# Opposite Corners Maths Coursework Thanks guys, I hope you guys can help, 'cause I am bummed right now. I've got "For any square on the 10 x 10 grid, we would have to make a formula for an ‘n x n’ square.The thing is I expanded the brackets of the formulas for (top left corner x bottom right corner) and (top right corner x bottom left corner) and found the difference, but I expanded wrong, yet I still got a formula that worked like a beast, like, everytime, but now I've redone it, it doesn't work! If ‘n’ is the number of squares across the square, the formula should be the difference between (x n-1)(x 10n-10) and x(x 10n-10 n-1) These two equations with expanded brackets look like this: x² 11nx-11x 10n²-20n 10 And x² 11nx-11x Making the clear difference between them, 10n²-20n 10, which can be simplified to 10n(n-2) 10" But this formula, when used on 34x48 and 44x38 gets: 90, when it should clearly be 40!These will give me a clearer picture of what is involved in this investigation.

I print off in a mini-booklet (A5 booklet) that students can stick into their books after I've marked it.

Also includes 'adaptations' of the problems to be used by students to extend learning.

Well, the coursework is the one where there is a 10 x 10 grid, with a box drawn on it, and you have to find the different between the (top left corner x bottom right corner) and the (top right corner x bottom left corner).

I have handed this to my old maths teacher once, and he took aaaaaaaages to mark them, and has now left Can anyone help me get the formulas for: 1. the rectangle on a 10x10 grid and from there I'll be able to work out the rest.

12 13 14 15 22 23 24 32 33 42 = 230 Also from these formulae, when x is substituted with 4 and y is substituted with 6 (4 and 6 being the coordinates of the keystone of the step stair positioned higher on the grid above), an answer of 650 is calculated 54 55 56 57 64 65 66 74 75 84 = 650 This confirms the formula 10 wy-0 w 10 x 10 can be used to calculate the stair total of a 3-step stair on a 10 by 10 grid. of squares high the stair is w = Width of grid (number of squares) Relationships between different stair heights on a 10 by 10 grid To find a pattern, I kept ‘n’ constant (n = 1) and I changed the height, ‘h’. but that’s about the point I got up to in my coursework.

Height (h) 1 2 3 4 5 6 Total (T 1) 1 14 50 120 235 406 Now I need to find the differences between these numbers: Height (h) 1 2 3 4 5 6 Total (T 1) 1 14 50 120 235 406 Difference 1 13 36 70 115 171 Difference 2 23 34 45 56 Difference 3 11 11 11 I repeated this with n = 33 Height (h) 1… If you want challenge, use the s-number as the top left of the stair shape…

S = Stair size, eg a 3 x 3 stair s = 3 G = Grid size, eg a 10 x 10 grid = 10 A = Amount of ‘n’ N = bottom left hand corner of shape in 2 steps: 1) (Sx (S 1) /2) = A 2) AN (G 1) x ( (sxsxs-s) /6) = THE ANSWER SOME EXAMPLE WORDINGS TO USE IN YOUR WRITE-UP… At the time I was not really experienced with liquor, but willing to ... 1 Number Grid From the formula (10 wy-0 w 10 x 10), when x is substituted with 5 and y is substituted with 1 (5 and 1 being the coordinates of the keystone of the step stair positioned lower on the grid above), an answer of 140 is calculated. aka the “Gregory Newton Formula.” I’ve searched on the internet for this formula and help on it… it’s like too complicated with all those wacky symbols.

[ (wy-w x) 3] [ (wy-w x) w] [ (wy-w x) w 1] [ (wy-w x) w 2] [ (wy-w x) 2 w] [ (wy-w x) 2 w 1] [ (wy-w x) 3 w] This can be simplified to: 10 wy-0 w 10 x 10 From these formulae, when x is substituted with 2 and y is substituted with 2 (2 and 2 being the coordinates of the keystone of the step stair positioned lower on the grid above), an answer of 230 is calculated. hotel I got out of the car crawling to the steps, and fell asleep there. So we were having our fun there and by this time I was tired of drinking beer, needed a little change ... 5 6 7 8 13 14 15 21 22 29 = 140 From the formula (10 wy-0 w 10 x 10), when x is substituted with 2 and y is substituted with 6 (2 and 6 being the coordinates of the keystone of the step stair positioned higher on the grid above), … The one my teacher taught is: (If the value of n = 0) s x (1 st Difference) [s (s 1) ]/2 x (2 nd Difference) [s (s-1) (s-2) ]/6 x (3 rd Difference) Ok I have almost no clue how to do this…

The numbers in the grid will go horizontally from left to right.

Text Box: In the square grids I shall call the sides N.

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