Lesson video

Hi there, my name is Miss Darwish.

And for today's math lesson, we are going to be exploring reflections and translations.

So, before we get started, if you just want to take yourself to a nice quiet place, ready for the lesson.

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

We're going to first look at four types of transformations, understand what they are.

Then, we're going to be looking at reflecting and translating shapes.

And then, we're going to be having a look, if they're the same or different.

Basically, just comparing reflecting and translating shapes.

Looking at the X and the Y coordinates.

And then, at the end of the session, there will be a quiz for you to complete as always.

So, let's get started.

So, before we start the lesson, you'll just need something to write with, pencil or pen, ferby pencil, a sheet of paper or a notebook and a ruler.

If you want to go and grab those three items, then we can start.

Okay, so when we talk about transformations, there are actually four types of transformations and they are, translation, reflection, rotation, and enlargements.

There are four things you can do to a shape to transform it.

So, to change something about it.

So we've got translation, a reflection, a rotation, or an enlargement.

And just for today's lesson, we're just going to be focusing on the first two.

So, we're going to be looking at a translation.

So, transforming a shape by translating it or transforming a shape by reflecting it.

So we're just focusing on those two today.

Okay, so in front of you, you've got some coordinates and a grid and you've got rectangle A and rectangle B.

So, it says A has been translated eight to the right.

Can you see that? We counted eight to the right.

So, if we translate shape A eight times to the right, we get to shape B, or we could also say, if we translate shape B eight squares to the left, we get to shape A of course.

So, there's two different ways we can say, we can say A has been translated eight spaces to the right and then we get to B.

Or we can say, shape B has been translated, eight spaces to the left and we get to A.

But, there's something else we could also say about moving from A to B or from B to A.

Can you think of anything else we could say? Let's have a look.

Can also say that, A has been reflected onto the y-axis.

If we reflect the shape onto the y-axis, where would we be? B a shape? Where would it be, okay.

Or what could we do to B if we reflect exactly the same reflect to B onto the y-axis, we would be at shape A, well done.

So, shapes haven't moved, have they? We've got shape A and we've got shape B, two rectangles.

And we've actually described four different ways that we could talk about the transformation without the shapes actually changing.

So, say them with me.

What's the first thing? A has been translated eight squares to the right.

So, the second one, that B has been translated eight squares to the left, well done.

The third one, A has been reflected onto the y-axis.

And what's the last one? B has been reflected onto the y-axis, well done.

So, this time let's move on.

Now, our shape A is slightly different to the last shape A.

This shape A is a what type of triangle? A right ankle triangle, well done.

Now, it says reflect A onto the x-axis and label it B.

So, we just think about how are we going to reflect A onto the x-axis.

So, with your finger, if we were to reflect shape A or triangle A onto the x-axis, where would it be? Have a point.

Let me give you 10 seconds.

Okay, let's see.

So it says, reflect A on the x-axis and label it B.

So there is B, well done.

And then we're going to reflect B onto the y-axis.

The vertical line is the Y-axis of course, and label it C.

So again, I'm going to give you 10 seconds.

Where do you think triangle C would go, off you go? Where would triangle C go? Reflecting B onto the y-axis.

Okay, let's have a look.

Do you get that right? So, that's where triangle C is.

And then, we've got something else to do, then reflect C onto the x-axis and label it D.

Again, I'm going to give you 10 seconds.

Where do you think triangle D would go off you go? Okay, should we have a look together? Where would triangle D go? So, we've reflected C onto the x-axis and we're going to label it D.

Is that what you thought triangle D would go? Well done if you got that right.

Okay, and then, there's one more thing to do.

It's now asking us to reflect D onto the y-axis.

Should I give you 10 seconds again? We're not labelling it though.

So, just where your finger point, if we were to reflect shape or triangle D onto the y-axis, where would it go, 10 seconds.

So, we would be back at shape A, wouldn't we? So, after four reflections, we are back at A, did you say that? So triangle A, we reflected it onto the x-axis and we got to triangle B.

Triangle B, we reflected it on the y-axis and we got triangle C.

And then triangle C.

We reflected on the x-axis.

We got triangle D and triangle D we reflected it on the y-axis.

And we were back at A.

So, after four reflections, we were back at A where we started, okay.

Now, we've got different shape A.

And this shape A is a what type of quadrilateral shape? It's a rectangle, well done.

Now, they're asking us to reflect A onto the x-axis.

Horizontal line is the x-axis.

Where do you think it will go? Give it a point.

Give you 10 seconds again, reflect A onto the x-axis.

Okay, should we have a look together? Now, It says, reflect A onto the x-axis and label the reflected shape B.

So, we're going to call that shape B, well done.

Now, we're going to do something else.

Reflect B onto the y-axis and label it C.

Should give you 10 seconds again.

Where would shape C go? Where would the quadrilateral C go? So, we're reflecting B onto the y-axis.

So, where would C be? Should we have a look together? Okay, well done, if you said that.

We're going to label it C and then we're going to look at A.

So can you find shape A and point to shape A.

Your finger and shape A, okay.

