Consider a blank m x n rectangular grid. Your goal is to shade in squares in the grid such that the following two restrictions are satisfied: No shaded squares are adjacent along an edge

All unshaded squares are connected along edges so that a continuous "path" can be found connecting any two unshaded squares For a specified grid size, what is the maximum number of squares that can be shaded following these restrictions?

I am in a Mathematical Reasoning class and have this problem due Friday. I have tried to complete it, but I am just going in circles. There are no notes from class on this problem - we are instructed to "try it."