Number Grid Coursework

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Index page.

Page 1: Title Page.

Page 2: Index Page.

Page 3: Investigation, 2x2 squares inside a 10x10number grid.

Page 4: Investigation, 3x3 squares inside a 10x10 grid.

Page 5: Investigation, 4x4 squares inside a 10x10 grid.

Page 6: Investigation, 5x5 squares inside a 10x10 grid.

Page 7: Formula of a 10x10 grid.

Page 8: Investigating Formula of 10x10 grid.

Page 9: Investigating, 2x2 and 3x3 squares inside an 8x8 grid.

Page 10: Investigating, 4x4 and 5x5 inside an 8x8 grid.

Page 11: Formula of an 8x8 grid and investigation of formula.

Page 12: Investigating Formula of an 8x8 grid.

Page 13: Investigating rectangles 2x3 and 2x4 on a 10x10 grid.

Page 14: Investigating rectangles 2x5 and Formula on a 10x10 grid.

Page 15: Investigating Formula of rectangles inside a 10x10 grid.

Number Grid Coursework.

Initial investigation.

In this assignment I will look at a 10x10 number grid. I will be looking at different equations and working out the formula for each.

Example

2

1

2

Equation

Total

x 12

2

2 x 11

22

I will also find the products and then minus them to get the difference.

Equation

Total

x 12

2

2 x 11

22

Difference

0

The difference is 10. I will investigate further to see if this is always the case for 2x2 squares.

2x2 squares

Equation

Total

2 x 23

276

3 x 22

286

Difference

0

2

3

22

23

Equation

Total

59 x 70

4130

69 x 60

4140

Difference

0

59

60

69

70

81

82

91

92

Equation

Total

81 x 92

7452

91 x 82

7462

Difference

0

Equation

Total

9 x 20

80

0 x 19

90

Difference

0

9

0

9

20

There is a pattern; the difference is always 10 for 2x2 squares. To prove these results algebraic equations can be used. When the value of X is replaced by a number the difference will always be 10.

x

x+1

x+10

x+11

Expression 1

x(x+11)= x2 +11x

Expression 2

(x+10) (x+11) = x2 +10x+x+10

= x2 +11x+10

x2 +11x+10

- x2 +11x

= 10

3x3 squares

2

3

4

2

3

4

22

23

24

Equation

Total

2 x 24

48

4 x 22

88

Difference

40

Equation

Total

6 x 28

68

8 x 26

208

Difference

40

6

7

8

6

7

8

26

27

28

58

59

60

68

69

70

78

79

80

Equation

Total

58 x 80

4640

60 x 78

4680

Difference

40

Equation

Total

71 x 83

6603

73 x 91

6643

Difference

40

71

72

73

81

82

83

91

92

93

There is also a pattern in the 3x3 number squares the difference is always 40. I have also done algebraic equations for this number square to prove that the difference is always 40.

x

x+2

x+20

x+22

Expression 1

x(x+2)= x2 +22x
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Expression 2

(x+2) (x+20) = x2 +40x+2x+20

= x2 +22x+40

x 2 +22x+40

- x2 +22x

= 40

4x4 squares

Equation

Total

2 x 35

70

5 x 32

60

Difference

90

2

3

4

5

2

3

4

5

22

23

24

25

32

33

34

35

Equation

Total

34 x 67

2278

37 x 64

2368

Difference
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