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I can explain how negative numbers are used on a coordinate grid.

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Licence

This content is © Oak National Academy Limited (2023), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Key learning points

Coordinates can include negative values
The x or horizontal value is always the first value in a coordinate
The y or vertical value is always the second value in a coordinate

Common misconception

Pupils can get mixed up with which comes first, the x or y axis, when reading/plotting coordinates.

There are lots of aide-mémoires to remember the order. However, regular practice using a stem sentence like the one in the lesson will help.

Keywords

Coordinates - Coordinates are a set of values that show an exact position.
Quadrant - Any of the four areas made when a plane is divided by an x and y axis.
Axis / axes - The x and y lines that cross at right angles to make a graph or grid.

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Hi there, I'm Mr. Tilstone and it's my great pleasure to be working with you today on a lesson all about negative numbers.

So if you're ready, let's begin.

The outcome of today's lesson is I can explain how negative numbers are used on a coordinate grid.

We've got some keywords that I'm going to introduce to you in a my turn, your turn style.

So are you ready? So my turn coordinates, your turn, my turn, quadrant.

Your turn, my turn, axis, your turn.

My turn, axes, your turn.

So it looks like the word axes, but it's axes in this case.

And let's see what those words mean.

Some of those might be familiar to you already.

So coordinates are a set of values that show an exact position they can be shown on a grid as pictured.

So have a look at that grid.

Does that look familiar? Do you remember doing any learning on that recently or in the past? Any of the four areas made when a plane is divided by an X and Y axis are called a quadrant.

The X and Y lines that cross at right angles to make a graph or grid are called axes, which is the plural of axis.

So this graph here, look, it's got an X axis.

It's got a Y axis, so it's got two axes.

Our lesson today is split into two cycles.

The first is using a two quadrant coordinate grid and the second using a four quadrant coordinate grid.

So let's start with the using a two quadrant coordinate grid.

Are you ready? You may have had some previous experience of using the Cartesian coordinate grid system.

What rules can you remember? Well here's what it looks like.

Can you think of any rules? Well, it's got two perpendicular lines, perpendicular, meaning meeting at a right angle, called axes.

That's one axis.

That's the other axis, it's got two axes.

The axes are numbered just like a number line.

You can see that one going from zero to five, the X axis and the other one also going zero to five.

The Y axis, they don't always go from zero to five.

They can go to all sorts of different numbers.

The horizontal axis is called the X axis.

And do you might have had some very recent experience of doing some graph work where we used X and Y axes.

That's X axis.

And the vertical axis is called the Y axis.

The point where the two axes intersect is called the origin and it's labelled with a zero.

So that zero point's called the origin.

Here it is.

Okay, so plotting and reading coordinates always begin at the origin.

So that zero point, the dot here is located three units to the right on the X axis.

So if you go from the zero using a horizontal line, that's three across, three along just like so.

And then two units up on the Y axis.

This might be ringing a bell to you.

Brackets are used to show the coordinates with a comma in between them.

So there's some specific punctuation that's used to show coordinates.

So this purple cross here is located at the coordinate three, two.

So notice the brackets, notice the comma, that's how they're written.

The X axis must be shown first and the Y axis must be shown second.

Otherwise it's showing different information.

So the green cross is at two, three.

So that's why it's important that we get them the right way round.

They're in two different positions.

They've got two different coordinates.

When plotting the coordinates, it might be helpful to use a stem sentence.

M, in the X direction, m, in the Y direction.

So here we've got three in the X direction, two in the Y direction.

And for the green one, see if you can figure that one out.

That is how many in the X direction? That's two in the X direction.

How many in the Y direction? Three, so two in the X direction, three in the Y direction.

Let's have a check.

Which of these options describes this coordinate? Choose all that apply.

So there's more than one answer here.

Is it A, at four, one? Is it B, one in the X direction, four in the Y direction.

Is it C, four in the X direction, one in the Y direction.

And is it D, one, four? Pause the video and give that a go.

What did you think? Did you manage to have a chat with those around you? Did you all come up with an agreement? Let's have a look at the answers.

Well, it is one in the X direction and then four in the Y direction.

So that's applying our stem sentence.

And to use the shorthand, the sort of brackets and comm system, it's one, four.

That's how we represent those coordinates.

So those were the two right answers.

Well done if you've got those two, you are on track, you're ready for the next part of the lesson.

Okay, so plotting the coordinate three, zero.

There's something different about this one.

Something that's a little bit tricky.

