Lesson video

Hello there, my name is Mr. Tilstone.

I hope you're well.

I hope you're having a great day.

Let's see if we can make that day even better by really acing this lesson, which is all about coordinates.

You might have had some experience in the past with coordinates.

Maybe you've even used a four quadrant coordinate grid, which is what we're going to be doing today.

If you're ready, I'm ready.

Let's begin.

The outcome of today's lesson is I can draw and complete simple shapes by plotting positions on the full coordinate grid.

So when we talk about the full coordinate grid, we mean four quadrants, positive and negative.

And our keywords today, my turn, coordinates, your turn.

My turn, quadrant, your turn.

And my turn axis or axes, your turn.

What do those words mean? Have you encountered them before? Would you like a reminder? Let's have a look.

Coordinates are a set of values that show an exact position, and you can see a coordinate grid there.

Any of the four areas made when a plane is divided by an x and a y-axis is called a quadrant.

And today we're going to be looking at grids with four quadrants.

The x and y lines that cross at right angles to make a graph or grid are called axes, and axis is a plural of axis.

So when you look at that word, you might think it's pronounced axis.

No, it's axes.

And our lesson is split into two cycles, two parts.

The first will be plot points on the full coordinate grid and the second draw shapes on the full coordinate grid.

So if you are ready, let's start by thinking about and concentrating on plotting points on the full coordinate grid.

And in this lesson you will meet Alex and Aisha.

Have you met them before? They're here today to give us a helping hand with the maths and very good they are to.

So here is four quadrant coordinate grid.

Is it ringing any bells? Have you used one of these before? Have a look at it.

See what you can notice.

Look at the axes.

Look at the labels of the axes.

So both axes in a coordinate grid can be extended past 0.

It could be thought of as two perpendicular number lines each showing positive and negative values.

So can you see that? Can you see like a horizontal number line that's got negative and positive values on? And then 0 in the middle of it.

And then can you see a vertical one that's the same? That's essentially what they are.

So the grid is referred to in terms of its four quadrants.

That's the first quadrant, second quadrant, third quadrant, and fourth quadrant.

And we could think of it a different way.

We could think about whether each quadrant has got a positive x value or a negative x value or a positive y value or a negative y value.

So here we've got positive x direction, positive y direction.

That's how we can describe the first quadrant.

So all the values in that quadrant are always positive.

Sometimes referred to as a first quadrant.

And here we've got a negative x direction.

So if you look at that x sort of number line, the axis, this goes into the negative number.

So this is a negative x direction, but still positive y direction.

And all the coordinates in this quadrant have an x value less than 0, but a y value greater than 0.

So it's a mixture.

Where do you think we're going now? So see if you can make a prediction.

The third quadrant, what's that going to look like? Look at the values on it.

That's a clue.

Negative x direction, negative y direction.

In this quadrant, both axis are negative.

And what about that last one? How do you think we can describe that? Hmm, it's the fourth quadrant.

This one's got a positive x direction.

We can see that from the axis and a negative y direction, we can see that from the axis.

In this quadrant, the x value is greater than 0, but the y value is less than 0 wherever you plot your coordinates.

So let's have a look at this coordinate.

This is a positive, positive one.

Can you read it? Well, let's investigate.

So here it's 3, 5.

So we always start with the x value, which is 3.

And then the y value, which is 5.

So that's 3, 5.

Remember to use the brackets as we've done here and remember about the comma.

So that's positive x quadrant and positive y quadrant.

3 along and 5 up.

What about this one then? How does that coordinate change? It's got something in common.

Can you see what it's got in common? They share the same y value, but look at the x value.

How's that changed? That's become -3.

So that's now -3, 5.

That's in the negative x quadrant and the positive y quadrant.

And that's reflected in the coordinates.

So that's -3 along, and that's 5 up.

What about here? Again, that's got something in common with the previous coordinate, but something different.

What can we say? That's -3, -5, both values negative there.

And we've gone -3 across and -5 down.

And what about this one? How can we describe this one? That's 3 across and -5 down, so 3, -5.

3 across and -5 down.

Let's see how much you've understood and if you are ready for the next part of the learning.

In which quadrant will you find coordinate -4, 1? A, B, C, or D? Pause the video.

What did you think? Was it A? Was it B? Was it C? Was it D? Well, it's -4, so it can't be A because it's got a negative value.

In can't be C can it? Because that would be both negative value.

So it's going to be B or D.

Remember we look at the x value first.

It's B, that's where you would find -4, 1.

<v ->4 across and 1 up.

