Lesson video

Hi there, my name is Miss Darwish, and for today's math session, we're going to be looking at reflecting shapes onto coordinates, especially on the first two quadrants.

But before we get started on today's lesson, if I can just ask you to make sure or take yourself to a nice, quiet environment ready to start the lesson.

Hi, there.

So the agenda for today is, first of all, we're just going to recap on reflection just to see what you already know about reflection, and what you can remember.

And then we're going to have a look at vertical lines of reflection, and then horizontal lines of reflection, and then of course at the end, as always, there will be a quiz for you to complete on today's learning.

So let's get started with the lesson.

Okay, for today, you will just need a pencil, something to write on paper, square paper, plain paper.

Anything will do, and a ruler.

If you want to go and grab those things, then we can stop.

Okay, just to recap on what reflection is so when we flip an image across a line of reflection, that image is then reflected, okay? So another synonym for reflection can be just to flip something.

So to flip an image to reflect an image.

Okay, let's have a look at some examples of reflection.

So here is an example, can you see the reflected line? So the reflected line is vertical.

Can you see that? And then the shape that we have, that has already been reflected has got how many vertices? It has got four vertices, well done.

And you can see each one is in a different colour to show you where it would be reflected.

So the original purple point is then reflected onto the other purple point, and then the black, the blue and the green.

So, I want you to count for me how many squares away is it from the purple coordinate to the line of reflection? Three squares away.

Good.

So from the other purple coordinate to the line of reflection that also has to be three squares.

Good.

What about the green? How many squares away is the green coordinate from the line of reflection? Can you count that for me? Six squares away, well done if you said that, and then from the line of reflection to the other reflected green point, there are also six squares, okay? So, when we are reflecting a shape, I've got two examples for you, A and B.

One of them shows a shape being reflected.

The other one does not show a shape being reflected.

Which one is correct? Which one, A or B, shows a reflected shape? I'm going to give you 10 seconds to have a think, and then I want you to point to either A or B, which one correctly shows a reflected shape? Okay, five, four, three, two, one.

You picked which one? A or B? Well done if you said that A is correct.

Let's have a look at A.

So, I've chosen just one of the many vertices on the shape, and again we're going to count how many squares away, and then to see that if it's correctly being reflected onto the other side, okay? We can also choose another point.

So another coordinate, and you can see the black is just one square away from the line of reflection, and its reflective point is also one square away.

So A was correct.

Okay, let's have another go.

Which one has been correctly reflected? Is it A or is it B? Going to give you 10 seconds to point A or B is correctly reflected? Okay, time's up.

Let's have a look.

Well done.

If you said B, they're exactly the same reason, you can see that the line of reflection is horizontal, and that B has been reflected, and we can count how many squares away from each of the vertices until the line of reflection to check.

Okay.

So, you can see a right-angled triangle on this grid.

I want you to think what are the coordinates? What are the coordinates? So I've marked the vertices for you.

So if you want to quickly just on your piece of paper or your notepad, just jot down what are the three coordinates of this right-angled triangle? Okay, I'll give you six more seconds.

Okay.

Let's have a look together.

You can check.

So we have got the point,.

Well done if you said is one of the coordinates.

We've also got.

Well done if he said that as well, and then the last one is, what's the last one tell me? Excuse me.

So well done if you got those three coordinates correct.

Now, let's move on and see what we need to do.

Can you spot the line of reflection? Is it vertical or is it horizontal? Is the line of reflection vertical or is it horizontal? Well done.

The line of reflection is vertical.

We can see that there.

So, now we can see the line of reflection is vertical, we want to reflect this right-angle triangle across that vertical line of reflection.

What will the new coordinates be? Where will the shape go? What would it look like? Let's have a look at this together.

Okay, so first of all, I've just labelled my vertices A, B, and C just to make it easier to see where each point goes.

So, how many squares are there between A, and the reflected line? Can you count them for me? So just choose a one point A, just going to take it one at a time, one coordinate at a time and count.

So there are seven squares from point A until we reach the line of reflection, well done.

So that means that A' must also be seven squares away till the line of reflection well done.

Okay, where do you think B' will go? So remember B is the original point, and B', we add a dash to the letter when we've reflected to the new coordinate.

Where do you think B' will go and why? Okay.

Should we see if you're right? Ready, put your finger where you think it will go.

Okay, well done if you got that right, and then what about C'? How many squares away is C from the line of reflection count them for me.

Three squares away from the line of reflection.

So C' must also be, three squares away from the line of reflection.

