Year 4: Reading coordinates
Part of the Year 4 coordinates and translation chapter. Chapter overview · whole chapter on one page · Download worksheet (PDF) · Answers (PDF)
Reading coordinates
Imagine you are at the front door of a school. To get to your classroom, you walk along the corridor first. Then you go up the stairs. Coordinates work in the same way. They are two numbers that tell you exactly where a point is on a grid: along first, then up.
The two number lines are called the axes. The x-axis goes along the bottom. The y-axis goes up the side. They meet at the origin, which is the point (0, 0). Every point is counted from the origin. The grids in this chapter show the top-right part of the full coordinate grid, where all the numbers are 0 or bigger. This part is called the first quadrant.
We write the coordinates in brackets with a comma between them: (4, 3). The first number is the x-coordinate (how far along). The second number is the y-coordinate (how far up). On these grids the numbers are written on the lines, not in the squares. A point is where two lines cross.
Some points are on an axis. A point on the x-axis has 0 for its up number, like (5, 0). A point on the y-axis has 0 for its along number, like (0, 4). The origin has both numbers zero: (0, 0).
Key ideas
- Coordinates are written (along, up), in brackets, with a comma. The first number is the x-coordinate. The second number is the y-coordinate.
- The origin is (0, 0). The x-axis goes along. The y-axis goes up.
- Always go along first, then up: “along the corridor, then up the stairs”.
- Points on the x-axis have y = 0. Points on the y-axis have x = 0.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.A is above the number 4 on the x-axis.
Along = 4 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.A is level with the number 3 on the y-axis.
Up = 3 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.A = (4, 3)
Check. Start at (0, 0). Go 4 along and 3 up. You arrive at A. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.B is above the number 5 on the x-axis.
Along = 5 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.B is on the x-axis, so we go 0 up.
Up = 0 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.B = (5, 0)
Check. Start at (0, 0). Go 5 along and 0 up. You arrive at B. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Go along first, then up. The letter you land on is the answer.
- Start at the origin. Every position is measured from the point (0, 0).(0, 0)
- Go 6 along the x-axis. The first number is the along number.(6, 5): along = 6
- Go 5 up. The second number is the up number.Up = 5
- Read the letter at the point. We stop where the two moves meet.The letter is C.
Check. Point C is 6 along and 5 up, which is (6, 5). ✓
Watch out. Do not go up first. The first number is always the along number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.S is above the number 9 on the x-axis.
Along = 9 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.S is level with the number 7 on the y-axis.
Up = 7 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.S = (9, 7)
Check. Start at (0, 0). Go 9 along and 7 up. You arrive at S. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The first number says how far to go along. The second number says how far to go up.
- Look at the first number. The first number is the along number (the x-coordinate).(6, 2): first number = 6
- Look at the second number. The second number is the up number (the y-coordinate).(6, 2): second number = 2
- Write the moves. Start at the origin, go along first, then up.Go 6 along and 2 up.
Check. Start at (0, 0), go 6 along and 2 up: you are at (6, 2). ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the point P carefully, along first and then up. Compare with what Zainab wrote.
- Read point P. Look down to the x-axis, then across to the y-axis.P is above 3 on the x-axis, so along = 3.
P is level with 5 on the y-axis, so up = 5. - Write the coordinates. Along first, then up.P = (3, 5)
- Compare with Zainab’s answer. Zainab wrote (5, 3). That means 5 along and 3 up. This is a different point.The point (5, 3) is shown in blue below.
Check. (3, 5) means 3 along and 5 up. That is where P is. ✓
Watch out. Zainab put the up number first. Always say the along number first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates of all the points. Then look for two that have the same first number (x).
- Write the coordinates of every point. We read each point: along first, then up.A = (2, 6)
B = (5, 3)
C = (2, 2)
D = (8, 3)
E = (7, 7) - Look at the x-coordinate (the first number). Two points that have the same number here are on a straight line.The x-coordinate 2 is in A and in C.
- Write the answer. Points with the same x-coordinate are in a vertical line. Points with the same y-coordinate are in a horizontal line. The orange line joins them.A and C
Check. A and C both have x = 2. ✓
Watch out. Compare the correct number: first number for x, second number for y.
