Lesson video

Hi there, my name is Miss Darwish, and today's Math lesson we are going to be further exploring translations and reflections using coordinates.

But before we start the lesson, if you could just take yourself to a nice quiet place, so you're ready to start.

Okay, the agenda for today's lesson is first of all, we're just going to recap on what the four types of transformations are.

And then we're going to be looking at reflecting and translating shapes onto coordinates, and then knowing the difference just by looking at the coordinates.

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

So you will need for today's lesson, a pencil, a sheet of paper, or a notebook, something to write on, and a ruler.

If you would like to go and grab those things, then we can start the lesson.

Okay, reflections.

So I've got the coordinates for the vertices of a triangle, two one, two three, and four one.

Can you see that? And what's that triangle labelled as? Triangle A.

So triangle A has the vertices, say them with me two one, two three, and four one.

Well done.

Okay.

Now the point two one, reflects to two minus one.

And two three, reflects to two minus three.

I'm just going to stop there.

What are we reflecting on? Are we reflecting on the x-axis or are we reflecting on the y-axis? And how do you know? Okay, we are reflecting on the x-axis, and how do we know? Because the x-coordinate has stayed the same.

We've gone from two to two, oh, we've gone from a two to a two.

So two one, reflects to two minus one, and then two three, reflects the two minus three.

Now I want to see if you can see a pattern here.

What about four one, on the original A triangle? What does that reflect to? What do you think four one.

We should have a look together.

So that reflects to four minus one.

Well done if you said that.

So four one reflects to four minus one.

Now I'm going to ask you a question.

What have you noticed between the original coordinates, and then after we reflect them.

What's the same, and what's different? If you got any ideas, jot these down for me.

So two one, reflects to two minus one, two three, reflects to two minus three, four one, reflects to four minus one.

What's the same and what's different? So what's the same first of all tell me.

The x-coordinate has stayed the same, and why? Because we have been reflecting onto the x- axis, well done, and then what has changed? The y-coordinates changed.

But there's something that's the same about the y-coordinate though, although it's changed.

So it's gone from one to minus one, three to minus three, and one to minus one.

Something's changed, and something's also the same.

The actual digit is the same, so one, one, but the sign in front of the digit, we've gone from a positive to a negative.

So the actual signs changed, but the digit has stayed the same.

And this has happened when we reflected, Okay, let's have a look at another example.

Nine three, nine five, and 11 three are coordinates of a triangle.

When this triangle is reflected onto the x-axis, then what are the new reflected coordinates? So we've got a triangle, and the coordinates of three of the vertices are.

say them with me, nine three, nine five, and 11 three.

And we're going to reflect this triangle onto the x-axis.

Like the example before, we also reflected the triangle onto the x-axis, didn't we? So what are the new coordinates going to be? Okay, before you answer that question tell me, what's going to stay the same if we are reflecting onto the x-axis, what's going to stay the same? The x-coordinate is going to stay the same, well done.

Okay, so the x-coordinate is going to stay the same.

What else is going to be the same? And what's going to be different? Okay, should we have a look together? So nine three, reflects to nine minus three.

Nine five, reflects to nine minus five.

Can you see that the x-coordinate has stayed the same and the actual digit of the y has stayed the same, but the sign has changed.

We've gone from positive three to negative three.

So coming from a positive integer to a negative integer, five to minus five.

and 11 three is then going to be reflected to become.

11 minus three, well done if you said that, simple.

So actually the second example, we didn't have the coordinates and we couldn't actually see the shape in front of us, but we didn't need to.

Just by looking at the coordinates and understanding and knowing if it's reflected onto the x-axis or the y-axis, we can guess and see what's going to happen with the coordinates.

In both examples were reflected on the x-axis, and that's why what didn't change? The x-coordinate did not change.

And what if the question also had all asked us to reflect on the y-axis, what would not change? The y-coordinate would not have changed, that would have stayed the same.

Okay, let's move on.

So minus three two, minus three three, minus two two, and minus two three, are coordinates of a square.

So these four vertices are for a square this time.

When this square is reflected onto the x-axis, so we're look at the x-axis again, then what are the new reflected coordinates? So tell me, because we're reflecting onto the x-axis, what is not going to change? The x-coordinate.

And we're reflecting onto the x-axis remember.

So what might change and what might be similar with the y-coordinate? Let's have a look.

Minus three two, reflects to minus three minus two.

Minus three three, reflects two minus three minus three.

Because again, we reflected the square onto the x-axis.

The x-coordinate did not change.

That stays the same, okay? And the y, the actual digit stay the same, but the sign has changed.

