# Lesson video

In progress...

Hi there, my name is Miss Darwish, and for today's maths lesson, we are going to be exploring missing lines of symmetry.

But before we get started, if I could just ask you for a favour, if you just want to take yourself to a nice quiet place, ready to start the lesson.

So the agenda for today's lesson is the following.

First of all, we're just going to recap on reflections, and then we're going to be looking at finding the mirror line between a few options, and then we're going to have a look at missing lines of reflection and how to find them.

And then at the end, of course, as always, there will be a quiz for you to do on today's learning.

So, before we start the lesson, you will need a sheet of paper or a notebook, pencil and a ruler.

So if you want to go and get those things, we can start the lesson.

Okay, let's start.

So reflections, in front of us, we have got a grid with some coordinates, and we've got two shapes, and one of the shape has been reflected onto the other.

Can you see that? Now, the only thing that's missing is what? We know these shapes are reflections of each other because we've been told that.

But, what's missing is a mirror line, or a line of reflection.

So we can call it a line of reflection or we could also call it a mirror line, and we can call it a mirror line because if I was to grab a mirror and place it on that line, it would show us what the shape would look like if it's reflected.

Okay, so, is this the correct mirror line, now that I've just added a mirror line? Is it correct? Yes or no, what do you think? Why is it right? Why is it wrong? What do you think? Okay.

Now, is this correct? This one or this one's the correct mirror line, or neither, and why? What about this one? Yeah, that one looks about right.

Why does that mirror line look right? If we look at the first mirror line, it's not really halfway between both shapes, is it? And if we choose one of the points on that shape, and we were to reflect it, it wouldn't reflect the exact same place.

And we wouldn't get that here either.

But if we have a look at this, if you choose one of the points, we can see that there's four squares away from the mirror line, or the line of reflection, and also where it's been reflected is also four squares away.

Can you see that? Okay, so this is the correct mirror line that we're missing.

Okay, below, two of the shapes are reflected.

Okay, again, what's missing? All, so the mirror line's missing, or we can also say the line of reflection.

We can call it the line of reflection or the mirror line.

So where do you think it goes? Have a think.

Maybe you want to grab your ruler and place it on the screen, as to where you think it might go, the line of reflection or the mirror line.

Okay.

Should we have a look together? I've given you three options now.

I'm not going to tell you the answer straight away.

So there's option A, option B and option C.

I wonder, was your ruler a placed on either A, B or C? Okay.

Let's go through each of the options.

So, let's have a look at A first of all.

The triangle has three vertices, correct? I've chosen just one of these, and I've marked it with a black X.

Can you see that? Okay.

So, this point is three squares away from mirror line A.

Can you count to three squares? Okay, good.

Now, it's reflected point, I've also marked with an X.

Is that three squares away from the mirror line? It's not three squares away from the mirror line.

So is A the mirror line? No, we don't think it's A.

So let's check the next one.

Let's check B.

Okay.

We check B.

Again, the first thing I did was point out we know a triangle has three vertices.

I'm just going to pick or choose one of those three.

So I have picked the same one as I did when I was checking A.

How many squares away is it from the mirror line? It's five squares away from the mirror line.

Well done.

And can you see where it's same reflective point is? I want you to put your finger there.

Have you found it? Okay.

Let's have a look.

So this point is five squares away from the mirror line, mirror line B.

It's reflective point is also five squares away from mirror line B.

What does that tell us? Could the line of reflection B, or mirror line B, be the correct one? Okay.

Let's check the other vertices just to be sure.

So we're going to pick another one, so that's another point.

This is also how many squares away from the mirror line? Five squares away from the mirror line.

Well done.

And can you find the same point on the other side? It's reflected point is also five squares away from the mirror line.

Well done.

Okay.

Let's have a look at the last one.

We're checking the last vertices.

How many squares away is it from the mirror line?? Can you count them for me? Three squares away.

Well done.

And it's reflective point is also three squares away from the mirror line.

So have we found our mirror line? We have on hopefully by line B is where you had your ruler.

If you didn't, then don't worry.

Now we know how to check now.

Okay.

Let's look at another example.

So, it says, where is the mirror line? I've given you two shapes.

The ones is a reflection of the other.

Where do you think the mirror line might go? I'm going to give you some thinking time.

Okay.

Should we go through it together now? Giving you some thinking time, maybe you got an idea as to where you might think the mirror line might go.

Let's have a look together.

So, step one, this is my method or my recipe of doing this.

So first of all, step one is to find one of the vertices.

Anyone.

It really doesn't matter which one you pick.

This is the one that I've chosen.

You might choose a different one.

So I've picked it.

Now, you've also got to find where would that point be when it's reflected on the shape? So we look at the reflected shape, and I want you to find the exact same point.

So I've marked both of them.

