How Dot Arrays on Grids Cause Confusion

A few days ago during math tutoring, a 6th grader was having trouble counting the length and width of a rectangle on a grid. When shown a rectangle 4 units wide and 2 units long, she said the area was 15 square units! The error was caused by counting the intersection points instead of the spaces. Consider the following figures.

Some curriculum materials include practice with making dot arrays on a grid for multiplication. Students who make these arrays may then be confused about finding the length of a segment on the grid. In Common Core, students are expected to draw and count arrays of squares. This is a better approach because students are less confused and it leads perfectly into the concept of area.