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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

Join now!


10 X 10 NUMBER GRID CONCLUSION

I have noticed a relationship within my results. The result, which is after a result, is the box sizes squared number, multiplied by 10 (as shown colour co-ordinated within the final result table). Therefore, the formula for a 10 x 10 number grid with multiples of 1 and heights and widths of n is…

(n – 1)(n – 1) x 10

To further my investigation, I’m going to change the shape, which contains the numbers being multiplied. I am going to use a rectangle, which has a width of n and a height of 2.


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