Lesson video

Hi ethics, we're starting a new topic this week, coordinates and shapes.

Today, we'll be learning to describe coordinate positions on a grid.

All you'll need is a pencil and a piece of paper.

Pause the video and make sure you have your equipment ready.

Today's agenda will be describing coordinate positions on a grid, starting with a quiz to test your knowledge of coordinates already.

Then you'll go on to describe the position of coordinates, then explain quadrant rules before doing some independent learning and a final quiz to test your knowledge.

So let's start with our initial knowledge quiz, pause the video and complete the quiz.

Great work.

Now here's what you do now.

There some key vocabulary down the right hand side.

I would like you to use the image to help explain each the of vocabulary words.

Pause the video while you make some notes.

So our first word is coordinate.

These are a set of values that describe the position on a grid.

And we'll come on to how to use coordinates in a moment.

The second word is point.

These are our points on the grid.

They Mark a specific coordinate position.

To plot is to draw on the grid.

To draw your points onto the grid.

Axis, so the first one is the singular.

So we have the x-axis.

Sorry, we have the x-axis.

It's the one that goes across the horizontal axis.

And we have the y-axis.

It's the one that goes down the vertical.

And then axes.

This is the plural.

So that's when we're talking about both the x and the y-axis together.

So these are our axes.

Quadrant refers to the four quarters of the coordinate grid.

So the grid is split into four parts.

And if you think about the word quadrilateral, which is the four sided shape, we know that this prefix quad means four.

And then position is where a coordinate is placed on a grid.

So now we're going to describe the position of coordinates.

We'll do the red and the blue ones together, and then you'll do the purple and yellow ones independently.

So, we always start with the x-coordinate.

And we write our coordinates in brackets.

So it's x first followed by a comma and then a y-coordinate.

Our is the horizontal axis or across the grid.

So we go across first to where our point lies on the x-axis.

So this one is at six.

So we know that the coordinate on the x-axis is six, and then we go up the y-axis and we can see that this is at four.

So if I just demonstrate that, so we can see that this one is at six on the x-axis and it's at four on the y-axis.

So the point is that position brackets six at first comma four.

So this red dot is that position six four.

And you may have learned it as you go along the corridor first either this way or this way, and then up or down the stairs.

let's do the blue one together.

So the x-coordinate of the blue point.

If I go along the corridor, I can see that it's here.

It's going meeting down here.

And this is halfway between two and four.

So this must be three.

And the y-coordinate, if I go down the stairs this time it's here.

This is halfway between minus eight and minus 10.

So it must be minus nine.

So x comes first, it's at point 3 comma minus nine.

And I can annotate that on the grid.

Three minus nine.

So use this language structure here and have a go for the purple dot and then the yellow dot.

Pause the video now.

So we can see if we go along the corridor that the purple dot is in line with this point on the grid.

And you may have to draw your dotted lines on it first, and then you'll have to do that last as you get more skilled.

It's halfway between minus two and minus four.

So the x-coordinate, which always comes first is minus three.

Then the y-coordinate up the stairs is eight.

So it's minus three eight.

And your yellow one, we're going along the corridor this way, we go on the horizontal axis first, the x-axis.

We can see that that is at minus eight.

And then down the stairs, the y-axis it's at minus two.

Let's have a look at some more.

We're looking at the blue point here.

How can we describe the position of this point and how can we record it? So we remember that we have x and then y and they're in alphabetical order.

So that's also helpful.

And if it's not labelled, you might want to label your axes.

X is across, it's literally across, and then y is the vertical.

So if I go along the corridor, I can see that this is at zero on the x-axis.

So the x-coordinate is zero.

And I go up or down the stairs, I can see that it's actually also at zero on the y-coordinate.

So the blue dot is at the position zero.

This is called the origin.

Now these coordinates will also have part of it at zero.

So let's have a look at this one first here.

So the x-coordinate.

If I go along the corridor along the x-axis, I can see that it's at four and then I'm going up or down the stairs.

What I can see that it doesn't go up the y-axis or down.

It it's actually at zero.

So this point is at four zero.

And I can label this on here.

Now this other point, first of all, I go along the x and I can see that it is at zero on the x-axis.

So the x-coordinate is zero.

And as I go up the stairs, I can see that it is at four on the y-axis.

So we can see that these have got the same numbers in their coordinate positions, but then the other way round.

So when you have a coordinate that is on an axis, you are going to have a zero in that coordinate position.

So now I want you to pause the video and find the errors.

Mariam has described the position of these coordinates, but she's made some errors.

Can you correct them? So let's start off with A.

A is incorrect.

Let's find out why.

if I go along the x-axis, I can see that the x-coordinate is eight.

So it's not minus eight, it's eight.

And then I go down the stairs for this one, along the corridor, then down the stairs, I can see that it's at position minus four.

