NUMBER GRID COURSEWORK
10 X 10 NUMBER GRID
2 x 2 BOX
12 13
22 23
22 x 13 = 286
12 x 23 = 276
286 – 276 = 10
89 90
99 100
99 x 90 = 8910
89 x 100 = 8900
8910 – 8900 = 10
72 73
82 83
82 x 73 = 5986
83 x 72 = 5976
5986 – 5976 = 10
66 67
76 77
76 x 67 = 5092
77 x 66 = 5082
5092 – 5082 = 10
I have noticed that the outcome is always 10.
2 x 2 BOX ALGEBRA
a a+1
a+10 a+11
(a + 10)(a + 1) = a² + a + 10a + 10 = a² + 11a + 10
a(a + 11) = a² + 11a
(a² + 11a + 10) – (a² + 11a) = 10
3 x 3 BOX
68 69 70
78 79 80
88 89 90
88 x 70 = 6160
90 x 68 = 6120
6160 – 6120 = 40
18 19 20
28 29 30
38 39 40
38 x 20 = 760
18 x 40 = 720
760 – 720 = 40
3 x 3 BOX ALGEBRA
a a+1 a+2
a+10 a+11 a+12
a+20 a+21 a+22
(a + 20)(a + 2) = a² + 2a + 20a + 40 = a² + 22a + 40
a(a + 22) = a² + 22a
(a² + 22a + 40) – (a² + 22a) = 40
4 X 4 BOX
31 32 33 34
41 42 43 44
51 52 53 54
61 62 63 64
61 x 34 = 2074
64 x 31 = 1984
2074 – 1984 = 90
1 2 3 4
11 12 13 14
21 22 23 24
31 32 33 34
31 x 4 = 124
34 x 1 = 34
124 – 34 = 90
4 X 4 BOX ALGEBRA
a a+1 a+2 a+3
a+10 a+11 a+12 a+13
a+20 a+21 a+22 a+23
a+30 a+31 a+32 a+33
(a + 30)(a + 3) = a² + 3a + 30a + 90 = a² + 33a + 90
a(a + 33) = a² + 33a
(a² + 33a + 90) – (a² + 33a) = 90
5 X 5 BOX
56 57 58 59 60
66 67 68 69 70
76 77 78 79 80
86 87 88 89 90
96 97 98 99 100
96 x 60 = 5760
100 x 56 = 5600
5760 – 5600 = 160
6 7 8 9 10
16 17 18 19 20
26 27 28 29 30
36 37 38 39 40
46 47 48 49 50
46 x 10 = 460
50 x 6 = 300
460 – 300 = 160
10 X 10 NUMBER GRID RESULTS SO FAR
I’ve spotted a pattern. I predict that the result for the 6 x 6 box will be 250. This is because each time the box size increases the result goes up 20 more than it went up last time.
6 X 6 BOX
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
51 x 6 = 306
56 x 1 = 56
306 – 36 = 250
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 66
71 72 73 74 75 76
81 82 83 84 85 86
91 92 93 94 95 96
91 x 46 = 4186
96 x 41 = 3936
4186 – 3936 = 250
My prediction was correct. However I will make a 2nd prediction. I predict that the 7 x 7 box will have the result of 360.
7 X 7 BOX
1 2 3 4 5 6 7
11 12 13 14 15 16 17
21 22 23 24 25 26 27
31 32 33 34 35 36 37
41 42 43 44 45 46 47
51 52 53 54 55 56 57
61 62 63 64 65 66 67
61 x 7 = 427
67 x 1 = 67
427 – 67 = 360
31 32 33 34 35 36 37
41 42 43 44 45 46 47
51 52 53 54 55 56 57
61 62 63 64 65 66 67
71 72 73 74 75 76 77
81 82 83 84 85 86 87
91 92 93 94 95 96 97
91 x 37 = 3367
97 x 31 = 3007
3367 – 3007 = 360
My 2nd prediction was also correct.
10 X 10 NUMBER GRID FINAL RESULTS