Number Grid Investigation

3888 WordsJan 23, 200816 Pages
The Patterns, Rules and Formulae Found in a Number Grid For this coursework I shall investigate and explain thoroughly the patterns, rules and formulae found in a number grid when placing a square at any point in the grid, multiplying the top left and bottom right corners and the top right and bottom left corners and finding the difference. I will look at all the variables and use systematic methods when doing this. Suggested Variables: Width of grid Size of Square Multiplication Tables Width of Grid: Does the width of the grid make a difference to formulae? I shall keep the size of the square at a constant (2 x 2) Width of Grid size 10) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22…show more content…
Now I shall try to answer the question "does this differ with a different size grid?" I shall try to fill the table shown underneath to get a clear view on all the data and try to see a formula from this data. Grid Width Difference 4x4 10 3x3 9 2x2 8 Square size 2x2 grid width 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 12 x 23 = 276 22 x 13 = 286 286 - 276 = 10 I shall now use letters to prove this correct X X+1 X+10 X+11 X(X+11) = X² + 11X (X+1)(X+10) = X²+11x+10 (X²+11x+10) - (X²+11X) = 10 Square Size 2x2, Grid Width 9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 21 26 27 11 x 21 = 231 20 x 12 = 240 240 - 231 = 9 I shall now use letters to prove this correct X X+1 X+9 X+10 X(X+10) = X² + 10X (X+9)(X+1)=X²+10X+9 (X²+10X+9) - (X²+10X) = 9 Square size 2x2, Grid Width 8) 1 2 3 4 5 6 7 8 9 10 11 12 13
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