Watch out
Along first, then up. (2, 6) and (6, 2) are not the same point. Also, the numbers are on the lines, so count the lines from the origin, not the squares. The origin is (0, 0), not (1, 1).Exercise 10A Reading and writing coordinates
Non-calculatorKey words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.A is above the number 2 on the x-axis.
Along = 2 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.A is level with the number 3 on the y-axis.
Up = 3 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.A = (2, 3)
Check. Start at (0, 0). Go 2 along and 3 up. You arrive at A. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.B is above the number 5 on the x-axis.
Along = 5 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.B is level with the number 1 on the y-axis.
Up = 1 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.B = (5, 1)
Check. Start at (0, 0). Go 5 along and 1 up. You arrive at B. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.C is above the number 1 on the x-axis.
Along = 1 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.C is level with the number 5 on the y-axis.
Up = 5 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.C = (1, 5)
Check. Start at (0, 0). Go 1 along and 5 up. You arrive at C. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.D is above the number 6 on the x-axis.
Along = 6 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.D is level with the number 4 on the y-axis.
Up = 4 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.D = (6, 4)
Check. Start at (0, 0). Go 6 along and 4 up. You arrive at D. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Go along first, then up. The letter you land on is the answer.
- Start at the origin. Every position is measured from the point (0, 0).(0, 0)
- Go 3 along the x-axis. The first number is the along number.(3, 2): along = 3
- Go 2 up. The second number is the up number.Up = 2
- Read the letter at the point. We stop where the two moves meet.The letter is A.
Check. Point A is 3 along and 2 up, which is (3, 2). ✓
Watch out. Do not go up first. The first number is always the along number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Go along first, then up. The letter you land on is the answer.
- Start at the origin. Every position is measured from the point (0, 0).(0, 0)
- Stay on the y-axis. The first number is the along number.(0, 5): along = 0
- Go 5 up. The second number is the up number.Up = 5
- Read the letter at the point. We stop where the two moves meet.The letter is B.
Check. Point B is 0 along and 5 up, which is (0, 5). ✓
Watch out. Do not go up first. The first number is always the along number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Go along first, then up. The letter you land on is the answer.
- Start at the origin. Every position is measured from the point (0, 0).(0, 0)
- Go 4 along the x-axis. The first number is the along number.(4, 0): along = 4
- Do not go up. The second number is the up number.Up = 0
- Read the letter at the point. We stop where the two moves meet.The letter is D.
Check. Point D is 4 along and 0 up, which is (4, 0). ✓
Watch out. Do not go up first. The first number is always the along number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Go along first, then up. The letter you land on is the answer.
- Start at the origin. Every position is measured from the point (0, 0).(0, 0)
- Go 7 along the x-axis. The first number is the along number.(7, 3): along = 7
- Go 3 up. The second number is the up number.Up = 3
- Read the letter at the point. We stop where the two moves meet.The letter is G.
Check. Point G is 7 along and 3 up, which is (7, 3). ✓
Watch out. Do not go up first. The first number is always the along number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The first number says how far to go along. The second number says how far to go up.
- Look at the first number. The first number is the along number (the x-coordinate).(5, 2): first number = 5
- Look at the second number. The second number is the up number (the y-coordinate).(5, 2): second number = 2
- Write the moves. Start at the origin, go along first, then up.Go 5 along and 2 up.
Check. Start at (0, 0), go 5 along and 2 up: you are at (5, 2). ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The first number says how far to go along. The second number says how far to go up.
- Look at the first number. The first number is the along number (the x-coordinate).(3, 6): first number = 3
- Look at the second number. The second number is the up number (the y-coordinate).(3, 6): second number = 6
- Write the moves. Start at the origin, go along first, then up.Go 3 along and 6 up.
Check. Start at (0, 0), go 3 along and 6 up: you are at (3, 6). ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The first number says how far to go along. The second number says how far to go up.
- Look at the first number. The first number is the along number (the x-coordinate).(7, 0): first number = 7
- Look at the second number. The second number is the up number (the y-coordinate).(7, 0): second number = 0
- Write the moves. Start at the origin, go along first, then up.Go 7 along and 0 up.
Check. Start at (0, 0), go 7 along and 0 up: you are at (7, 0). ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The first number says how far to go along. The second number says how far to go up.