So eight minus four.

She'd got the x-coordinate wrong.

Let's look at B.

Along the corridor to 10.

So the x-coordinate is correct.

And up the stairs to four.

So this one is correct.

C, I go along the x-axis to five.

So that's not correct.

I can see that the x-coordinate is five.

And I go down the stairs down the y-axis to minus seven.

So you can see here that what the person did was they went down the y-axis first, and then the x-axis.

So they got these coordinates the wrong way round.

The D, I'll go along the x-axis.

I can see that it's halfway between minus six and minus eight.

Well, that's actually the minus seven.

So this person might, what Mariam has done is read the scale wrong here.

So if you have gaps like this, you may find it helpful in those gaps to put the correct numbers.

And then I can see that going down the y-axis, it's halfway between minus two and minus four, which is actually minus three.

So you need to read the scale really carefully.

E, well there's only one coordinate.

So this must be incorrect.

We always have to have both an x and a y-coordinate.

So for E, I can see that on the x-axis, I go along it's at minus two.

So that is the x-coordinate.

And then when I go on the y-axis I can see that it doesn't go up or down the y-axis stays at zero.

So Mariam forgot to put in her zero for her y-coordinate.

F, I'm going along to minus 10.

So that's correct.

And up to nine.

So this one is correct.

So hopefully you saw those errors and realise what the error was in each case.

It was just one small thing done incorrectly, but the most important thing to remember is that you put your x-coordinate before your y-coordinate.

Now, let's look at quadrants.

So we say coordinate grid was split into quarters into four parts.

And we're going to look for some patterns now.

So when we're looking at this, this is we'll call this the bottom left quadrant.

We want to know what is the rule about coordinates in this quadrant.

So if we look at this one here, we can see that this is at minus seven, and then we go down, it's at minus three.

So what we've got here is we've got a negative at x and a negative y-coordinate.

Now is that always the case? Let's put another one in here.

So this is at minus four minus five.

So it looks like it's going to be a constant pattern.

We'll put one here that says minus eight minus eight.

So, we can say that any coordinate in the bottom left quadrant will have a negative x-coordinate and then negative eight coordinate.

And this will help us to sense check things later on.

And I'll come onto more about what that means in a minute.

Let's look at another quadrant.

For top left.

This one has got minus 10 for it's x-coordinate, and we go up to nine for the y.

So what it looks like is negative x and positive y.

Let's just check with a couple more.

Put one here.

So we go along the x-axis, which is minus six and up the y-axis, which is four.

So yes, again, we have a negative x and a positive y.

And we can see that when we go into this quadrant, we go this way along the x-axis, which is all negative numbers, and we go up to the y-axis, which has positive numbers.

So we can generalise that this will always be negative x and positive y.

Have a look at the top right quadrant and see if you can work out the rule.

So this one is at 10 on the x and four on the y-axis.

So we've got a positive x and a positive y-coordinate.

Because when we go this way from zero on the x-axis, these are positive numbers and the same with the y.

So finally have a look at the bottom right quadrant.

What is the rule for this one? So this one, we go along the corridor or along the x-axis to four, and then down the y-axis to minus three.

So this is positive at x negative y.

So here are all of our rules together.

You can see now what you're going to have in each quadrant on your coordinate grid.

So let's have a look at these coordinates.

Without plotting them, can we decide where they are going to go in the grid? So let's do the first one together.

Minus two four.

Minus two, so that's a negative x-coordinate.

So it's going to go in one of these two.

And four is a positive y-coordinate.

So this one must be top left.

Have a go at the other three, by yourself.

Pause the video while you work out, which quadrant the coordinates belong in.

So minus six minus eight had negative x.

So one of these two.

And negative y.

So this one must've been bottom left.

One minus two.

That's a positive x and a negative y.

So this one is bottom right.

And then last one, four six is positive x and y.

So it's top right.

Now, it's helpful to know these rules, because then you can very quickly realise where you've made a silly mistake.

If you've maybe done y before x by mistake, you can think, actually, I know that doesn't look right, because I know that if it's positive x and y, it must go in the top right.

Or if it's negative x and y, it must go on bottom left.

So these are helpful rules to remember.

Now, it's time for you to do some independent learning.

Pause the video, and complete the task.

And restart once you're finished so that we can go through the answers together.

And for your first question, you were asked to write the coordinates of each point.

For A, we went along the x-axis to the left to minus seven, and then up y-axis to five.

B, we went along the x-axis and it was further on then it was labelled.

So you have to label that one in there as well.

So that was minus 12.

And then down the y-axis to minus six.

And here we can see, we knew that this one was going to have negative x and negative y and here we have it.

Think about all quadrant rules.

We knew that C will have negative x and negative y.

So we can just make sure when we're doing our answers along to minus three, and down to minus three.