We've gone from a positive two to a negative two, positive three to a negative three.

The other two coordinates of the vertices, minus two two, reflects to minus two minus two.

Minus two three, reflects to minus two minus three.

So there you can see all the x's stayed the same, and the y has just slightly changed because we were reflecting on the x-axis.

The sign in front of the digit has changed.

So, okay.

So now can you spot and see what's going to happen when we reflect onto an x-axis or a y-axis.

Remember if we were reflecting onto the y-axis, it would have be the y-coordinate that did not change, okay? Okay, let's move on to translations now.

So we have got a triangle, a right-angled triangle, and we've labelled that A.

Two one, two three, and four one are vertices of a triangle.

Can you see that? Okay.

Triangle A translates down five.

So we've translated triangle A, five squares down.

So the point two one, has translated to two minus four.

Two three, has translated to two minus two, and four one, has translated to four minus four.

I'm going to go back through that.

What has stayed the same with these translations? So we've moved down, or stayed the same.

Two one, to two minus four.

The x-coordinate, well done, has stayed the same.

Two two, nothing's changed there.

Why is that? Why has the x-coordinate not changed, when we've translated down? Okay.

Because we're moving down.

And because we're moving our shape down, the only thing that's changing there, will be the y-axis.

Correct.

But actually, if we have a moving right or left, then the x would change, cause the x-axis is a horizontal line.

So because we're moving down, that is vertical.

It's a vertical move, so the y would change.

So the x is staying the same, and we can see that.

And the y is changing, it's decreasing.

It's getting less by three.

Cause we said, we're going to move it down.

Sorry, by five.

I made a mistake.

We're moving it down by five, okay.

So two one.

So the y-coordinate one, if we subtract five, zero minus one, minus two, minus three, minus four.

We've subtracted five, we get to minus four.

And two three, translates to two minus two.

The x-coordinate stays the same, and the y-coordinate it decreases by five.

So you go from three, two, one, zero, minus one, minus two.

And let's check the third one.

Four one, translates to four minus four.

Again, the x-coordinate does not change.

And the one we subtract five, zero, minus one, minus two, minus three, minus four.

We've subtracted five, and we've got to four minus four.

Okay.

Now, again I'll show you an example with the coordinates and the grid, so we can see it this time, we're just going to focus on what the coordinates actually say.

Nine three, nine five, and 11 three, are coordinates of a triangle.

So I've got the coordinates of a triangle, three vertices of a triangle.

What are they? Say them to me.

Nine three, nine five, and 11 three.

Well done.

When this triangle is translated down by three, what are the new translated coordinates? So again, we're moving down.

What's going to change, the x-coordinate or the y-coordinate, and why? We're moving the shape down.

Good, if we're moving the shape down, the y is going to change, not the x, the x will stay the same.

Let's have a look.

So nine three, translates to nine zero, because the x coordinate has stayed the same, Remember cause we're moving the shape down.

So because we're moving the shape down, the y-coordinate has decreased by three because we've translated it down by three, and three subtract zero.

Three subtract three, sorry, is equal to zero.

Let's look at the next one.

Nine five, translates to nine two, why? Tell me why, what's changed, what stayed the same.

The x has stayed the same, and the y-coordinate five has decreased by three, which gave us two, good.

The next one, 11 three, translates to 11 zero.

Oh, and that's it.

Okay.

Now we've seen examples of translations and reflections.

So this time we're going to guess if this is a translation or a reflection, are you ready? So triangle A has the following three vertices, two four, two three, and three three.

Okay.

So we don't know what type of transformation this is, okay? We just know about the triangle so far.

We want to know, is it a translation or is it a reflection just by looking at the coordinates.

Bit of a game.

Triangle A is transformed as the following.

So two four, becomes minus two four.

What's the same, and what's different? Two four, has transformed to minus two four.

But y has stayed the same.

And what about the x? The digit is the same, but the sign's different.

Let's look at the rest.

Two three, is transformed to minus two three.

Again, what stayed the same? The y-coordinate stayed the same.

The digit for the x-coordinate stayed the same, but the sign's different.

And then three three, is transformed to minus three three.

What stayed the same? Again the y stayed the same.

The actual digit of the x stayed the same, but the sign changed.

Does that sound familiar to an example we've seen before? Bit of familiar.

Translation or reflection, what do you think? Should we do a T for translation, or just to a small R for reflection? So Tell me, translation or reflection.

Three, two, one, show me.

It's a reflection.

Do you remember when we looked at the examples where the x and the y, basically the digits are the same, but depending on whether you reflect on the x or the y.