Have you spotted what it is? It's the zero part, right? But let's use our stem sentence.

So, mm, in the X direction, mm, in the Y direction.

So what is that? That's three in the X direction.

But how many is it in the Y direction? How far up has it gone? Hasn't gone up at all has it? So it's zero.

So that's three in the X direction, zero in the Y direction.

What would the coordinates be? Three, zero, okay.

What about this one? Plotting the coordinate zero, three.

Let's do a check, what do you think? Use that stem sentence.

Talk to your partner, pause the video.

Okay, so we're gonna plot zero, three.

Let's have a look.

So that is zero in the X direction.

So it hasn't gone anywhere on the X direction, but three in the Y direction.

And that's where we would plot it, just there.

That's where zero three is.

In the same way that vertical number lines can be extended past zero to include negative numbers, the axes can be extended.

So let's now focus our thoughts on negative numbers as well as positive.

Here we go.

So we've extended one of those axes.

We've extended in fact the Y axis, the coordinate grid now has two quadrants.

Before it had one quadrant, now it's got two, two different sort of zones, if you will.

The STEM sentence, mm, in the X direction.

M in the Y direction can still be used when plotting and reading coordinates.

Here we go, look, so this first coordinate is what do you think in the X direction and what in the Y direction? That is one in the X direction and negative two in the Y direction.

So we've got our first negative number and we'd write that just like that with brackets and the comma.

So one, negative two, let's look at another example.

So we've got a new coordinate here.

So look at the purple cross please.

This time, it's one in the X direction and negative three in the Y direction.

Note that the X coordinate has not changed.

So it's still one across, it's the Y coordinate that's changed.

So that gives us one, negative three.

That's how we write that.

And once again that we've got a new coordinate, this time it's one in the X direction, negative four in the Y direction.

And that's how we write that, one, negative four.

So in the X direction, in the Y direction.

What do you think we've got this time? Let's have a look.

Have a think about that.

We've got zero in the X direction, it hasn't gone anywhere.

And negative three in the Y direction.

And that's how we write that zero, negative three.

So the zeros can be quite tricky on coordinate grids.

So they're something to be mindful of.

We've got a generalisation and we're gonna chant it.

I'll say it, we'll say it, then you say it.

And it is as follows, when the Y coordinate is negative, the point is positioned below the X axis.

Let's say that together, are you ready? When the Y coordinate is negative, the point is positioned below the X axis.

Now just you're going to say it.

Ready, go.

Fantastic, here we go.

Two different examples of the Y coordinate being negative and positioned below the X axis.

Let's do a check.

Use a stem sentence to describe the position of the cross.

Write the coordinates using the brackets and a comma.

So remember those two pieces of punctuation.

So m in the X direction, m, in the Y direction.

Pause the video and have a go.

How did you get on? Did you have the chance to confer with a partner and agree on an answer? Let's have a look, well, that is five in the X direction, negative four in the Y direction, and we write that as follows, five, negative four, the brackets and the commas.

If you've got that question right, you're on track, you're doing well, you're ready for the next part of the learning, congratulations.

Let's do another check.

Use a stem sentence to describe the position of the four crosses.

Write the coordinates using bracket and the comma.

And then have a think about this, what do you notice? So it's M in the X direction.

M in the Y direction.

Pause the video, remember to talk to your partner if you've got one.

And let's see what you can come up with.

Let's have a look then, so what do you notice? The crosses all have the same Y coordinate.

So they've all got negative two for the Y coordinate, and they're all on a line parallel to the X axis.

If you said that, very well done.

So A is one, negative two, B is two, negative two C is three, negative two and D sorry, is four, negative two.

Very well done if you've got all of those right.

Similarly, the X axis can be extended past zero to make a different two quadrant coordinate grid.

So before we extended the Y axis, now we're going to extend the X axis.

Here we go.

So now the X axis contains negative values.

Let's have a look at this coordinate.

We could still use our wonderful stem sentence.

In the X direction, m, in the Y direction.

You might want to give that a go before I tell you.

Okay, so we've got negative three in the X direction and one in the Y direction, and that gives us the coordinates negative three, one.

Just like that, just as follows.

So it's just the same as before, but with a different negative axis.

Okay, what about this one then? M in the X direction, in the Y direction, what could it be this time? I think it might involve that tricky zero.

Let's have a look, this time it is negative four in the X direction and zero in the Y direction.

And that's how we write it.

The same stem sentence can be used to plot a point on the grid from a pair of coordinates.

So plot a coordinate at negative five, four.

So have a look at the coordinate grid.