D, as this is on the line, we know that one of the coordinates will be a zero.

So we go along and that actually goes to minus one.

It's not labelled on that.

Minus one.

And then if we go up or down the y-axis, we can see that it doesn't go up or down.

It stays at zero.

So this is minus one zero.

E, again, it's on one of the axes.

So we're going to have zero as one of our coordinates.

Going along the X axis, we can see that it go pass zero.

So it starts at zero, and we go up the y-axis all the way up to seven.

So that one is zero seven.

G, is in the top right quadrant.

So we know it's going to have positive x and positive y.

And we go along to four and up to three.

So that's four comma three.

H is on an axis.

So it's going to have a zero as one of its coordinates.

We go along the x-axis and it stops at three.

And then we know it doesn't go up or down, the y it stays at zero.

I, I missed out F.

I'm missing up my alphabet here.

E, F there we go.

F is in the top right.

So that should be positive x and positive y.

So it goes all the way along to 11 and up to six.

And now I've done G, H.

I'll go to I.

Bottom right.

That will be positive x negative y.

I go all the way along to five on the x-axis and down to minus eight on the y-axis.

And finally J, along to 10 and down to minus six.

That's a 10.

There we go.

On question two.

Here, you were asked to find the final vertex of a rectangle.

Now we haven't explicitly learned how to do this, but what you should have been able to do is visualise a rectangle.

So you may have drawn maybe just in your head, the lines on that.

So we know that the final one is going to be going down here.

It's going to be in line with the C and in line with the A vertex.

So it's going to go here.

And it's also important, you can just check this by seeing how many units high it is.

So this is one, two, three, four.

Does it match the other side? One, two, three, four.

Yes, it does.

And then the length of A, one, two, three, four, five, six, seven, eight, nine.

So it should be the same along the bottom, one, two, three, four, five, six, seven, eight, nine.

That's correct.

And it looks like a rectangle.

Let's have a look at the coordinates.

So we go along the x-axis to minus five, and we doesn't go up or down the y-axis.

It stays at zero.

So your coordinates for point D were minus five zero.

Question three is similar question where you need to find the last vertex of the square.

So again, you need that it has to be inline with B and C.

So it's going to go here and you can check as well that these sides are one, two, three, four units long, and obviously all sides in the square equal.

So each of these is four.

You minus two.

So your coordinates for point D were three minus two.

Question four, you were given two vertices of an isosceles triangle, and you were given some extra information.

Was that point C had the same y-coordinate as point B.

Now, I'll tell you in a minute why that was important.

Let's find the coordinates of A and B.

So, A along the x-axis is minus six, up the y-axis is five.

B, along the x-axis is minus nine and down the y-axis is minus four.

So we're being told that C has the same y-coordinate as B.

So C is going to be something minus four.

So we know that it's going to be on this line here, but we need to figure out where it will be on the x-axis.

The reason that we are given that information was because there are multiple ways to draw an isosceles triangle on here.

And we'll solve this, and then I'll show you what that could've looked like.

Now, the most important thing here was to find how many units wide it should be.

So it's three halfway along it's three wide.

And that's in line with the top vertex.

So we need to go three further along for it to be an isosceles triangle.

So our final vertex should have gone here.

And therefore that is at minus three minus four.

Minus three minus four.

And there we have a completed isosceles triangle.

Now, the reason we were given this information was because we could have put an x somewhere around.

Yes it's not accurate, but somewhere around there to make an isosceles triangle.

That way or somewhere down here to make it the other way.

So there were multiple possibilities, which is why this extra information was given to you.

And for question five, this is touching on something that we're going to be learning about later on this week.

So we haven't been given the size of the square, but we've got to work it out ourselves.

So here is a square on the coordinate grid, and we've got to find out the coordinates of A and B.

We need to use the x-coordinates that we know to figure out the length of one side.

So we can see that these ones, the C and D are at the same point on the y-axis.

But on the x-axis, C is at two and D is at six.

So the difference between two and six is four.

So that means that the square is, we'll call them units because it's not centimetres it's units on the grid.

So this square is four units wide.

So it must also be four units in length, as well as width.

Now, we can see that A is at the same position as C on the x-axis.

So it's going to have same coordinate as C in the x position.

But now it's gone up four units higher on the y-axis.

So we added four to the y-coordinate, which gets us to nine.

So A is that two on the x and nine on the y.

For point B, it's at the same position on the x-axis as D is.

So it's still at six.

But it's gone four units high up on the y-axis.

So five plus four is nine.

So it's at six nine.

We'll be looking more at questions like this later on in the unit.

Great work, now it's time for your final quiz.

Pause the video and complete the quiz, and then click restart once you're finished.

Great work today.

In our next lesson, we'll be translating simple shapes.

It would be really good, if you can try and get hold of some grid paper that looks like your maths book at school.

I'll see you then.