• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3

# Corner to corner

Extracts from this document...

Introduction

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.

## C x B and then subtract A x D

 A B C D

E.g.

 2 3 12 13

(On 10 x 10 square)

2x13=26

3x12=36

36-26=10

If I move the 2

Middle

6643-6603=40

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

 Length of Square Difference 2 10 3 40 4 90 5 160 6 250 7 360 8 490 9 640 10 810

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

Conclusion

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.

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

# Related GCSE Number Stairs, Grids and Sequences essays

1. ## Investigation of diagonal difference.

1 1 + (3 - 1) = 3 1 + ((2 - 1) 10) = 11 1 + ((2 - 1)10) + (3-1) = 13 => The solutions give the correct final products and the corner values are the same as the corner values of a 2 x 3 cutout on a 10 x 10 grid.

2. ## What the 'L' - L shape investigation.

Note that 4 is the grid square and 8 is double the grid size and two rows up. The sum of the shape above gives me the last part of the formula, which is -9: 1 + 2 + (-4)

1. ## Algebra Investigation - Grid Square and Cube Relationships

Summary Boxes and Grid Size of 'g' 5x5 Grid Algebraic Summary Box: n n+w-1 n+5h-5 n+5h+w-6 Overall difference calculation: 5hw-5h-5w+5 6x6 Grid Algebraic Summary Box: n n+w-1 n+6h-6 n+6h+w-7 Overall difference calculation: 6hw-6h-6w+6 7x7 Grid Algebraic Summary Box: n n+w-1 n+7h-7 n+7h+w-8 Overall difference calculation: 7hw-7h-7w+7 gxg Grid As can

2. ## The problem is to investigate the differences of corner numbers on a multiplication grid.

= 10 (25x34)-(24x35) = 10 (63x72)-(62x73) = 10 (58x67)-(57x68) = 10 (90x99)-(89x100)=10 For all of these you can that the difference is a constant 10, so anywhere you put a 2x2 square on a 10x10 grid you will always get the same difference of ten.

1. ## number grid investigation]

I will now investigate to check if all examples of 3x3 grid boxes demonstrate this trend in difference. I will conduct this research using another 2 of these boxes from the overall cardinal10x10 number grid. My predication also seems to be true in the cases of the previous 2 number boxes.

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. ## For my investigation I will be finding out patterns and differences in a number ...

All the differences are underlined and in bold. 1 2 3 4 5 6 11 12 13 14 15 16 21 22 23 24 25 26 31 32 33 34 35 36 41 42 43 44 45 46 51 52 53 54 55 56 1 x 56 = 56 51

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.

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