• 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
4. 4
4

# You are given a 9x9 number grid with a 2x2 square on it. Investigate when pairs of diagonal corners are multiplied and subtracted from each other.

Extracts from this document...

Introduction

Douglas Carter

Mathematics Coursework

Problem:

You are given a 9x9 number grid with a 2x2 square on it. Investigate when pairs of diagonal corners are multiplied and subtracted from each other. Come up with an algebraic formula that gives the difference for any size square/rectangle on any size grid.

Method:

Starting with the problem given, a 9x9 number grid with a 2x2 square on it, I gave each number in the square its equivalent in algebra.

If the first number is a the number grid would be as follows…

This can be used to make a formula that gives the difference (Dif) when diagonals are multiplied and subtracted from each other, for a 2x2 square on a 9x9 grid, where 9 represents the width of the grid and a

Middle

I found similarities between the differences when looking at them written in different ways. For a 9x9 grid and different sized squares I got the following table of results:

This shows that the difference is relative to the grid width but increases as the size of the square increases in similar steps but faster and with more effect.

Using the formula I found that there is a pattern in the increase in difference of rectangles, such as 2x3, 3x4, etc… I have tabulated the results.

From looking at what I have tried I saw that in order to get a universal formula for the difference of any size square/rectangle on any size grid, both the grid width, width, and

Conclusion

By inserting these variables into my basic

formula above I developed the following

universal formula:

Using this formula I tested a square and rectangle on a 9x9 grid.

2x2 square on a 9x9 grid:

Dif = l(py-y-p+1)²

= lpy-ly-lp+l

= 2x2x9-2x9-2x9p+9

= 9

2x3 rectangle on a 9x9 grid:

Dif = l(py-y-p+1)²

= lpy-ly-lp+l

= 2x3x9-2x9-3x9p+9

= 18

The formula is…

(width of grid) x (area of square/rectangle) - (width of square/rectangle) - (height of square/rectangle) + (width of grid)

This gives the difference for any size square/rectangle on any size grid.

I tested the formula on a large random sized grid with a random sized rectangle.

3x9 rectangle on a 49x49 grid:

Dif = l(py-y-p+1)²

= lpy-ly-lp+l

= 3x9x49-3x49-9x49p+49

= 784

Conclusion:

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. ## Number Grid Aim: The aim of this investigation is to formulate an algebraic equation ...

3 star(s)

97263 - 97244 = 19 5. 305 x 325 = 99125 306x 324 = 99144 ? 91444 - 99125 = 19 Once again, I can conclude that the difference between the cross multiplied products is the size of the grid; 19. To confirm this, the number 19 has been inserted into the formula to prove that this is correct.

2. ## &amp;quot;Multiply the figures in opposite corners of the square and find the difference between ...

This is where we can make formulae from the results of the table. The formula should connect the size of the square (n) which will be the length of one side of the square to the difference and save the hassle of the working out.

1. ## Investigation of diagonal difference.

size grids as this may be of use to me when trying to find a general formula. I will now look at 2x2 cutouts in different size grids. What is the diagonal difference of a 2 x 2 cutout on an 8 x 8 grid?

2. ## For other 3-step stairs, investigate the relationship between the stair total and the position ...

49 57 58 59 60 61 12 Formula: 15x-200 23 24 1: 15x56-200= 640 34 35 36 2: 12+23+34+45+56+24+35+46+57+36+47+58+48+59+60= 640 45 46 47 48 56 57 58 59 60 18 Formula: 15x-220 30 31 1: 15x66-220= 770 42 43 44 2: 30+42+54+66+43+55+67+56+68+69+18+31+44+57+70= 770 54 55 56 57 66 67 68

1. ## Maths - number grid

the above calculations it can be assumed that they are correct, I will use algebra to prove this. (s+5)(s+30) - s(s+35) s(s+30) +5(s+30) - s - 35s s +30s+5s+150 - s -35s =150 I find it very difficult to see any major trend, this is because I am randomly selecting

2. ## Investigate The Answer When The Products Of Opposite Corners on Number Grids Are Subtracted.

out other number grid answers and a pattern might present itself from the graph. From the graph, I have realised that you cannot find out other answers accurately because the line is not linear. It is a curve so the next answer could be anything.

1. ## Investigate the difference between the products of the numbers in the opposite corners of ...

1 2 3 11 12 13 21 22 23 1 x 23 = 23 3 x 21 = 63 63 - 23 = 40 8 9 10 18 19 20 28 29 30 8 x 30 = 240 10 x 28 = 280 280 - 240 = 40 I can

2. ## Number Stairs - Up to 9x9 Grid

On a 10 by 10 number square grid 91 92 93 94 95 96 97 98 99 100 81 82 83 84 85 86 87 88 89 90 71 72 73 74 75 76 77 78 79 80 61 62 63 64 65 66 67 68 69 70 51

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