So I want you to put your finger up before I reveal the answer, and see if you got it right, where it would C' go? And five, four, three, two, one.

Did you get it right? Well done if you got it right.

So now we've got A', B' and C' dash.

Can you see how the shape's now being reflected? Okay.

Let's have a look at point A.

So that's the original point before we reflected anything.

The coordinates are , and then A', so the same point when it was reflected is.

What's the same and what's different between the coordinates? So what's the same? What didn't change between A and A'? The y didn't change, did it? Still four on A and four on A'? And what about the x? That changed, went from minus five to nine.

Interesting.

Did you have a look at B and C, and see if the same thing happened or not? Okay, so point B , those were the coordinates, and then B', the coordinates when we reflected B are now,.

So again, what stayed the same? The y stayed the same.

Exactly the same like the A.

Interesting.

What would you think will happen when we look at and compare C, the coordinates of C and the coordinates of C'? Let's have a look.

So C is , and C' is.

So did the same thing happen? Yes.

When we reflected the shape, the y or the coordinates did not change.

Why is that? Why did the y not change? Okay.

When the line of reflection is vertical, y stays the same.

Can you see a y axis in green? Can you see that? The y axis? It's almost similar to the line of reflection, they are both vertical.

That's why they're similar.

They're both vertical.

So when our line of reflection is vertical, the same as the y axis, the y does not change.

Okay? The y stays the same.

Let's have a look at another example.

Okay.

This example that we're about to look at, the line of reflection, is it a vertical or is it horizontal? It's horizontal.

So what do you think? Let's have a look and see what happens.

So again, we've got a right-angled triangle, and we need to reflect this shape onto a vertical line of reflection this time.

Okay.

So, what would the new translated coordinates be? What do you think will stay the same? Jot down what you think, what your predictions are, and then we'll check at the end if you're right or wrong, okay? Give you a few more seconds to jot down what you think will stay the same with the translate, with the reflected coordinates? Okay.

Let's have a look.

So, A is just one square away from the line of reflection.

So A' is also just one square away from the line of reflection.

Where do you think B' will go? Where do you think B' will go? Okay.

Let's see if you're right.

Hold on.

And what about C'? Where do you think it will go? Put your finger where you think it will go? C'.

Let's check.

Okay, well done.

Just look at the coordinates.

Now let's take a closer look.

So, point A is.

A' is.

What stayed the same, the x or the y? The x stayed the same this time, but the y changed.

Let's have a look at B and B'.

So the coordinates of B , and B'.

What stayed the same? The x stayed the same, the y did not, and then C and C'.

So C the coordinates are , and C' the coordinates are.

What stayed the same? The x.

So tell me what was your prediction? Did you predict that the x would stay the same this time, and that the y would change? Why did the x data stay the same this time? But in our previous example, it was the y that stayed the same.

So why, what changed? Okay.

Of course, what changed is that this time, our line of reflection is horizontal, before it was vertical.

So because it's horizontal, again, it looks similar to our x axis, the x axis is horizontal, our line of reflection is horizontal, and that means that the x will stay the same.

Okay.

Now it's time for you to pause the video to complete your task but before you do, I'm just going to go through the independent task with you quickly.

So before you have to reflect the shape, I want you to write down the coordinates that you think will change.

So you can see where the line of reflection is but do this please before you actually come to reflect the shape, okay? And then of course you can check after.

Okay.

Now you can pause the video, and then once you've had a go at that task, come back and we will go through the answers.

Okay, welcome back.

Hopefully, you found that okay, not too tricky.

Let's go through the answers together.

So, you can see that the line of reflection is horizontal.

So what did you predict? Which coordinates did you predict would not change? The x coordinates because our line of reflection is horizontal, as you can see.

So, our x axis is also horizontal.

So the x coordinates should have stayed the same.

Let's check.

Okay.

So you can see that.

So if we just do take two coordinates at a time, two points at a time.

So we've got , one of the original ones reflects to.

Well done.

And reflects to.

If you got those two right, give it a tick, and we'll look at the next two.

Okay.

Now we've got reflects to , and reflects to.

So check these two vertices, coordinates, and give it a nice big tick if you got that right as well.

And then we'll look at the last two.

So, sorry, reflects to , reflects to.

Well done if you said that.

Give yourself a really big tick.

Okay.

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

I would love to see the work that you completed today.

Now, just want to say well done, and all the brilliant learning that you have done today on reflecting shapes on coordinates.

Now I would like you to go, and have a go at completing the quiz, and good luck.