Navigating Spaces in Grids

A grid is made of squares arranged in straight lines that go across and up and down. The lines that go across are called rows, and the lines that go up and down are called columns. Every square in a grid sits inside exactly one row and one column, which is what makes it possible to find any square by describing where it is.

Navigating spaces in grids means using rows, columns, and simple directions, such as up, down, left, and right, to find a square, describe where something is, or explain how to move from one square to another. This skill shows up everywhere, from city maps and seating charts to spreadsheets and, later on, the coordinate plane.

To find a square in a grid, it helps to count in two steps. First, count across the grid to find the right column. Then count up or down to find the right row. Doing both steps together tells you exactly which square is being described.

In the grid above, the yellow square is in column 4 and row 3. Saying "column 4, row 3" or "row 3, column 4" both describe the exact same square, as long as everyone agrees on which number comes first.

Once a square can be named using its row and column, the next step is describing how to move from one square to another. Movements in a grid are usually described with four simple directions: up, down, left, and right. Each move changes either the row number or the column number, but not both at the same time.

For example, moving right one square keeps you in the same row but shifts you to the next column. Moving down one square keeps you in the same column but shifts you to the next row.

Worked Example

Suppose a marker starts at column 1, row 1, the top left square of a grid. To reach column 4, row 3, describe the path using directions and counts.

Step 1: Move right 3 squares to reach column 4, row 1.

Step 2: Move down 2 squares to reach column 4, row 3.

The full path can be written as "right 3, down 2." Grids can also be navigated in a different order, moving down first and then right, and the marker will still land on the same final square.

Besides counting rows and columns, grids can be described using position words such as above, below, next to, between, and beside. These words work alongside the earlier skill of describing where an object is compared to another object, which is covered in describing relative positions of objects. In a grid, a square that is above another square is in the same column but an earlier row, while a square that is beside another square is in the same row but a different column.

Grid navigation connects to many other topics in geometry. Being able to track rows and columns carefully supports skills like recognizing how shapes fit together, as practiced when composing and decomposing 2D shapes, and it also builds the careful counting habits needed when learning to sort 2D shapes by attribute. Later on, this same idea of counting across and up or down becomes the foundation for plotting points on a coordinate plane, where every point is described by two numbers in a fixed order.

When practicing grid navigation, always double check two things: which direction was counted first, across or up and down, and whether the count started from the correct square. A small mistake in either step can land on the wrong square, even if the number of moves is correct.

Related lessons

• Math 2