</v> That's in the negative x quadrant and the positive y quadrant.

Okay, it's time for some practise.

I think you're ready for this.

One task, plot these coordinates.

You might even want to plot some more and test your friend after if you've finished that.

So good luck with that and I'll see you soon for some feedback.

Welcome back.

How did you get on? Are you starting to feel confident with plotting these coordinates on the four quadrant grid? Let's have a look.

So let's start with 3, 4, that's there.

This is -2 5.

This is a tricky one, next, -4, 0.

It's actually on the axis.

There we go.

So -4 across, but nothing, 0 up or down.

And then we've got 5, -3 and another tricky one with a 0, they're always a bit tricky.

That's 0 across on the x axes, but -5 down.

So that's where that one would be.

And then we've got 2, 1 and -1, 5.

So very well done if you've got all of those.

You're ready for the next cycle, which is drawing shapes on the full coordinate grid.

These are the vertices of a quadrilateral.

The first two coordinates have been plotted and a line drawn to join them.

So it's a quadrilateral.

So how many sides? Four.

How many vertices? Four.

And we've got those four vertices here as coordinates and we've got two of them plotted.

So you can see 2, 3 plotted in the positive positive quadrant.

You can see -3, 3 plotted.

Now we need to see if we can complete the shape and plot those other two coordinates.

So let's start with -5, -3, what do you notice? Both negative.

So which quadrant will that be? Quadrant three.

So -5 across and -3 down.

Let's have a look.

There we are, that's -5, -3.

And one more.

We're going to look at 4, -3.

So that's 4 across and -3 down.

Now we've got to complete the shape and name the quadrilateral.

So what would you do now? It's a bit like joining the dots this isn't it? Gonna join the vertices to create the sides.

Let's have a go.

Tell me if this is correct.

Am I on the right tracks do you think? No, I'm not.

I've joined the wrong vertex.

It won't form a quadrilateral.

What about now? Am I on the right tracks now? Yes.

And I can keep going and join these two vertices.

And finally these two vertices.

And now I've got a quadrilateral.

Can you name it? Well, let's have a look.

It's got one pair of parallel sides.

It's a trapezium.

These coordinates are the vertices of a polygon.

What do you notice about the coordinates? Let's have a look at them.

We've got 4, 0, -2, 0, <v ->2, -4, 4, -4.

</v> Do you notice anything? Hmm.

I notice that some of those numbers came up more than once.

Can we make predictions about the properties of the polygon based on that? Well these two coordinates share a y value of 0.

So they're both on the x axis.

Okay, so that's a bit of a clue.

The points could be joined by a horizontal line.

Hmm.

Now let's have a look at the other two coordinates.

They've got something in common too, haven't they? These two coordinates also share a y value, meaning there's another horizontal line.

So we've got two horizontal lines in this shape.

So that should be starting to narrow it down a little bit.

It would be lower than the other horizontal line? Yes.

Why is that? Because it's got negative values.

What could the shape be, I wonder? Well, it's got four vertices.

We know that.

It's got two horizontal sides.

We know that.

Let's think of all the shapes that fit that description.

Well, the shape could be a parallelogram, could be a rhombus, could be a trapezium, could be a square, could be a rectangle.

Hmm.

I think we need more information.

So what else do you notice about these coordinates? Does anything else jump out at you? Hmm, look carefully.

Do what a good mathematician does and notice.

Anything? Well the x coordinates in each pair are six units apart.

So we've got 4 and -2, they're six apart and -2, 4, they're six apart.

This means that the two sides are equal in length.

So it's got four vertices, it's got two horizontal lines.

The lines are equal in length.

We've got another clue.

There's still lots of possibilities of what the quadrilateral could be.

Now whilst those x coordinates are six units apart, the y coordinates are four units apart, hmm.

So one of the pairs of size must each be six units long and the other pair four units long.

So they're not equal.

Okay, so in the quadrilateral, not all sides are the same length.

Could it be a parallelogram? Yes, it could still be that.

Could it be a rhombus? No, because they are all the same length sides.

Could it be a trapezium? No, it couldn't be a trapezium anymore.

Could it be a square? No.

Could it be a rectangle? Yes, it could be.

So I think we've narrowed it down to parallelogram or rectangle.

So let's keep digging.

Let's plot.

So that's 4, 0, that's -2, 0, that's -2, -4 and that's 4, -4.

I think you could hopefully see what that is.

Can join those vertices together and we've got a rectangle.

The shape is a rectangle.

Three of the four coordinates for a quadrilateral have been drawn.

Can you see three there? I wonder where the final vertex will be.

