Difficulties and Challenges Involved in the Chess Board Problem

As a student, I solved the problem first by counting individual squares and then realizing  that there was a pattern. Using the pattern, I was able to solve the problem relatively quickly.

As a teacher, I can see students finding difficulty when trying to determine the number of squares larger than the 1x1 squares. Counting these becomes difficult past this stage as the squares begin to overlap. I would encourage an approach involving finding patterns. To guide them, I could start by helping them with the first step in determining a pattern.

To modify this problem to make it more difficult, you could add another dimension and ask for the number of cubes in a 8x8x8 cube. or ask for the number of triangles in a similarly structured triangle where patterns would be more difficult to find.