- Look at the first number. The first number is the along number (the x-coordinate).(4, 4): first number = 4
- Look at the second number. The second number is the up number (the y-coordinate).(4, 4): second number = 4
- Write the moves. Start at the origin, go along first, then up.Go 4 along and 4 up.
Check. Start at (0, 0), go 4 along and 4 up: you are at (4, 4). ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The x-axis is the line that goes along the bottom of the grid. It is the horizontal line.
- Remember what the x-axis does. We go along the x-axis first when we read coordinates.The x-axis goes along the bottom.
- Look at the letters on the picture. A is on the bottom line. B is on the line going up the side.A is on the line going along the bottom.
- Write the answer. The x-axis is line A.
Check. The x-axis is the one we count along first. ✓
Watch out. x goes along. y goes up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The y-axis is the line that goes up the side of the grid. It is the vertical line.
- Remember what the y-axis does. We go up the y-axis second when we read coordinates.The y-axis goes up the side.
- Look at the letters on the picture. B is on the line going up the side.B is the line going up.
- Write the answer. The y-axis is line B.
Check. The y-axis is the one we count up. ✓
Watch out. x goes along. y goes up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The origin is the point where the x-axis and the y-axis meet. It is the start for all coordinates.
- Find where the two axes cross. The two lines meet at the corner.They meet at point C.
- Say its name and coordinates. The point where the axes meet is called the origin.C is the origin, (0, 0).
Check. Going 0 along and 0 up leaves you at C. ✓
Watch out. The origin is (0, 0), not (1, 1).
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Write the along number first and the up number second, inside brackets.
- Find the along number. The along number is the x-coordinate. It goes first.Along = 3
- Find the up number. The up number is the y-coordinate. It goes second.Up = 4
- Write them in brackets, along first. Put a comma between the two numbers.(3, 4)
Check. Start at (0, 0). Go 3 along and 4 up. ✓
Watch out. Do not write the up number first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Write the along number first and the up number second, inside brackets.
- Find the along number. The along number is the x-coordinate. It goes first.Along = 6
- Find the up number. The up number is the y-coordinate. It goes second.Up = 1
- Write them in brackets, along first. Put a comma between the two numbers.(6, 1)
Check. Start at (0, 0). Go 6 along and 1 up. ✓
Watch out. Do not write the up number first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Write the along number first and the up number second, inside brackets.
- Find the along number. The along number is the x-coordinate. It goes first.Along = 0
- Find the up number. The up number is the y-coordinate. It goes second.Up = 5
- Write them in brackets, along first. Put a comma between the two numbers.(0, 5)
Check. Start at (0, 0). Go 0 along and 5 up. ✓
Watch out. Do not write the up number first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Write the along number first and the up number second, inside brackets.
- Find the along number. The along number is the x-coordinate. It goes first.Along = 8
- Find the up number. The up number is the y-coordinate. It goes second.Up = 8
- Write them in brackets, along first. Put a comma between the two numbers.(8, 8)
Check. Start at (0, 0). Go 8 along and 8 up. ✓
Watch out. Do not write the up number first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. The origin is the point where the two axes meet. We start counting every position from it.
- Find where the axes meet. The x-axis and the y-axis cross at the origin.It is at the very corner, with nothing to count.
- Count along and up. We go 0 along and 0 up.Along = 0, up = 0
- Write the coordinates. Along first, then up.The origin is (0, 0).
Check. You do not move at all, so you stay at (0, 0). ✓
Watch out. The origin is (0, 0), not (1, 1).
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. A point on the x-axis is on the bottom line. It has not gone up at all.
- Find the along number. The point is 5 along the x-axis.Along = 5
- Find the up number. The point is on the x-axis, so it is 0 up.Up = 0
- Write the coordinates. Along first, then up.The point is (5, 0).
Check. Every point on the x-axis has y = 0. ✓
Watch out. The second number is 0 on the x-axis, not the first.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. A point on the y-axis is on the line going up the side. It has not gone along at all.
- Find the along number. The point is on the y-axis, so it is 0 along.Along = 0
- Find the up number. The point is 3 up the y-axis.Up = 3
- Write the coordinates. Along first, then up.The point is (0, 3).
Check. Every point on the y-axis has x = 0. ✓
Watch out. The first number is 0 on the y-axis.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.S is above the number 3 on the x-axis.