And we can see this has been reflected onto the y.

How do we know that this reflection was on the y-axis? Because the y-coordinate stayed the same.

The x stayed the same, but the digit.

but the actual.

the sign for the digit changed.

We went from a positive to a negative.

So that has been reflected onto the y-axis.

Well done, if you said R for reflection.

Okay, let's have a look at another one.

Triangle A has the following three vertices, two four, two two, and four two.

Triangle A.

so we've got two four, transforms to two minus two.

What stayed the same, what's changed? The x is the same, the y is different.

The y has decreased.

Two two, is transformed to two minus four, and four two, is transformed to four minus four.

So T for reflection or an R.

Oh, sorry, made a mistake.

T for translation, or R for reflection.

Which one do you think it is.

And show me in three, two, one.

So it's been translated down by six.

Can you see that? And we guess from the coordinates, because usually when something's been reflected on the x or the y-axis, the digits are exactly the same.

It's just either the x or the y.

The sign changes either positive to a negative, but we didn't get this, did we? So it has been translated by six.

And we know this, because the y-coordinate has decreased by six.

Four take away six is equal to minus two, two take away six is equal to, minus four, and two take away six is equal to minus four.

Well done, if you said that.

Okay, now it's time for you to pause the video, and have a go at your task.

Once you've had a go and checked through, then come back and we'll go through the answers together.

Good luck.

Okay, welcome back.

How was that? Did you find that okay? Let's have a look.

So I left you with a question about three different types of transformations.

Oh, sorry.

Three different types of transformations.

So we had.

Let's just look at one at a time.

One one, transforms to minus one one, one three, transforms to minus one three, two one, transforms to minus two one.

So we've got three coordinates of three vertices and that would indicate it's a triangle, right? So one one, minus one one, one three, minus one three, two one, minus two one.

What stayed the same in these coordinates? The y has stayed the same, hasn't it? And the x has it completely changed? The sign has changed.

It is a different number.

The sign has changed, but the digit is the same.

It's gone from one minus one, one minus one, two minus two.

So is that a translation or a reflection? A reflection, and what stayed the same? The y stayed the same.

So it has been reflected onto the y-axis, okay.

So we've got the x-axis and the y-axis.

We can see it's being reflected onto the y-axis because one one, has been reflected to minus one one.

The y-coordinate has stayed the same throughout.

Can you see that? Okay, well done If you said reflected onto the y-axis, give yourself a big tick.

Okay, let's look at the next one.

These all seem to be triangles, how do we know? Because they've given us three coordinates of three vertices.

So we've got one minus two, transforms to one four, one minus four, transforms to a one two, and four minus four, transforms to four two.

Have all the digits the same.

So is it a translation or reflection? Some of the digits have changed, haven't they? So that would tell us it's not a reflection onto the x or the y-axis.

So it must be some kind of translation.

Let's see what kind of translation exactly.

What's changed the x or the y-coordinate? The y-coordinate has changed.

This is the y-coordinate, right? We've gone from minus two to four.

Has that increased or decreased? Minus two to four.

Is that increase as it got bigger, or as it got smaller? It's increase, so we're moving up the y-axis.

So is the shape being translated down or up? It's being translated up, let's have a look.

So one minus two, translates to one four, one minus four, translates to one two, four minus four, translates to four two.

They have been translated up by six.

And we know that just by looking at the y-coordinate, it's increased.

It's gone up by six each time.

Well done if you said that.

Give yourself a big tick if you got that right.

Okay, and then the last one, another triangle.

Minus five two, transforms to minus five minus two, minus five four, transforms to minus five minus four, minus three two, transforms to minus three minus two.

Does that look like a translation or a reflection just by looking at those digits? Definitely looks like a reflection because the digits.

the actual digit itself, they haven't changed.

It must be a reflection.

Question is, onto the x or onto the y? Will it stay the same.

The x has stayed the same, so it must be reflected onto the x-axis.

Well done, if you've got that right.

Give yourself another big tick.

Okay, well done.

If you would like to share your work with Oak National, then please ask your parent or your carer, to share your work onto Twitter, and to tag @OakNational, and to use the #LearnWithOak.

I would love to see the learning that you did today.

So before I leave you to go and complete the quiz for today's session, I just want to say a really, really big, well done on all the brilliant learning that you have done today.

It's definitely not easy trying to guess if it's a translation or a reflection just by looking at the coordinates without having a grid.

So what you did today, was super hard work, so just a brilliant then, well done.

So before I leave you to complete the quiz, I'm just going to say good luck, and I will see you soon.