counting the squares "helps me to mark each vertex, "now I can join them with straight lines." And she's successfully reflected the shape, it's another really good strategy to remember from Sofia.

And Jacob says, "Great reflection, we've created an octagon." It's an irregular octagon, isn't it? But it does have eight sides and lots of right angles.

Jacob changes the line of symmetry and draws another shape for severe to reflect.

She says, "I need to reflect each vertex." So she's looked at this vertex, it's three dots along and three dots down, so she can plot a point.

And the other one is three dots along and three dots down as well, or three dots down and three dots along, depends which way you looked at it.

"Counting the squares helps me to mark each vertex, "now I can join them with straight lines." Now I know there aren't actually any squares on there but if you imagine the dots join together to create a squared grid, each of those dots would be the vertices of those squares, so we can think about it as a squared grid of dots.

Jacob says, "Good work again, Sofia, "we have created a hexagon." Time to check your understanding.

Is this statement true or false? When you reflect this shape, you will create a triangle.

True or false? And can you explain why? Pause the video, have a go, and when you're ready for some feedback, press play.

What did you think? It's true, isn't it? Start by reflecting the vertex, then join them with straight lines, and you can see that this shape forms a triangle when it is reflected.

So we've gone all the way across to the mirror line, the same number of dots down to plot our point and now we can join it up with the remainder of the shape, and we've created a larger triangle.

Can you see? It's a right angle triangle.

And it's a right angled isosceles triangle because the sides that we've reflected must be the same length as the side that we started with.

Time for you to do some more practise.

Question one, you're going to reflect each shape in the diagonal line of symmetry, and can you name each polygon that's been created? And for question two, how many different quadrilaterals can you create by reflecting a shape in a diagonal line of symmetry? And Jacob says, "I've shown you how to create a square.

"How could you create a rhombus, a kite, "a rectangle, or a trapezium?" Pause the video, have a go at creating some reflected polygons, and when you're ready for some feedback, press play.

How did you get on? So for question one, you were given some shapes to reflect.

So the first one you reflected created a square, the second one created an octagon.

The next one created a hexagon.

And then onto the bottom row, we created another octagon, a hexagon, and finally a rectangle.

Did you use Sofia's strategy of plotting the vertices to make sure that you reflected your shapes accurately? And in question two, you are going to choose the shapes that you reflected.

So could you create those shapes that Jacob challenged you to? He says, "This is how I created some different quadrilaterals.

"Did you find any different ways to create these shapes?" So he has created a square, a rhombus, a kite, another kite, a trapezium, another trapezium, and a rectangle.

And just something to remember, that some 2D shapes can have more than one name.

For example, the square that Jacob drew could also be described as a rectangle because it has four rectangles, a kite because it has two pairs of adjacent sides that are equal in length, and a thrombus because it has four sides the same length and two pairs of opposite angles that are equal.

I hope you enjoyed creating all those shapes and we've come to the end of our lesson.

We've been exploring diagonal lines of symmetry.

So what have we been thinking about learning about today? Well, we've learned that a line of symmetry does not have to be vertical or horizontal, you can reflect shapes on a diagonal line of symmetry.

You can reflect a shape by counting the position of each vertex and making a mark, then joining the marks with straight lines, and that's a really good strategy to remember.

And each vertex of a shape will be the same distance from the line of symmetry when this is reflected.

I hope you've enjoyed reflecting shapes and exploring diagonal lines of symmetry.

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

Bye-bye.