Along = 3 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.S is level with the number 8 on the y-axis.
Up = 8 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.S = (3, 8)
Check. Start at (0, 0). Go 3 along and 8 up. You arrive at S. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.P is above the number 8 on the x-axis.
Along = 8 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.P is level with the number 9 on the y-axis.
Up = 9 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.P = (8, 9)
Check. Start at (0, 0). Go 8 along and 9 up. You arrive at P. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.L is above the number 6 on the x-axis.
Along = 6 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.L is level with the number 4 on the y-axis.
Up = 4 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.L = (6, 4)
Check. Start at (0, 0). Go 6 along and 4 up. You arrive at L. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.F is above the number 9 on the x-axis.
Along = 9 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.F is level with the number 2 on the y-axis.
Up = 2 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.F = (9, 2)
Check. Start at (0, 0). Go 9 along and 2 up. You arrive at F. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates of all the points. Then look for two that have the same first number (x).
- Write the coordinates of every point. We read each point: along first, then up.A = (2, 6)
B = (5, 3)
C = (2, 2)
D = (8, 3)
E = (7, 7) - Look at the x-coordinate (the first number). Two points that have the same number here are on a straight line.The x-coordinate 2 is in A and in C.
- Write the answer. Points with the same x-coordinate are in a vertical line. Points with the same y-coordinate are in a horizontal line. The orange line joins them.A and C
Check. A and C both have x = 2. ✓
Watch out. Compare the correct number: first number for x, second number for y.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates of all the points. Then look for two that have the same second number (y).
- Write the coordinates of every point. We read each point: along first, then up.A = (2, 6)
B = (5, 3)
C = (2, 2)
D = (8, 3)
E = (7, 7) - Look at the y-coordinate (the second number). Two points that have the same number here are on a straight line.The y-coordinate 3 is in B and in D.
- Write the answer. Points with the same x-coordinate are in a vertical line. Points with the same y-coordinate are in a horizontal line. The orange line joins them.B and D
Check. B and D both have y = 3. ✓
Watch out. Compare the correct number: first number for x, second number for y.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read point A carefully, along first. Then compare it with what Noah wrote.
- Read point A. Look down to the x-axis for the along number, then across to the y-axis for the up number.A is above 2 on the x-axis. Along = 2.
A is level with 6 on the y-axis. Up = 6. - Write the right coordinates. Along first, then up.A = (2, 6)
- Find Noah’s mistake. Noah wrote (6, 2). He wrote the up number first.Noah wrote the up number before the along number.
Check. (6, 2) is 6 along and 2 up. That is a different point from A. ✓
Watch out. Along first, then up.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates carefully. The first number is along (x) and the second number is up (y). Then decide if the statement is true.
- Look at the statement. We want to know if it is true or false.(6, 2) is further right than (2, 6).
- Compare the along (the x-coordinate, the first number). Further right means a bigger along number. Higher up means a bigger up number.(6, 2): 6
(2, 6): 2
6 is bigger than 2 - Decide. The statement is true.
Check. Check with a picture: the along number comes first. ✓
Watch out. Along is the first number. Up is the second number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates carefully. The first number is along (x) and the second number is up (y). Then decide if the statement is true.
- Look at the statement. We want to know if it is true or false.(5, 1) is higher up than (1, 5).
- Compare the up (the y-coordinate, the second number). Further right means a bigger along number. Higher up means a bigger up number.(5, 1): 1
(1, 5): 5
1 is smaller than 5 - Decide. The statement is false.
Check. Check with a picture: the along number comes first. ✓
Watch out. Along is the first number. Up is the second number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates carefully. The first number is along (x) and the second number is up (y). Then decide if the statement is true.
- Look at the statement. We want to know if it is true or false.(3, 4) is higher up than (3, 1).
- Compare the up (the y-coordinate, the second number). Further right means a bigger along number. Higher up means a bigger up number.(3, 4): 4
(3, 1): 1
4 is bigger than 1 - Decide. The statement is true.
Check. Check with a picture: the along number comes first. ✓
Watch out. Along is the first number. Up is the second number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the coordinates carefully. The first number is along (x) and the second number is up (y). Then decide if the statement is true.
- Look at the statement. We want to know if it is true or false.(2, 5) is further right than (6, 5).
