• 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
5. 5
5
6. 6
6
7. 7
7
8. 8
8

# Investigating how the numbers worked on a number grid.

Extracts from this document...

Introduction

Maths GCSE Coursework

Kaleigh Mills

Investigation

I was given the task of investigating how the numbers worked on a number grid. This is what I did to find out:

I chose a grid of four numbers and I multiplied the Top Left (TL) by the Bottom Right (BR) then I did the same with the Top Right (TR) and the Bottom Left (BL). I then found out the difference between the two outcomes.

 n n+1 n+10 n+11

E.g.

 12 13 22 23
 44 45 54 55

After trying a few 2 x 2 grids I then went on to do some 3 x 3 grids.

 n n + 2 n + 20 n + 22

E.g.

 61 62 63 71 72 73 81 82 83
 5 6 7 15 16 17 25 26 27

## n

n+3

n+ 30

### n+

33

n(n + 33) = n2 + 33n

(n + 3)

Middle

53

54

55

56

63

64

65

66

67

73

74

75

76

77

83

84

85

86

87

94

95

96

5

6

7

8

#### 9

15

16

17

18

19

25

26

27

28

29

35

36

37

38

39

46

47

48

##### 49

After testing a lot of grids I have discovered that the rule for a square of any size is

(n-1)2x10. To prove this I am going to test it for a 6 x 6 grid.

Prediction

I predict that for a 6 x 6 grid the difference will always be 250.

For a 6 x 6 grid the algebraic formula is:

n(n + 55) = n2 + 55n

(n + 5)(n + 50) = n2 + 55n + 250

Difference = 250

Testing

 2 3 4 5 6 7 12 13 14 15 16 17 22 23 24 25 26 27 32 33 34 35 36 37 42 43 44 45 46 47 52 53 54 55 56 57

By predicting what the outcome would be with

Conclusion

6 x 6 grid

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
 7 8 13 14
 22 23 24 28 29 30 34 35 36

After testing a few square grids from a 6 x 6 grid I found the differences to be 6 and 24, these are both multiples of 6. Therefore I have now proved that my prediction is correct.

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

To do this I am going to look at the change in the L-Shape when it is rotated. I will start by doing a diagram of the four rotations that are possible using a standard L-Shape. 1 2 3 4 5 6 7 8 9 10 11 12 13 14

2. ## Number Grids Investigation Coursework

Table of Results for Rectangles My next job is to put all my results for rectangles in a table, to look for potential patterns and formulae. Length of Rectangle (m) Width of Rectangle (n) Difference (D) 2 2 10 2 3 20 2 4 30 2 5 40 Obviously, the

1. ## Number Grid Investigation.

+ (TR X BL) Firstly in a 2 X 2... 31 32 41 42 (TL X BR) + (TR X BL) = 2614 70 71 80 81 Product difference = 11350. The product difference is not the same. I do not see that changing the calculations will have any effect on my formulas.

2. ## Number Grid Coursework

(16 + 5)(16 + 60) - 16(16 + 60 + 5) 21 x 76 - 16 x 81 1596 - 1296 300 (N.B. also = 10 x 5 x 6 = 10[p - 1][q - 1]) 7) Justification The formula can be proven to work with the following algebra (where

1. ## Maths - number grid

major trend forming, I am going to increase the size of my rectangles to and 8x5. 30x63 - 23x70 1890 - 1610 Difference = 280 I am confident that the defined difference of 280 for any 8x5 is correct. I will use algebra to ensure this is true.

2. ## Number Grid Investigation

10 (4x4 - 1)...10 (3x3) = 90, this is correct as I proved earlier that the difference for a 4 x4 square is 90. The formula which works for any size square on the 10 x 10 number grid is: 10 ( a - 1 )2 I am now going to investigate rectangles on the 100 grid.

1. ## number grid

After looking at my table I have found out that the difference between, the product of the top left number and the bottom right number, and the product of the top right number and the bottom left number is always 10 in a 2 X 2 grid.

2. ## Mathematical Coursework: 3-step stairs

Therefore I'm able to find the total number of the 3-step stair by just adding 6. However this technique would restrict me from picking out a random 3-step stair shape out of the 9cm by 9cm grid. As I would have to follow the grid side ways from term 1 towards e.g.

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