How many squares are there on a chess board

1
How many squares are there on a chess board?
Well lets investigate!
2
Well, that is easy!
A chess board has 8 squares along..
and 8 squares down
8 X 8 64
3
Well done, you know your square numbers!
1 x 1 1 2 x 2 4 3 x 3 9 4 x 4 16 5 x 5
25 6 x 6 36 7 x 7 49 8 x 8 64 9 x 9
81 etc..etc..
4
But the answer is still wrong.
4
Miss.Miss. The whole board is a square! So
there are 65.
4
Well done Johnny, youre thinking on the right
lines.
5
But the answer is not quite right.
Go into groups and investigate.
What did you find out?
6
Blue table, what did you find out?
Well Miss, there are lots more squares, look..
A 2 by 2 square, and there are lots of them.
And we worked together and found there are 49 2
by 2 squares!
7
Green table, what did you find out?
Well Miss, there are lots more squares, look..
A 3 by 3 square, and there are lots of them.
And we worked together and found there are 36 3
by 3 squares!
8
Yellow table, what did you find out?
Well Miss, there are lots more squares, look..
A 4 by 4 square, and there are lots of them.
And we worked together and found there are 25 4
by 4 squares!
9
So the tables continued...
Red There are 16, 5 by 5 squares.
Purple There are 9, 6 by 6 squares.
White There are 4, 7 by 7 squares.
Well done class, lets put our findings together.
10
1 x 1 1 Thats the big board. 2 x 2 4
7 by 7 3 x 3 9 6 by 6 4 x 4 16
5 by 5 5 x 5 25 4 by 4 6 x 6 36
3 by 3 7 x 7 49 2 by 2 8 x 8 64
Thats all the squares
4
Well done, you know your square numbers!
11
So, 64 49 36 25 16 9 4 1
equals
204
4
12
So, how many squares are there on a chess board?
It depends on your level of learning.
With a little help from your friends...
64 or 204