Number grids.
By Nicole Highfield.
The aim of this investigation is to find the differences of N x N squares that are inside a 10 x 10 grid (shown bellow) then to see if there is a rule or pattern that will connect the size of the N x N to the size.
To be able to find the difference of an N x N square, I will start at the smallest one, which is 2 x 2. The corners have to be multiplied together in a diagonal way. My 2 x 2 square is: -
2 x 23 = 276
3 x 22 = 286
Then to find the difference I have to minus the smallest answer from the biggest one. This is the to find the differences in all squares.
286 - 276 = 10
Using 2 x 2 array (square) of number I have found a difference between the two corners, this is a difference of ten. I will check this by doing some more 2 x 2 arrays, and work my way to bigger squares so that the investigation does not get complicated.
88 89
98 99
88 x 99 = 8712
89 x 98 = 8722
8722 - 8712 = 10
55 56
65 66
55 x 66 = 3630
56 x 65 = 3640
3640 - 3630 = 10
72 73
82 83
72 x 83 = 5976
73 x 82 = 5986
5986 - 5976 = 10
From doing these three checks I have found that the difference in a 2 x 2array is ten, to be completely sure that it is ten in any place in the 10 x 10 grid I am going to put it into a N x N formula.
By Nicole Highfield.
The aim of this investigation is to find the differences of N x N squares that are inside a 10 x 10 grid (shown bellow) then to see if there is a rule or pattern that will connect the size of the N x N to the size.
To be able to find the difference of an N x N square, I will start at the smallest one, which is 2 x 2. The corners have to be multiplied together in a diagonal way. My 2 x 2 square is: -
2 x 23 = 276
3 x 22 = 286
Then to find the difference I have to minus the smallest answer from the biggest one. This is the to find the differences in all squares.
286 - 276 = 10
Using 2 x 2 array (square) of number I have found a difference between the two corners, this is a difference of ten. I will check this by doing some more 2 x 2 arrays, and work my way to bigger squares so that the investigation does not get complicated.
88 89
98 99
88 x 99 = 8712
89 x 98 = 8722
8722 - 8712 = 10
55 56
65 66
55 x 66 = 3630
56 x 65 = 3640
3640 - 3630 = 10
72 73
82 83
72 x 83 = 5976
73 x 82 = 5986
5986 - 5976 = 10
From doing these three checks I have found that the difference in a 2 x 2array is ten, to be completely sure that it is ten in any place in the 10 x 10 grid I am going to put it into a N x N formula.