We've got 3, 2.

Can you see that? We've got -3, 1.

Can you see that one? And we've got 2, -4.

Where could the final coordinate be plotted and what shape would be formed.

And is there more than one answer? Well yes, I think there is, don't you? There's lots and lots of places that could go and the shape will change depending on where it does go.

Now John thinks he can form a square.

What do you think? Is that right? Different quadrilaterals can be made depending on the position of the last coordinate.

<v ->4, 5 makes any irregular quadrilateral.

</v> There we go.

So it's got four sides, but it's irregular.

They're not all the same size sides.

There we go.

It's not square though.

How about if we put it there? <v ->3, -4 will create a kite.

</v> Let's have a look at that.

Yes, not a square though.

What about if we put it here? <v ->4, -5 will create a parallelogram</v> but still not a square.

Joining these vertices does not create perpendicular sides and that's what squares have got.

So in fact, Jun's incorrect.

So it can make lots of different quadrilaterals, but square's not one of them.

Let's have a quick check.

Name the shape that will be created if these coordinates are plotted.

Can you predict first by noticing the coordinates like good mathematicians do? Okay, so you've got 4, 1, -2, 1, <v ->2, -5 and 4, -5.

</v> What shape will that be? Pause the video.

Let's see, well that is where the coordinates will go and it makes a square.

As you can see, the side lengths are the same.

And you might have noticed that by looking at the coordinates and how far apart they were.

So well than if you did.

It's time for some final practise, you're doing really well.

Number one, these are the vertices of a quadrilateral 3, 1 that's plotted already.

<v ->2, 1 that's plotted.

</v> <v ->5, -3, that's not plotted.

</v> And 0, -3.

Complete that shape and name the quadrilateral.

Number two, what shape could these coordinates form? Make a prediction and then plot the shape to see if you were correct.

So notice first and then predict based on that and then plot them and see if you were right.

Number three, on each grid two of the four vertices of a quadrilateral are given.

Form the shape stated and give the coordinates of the other two vertices.

Some of the shapes have more than one possibility, so you might like to give more than one.

Here we go.

So that's A, that's a square.

Two of them have been plotted.

What could the other two be? And B, that's a trapezium or the first two coordinates or vertices of a trapezium 4, 1 and 1, 4.

Where could the other ones go? And we've got the parallelogram, that's 4, 1 and 1, 4.

Where could the other ones go? Is there more than one answer? And D, that's a kite.

We've got 4, 1 and 1, 4 again, but where could the other coordinates or the other vertices go? Pause the video, have fun with that and I'll see you soon for some feedback.

Welcome back.

Let's have a look.

Let's give you some answers.

Number one, these are the vertices of a quadrilateral.

So we've got 3, 1 or -2, 1, <v ->5, -3 and 0 -3.

</v> Complete the shape and name the quadrilateral.

Well there's a shape and it's a parallelogram.

And number two, two of the y coordinates are identical and so are a different two, meaning two horizontal lines.

The x coordinates are all different.

So the other lines are not horizontal.

The shape could therefore be another parallelogram.

So well done if you said that.

And number two, there's 1, 3 there's -5, 3, there's -2, -5, and there is 4, -5.

Here we go.

It's a different parallelogram.

and A, that's the only way to complete that square.

<v ->2, 1 and 1, -2.

</v> Well then if you got that.

And the square of course was in a different orientation.

And for B, that's one example of a trapezial.

There were other possibilities.

But we've gone here for -2, 4 and 4 -2.

Now it's got one pair of parallel sides and one that's not.

And see another example.

There are other possibilities.

We've gone here for -5, 4 and -2, 1.

And that's made a parallelogram.

And here's a kite.

And for example, you could have gone for 4, 4 and -3, -3 and that would've formed the vertices of a kite.

We've come to the end of the lesson.

You've done really well today.

Well done.

Today's lesson have been drawing and completing simple shapes by plotting positions on the full coordinate grid, all four quadrants.

Coordinates can exist in all four quadrants of a grid.

And they show the exact position of something, be it positive or negative.

So the example on the right shows 2, -3.

And the format is always like this in brackets x, y.

Giving the distances along the x and y axes, shapes can be drawn on the grid using given coordinates.

And that's exactly what you've done today.

So well done.

And that is the end.

Give yourself a pat on the back.

It's well deserved.

And breathe a sigh of relief.

That's also well deserved.

Your maths lesson is over.

Have really enjoyed it and I hope I get the chance to work with you again on another math lesson in the near future.

But until then, have a great day, whatever you've got in store, take care and goodbye.