Many (seemingly daunting) problems in mathematics can be broken down into smaller, more manageable ones where the results can then be collected to solve the original question. Here, we partitioned the original question into 8 smaller ones and then compiled the results in an efficient manner by employing the sum of squares formula. Some possible extensions for this problem are:
- number of squares in a larger board (9x9, 10x10, 100x100, NxN)
- number of squares in a rectangular board (MxN)
- number of non-square (PxQ) rectangles instead of squares, P<Q.
- number of cubes in 3 dimensional board (8x8x8, NxNxN)
Beautifully done, Jordan! I like your 'red dot' technique as a very visual way of counting the squares, and finding the summation formula would be a good activity to help senior high school students get accustomed to sigma notation. Very comprehensive extensions too! Thanks for this great work.
ReplyDelete