Lesson video

Hi there.

My name is Miss Darwish and I am a primary school teacher from West London.

So for today's lesson we are going to be translating some points and shapes on using coordinates.

So before we get started, if you can take yourself to a nice quiet area, ready for today's lesson.

Hi there.

So the agenda for today's lesson is as follows.

We're going to recap coordinates, looking at different quadrants and then we're going to be looking at translating some points and shapes and then we're going to have a go at something a bit trickier, translating points without a grid.

And then of course at the end, there will be a quiz for you to do.

So let's get started with the lesson.

So you will need a pencil, a piece of paper or something to write on is fine and a ruler.

So let's just remind ourselves with the four quadrants when we have an X axis and a Y axis.

So you can see in the first quadrant both X and Y are positive.

In the second quadrant, X is negative, but Y is positive.

In the third quadrant both X and Y are negative, good.

And in the fourth quadrant, X is positive and Y is negative.

Okay, here is a shape, a quadrilateral.

What are the coordinates? So let's find the four vertices.

What are the coordinates? If you want to say them out loud if you want to write them down, then you can have a go.

Let's have a look together.

So here are the four vertices that I have marked.

First of all, that's almost like my step one, that I like to do personally, before I can start thinking about what the coordinates are.

Okay, so we've got -4, 1 and then we've got -2, 1.

And then we've got -5, -3.

And the last one is -1, -3.

Hopefully you can see that, nice and clearly.

So now we've got the four coordinates.

Now we're going to think about translations.

Now, translating this shape.

If this shape was translated, four spaces to the right, four spaces to the right, what would the new coordinates be? So we want to translate the shape.

So the shape doesn't move.

Remember the orientation doesn't move, the size of the shape doesn't move.

The only thing that changes is where the position of the shape.

So what would the new coordinates be if the shape was translated four to the right? What do you think? Let's have a look.

So, if it was translated four to the right, then let's have a think.

So that's one, count with me.

So you see what we've done there.

We're going to translate it four spaces to the right.

One, two, three, four.

So all of the points have moved four spaces to the right.

And that is where the shape would be.

So the shape's position has moved.

And again, we can see clearly the four vertices or the four coordinates.

So the translated coordinates are now, we've got 0, 1 and we've got 2,1.

We've got -1, -3 and 3, -3.

Well done if you said that.

Okay, here's a triangle.

What are the coordinates? So what was that step one that I told you before that I like to do? Find the three vertices.

Okay, so here's the first vertice, one of them.

So we've got three vertices, 'cause it's a triangle.

So the first point is 4, 4.

And then we've got 4, 2.

What's the last one? Tell me the coordinate.

What's the last one? 6, 2.

Well done if you said that.

6, 2.

Okay, now we need to translate the shape.

Five spaces down.

So can you do that for me? So you want to translate the shape five spaces down.

So, again, we need to identify the three vertices and move them down.

Let's do that together.

There they are.

Okay, are you ready to count with me? One, two, three, four, five.

And what are the new coordinates? What do you think the new coordinates are? Jot these down for me.

They're all in the fourth quadrant.

So if you've done that, then you should notice that your three coordinates or have a positive X or Y.

X, 'cause it's in the fourth quadrant, a positive X and a, what about the Y? Negative Y, well done.

So we've got 4, -1, 4, -3 6, -3 So they've all got positive X and a negative Y.

Because all the coordinates of the translated triangle they've from being in the first quadrant to the last or the fourth quadrant.

Okay, so let's have a think about negative numbers.

So you could see an X axis, correct? And I've marked the X axis at -2, 0 We're just going to leave the Y axis for now.

But this point is -2, 0.

Zero because it's not on a Y axis and minus two on the X axis.

So if I was to move this point one space to the right, it would be minus two, add one.

So it would be the new translated point.

and minus two add one is equal to minus one.

Did you see the move that we made there? I'll show you again.

So minus two, if we're told that a shape or a point in this case, moves one space to the right.

So we're going this way, we're adding one.

So it's closer to zero.

So we've got minus two, add one is equal to minus one.

Did you see that on the number line? Okay, right now we're going to go back to our point -2, 0.

And this time, our coordinate is being translated two spaces to the right.

So our coordinate is being translated two spaces to the right.

If we're moving right or left only the X axis changes.

But if we move it to the right, we are adding, and if we're moving to the left, we are subtracting.

So this time we're moving to the right by five.

