Coordinates and Position
A grid coordinate system
A grid coordinate system is built from two number lines, called axes, that cross at right angles. The horizontal axis runs across and the vertical axis runs up, and they meet at a point called the origin, written as the coordinates zero, zero. Evenly spaced gridlines divide the space into a grid, and each line is numbered from the origin. Once the axes are drawn and numbered, every position in the space can be named exactly. The grid turns an empty space into a map where any point has its own address.
Reading the coordinates of a point
A point on the grid is named by its coordinates, a pair of numbers written in brackets and separated by a comma. By convention the first number is read across from the origin along the horizontal axis, and the second is read up the vertical axis. A point three across and two up has the coordinates three, two. The order matters, because three, two and two, three are different points. Reading coordinates means finding how far across and how far up a point sits, then writing the two numbers in the right order.
Plotting a point from coordinates
Plotting works the other way around: starting from a pair of coordinates, the point they describe is found and marked. To plot the coordinates four, one, count four spaces across from the origin and then one space up, and mark the point where those meet. Following the across-then-up order every time makes plotting reliable, so the same coordinates always land on the same point. Plotting and reading are inverse skills, and together they let positions be both recorded as coordinates and recovered from them.
Describing position and movement
Coordinates also describe movement from one point to another. Moving from the point one, one to the point four, three means going three spaces across and two spaces up, because the first coordinate changes from one to four and the second from one to three. Describing a move this way breaks it into a horizontal part and a vertical part, each read from the change in a coordinate. The same idea describes a journey on a map as a series of moves, so a path across the grid can be written down and followed exactly.
Using directional language
Alongside coordinates, directional language describes position and movement in words. Directions such as left and right, up and down, or the compass points north, south, east and west say which way to face or move. Saying that one place is two squares east and one square north of another locates it, and instructions like turn and move forward guide a path step by step. Directional language and coordinates work together: the words give the sense of direction, and the coordinates give the exact amount.
Locating and moving with confidence
Locating and moving with coordinates comes down to a clear system: set up numbered axes meeting at the origin, read a point as how far across and how far up, plot coordinates by counting across then up, and describe movement as changes in the coordinates or in directional words. With these habits a child can name any position, plot any point, and describe a path across a grid, ready for the maps, transformations and coordinate planes of later mathematics.