Coordinates: Mapping Positions on a Grid
What Are Coordinates?
Coordinates are a pair of numbers that help us find a point on a plane. Sometimes one of the numbers is replaced with a letter — like in the game of Battleship or when labeling the squares on a chessboard. Other times both are numbers, like when we use GPS coordinates to find a location in a forest.
In some cities, maps are organized in a similar way. In New York, for example, streets run east to west and are numbered, while avenues run north to south and are numbered too. To find a place, you just locate the right street and the right avenue — that’s your spot.
Why Does It Matter for Kids?
Kids and teens with stronger spatial reasoning tend to do better in math and science. In elementary school, the importance of these skills is often underestimated. Yet maps, diagrams, graphs, and many other everyday tools rely on coordinates — even though the topic itself gets very little time in the curriculum.
Research shows that by the age of four, children can already use the relationships between lengths and angles to match a map to real space. However, they still struggle to tell a shape from its mirror image, which often leads to symmetry mistakes.
In another study, kids aged seven to eleven used a virtual coordinate trainer. Compared with a control group, they showed significant gains in math skills — not only in tasks involving coordinates, but also in arithmetic areas that depend on understanding the number line.
How Do We Teach?
A simple drawing of a house usually looks the same: a square for the walls and a triangle for the roof. But today only a few children actually live in small houses with pointed roofs. Most live in apartment buildings and already know that buildings have entrances and floors.
We build on that knowledge to introduce the idea of a basic coordinate system, where each window in a building can be described by its entrance number and floor number.
The very first tasks are simple: find the top floor of the building and check whether the light is on there.
Tables and coordinates
Top floor
Later, entrances use letters for labeling. Kids look for the top window in entrance A, for example. Step by step, they begin to work with a full grid, such as finding the cell marked B4.
We also practice chess notation, first on a small board (4×4), then on a real one (8×8). Kids learn about the moves of different pieces: the pawn, the bishop, and the king. To help them navigate the board, we use the image of an arrow flying in a straight line. They have to decide whether that arrow will hit the target placed on a given square.
In a game where kids steer a small boat, work with coordinates reaches its most advanced form. Kids use their hands to guide the boat: the left hand controls the vertical coordinate, and the right hand controls the horizontal one. At first, the boat moves along straight horizontal and vertical paths, so the hands move one after the other. As the tasks get harder, diagonal paths appear, and the hands need to move at different speeds. In the most challenging levels, the boat follows smooth, curved lines that require full coordination.
Tables and coordinates
Coordinates
Tables and coordinates
Coordinates
Tables and coordinates
Chess notation (4х4)
Tables and coordinates
Chess moves (pawn)
Tables and coordinates
Chess moves
Coordinates
Coordinates: movement along grid lines
Big Ideas
Coordinates are part of everyday life. We often hear people say, “Drop me your location.” When we share it, we’re actually giving the coordinates of a point on the Earth’s surface — its latitude and longitude. To describe where an airplane is in the sky, we need one more coordinate: its altitude.
The rectangular coordinate system plays a key role in high school math. In geometry, students learn how to find the coordinates of a midpoint, how to write the equation of a line on a plane, and later, the equation of a plane in space.
In algebra, coordinates help us show how numbers and relationships look visually. Graphs display functions — and those functions can describe almost anything. A graph might show the distance of a car from its starting point, the temperature of the air, the magnitude of an earthquake, or even the population of the Earth. By looking at a graph, it becomes easy to see what is happening: whether things are heating up, cooling down, growing, or shrinking.
