• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Corner to corner

Extracts from this document...


The investigation was corner to corner, which means that within a four sided shape on a table of numbers you had to multiply the top left corner with the bottom right corner and then the bottom left corner with the top right corner, you then had to find the difference between the two multiplication’s. image00.png

C x B and then subtract A x D










(On 10 x 10 square)




If I move the 2

...read more.



Here is a table for the difference for a ten by ten grid:

Length of Square




















The difference is calculated by the (length of the square – 1)² x10, that is how I was able to calculate the other differences of the different length of square.

(L-1)² x 10= difference [algebraic form]

L = length of the square

The limitations with this formula are that the shape has to be a square, the length of the grid has to be 10 and the constant difference between each number has to be 1.

(n + a (L-1)) x (n + (L-1)) – (n x (n + a (L-1) + (L-1)= difference

I then simplified the above equation to make:

a( L² -2L + 1) = difference

a is the number of how many the grid goes across

...read more.


I have found that the formulae for the square and the rectangle are very similar but in the rectangle formula the height of the rectangle is included but for a square the height is the same as the length so the height value is not needed in the square formula. So a formula for four sided shapes on a grid of numbers with a constant difference of 1 is a (Lh – h – L + 1), the a is how much the grid goes across, the h is the height of the shape and the L is the length of the shape.


Rather than simplifying the formulae step by step I have jumped from the starting formula to the ending one, in the future I shall simplify my formulae step by step.

...read more.

This student written piece of work is one of many that can be found in our GCSE Number Stairs, Grids and Sequences section.

Found what you're looking for?

  • Start learning 29% faster today
  • 150,000+ documents available
  • Just £6.99 a month

Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

See related essaysSee related essays

Related GCSE Number Stairs, Grids and Sequences essays

  1. What the 'L' - L shape investigation.

    Therefore, we have 5L -9 present in the formula. I will use this formula to verify its correctness and to look further for additional differences. Number In Sequence Formula Formula Equation Results L-Sum 1 5L -9 (5 x 9) - 9 36 36 2 5L -9 (5 x 10)

  2. number grid investigation]

    It is the sum of these that equal the bottom right, or: Formula 1: Bottom Right (BR) = Top Right (TR) + Bottom Left (BL) As also shown by the summary boxes and examples above, the formula for the top right number remains constant, and is linked with the width,

  1. Algebra Investigation - Grid Square and Cube Relationships

    w, of the box in the following way: Formula 2: Top Right (TR) = Width (w) - 1 It is also evident from the examples calculated that the bottom left number is also linked with the height, w, (the width and height are always equal, due to the dimensions of the box producing a square)

  2. Opposite corner

    anywhere in the 100 sqaure grid the difference is always going to be 20 Now i am going to choose a rectangle from the 100-sqaure grid 2 by 3 horizontally 45 46 47 48 55 56 57 58 The products of the number in the opposite corner of this rectangle

  1. I am doing an investigation to look at borders made up after a square ...

    6 5 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 1 1 1 2 3 4 5 6 6 5 4 3 2 2 2 2 2 3 4 5 6 6 5 4 3 3 3 3 3 4 5

  2. Number Grid Investigation

    will now check another 3 x 3 grid to see if the pattern continues: 27 28 29 37 38 39 47 48 49 27 x 49= 1323 Difference = 40 29 x 47= 1363 A pattern seems to be forming the difference is 40 on both of these 3x3 squares; however I will try another square to convince me.

  1. Investigation of diagonal difference.

    a trend for all of the 2x2 cutouts in a 10x10 grid. From this I will be able to calculate the diagonal difference of a cutout anywhere on the grid, as n is independent of where the cutout is on the grid.

  2. This investigation is about finding the difference between the products of the opposite corner ...

    NxN N(N - 1)2 Predict + check Looking at the patterns of numbers from my tables of results it appears for a grid size of NxN the difference is N(N - 1)2. I predict that for a 10x10 grid the difference will be 10 x 92 = 10 x 81 = 810.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work