Lesson video

Hola! No, it's not Spanish lesson, It is a maths lesson and my name is Mrs. Buckmire And today I'll be teaching you about mixed transformations.

It could be helpful to have a pencil.

You do need paper.

If you don't have a pencil, just use a pen and let's begin.

Okay.

So before you to try this, I want you to copy the diagram, and then reflect S in the lines, L one L two and L three.

Then, I want you to select two of the reflected shapes, and describe the transformation between them.

Okay? Pause the video and have a go.

Okay, So I put in TUV, hopefully you can see them.

I'll even, probably go over them a bit.

So for B, that was in the line of reflection L one.

So we can see that each point, this is one aways, this one's going to be one aways there, this one, one away.

So one away.

So it's there.

And then we can kind of imagine that other point.

So it ends up like that.

The T, so T, use an L two.

So this was one, this was one.

So that's why it ends up over here.

And for you, it is looking at the diagonal.

So we don't need these anymore, looking at diagonal here.

So this is one diagonal way.

So one diagonal ends up here, and this one is two diagonals away.

So two diagonals, it ended up here.

And this one, let's say, it's like, if we go one and three of a rectangle, so it's also going to be one and three away.

So it ends up here and this, by the way, I'm reflecting the line L three and here it is like across.

There's going to be across as well.

So it ends up here, which kind of makes sense.

So it looks like this.

So there are our reflected shapes.

Lets rub out everything else that we don't need.

Okay.

So now we select two of them, and we need to describe the transformation between them.

So T to U is a 90 degrees clockwise rotation centre.

T to V is a 180 degrees clockwise rotation centre.

And that one doesn't matter, it can be clockwise, anti-clockwise, U to V would be at 90 degrees clockwise rotation.

So you could have slightly different ones, maybe 200, anti-clockwise, one 90 degrees clockwise.

You remember that? Yeah? But maybe you will notice something.

So from S to T and S to U, and it's to view our reflections, and now from T to U, T to V, we have some rotations.

Interesting.

Okay, So I want us to kind of explore different ways to transform one, the squares onto the other.

So you can choose which square is going to be the object, and which one's going to be the image.

And then I want you to complete their description.

So this person said, I reflected, Hmm.

What could they have finished it off with? I rotated, I translated.

So pause the video and think, how could I transform one of the squares onto the other with these sentence starters? Okay.

So for, I reflected, it could be, so let's say, I'm going to say that I'm going from this A to B.

So that's what my answer gives me.

If you did B to A, that's fine, you can think about how it would be similar.

So, I reflected.

Well, the mirror line needs to be exactly in the centre.

So it looks like it's going to be there.

So if I just take a coordinate, this one is going to be , this one's going to be , This one's going to be , So therefore it must be in the line.

Y equals three.

I rotate it.

I always find rotations a little bit harder.

So where can it rotate? Hmm.

There are lots of options, actually.

Let's use here.

If I choose this to be the centre, as that's like a one diagonal away.

So when it turns to here, that's a 90 degree turn, isn't it.

So might we turn that way.

Clockwise.

So 90 degree clockwise turn about ? Yeah.

What about I translated? So if I'm going from, let's say A to B, it goes, let's see, here's a point.

And this is the correspondent.

Remember it must be the correspondent vertex.

So it goes one, two, three, upwards.

So three up,.

So if you did it the other way, if you were going to B to A, what would the vector be? Excellent! It would be , because we're going three down.

And the blind reflection will be staying the same, what about the rotation? Oh the rotation actually, I did B to A, so if it was A to B, it should be, it would be anti-clockwise.

Actually I just put 90 degrees for the centre, but if it was B to A, this one would be clockwise.

That's what we said.

And if it was A to B, it would be anti-clockwise.

You need to be very careful.

Remember rotation.

You need an angle, a direction and a centre.

That's why you should check your work.

Okay.

You were ready for the independent tasks and you're not going to make those same mistakes.

You're going to write down a single transformation that maps A onto R, A onto P, A onto Q and A onto S.

This is on the worksheet as well.

