﻿Hello, and welcome to this lesson with me, Dr. Saada. In today's lesson, we will be learning about the 2-D coordinate axes. For today's lesson, you need a pen and paper. Please take a moment now to clear away any distractions, and find a quiet place where you won't be disturbed during the lesson. Okay, when you're ready, let's begin. I would like you to try this question. Which of the points below can be joined using the L below? If you look at the diagram, you've got something that looks like an L inside a green box. Imagine the L is on a tracing paper, so you can place it however you want over the points. Which points can you join together using that L? If you feel confident about this, please pause the video and have a go at it. If not, don't worry. I'll give you some support. Okay, so for support, I'm going to ask you to imagine moving that L from there and trying to put it next to the letter C, and rotate it around. Where would it fit? Mm, good thinking. It would look like this, wouldn't it? Now, pause the video, and have a go. How many points were you able to join using the L? Really interesting. Well done. Let's have a look at the ones I've done here. Connect this one, C to E. I connected B to F, D to G, and H to E. Did you get the same answers? Good job. Well done. We use coordinates to describe the position of a point. A coordinate consists of two values, the x-coordinate and the y-coordinate. The x-coordinate describes the horizontal location, and the y-coordinate describes the vertical location. When we want to write the coordinate, this is how we write it. So we write, we start with the bracket, and then we have x, the x-coordinate, comma, and then the y-coordinate. And then we remember to close the brackets. That's how we write coordinates. If we look at the grid here, there is a really important point on the grid, and that is this point here. 'Kay, and this point is called the origin, and it has, so it's called the origin, and it has the coordinate zero, zero. The reason for this is at this point, at the origin here, it's on the zero on the x-axis and it's on the zero on the y-axis. So it has the coordinate zero, zero. Okay, now let's have a look, and we're going to start with this point here. 'Kay, so we are going to write down the coordinates for each of these points, and we are going to have a little chat about them as we write them, as we go along. Okay, so the coordinate of the first point that I have just marked here, if we read the value on the x-axis, it's one, so it has the coordinate of one, zero. Because on the y-axis, it's still here. We didn't go up. We didn't go down on the y-axis at all. Okay, so it has the coordinate one, zero. Now, the second point, let's look at this point here. If I want to write the coordinate of this point, on the x-axis, it's on number four. That's four. On the y-axis, it's at three. So the coordinate is four, three. Next point, this one here, 'kay, it has the coordinate three on the x-axis. That's three. And along the y-axis, it's four. So it has the coordinate three, four. Now, there's something really important about the three points that I have just labelled here. They are all on or in the first quadrant, quadrant number I. All the x-coordinates and the y-coordinates are positive. There's one more, actually, that lies right in between quadrant I and quadrant II, and it's this one here. What's the coordinate of this one? And you have to be really careful with this one. Okay, on the x-axis, it's at zero. So the coordinate is zero. And on the y-axis, it's at one. So it's zero, one. Now, let's move on to quadrant number II, which is this quadrant here, so this part of the grid. And we're going to write down the coordinates of each of the points. We will start with this point here. What's the coordinate of this point? If we read the x-coordinate, it's negative three, and y-coordinate is four. So the coordinate of the point is negative three, four. Let's read this one here. 'Kay, we do exactly the same thing. On the x-axis, it's at negative four. So we have negative four. And along the y-axis, it's at three. Next point, which is this one here, so on the x-axis, it's at negative one. Well done. And on the y-axis, did we go up or down? We didn't, so it's at zero. So negative one, zero. Now, moving on, this is our third quadrant. Okay, so this is our third quadrant. We're going to find the coordinate of this point here to start with. What's the coordinate of this one? If we check the x-coordinate, the x-coordinate is negative four. And the y-coordinate is negative three. Next one, so this point here, the x-coordinate is negative three. Well done. And the Y coordinate is negative four. Really good. And next one, we're going to do this point here. I'm going to write the coordinate for it here, so I've got a bit more space. What's the x-coordinate? It's at zero on the x-axis. Well done. And y-coordinate, it's at negative one. And the last two points that we have, this point here, what's the coordinate? We go up. It's four on the x-axis, and it's negative three on the y-axis. And this point here, it's? Excellent. Three, negative four. It's at three for the x-axis and negative four on the y-axis. 