How many squares are in a checkerboard? By :Gloria Gonzalez By :Gloria Gonzalez And Ieni Vargas And Ieni Vargas

How many squares are in a checkerboard? oLet's see if we can get you started and then YOU can come up with the answer. oThis question implies "squares of any size." How about if we make a Table and collect our data; we might find a pattern going on. oIf you look at the smallest size square on a checkerboard, we can call that a 1 unit by 1 unit square. There are 64 of that size.

The next size square is a 2 unit by 2 units square. It's okay to use These more than once in different new squares. The top left-hand corner Has 4 of the 1x1's which make a 2x2. See it? Good, then move right One square and find a new 2x2 made with two of the 1x1's you just used And two 1x1's right next to them. Likewise you can shift down just one Row and use two that you've already used. Count all of these 2x2's. You should come up with 49.Our table would look like this: Size number of squares 1*1 64 2*2 49 3*3 4*4 Ect..

You go ahead and complete this table. After you're done you still have To add up the right hand column to get the total number of squares on a Checkerboard. Let's get back to the question of a pattern. Is there anything you? Notice about the numbers in the right hand column? Is there a relation To the number of 1x1 squares on a side of the checkerboard? 2x2's? Etc.? Say you have an 8x8 checkerboard. There are many other little and Big squares inside of that so counting them all how many are there? (E.g. counting all the 1x1, 2x2, 3x3, 4x4, 5x5, 6x6, 7x7, 8x8).

Suppose you have a square checkerboard of some other size - not 8x8 –What is the easiest way to find how many squares there are in it? Make sure that when you are done you will be able to find the number Of squares in any size checkerboard within 2 minutes. I tried counting the squares individually, but that wouldn't be quick Enough for 12x12. Could you please give me some tips for how to Approach this problem?

THANKS FOR YOUR TIME.