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First of all I decided to investigate using the same size steps on an 8 x 8 number grid.Here is what I found out: x x 1 x 2 x 8 x 9 x 16 = 6x 36 Therefore as you can see above the formulas for the three step stairs on different sized number grids do not seem to be exactly the same (other than each time the multiplication of ‘x’ has been the same).So for the three step total on any size grid the formula is; 6x 4g 4 Different Stair Sizes Next I shall investigate different stair sizes and the formulas for their totals.
Part 1- Three Step grid I have investigated the three step stair (some of my findings can be viewed on the graph paper in the back).
During my investigation I believe that I have worked out the formula for the total inside the three step stairs on a 10 x 10 grid.
I shall do this by experimenting with the size of the grid corresponding to the size of the stairs used in the grid.
I shall try to work out the formulas by recognising any similarities in the results obtained.
I have shown this below representing the grid size by using the letter ‘g’.
x x 1 x 2 x g x g 1 x g g = 6x 4g 4 After checking this formula to see if it works for each size of grid it has been proven that it does work.
In this investigation it has also been proved that wherever the stairs are in the grid the formula for their total still applies.
Part 2 – Other Steps on Other Number Grids Now that I have finished the three step stair on just a 10 x10 number grid I shall go on to changing first the grid size and then the steps size.
Although the corner number affects the multiplication of x, it does not affect the number 4 which always remains the same no matter what the corner number is.
So, the three step stairs could be located anywhere in the grid and the only part of the formula that will change is the amount of times that you multiply x.