'Kay, so it's really important to note that all the points that we have in this part of the grid, so in this part of the grid, all of the points that are on this part here, okay, all of these are in quadrant I. The x- and the y-coordinates are both positive. All the points that are on this part of the grid, so all of this area here, any point that is in that area, that is the second quadrant of the grid. The x-coordinate is negative, and the y-coordinate is positive. The third quadrant is this one here. 'Kay, and what's really special about it is that any point that is in that quadrant has a negative x- and a negative y-coordinate. And the fourth one obviously is this one here. And it has a positive x-coordinate, but it has a negative y-coordinate. And for the second part, give the coordinates of a point that would be off the grid shown. You can see that the grid that I have here provided, it goes up to positive seven, and it goes to a minimum of negative seven and up to positive six on the y-axis and negative six on the y-axis. However, we can have points outside the scope of this grid. So I can have a point that has the coordinate of eight, 10. I'm not really limited to this. Just the grid that I provided here had this limitation, but we can have points outside the grid. I can have something like negative 100, negative 11. Okay, I can also have decimals. So I can have 25.5, 3/4. So I can have decimals. I can write it as a fraction form. It really doesn't matter. So we can have so many different points that are not necessarily now shown on the grid. And now it is your time to practise independently what we have learned together. So pause the video, and have a go at the independent task. Great. Let's mark question number one. I want you to mark and correct the work. If you've made a mistake, it's really, really important that you correct it. So let's have a go at this together. Question one, state the coordinate for each of the points. And you had the grid with some points on it. Let's start, and let's do them in alphabetical order. So we'll start with point A. What did you write down? Excellent. Three, two. What did you write down the coordinate for point B? Good job. It's five, negative three. What did you write down for C? Really good. Negative four, negative three. What about point D? Excellent. Negative four, four. And for E? Really good job. Zero, six. Point F? Great job. Negative seven, one. Now, I wonder what you wrote down for G because that was the one that I thought, "Ooh, really interesting." If we look at G, where is it on the x-axis? If I draw a line, it's not actually on four and it's not on five. It's between and right in the middle, between four and five. So the x-coordinate must be? Good job. And what about the y? If I draw a line here to try and read it off, it's between three and four and therefore? Excellent. So the coordinate of G is at 4.5, 3.5. Really good. Now, part b, describe the journey from B to A, and there are so many ways that you could have tackled this part. Now let's have a look at what I've done here. From B, so I went to point B, and I drew a journey to A. I said to myself, "Let me describe it." What have I done to get from B to A? I went left two and up five, and that, as simple as that. You could have gone up first and then left, and that will also get you to point A. What about the journey from A to B? A to B, I went right twice. 'Kay, so I went right two and five down. You could have done the opposite, as in five down and then done right two. Good job. Right seven, up five describes a journey between which two points? What did you write down? Good job. If you go up five, right seven, you get the journey from C to A. Plot and label the points X, three, negative two. What would that be? Good. Three, negative two. Can you see here, I plotted the point using an X, and then I named it. So I wrote down that capital X. What about Y, six, negative two? So you go to six on the x-axis. You go down two places. There we go. What about Z, negative six, negative two? Negative six on the x-axis, so we go to negative six on the x-axis and then down to negative two, and that is that. Excellent job. Okay, question two, the image below is taken from a section of a coordinate grid. Find the coordinates of the points A, B, and C. Now, if you look at the grid clearly, now, if you look at the grid carefully, you're not given the x- or the y-axes. 'Kay, you're given two points that have coordinates three, 10, and one of them has five, 11 as its coordinates. Now, we need to use those two points to find the coordinates of the other three. So let's have a look at what is it that we know. We know that this point has an x-coordinate of three. This point has an x-coordinate of five. So right in the middle, between them, this line here must have an x-coordinate of four. Good job. Now, we don't know the y-coordinate yet, so let's look at what y-coordinates we know. We know that this point has a y-coordinate of 10, and this point has y-coordinate of 11. So this tells me that this line here has a coordinate of 11. This one has a y-coordinate of 10. This one has a y-coordinate of nine. And this line has a y-coordinate of eight. And therefore, point B has the coordinate four, eight. Really good. Now let's look at point A. We can already see that it has a y-coordinate of nine. What is its x-coordinate? It's one away from the five, 11, so it must have an x-coordinate of six. Really good. What did you get as the coordinate