Where do you think negative five, four will be? Well, it's negative five in the X direction, so that's negative five in the X direction and then it's four in the Y direction.

So we need to go up four and there we go.

That's where we would plot negative five four, just there.

And that's how we write it.

Negative five, four.

Let's do a check.

Which of the following correctly describes the position of the cross? Is it two, four? Is it four, two, is it four, negative two, or is it negative two, four.

Pause the video, have a chat to your partner if you've got one, and we'll give you an answer in a second.

Well, as always, I'm thinking about my X axis first, and the X axis is showing negative two and then a Y axis second, and they go alphabetically.

You might notice X is followed by Y in the alphabet and it is when you're doing coordinates.

So X first, Y, second.

So negative two is the X axis and then four is the Y axis.

So that is our correct option.

Well done if you've got that.

Time for some independent practise, do you think you can handle it? I think you can, in fact, I know you can.

So number one, what coordinates are being shown here? So you've got A, B, C, and D.

What are the coordinates? And we've helped you out by giving you the brackets and the commas already.

You've just got to fill in the blanks.

For E, what do you notice about points A and C? Is this something that they've got in common perhaps? And then, what do you notice about points B and C? And for number two, what coordinates are being shown here? So you've got A, B, C, and D.

And number three, what do you notice about points A, B, and C? And number four, what do you notice about about points B and D? So give that a go.

Very best of luck and I will see you quite shortly for some answers.

How did you get on with that? Let's have a look.

So number one, A, so we've got one, negative four, B three, four C, three, negative four, D, four, negative three.

E, you might have put something like A and C have the same Y coordinate.

And for F you might have put something like B and C have the same X coordinate so they've got things in common.

For number two, the coordinates being shown here.

So A is negative five, two, B is negative two, two, C is two, two and D is negative two, four.

So number three, A, B, and C all have the same Y coordinate.

And number four, B and D have the same X coordinate.

So they share a coordinate.

Are we ready for the second cycle? That is using a four quadrant coordinate grid.

So I wonder if you can picture what that would look like before I even show you.

Let's have a look.

Both axes can be extended past zero.

So before we've extended either the X axis or the Y axis, but this time we're extending both.

And the grid is referred to in terms of it's four quadrants.

So you can see there it's got four sort of zones.

One, two, three, four.

You might have heard words that have got quad in them before like quad bike.

That's got four wheels.

So that's the first quadrant, second quadrant, third quadrant and fourth quadrant.

Let's see what you can remember about coordinate grids then because although this is a new kind of grid for you, it's got the same features as before.

So we're looking for the X axis, the Y axis, the origin, and the first quadrant.

Can you describe where those are? Pause the video and talk to your partner if you can.

Let's have a look.

So the X axis is here.

This one going across, the Y axis is here.

The one going up and down.

The origin is here, zero, zero.

And the first quadrant is just here, so well done if you've got all those four features, you've understood the features of a four quadrant coordinate grid, well done.

So let's have a deeper look at our four quadrant grid, shall we? Well, in our first quadrant here, we've got a positive X direction and a positive Y direction.

So both axes are positive, that is greater than zero.

You will not need to use a negative symbol for anything that appears in that quadrant.

And then we've got a negative X direction, a positive Y direction.

So all of the coordinates in this quadrant have an X value less than zero.

So you will need a negative symbol, but a Y value greater than zero.

And then this is our zone that both our quadrant that both of the coordinates are negative.

So we've got a negative X direction, negative Y direction, both axes are negative.

So you'll need two negative symbols when describing the coordinates there.

And then finally, we've got a positive X direction and a negative Y direction.

In this quadrant, the X value is greater than zero, but the Y value is less than zero.

So let us investigate how the negative symbol changes the position on the four quadrant grid.

So here we've got four, three.

So positive, positive.

Here we've got those same digits, but with a negative symbol.

You can see it's a totally different position or at least on one of the axes it is.

So this time it's negative four, three.

So it's a negative X quadrant, a positive Y quadrant.

Let's use those same digits again.

But this time both of them have got a negative symbol.

So that's negative four, negative three.

So again, a different position, negative X quadrant, negative Y quadrant.

And then finally we've got four negative three.

So it's the same digits.

It's been the same digits on all four examples, four, three.

But the negative symbol changes the position.

That's a positive X quadrant and a negative Y quadrant.

Let's do a check, in which quadrant will you find the coordinate one, negative five.

Is that going to be A, B, C, or D? Pause the video.

Let's have a look, one, negative five is in D.

And there it is.

So if you've got that, brilliant, you're on track.

Got a positive X quadrant and a negative Y quadrant.

Just like with number lines, values can exist in between the intervals.

So have a look at this one.

You might notice it's not on any of the lines, the grid lines.

There's not sit in either the X grid line or the Y grid line, but it sits in between them and it has got a value.

So we can't describe it as three for the X coordinate because it's further than three and we can't describe it as four because it's not as far as four.

It's halfway between them.

Halfway between three and four.

So it's 3.

And let's have a look at the Y axis.

It's again, it's not on negative four, is it? It's not on negative five, but it's in between them.

So what could it be halfway between them? So it's at negative 4.

So there we go.

So that gives us the coordinates 3.

5, negative 4.

Let's do a check.

What are the coordinates of the cross just here, pause the video.

Okay, so you can see that once again, one of them this time, not both, but one of them lies in between two negative numbers in this case.

Here we go, so the X axis look, it's in between negative three and negative four.

So that's negative 3.

5, negative two.

Really big well done if you've got that.

Time for some final practise.

So number one, plot these coordinates.

Some have got negative values and a lot of them have got negative values.

And so have a think about where they belong on the grid.

Number two, plot these coordinates, what shape do they form? Pause the video and very best of luck.

How did you get on with that final task? Well, let's have a look at these coordinates.

So two, five is just here, negative three, four is here.

Negative five zero is just there, negative four, negative five is just here.

Four, negative two is just here, zero negative three is here.

And negative 2.

5, negative 1.

5 is just here.

And that was a really tricky one.

So well done if you've got that one.

And number two, plot these coordinates.

What shape do they form? They form a rectangle and it looks just like that.

We're coming to the end of our lesson.

So today we've been explaining how negative numbers are used on a coordinate grid.

Coordinates can exist in all four quadrants of a grid.

They show the exact position of something.

So today we looked at one quadrant grids at the start and then two quadrant grids, one where the X axis was extended and a different one where the Y axis was extended.

And then finally we looked at the four quadrant grids, like the one you can see on the screen, they're written using brackets and commas.

The example on the right shows two, negative three.

The format is always XY, given the distances along the X and Y axes.

And that stem sentence I think is really useful.

So m on the X axis, m on the Y axis, welded on today's achievements.

Hopefully I'll be able to work with you again soon.

Until then, take care and goodbye.

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" } ], "id": "9075a6f1-60f2-4fe1-4978-545d1749b469", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "Tick all the statements that are true." }, "questionType": "Multiple choice", "correct": [ { "text": "−3 is greater than −4." }, { "text": "3 is greater than −3." }, { "text": "3 and −3 have the same distance from zero." } ], "choices": [ { "text": "−3 is greater than −4." }, { "text": "−4 is greater than −3." }, { "text": "−3 is greater than 3." }, { "text": "3 is greater than −3." }, { "text": "3 and −3 have the same distance from zero." } ], "id": "1ce274bd-aae6-84c4-7e50-0e1b53b2e400", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "Put the following numbers into descending order." }, "questionType": "Ordering", "elements": [ { "order": { "text": "1" }, "item": { "text": "1" } }, { "order": { "text": "2" }, "item": { "text": "0.75" } }, { "order": { "text": "3" }, "item": { "text": "0" } }, { "order": { "text": "4" }, "item": { "text": "−1" } }, { "order": { "text": "5" }, "item": { "text": "−1.5" } } ], "id": "06f026bd-47de-99c8-dd3a-744502d9d385", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "What number is exactly halfway between −10 and −9?" }, "questionType": "Multiple choice", "correct": [ { "text": "−9.5" } ], "choices": [ { "text": "There is no number between −10 and −9." }, { "text": "−9.5" }, { "text": "−10.5" }, { "text": "−9.25" }, { "text": "−9.75" } ], "id": "ee9f03b6-4972-2922-a73f-ac15b7ba8233", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" } ], "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 5", "topic": null, "unit": "Negative numbers", "lessonCount": "10", "age": [ 9, 10 ], "gradeId": "age_9_10", "gradeStage": "Key Stage 2", "lesson": "Explain how negative numbers are used on a coordinate grid" } }, { "id": "156ce3dd-46a2-0d0d-2225-17ea5abe4512", "type": "Resource", "resourceType": "Quiz", "title": "Explain how negative numbers are used on a coordinate grid", "quizType": "Exit quiz", "items": [ { "type": "Question", "question": { "text": "Match the keyword with the definition." }, "questionType": "Matching", "pairs": [ { "left": { "text": "coordinates" }, "right": { "text": "a set of values that show an exact position" } }, { "left": { "text": "quadrant" }, "right": { "text": "any of 4 areas made when a plane is divided by x and y axes" } }, { "left": { "text": "axes" }, "right": { "text": "the x and y lines that cross at right angles to make a grid" } } ], "id": "1c257e12-a168-abab-02b8-3a2dce5c3722", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "Using brackets and a comma, give the coordinates of the cross marked on this two quadrant grid.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1701269466%2Fijmwzqsw3exb8fyezlri.png&w=640&q=75", "imageKey": "156ce3dd-46a2-0d0d-2225-17ea5abe4512/question/4fc01f6e4499e0a00ba033670368b559.png" }, "questionType": "Short answer", "correct": [ { "text": "(0,−4)" }, { "text": "(0, −4)" }, { "text": "( 0, −4 )" }, { "text": "(0,−4 )" }, { "text": "( 0, −4)" } ], "id": "74f5b3a8-f245-2f1e-56e1-29ce1307ce28", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "Match the letters with the quadrant descriptions.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1701269467%2Frvsa5d0fzuxgrugvz6r3.png&w=640&q=75", "imageKey": "156ce3dd-46a2-0d0d-2225-17ea5abe4512/question/cf1c4003e8f88989f53535d1c683d0b9.png" }, "questionType": "Matching", "pairs": [ { "left": { "text": "a" }, "right": { "text": "positive x direction, positive y direction" } }, { "left": { "text": "b" }, "right": { "text": "negative x direction, positive y direction" } }, { "left": { "text": "c" }, "right": { "text": "negative x direction, negative y direction" } }, { "left": { "text": "d" }, "right": { "text": "positive x direction, negative y direction" } } ], "id": "7680b424-e54c-7f39-433a-e2b109b46049", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "In which quadrant will you find the coordinate (−2, 5)?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1701269467%2Frvsa5d0fzuxgrugvz6r3.png&w=640&q=75", "imageKey": "156ce3dd-46a2-0d0d-2225-17ea5abe4512/question/cf1c4003e8f88989f53535d1c683d0b9.png" }, "questionType": "Multiple choice", "correct": [ { "text": "b" } ], "choices": [ { "text": "a" }, { "text": "b" }, { "text": "c" }, { "text": "d" } ], "id": "b9f7653a-045d-ddb0-0649-33bb7e9e03cf", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "If the axes were extended, in which quadrant would you find the coordinate (18, −25)?", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1701269467%2Frvsa5d0fzuxgrugvz6r3.png&w=640&q=75", "imageKey": "156ce3dd-46a2-0d0d-2225-17ea5abe4512/question/cf1c4003e8f88989f53535d1c683d0b9.png" }, "questionType": "Multiple choice", "correct": [ { "text": "d" } ], "choices": [ { "text": "a" }, { "text": "b" }, { "text": "c" }, { "text": "d" } ], "id": "43e0f685-5de2-6ed7-b435-e2600002cde3", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" }, { "type": "Question", "question": { "text": "When joined together, the four crosses form a rectangle. Tick all of the coordinates that would be found inside the rectangle.", "image": "https://www.thenational.academy/_next/image?url=https%3A%2F%2Foaknationalacademy-res.cloudinary.com%2Fimage%2Fupload%2Fv1701269468%2Fcikroibnpxzahlw8pahk.png&w=640&q=75", "imageKey": "156ce3dd-46a2-0d0d-2225-17ea5abe4512/question/b5b6f1202d7e6e4a86dfef036de23134.png" }, "questionType": "Multiple choice", "correct": [ { "text": "(0,0)" }, { "text": "(4,2)" }, { "text": "(−2,−3)" } ], "choices": [ { "text": "(0,0)" }, { "text": "(2,4)" }, { "text": "(4,2)" }, { "text": "(−2,−3)" }, { "text": "(−3,4) " } ], "id": "f2805abd-a291-3405-06b6-339d8dd44fd6", "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434" } ], "lessonId": "48986f09-5c4d-b563-d855-7ea7ecdb6434", "meta": { "gradeStageId": "ks2", "subject": "Maths", "grade": "Year 5", "topic": null, "unit": "Negative numbers", "lessonCount": "10", "age": [ 9, 10 ], "gradeId": "age_9_10", "gradeStage": "Key Stage 2", "lesson": "Explain how negative numbers are used on a coordinate grid" } } ] }