We want to reflect A nine spaces to the right and five up.

So, to the right first, we are at shape C.

Let's have a look at that again.

So, we're at shape A.

We are reflecting it nine spaces to the right.

Can you count that for me? And then five up and what's happened.

We are at C.

So, there are actually two different ways of getting from shape A to shape C.

can you remember what they were? What was the first one? We reflected shape A, well done onto the y-axis.

And that bought us, sorry.

I made a mistake.

What did I say wrong? We reflected shape A onto the x-axis and that brought us shape D.

And then we reflected shape B onto the y-axis.

And that brought us to shape C.

So, we did two different reflections, didn't we? First on the x-axis and then on the y-axis.

And that got us the shape C.

So, that was one way to get from shape A to shape C.

And then, what was the second way? Remind me from A to C.

We reflected it nine to the right and five up, or how else can we say that? Five up and nine to the right, well done.

So, two different ways that we got from A to C.

Okay, we're going to play a bit of a game, you ready? This is called same or different.

So, I'm going to give you two different ways of doing something.

Can tell me if it gives us the same result or a different result, okay.

So, reflect A in the y-axis and label it to B.

That's just the first step.

So, I'll give you 10 seconds and point where you think shape B might go.

So, we're reflecting shape A on the y-axis.

Five, four, three, two, one.

Are you ready? Okay, that's where shape B would go.

And now reflect B on the x-axis and label it C.

I'll give you 10 seconds.

Where will shape C go? Okay, where would shape C will go? Let's see, well done If you got it right.

Now, we're going to look at shape A, okay.

So, first we reflected A onto the y-axis that brought shape B.

Reflected A onto the x-axis that bought us shapes C.

Now, we just need to look at shape A point shape A for me, brilliant.

Now, I want you to translate shape A five down and eight squares to the right.

So, five down first of all and then eight squares to the right.

And I want you to put your finger where that takes you to, Does it take you to shape C? yes or no? Is it the same as the reflection from A to B to C? Or is it different? What do you think? If it's the same one We need to do this, if you think it's different, I want you to do this.

If you're not sure.

Maybe do this, okay.

And five, four, three, two, one same or different what do you think? Okay, it's the same, well done.

Did you see that? So, when we reflected shape A to B to C, it was exactly the same.

And now we can't see shape C because A is covering it, because it's exactly the same as the translation.

So, now we've seen examples of how a reflection can be similar to a translation.

Okay, so translating A down five and right eight is the same as reflecting A onto the y-axis and then reflecting it onto the x-axis.

I'm just going to give you a few seconds to read that through again.

Okay, right, well done.

Now, I'm going to ask you just to pause the video and have a look at the independent task for me.

Try your best with it, and then come back and we'll go through the answers together, good luck.

Hey there, welcome back.

How did you find those? Were they okay? Okay, should we go through the answers together now? Let's have a look.

So, this is the question that I left you with.

It says, first of all, draw a square at minus four, one, minus two, one minus four, three, and minus two, three.

So, we've got the coordinates of four vertices of a square.

So, hopefully it was easy as just plotting them onto the grid.

And then once you've done that, it asks you to reflect the square onto the x-axis name it B and then reflect B onto the y-axis label it C and then how many different ways can you write down to describe these transformations between the squares? Okay, let's have a look at, what your square should look like first of all, before we transform anything.

So, is this something similar to what your square look like? So, we've got minus four, one minus two, one, and then the vertices at the top minus four, three and minus two, three.

So, let's just check the original square first of all, before we look at the transformations.

Okay, is that what your square look like, right.

Let's have a look at the transformations now.

So, B reflect the square onto the x-axis and that's what it should look like.

So, now you'll have the coordinates minus two, one minus four, one minus two, three, and minus four, three.

So, just check that, that's what your B look like.

Get it, take if it did.

Okay, let's move onto the next bit.

So, then we reflected B onto the y-axis and we labelled that square C.

So, the coordinates of the vertices for square C are two, minus one, two, minus three, four, minus one and four, minus three.

Okay, now if we translate the original square down four and right six, we get to C.

Did you have that as well? So, we're looking at different ways from getting the two from the original square to B.

Or from the original square to C.

Or between even B and C.

So, to go from the original square to C, we could have described that transformation as a translation and said that we go down four and right six.

We get to C or right six down four.

Doesn't matter about the order.

If you did get that, give that a tick.

Okay, if we reflect B onto the y-axis of course, then if you can see that dotted line.

So, the y-axis would be our mirror line and then we would get to square C of course, did you get that? And obviously if we reflect C onto the y-axis, we would get to B works both ways.

Okay, well done on all the hard work that you did.

If you would like to share your work with Oak National, then please ask your parent or your care, to share your work on to Twitter and ask them to tag @OakNational and to use the hashtag learn with Oak.

I would love to see all the work that you did today.

Now, before I leave you to get on the quiz, I just want to say a really, really big, well done, on all the brilliant learning that you have done today on coordinates to connect two types of transformations.

And I know it's not easy when we mix both together, reflections and translations.

So super, super well done to you.

And I'm just going to leave you there and say good luck with the quiz.