So let's have a think.

One, two, three, four and five.

So minus two, add five is equal to three.

Well done.

Okay, now we need to think about how to do this without a grid, without coordinates.

This is where it gets a bit tricky, but actually it's not that tricky once we know what we're doing.

So let's have a think about how we would do this without a grid.

So the point -4, 0 is translated for spaces to the right.

If it goes right or left only the X changes.

So the point -4, 0.

The zero because that's the Y, it stays the same.

We're only moving left and right.

In this case we're moving four spaces to the right.

So our X is on minus four, where would the new coordinate be? We are moving to the right.

So we are adding four.

So what's the new co-ordinate? Say it to me.

It would be on 0, 0.

So we've gone from minus four, add four is equal to zero.

And actually we can see on the number line but we don't need the number line, do we? Because we know if we're moving to the right, we are adding.

So if it's four spaces to the right, we add four.

If it's 29 spaces to the right, we add 29.

What if it's one space to the left? We take away.

If we're going to the left.

If we're moving 13 spaces to the left we would take away 13.

Okay, so, let me just move this.

When we transfer a point left or right.

Only the X coordinate changes.

Remember I said that to you? If we are moving, if a shape or a point is being translated either to the right or to the left, only the X coordinate changes because the X axis is a, what kind of line? Horizontal line.

But if we transfer a point up or down, what changes this time? If we translate a point upward down, the Y changes, not the X.

Because the Y axis, sorry, is on a vertical line, whereas the X.

So if you think about it, when you do this for X if we're translating a point left or right, the X is changing.

But this is Y.

The Y axis is a vertical line.

So if we move it up or down, then the Y is what changes.

Of course, when we transfer a point, of course when we transfer point up and down and left and right, then the X and the Y change, if we're doing both.

So I want you to remember that.

So what changes if I'm moving right and left? The X.

And what about if I'm moving up and down? The Y.

And what about both? If I do five right and six down? The X and the Y.

If I translate the point 9, 0 three right and two down, what will the new coordinate be? This is a bit tricky now because we don't have a number line.

We don't have a grid, let's think about it.

If I translate the point 9, 0 three right and two down? So if I move it, let's do this one step at a time, three right, what changes if I'm moving right or left? The X.

And two down? The Y will change.

Sometimes I like to colour coordinate things so it's easier for us to remember.

So nine is the X and the Y coordinate is zero.

So if I'm moving three right, we are doing nine and three.

If I'm moving two down, we would then do zero, take away two.

Okay, so the X would be nine, add three is equal to 12.

And the Y, zero take away two is equal to minus two.

So the new coordinates will be 12, -2.

See how we did that without needing to look at a number line or coordinate grid? It's just a matter of remembering when we're moving left and right, the X changes.

And when we have the.

If we all moving up and down, then the Y changes.

Now it's time for you to complete your task.

Good luck with the task and just do your best, have a go.

And then when you come back we will go through the answers together.

Okay, welcome back.

Hopefully you didn't find those too tricky.

Should we go through the answers together now? If you've got a red pen or something to mark with, that will be great.

Okay, let's have a look.

The question was.

So the question reads that a rectangle has the following vertices.

Obviously it's a rectangle.

There are four vertices 'cause it's a quadrilateral shape.

They are -4, 2 4, 1 1, 2 and -1, 1 Now this rectangle is translated four to the right and two down, what are the new vertices? It's okay if you needed to have a look at the grid, either to check or to have a go at, that's fine.

So remember, when we are translating four right, what changes? The X, brilliant.

And two down? The Y changes.

Let's have a look and see what this would look like using coordinates and then you can see if you were right.

This is what I managed to plot.

This is our rectangle.

So let's have a look.

We had four right and two down.

So one, two.

First we moved it down, only the Y changed.

And then we're going to move to the right.

Count with me.

One, two, three, four.

So we moved it two down, four to the right.

We can check our answers now.

So the point -4, 2 is now 0, 0.

The point -4, 1 is now 0, -1 1, 2 is now 3, 0 and -1, 1 is now translated to 3, -1.

Well done, if you got that, give yourselves a big tick.

If you'd like to share your work with Oak National I would love to see your work on coordinates that you did today.

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

We would love to see the work that you did today.

Now, before I say goodbye and leave you, don't forget to go and complete the quiz.

Good luck on the quiz.

Just a big, well done on all the fantastic learning that you have done today.

Be proud of yourselves.