Number Grid Investigation

Number Grid Investigation

Aim: My aim is to find out how the number of rows and columns in a

square, on a certain sized grid will affect the difference between the

product of the top left number and the bottom right number in the

square subtracted from the top right number and the bottom left

number.

Prediction: I predict that when you've got numbers in a square box in

a 10 by 10 grid, the difference will always be a square number because

the box is shaped as a square.

Method: Firstly, I'm going to work out the difference, in a 2 by 2

square in a 10 by 10 grid, between the two products that I get from

multiplying the top left number and the bottom right number in the

square by the top right number and the bottom left number. I am then

going to repeat this another 3 times but these times I will work out a

3 by 3 square, 4 by 4 square and a 5 by 5 square. After doing this, I

will try to find a formula that can find the difference in any sized

square. I will then decrease the size of the grid so that it becomes 9

by 9 and will then do exactly the same method as I did before and then

I will do this again but with a 5 by 5 grid. I will then work out

formulas for both of these grids, to find the difference. I will then

use algebra to prove that my formulas are able to work out the correct

difference. To investigate further I will do the whole investigation

again but with rectangles instead of squares.

This is a table to show the differences in squares in a 10 by 10 grid.

No. of Rows (r)

No. of Columns (c)

Difference

Formula

2

2

10

10(r-1)²

3

3

40

10(r-1)²

4

4

90