There are two questions, this independent tasks.

So, pause the video and go to the worksheet or look at it here and make sure you have all the information.

Pause and have a go.

Okay.

So this is page two of two.

I want you to write down three different transformations that could have transformed square X onto square Y.

So maybe square X onto square Y, square Y is the image.

Okay.

Pause and have a go.

Okay.

So let's do some feedback.

So A onto R, so I can see that actually, it's kind of like been flipped around.

So it looks like it's going to be a line, a reflection line here, that's a badly drawn line, but you understand me.

So this point is , this point is.

So it's going to be X equals one.

So the reflection in the mirror line X equals one, good, A onto P.

So P is in the same orientation, and the same size and everything.

So it's going to be translation by the vector , A onto Q.

Again, I can see it's been flipped around.

So this would be the mirror line.

So just some points would be like , ,.

Why? So it's reflection in the line.

Y equals three.

And A onto S, oh it looks like it's been turned.

It's not the same orientation.

So it looks like this might be the centre of rotation.

And it looks like it's been turned 180 degrees.

So 180 degrees turn rotation, even about.

So what is really important is that you say what it is, say its a reflection, say if its translation, say if its rotation.

And then for each one, remember the key information.

You can pause it and check.

Okay.

So write down three different transformations that could have transformed square X onto square Y.

Did you get a reflection in the mirror line X equals two? Did you get a translation by the vector ? And finally, rotation 180 degrees about centre , Well done if you've got those.

Pause and check if there's any you didn't get, make sure they're correct.

Right, we're ready for our explore task, now I want you to be exploring the different transformation that takes one square to the other.

And I want you to see, can you describe the transformation of one shape to another in three ways? So it could be B to C and three way B to D, C to A.

There are lots and lots of different ones you can do.

Okay.

Pause the video and have a go.

Okay.

If you had to go like, Oh, it's too hard.

I have no idea what I was doing.

I'm going to give you a hint.

And my hint is, you know that they're squares.

Okay.

So we know that each one is a square.

So actually, how, what do we know about the squares? Well, they are actually two by two squares.

So I want to know actually what each coordinators Vertex's.

So if you give the vertices of each one, that might massively help you, with figuring out what transformations you can create.

Okay.

And then maybe just focus on ones.

Maybe just focus on C to D, and actually the different ways of getting from C to D, just C to D first.

Okay.

Good luck with it.

Okay.

I'm going to do B to C, so you could have a reflection in the mirror line, X equals negative 4.

5.

Okay.

So that's the cause.

Let me just go through, actually, in case it's helpful.

Here, there were two by two.

So this one was , and this one was , and this one was negative, Oh, sorry.

.

Okay.

This one.

So we could add , And so what we're trying to see, B to C.

So this is the line of reflection, If we think about reflection here.

So it's going to be halfway between negative five, and negative four.

So that's how you get to negative 4.

5.

Okay.

It will be translation with what vector? So just take two core verticis that are corresponding.

So maybe this one and this one.

So how do we get them from one to the other? So the Y values the same, so it doesn't move up or down.

It's just the X value that changes.

Good.

It moves three spaces to the right.

So how is that as a vector? Excellent.

It's going to be.

Okay.

And then what about rotation? So it is rotation 180 degrees, about 4.

54.

So actually it's going to be rotating across this point.

So it's like halfway between the, from there to there, you can kind of imagine how that would work, its exactly halfway.

So actually because it's a square, it works out really nicely.

Now there are lots and lots of answers, so well done if you had any different answers.

I would love to see, there are lots of answers, especially for the last ones.

If you'd like to share it, please ask your parent or care to share your work on Instagram, Facebook, or Twitter, tag it at @OakNational, #learnwithoak.

And it doesn't just have to be today's lesson, if there's anything over the transformations, that you've done that you're really proud of, Please do share it.

You guys should be proud of yourself.

You've worked really hard today.

So just keep it up by doing the exit quiz, complete the exit quiz, and then you can tick off all those things that you've done really, really well.

Good luck with it.

Bye.