Okay? Now, step two.

Once I found both of my points, remember it has to be, they're not both random.

I pick one random point, any of the vertices, and then that exact same point on the shape.

I have to find where it is on the second shape.

Okay, on the reflected shape.

So once I've done that, step two is to count how many squares apart are they? Can you count them for me? Okay.

Hopefully you counted eight.

They are eight squares away from each other.

Can you see that? Can you guess what we might do next? Okay, so, we find the halfway point, and half of eight is equal to four, or we can say eight divided by two is equal to four.

And when I found half of it, I've marked it with an X.

Can you see that X? 'Cause I'm finding half way between both of the points and then what have I replaced it with? My line of reflection, or what else do we call it a line of reflection? A mirror line.

Well done.

So I've replaced it with my mirror line or my line of reflection.

Now let's just check.

So I'm going to look for that first point again, and I'm going to count one, two, three.

It is four squares away from the mirror line or the line of reflection.

Okay, so, now I'm going to count exactly the same.

How many squares away from the line of reflection to the reflective point? Four squares away as well.

Good.

Okay.

Let's have another look.

Different example now.

Where is the mirror line? I'm going to give you some thinking time.

Tell me where do you think it is? Okay.

What do you think? So, what was your step number one? What did you do first? Find a random vertice, one of the vertices of many.

Choose any one and then find its reflective point and try and find halfway, after we've counted how many squares.

Okay.

So, have I found the correct mirror line? Was that what you had as well? Okay.

All right, so we can say that this is halfway between both shapes, and both of the shapes, one is a reflection of the other shape.

Well done.

Okay.

Now things get a little bit trickier now.

Where is the mirror line? What do you notice? We've got a shape in the first quadrant, and a shape in the third quadrant.

Where do you think the mirror line might go, again? Just grab your ruler and place it somewhere.

Don't forget to count the squares.

Okay, let's have a look together.

So, what was asked at number one? Tell me.

Tell me what's step number one? Pick any of the vertices.

We've got three of them.

Pick any of them.

And then what do we do? On the reflected shape, I want you to find me right now, I want you to take your finger and point to where that reflective point is on the reflected shape.

Go.

Okay.

Let's see if you're right.

Were you right? Hopefully it's where your finger is.

Okay.

And then what's the next step that we do? What do we count? It's going to be a diagonal count.

Let's have a look.

How many did you count? Do you want to count them now? Let's count together, so one, two, three, four, five, six, seven.

Seven squares between both points.

So, what's the next step I do? I've counted between my original point and its reflected point and there are seven squares, and now I have to divide it by two or find half way.

So what's half of seven? Three and a half or 3.

5.

So that is where my mirror line or my line of reflection would go.

And then again, I'm going to pick the same point and count from that point to the line of reflection.

Should be three and a half squares, but let's count.

One, two, three, and a half, half, one, two, three.

Okay.

Hopefully my nice, easy step method is clear 'cause I like using it when I look at lines of reflection.

Okay, brilliant work you've done today.

Now I would like you to pause the video, and you have got a task to complete.

If you want to go and complete that, do the best that you can.

Stop the video and then come back, and we will go through the answers and check together.

Good luck.

Okay.

Welcome back.

Hopefully you found that okay.

Not teacher key.

Let's have a look at the answers together then.

Okay, before we go for the answers, let's just read through the question together, and then you can check your answers and mark them.

So, shape A has been reflected to shape B.

Draw the missing mirror line.

And then the second part of the question says that shape A has also been reflected to shape C.

Draw the missing mirror line.

So we've got reflection from shape A to shape B, and then shape A to shape C.

So we should have two mirror lines, using a ruler, obviously.

So, let's have a look.

Okay.

So, here is a mirror line, and which mirror lines this whole translating from shape A to shape C.

And again, if you choose one of the points on shape A, hopefully that you did this, or if not, then have a go at doing it now.

Choose any of the vertices and then find the equivalent one on the reflected shape and then count.

It should be the same amount of squares between your original shape and one of the vertices that you've chosen to the mirror line or the line of reflection.

And the same from the corresponding or the same point on the other reflected shape.

So if you want to count the squares and make sure, that's okay.

Okay, and then the second one we're reflecting from shape A to shape B is a vertical line that looks like this.

And again, exactly the same thing.

If you want to choose one or two of the vertices from shape A, find the matching or the corresponding ones onto shape B and, again, count how many squares away it is from the mirror line or the line of reflection.

And it should be exactly the same number of squares as in from the line of reflection to the point that matches the original point.

So make sure you check those, please.

Once you've checked them, make you give yourself a nice big tick.

Okay, so these are the two lines, the lines of reflection or the mirror lines that you should have on your answer sheet.

Well done, if you got those right.

Okay.

Share your work with Oak National, if you would like to, of course.