- Compare the along (the x-coordinate, the first number). Further right means a bigger along number. Higher up means a bigger up number.(2, 5): 2
(6, 5): 6
2 is smaller than 6 - Decide. The statement is false.
Check. Check with a picture: the along number comes first. ✓
Watch out. Along is the first number. Up is the second number.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.J is above the number 10 on the x-axis.
Along = 10 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.J is level with the number 9 on the y-axis.
Up = 9 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.J = (10, 9)
Check. Start at (0, 0). Go 10 along and 9 up. You arrive at J. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Start at the origin. Count how far along (the x-axis) and then how far up (the y-axis) to reach the point. Write the two numbers in brackets, along first.
- Start at the origin. The origin is the point where the x-axis and the y-axis meet. We count every position from here.(0, 0)
- Go along the x-axis. The first number tells us how far to go along (think: along the corridor first). Look straight down from the point to the x-axis.M is above the number 1 on the x-axis.
Along = 1 - Go up the y-axis. The second number tells us how far to go up (then up the stairs). Look straight across from the point to the y-axis.M is level with the number 11 on the y-axis.
Up = 11 - Write the coordinates. We always write the along number first, then the up number, in brackets with a comma between them.M = (1, 11)
Check. Start at (0, 0). Go 1 along and 11 up. You arrive at M. ✓
Watch out. Along first, then up. (3, 5) and (5, 3) are two different points.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Read the x-coordinate of each house. The x-coordinate is the first number.
- Write the coordinates of every house. Along first, then up.H = (3, 2)
J = (10, 9)
K = (7, 6)
M = (1, 11) - Compare the first numbers. The house furthest along has the biggest x-coordinate.3, 10, 7, 1
The biggest is 10. - Write the answer. House J has the biggest x-coordinate.
Check. J = (10, 9) is furthest along the x-axis. ✓
Watch out. Compare the first numbers, not the second ones.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Think about some examples. Try to find a case where the statement is true and a case where it is false.
- Think about what the first number means. We always go along first.The first number tells us how far to go along (x).
- Test it. Try (4, 1): the first number is 4, so we go 4 along.It works for every point.
- Decide. This is always true.
Check. (7, 2): 7 along. (0, 5): 0 along. ✓
Watch out. Test the statement with real coordinates.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Think about some examples. Try to find a case where the statement is true and a case where it is false.
- Try a point with the same two numbers. (3, 3) has the same number twice.(3, 3) → yes, both numbers are 3.
- Try a different point. (2, 5) has two different numbers.(2, 5) → no.
- Decide. It is true for some points and not for others.This is sometimes true.
Check. We found one point where it is true and one where it is not. ✓
Watch out. Test the statement with real coordinates.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Think about some examples. Try to find a case where the statement is true and a case where it is false.
- Think about the x-axis. A point on the x-axis has not gone up at all.Up = 0
- Test it. Try (6, 0) and (2, 0).Both have 0 as the second number.
- Decide. This is always true.
Check. (9, 0) is on the x-axis, and its second number is 0. ✓
Watch out. Test the statement with real coordinates.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Think about some examples. Try to find a case where the statement is true and a case where it is false.
- Write what each point means. The order of the numbers matters.(2, 7) = 2 along, 7 up
(7, 2) = 7 along, 2 up - Compare. They are in different places on the grid.They are different points.
- Decide. This is never true.
Check. Along 2 and up 7 is not the same place as along 7 and up 2. ✓
Watch out. Test the statement with real coordinates.
Key words. Coordinates are two numbers in brackets, like (3, 5). They tell us exactly where a point is. The x-axis is the line going along the bottom. The y-axis is the line going up the side. The origin is the point (0, 0) where the two axes meet.
Method. Think about each possible along number and each possible up number. Count them, then multiply.
- Find the along numbers. On the grid they can be 0, 1, 2, 3 or 4.0, 1, 2, 3, 4 → 5 numbers
- Find the up numbers. They can also be 0, 1, 2, 3 or 4.0, 1, 2, 3, 4 → 5 numbers
- Multiply. Each along number can go with each up number.5 × 5 = 25
Check. There are 5 columns of lines and 5 rows of lines. 5 × 5 = 25 crossing points. ✓
Watch out. Remember the 0 lines. The axes count too.