for point C? I wonder if we got the same answer. Really good job. So the answer is two, 12. It is one away from three, but to the left, so it's less by one. And it is one above the five, 11 point, so it has a y-coordinate of 12. Really good job. And this brings us to our Explore task. Write down the coordinates of points A to F. So the points are clearly labelled on the grid. The robot starts at A. Use code to make the robot move from, and I've given you a few points, so to move from A to B, B to C, C to D, D to E, and E to F. You should all be able to answer the first part of the question. So write down the coordinates of the points. Now, to write the code for the second part of the question, I want you to use the codes north, west, south, and east. Now, if you're feeling confident about this, pause the video and have a go. If not, don't worry. I will give you a hint. Okay, so if you're not too sure, we need to make sure that you know the directions, so you know where your north, your south, east, and west. So if you are going to the right, you're going to write east. And depending on the number of steps that you take, you'll write the number in that white box. If you're going to the left, you're going to write west. Or if you want the robot to move to the left, you're going to write west. If you want the robot to move up, you're going to write north. And if you want the robot to move down, you have to write south and the number of steps that you want the robot to take next to each word. 'Kay, now pause the video, and have a go. Okay, let's start marking the work. We're going to go through the points first. So A has the coordinate negative five, two. B has the coordinate negative one, five. C, five, five. What did you get for D? Really good job. Two, one. What about E? Excellent. Two, negative five. And what did you get for F? Really good job. Six, negative two. And now that we have the coordinates written down, we are going to check the code. So the robot is at point A and needs to move to point B. What code did you write down? I wonder. Good job. To get from A to B, the robot will need to move to the right four places and up three, which means the code is east four and north three. I know that some of you may have written north three first and then east four, and that's fine because the robot could have also gone up first and then right. So well done if you got this correct. Next one, B to C. Good job. So from B to C, the robot just needs to go east. If we count the places, it's six spaces, So six places, so east six. Next one, from C to D, the robot will need to go down four places and then to the left three places. So down is? Good job. And to the left is? Excellent. So it needs to go west three and south four or south four and then west three. Both are correct. D to E, the robot will need to go south, and that is six places. Well done. And the last one, what did you write down for E to F? 'Kay, let's look at the grid. To get from E to F, the robot will need to go right and then up. And that is east four, and then up means north three. 'Kay, and some of you may have written north first, so north three and then east four, and both are correct. Well done. You have done some fantastic learning today. So really good. Well done. There are three things that I would like you to do now. First, I would like you to look back at your notes from today's lesson and identify the three most important things that you've learned today. It is up to you what these three things are. Secondly, I would like you to do the exit quiz. It's really important, just to check your understanding. And three, I would love to see your work. So if you want to share your work with Oak National, please ask your parent or carer to share your work on Twitter, tagging @OakNational and #LearnwithOak. And now all I have to say to you is enjoy the rest of your learning for today. Bye!

Fill in the gap: We use a coordinate .............. to describe a location in 2-D space.

Fill in the gap: The ............. describes the horizontal location of a given point.

Fill in the gap: The ............. describes vertical location of a given point.

The origin is the point

What is the coordinate of point A in the image given below?

What is the coordinate of point B in the image given below?

What is the coordinate of point C in the image given below?

The 2-D coordinate axis

In this lesson, we will learn how to describe positions on a coordinate grid.


Maths

Y7 Maths

Key Stage 3

Year 7

Coordinates

Geometry

THEME

UNIT

Line segments

Finding midpoints

Solving geometric problems

Forming shapes from midpoints

Forming shapes from diagonals

Equations of lines

Exploring horizontal and vertical lines

What are the co-ordinates of point C?

Which point has the co-ordinates (5, -2)?

Describe the movement from B to A.

Which statement best describes line segments A and B?

Which line segments have equal length?

Which sentence correctly compares the lengths of the two line segments shown below?

Find the mid-­point of the points on the number line:

Fill in the gap: The equation .......... describes a line through every point with x-coordinate 4.

What is the equation for line C?

What is the coordinate of the midpoint of the line segment shown below?

Lesson overview:The 2-D coordinate axis

Core Content

Coordinates: