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
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