Shape & Space
Co-ordinates (First Quadrant)
3rd Class · 4th Class · 5th Class · 6th Class
- ✓By the end of this lesson students will be able to understand what co-ordinates are and their purpose.
- ✓By the end of this lesson students will be able to identify the x-axis, y-axis, and the origin on a grid.
- ✓By the end of this lesson students will be able to locate and read the co-ordinates of points in the first quadrant.
- ✓By the end of this lesson students will be able to plot points on a grid given their co-ordinates in the first quadrant.
- ✓By the end of this lesson students will be able to use co-ordinates to describe the position of objects or vertices of shapes.
Key concepts
Co-ordinates are a pair of numbers that tell you the exact location of a point on a grid. Think of it like a secret code to find a treasure!
A grid is a pattern of squares formed by horizontal and vertical lines. We use it to help us find and plot points. At primary level, we usually work with the first quadrant of the Cartesian plane.
The x-axis is the horizontal line on the grid. When you're finding a point, the first number in the co-ordinates tells you how far to move along the x-axis (how far 'across' you go).
The y-axis is the vertical line on the grid. The second number in the co-ordinates tells you how far to move along the y-axis (how far 'up' you go).
The origin is the starting point on the grid where the x-axis and y-axis meet. Its co-ordinates are always (0,0). You always start counting from here!
Co-ordinates are always written as an 'ordered pair' inside brackets, like this: (x, y). The 'x' number always comes first, and the 'y' number always comes second. The order is very important!
The first quadrant is the part of the grid where both the x-values and the y-values are positive numbers (or zero). This is the only quadrant we use at primary school level.
Key facts to remember
- 1Co-ordinates are always written as an ordered pair (x, y).
- 2The x-axis is the horizontal line (across), and the y-axis is the vertical line (up).
- 3You always start at the origin (0,0) when finding or plotting points.
- 4Always move along the x-axis first (right), then along the y-axis (up).
- 5The first quadrant uses only positive numbers for both x and y co-ordinates.
- 6Each number on the axis represents a 'unit' or 'step' from the origin.
- 7A point on the x-axis will have a y-co-ordinate of 0 (e.g., (3,0)).
- 8A point on the y-axis will have an x-co-ordinate of 0 (e.g., (0,2)).
Worked examples
Example 1
Look at the grid below. What are the co-ordinates of the star, the heart, and the circle?
Answer
Star: (3, 4) Heart: (1, 2) Circle: (5, 0)
Remember to always go 'across the corridor' (x-axis) first, then 'up the stairs' (y-axis)!
Example 2
Plot the following points on a grid: A(2, 3), B(5, 1), C(0, 4).
Answer
A grid with points A(2,3), B(5,1), and C(0,4) correctly plotted and labelled. Point C will be on the y-axis.
When a co-ordinate is 0, it means you don't move in that direction from the origin. For (0,4), you stay at 0 on the x-axis and move 4 up on the y-axis.
Example 3
Draw a rectangle on the grid by plotting the points P(1,1), Q(1,5), R(4,5), S(4,1) and joining them with straight lines.
Answer
A grid showing the rectangle with vertices P(1,1), Q(1,5), R(4,5), and S(4,1) correctly plotted and joined.
Joining the points in the correct order is important to form the intended shape.
Common mistakes
- ✗Mixing up the order of the co-ordinates, for example, writing (y, x) instead of (x, y). Always remember 'across then up'.
- ✗Starting to count from 1 instead of 0 at the origin. The origin (0,0) is the true starting point.
- ✗Not using brackets or a comma when writing an ordered pair, e.g., '3 4' instead of '(3, 4)'.
- ✗Counting the lines on the grid instead of the spaces/units from the origin.
- ✗Misreading the numbers on the axes, especially if the scale is not 1, 2, 3...
Exam tips
- ★Always use a ruler to draw your axes and any lines connecting points to ensure they are straight and accurate.
- ★Label your x-axis and y-axis clearly, and mark the numbers along them, especially the origin (0,0).
- ★When plotting, count carefully. You can use your finger to trace along the x-axis first, then up the y-axis.
- ★Double-check your answers! If you're finding co-ordinates, count across and up again. If you're plotting, check if your plotted point matches the given co-ordinates.
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