If you ask this question in any class,
the first thing which can come to our mind is " ohh if it is 8 by 8
chessboard, then we just need to do 8*8= 64 ",which is obviously wrong
Thinking of the number of squares is
not an easy task for everybody and it can be easier for students who visualize
it.
I found that it is easier to cut the squares and place it on the board and
since on a chess board the squares are of two colors (in my example it is black
and white) so I would recommend to use only one color. (My case I am using only
white)
While looking at an 8 by 8 board, we get only 1 square.
We can observe that from a 7*7 board, we obtained 4 squares
Now we can observed that there is a pattern of square numbers
8*8 board = 1 square
7*7 board = 4 squares
6*6 board =9 squares
So obviously 5*5 board will be = 16 squares
4*4 board= 25 squares
3*3 board = 36 squares
2*2 board= 49 squares
1*1 board = 64
and since we need to calculate the total, we add them and we get 204
squares.
By visually looking at the chessboard, it was easier to calculate the
number of squares. It is difficult to just say that there is a pattern/sequence
behind this problem.
I will extend the problem by asking the student about the number of
squares in a 10*10 chessboard and see if they understood the pattern.
I could even extend it to a 100*100 chessboard since now the students will know the pattern and I also thought we could even ask the students how many triangles we can get from that triangular chessboard shown below
I could even extend it to a 100*100 chessboard since now the students will know the pattern and I also thought we could even ask the students how many triangles we can get from that triangular chessboard shown below
Very nice tangible/ graphic tools for a solution, Deeya! I like the fact that you actually made the white squares and could show how they fit on the chessboard -- this is a powerful teaching tool because it is so visual and tangible. I like the extension you suggest as well. What would you think about extending it to a 100X100 chess board, by the way?
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