69x96=6624
5 by 5 grids
- 1x45=45
5x41=205
205-45=160
- 6x50=300
10x46=460
460-300=160
- 51x95=4845
55x91=5005
5005-4845=160
- 56x100=5600
60x96=5760
5760-5600=160
The table above shows that the answer always ends in 0 and the second difference will always be 20. Also the table shows all the numbers are multiples of 10. I am now going to predict the next two grids size by using the first method by looking at patterns and rules of the above table.
One of the first patterns I can see is the second difference is always repetitive. From this I can predict the next two grid sizes from
Looking at the patterns from above.
Method two
Is the formula which is;
(N-1)² x grid size
I am now going to predict 6 by 6.
N represents the grid size e.g. 6 by 6.
Then you – 1 so you go back down two the grid size which is 5 by 5. Then you times 5 by 5 which equals 25. With this answer you then time it by the actual grid size which is 10. After that you come up with 250.
I am now going to predict 7 by 7.
N represents the grid size e.g. 7 by 7.
Then you – 1 so you go back down two the grid size which is 6 by 6. Then you times 6 by 6 which equals 36. With this answer you then time it by the actual grid size which is 10. After that you come up with 360.
I am now going to test my predation, by doing the same thing as I did for the other number grids.
6 by 6 grids
- 5x60=300
10x55=550
550-300=250
- 11x66=726
16x61=976
976-726=250
- 31x86=2666
36x81=2916
2916-2666=250
- 35x90=3150
40x85=3400
3400-3150=250
7 by 7 grids
- 1x67=67
7x61=427
427-67= 360
- 4x70=280
10x64=640
640-280= 360
- 31x97=
3007
37x91=3367
3367-3007=360
- 34x100=3400
40x94=3760
3760-3400=360
In conclusion I have found out that my predictions where right. So now I’m going to do the same thing all over again but I am going to change the grid from 10 by 10 to 11 by 11.
Extension investigation for Number grid
The purpose of this investigation is to look at diagonal differences on different sizes of grids. I am going to do this by multiple the numbers in the corners of the grids and then subtracting there answers to get the over all difference. From my previous investigation I did a 10 by 10 grid.
To carry out this investigation I will start by extracting a 2 by 2 grid by my original 9 by 9 grid. I will then carry out by multiplying the corner numbers and subtracting the smaller number by bigger the number so I can gain an answer. To further this investigation I will extend the grid size to a 3 by 3 grid and I will be doing exactly the same method as the other grid. I will then continue this by extending the grid size to a 4 by 4, 5 by 5, 6 by 6 and so on.
2 by 2 grids
- 11x21=231
12x20=240
240-231=9
- 40x50=2000
41x49=2009
2009-2000=9
- 61x71=4331
62x70=4340
4340-4331=9
- 64x74=4736
65x73=4745
4745-4736=9
3 by 3 grids
- 1x21=21
3x19=57
57-21=36
- 13x33=429
15x31=465
465-429=36
- 34x54=1836
36x52=1872
1872-1836=36
- 47x67=3149
49x65=3185
3185-3149=36
4 by 4 grids
- 1x31=31
4x28=112
112-31=81
- 14x44=616
17x41=697
697-616=81
- 46x76=3496
49x73=3577
3577-3496=81
- 51x81=4131
54x78=4212
4212-4131=81
5 by 5 grids
- 1x41=41
5x37=185
185-41=144
- 5 x45=225
9x41=369
369-225=144
- 37x77=2849
41x73=2993
2993-2849=144
- 41x81=3321
45x77=3465
3465-3321=144
The table above shows that the answers are multiples of 9 and the second difference will always be 18. I am now going to predict the next two grids size by using the first method by looking at patterns and rules of the above table.
One of the first patterns I can see is the second difference is always repetitive. From this I can predict the next two grid sizes from
Looking at the patterns from above.
Method two
Is the formula which is;
(N-1)² x grid size
I am now going to predict 6 by 6.
N represents the grid size e.g. 6 by 6.
Then you – 1 so you go back down two the grid size which is 5 by 1. Then you times 5 by 5 which equals 25. With this answer you then time it by the actual grid size which is 9. After that you come up with 225.
I am now going to predict 7 by 7.
N represents the grid size e.g. 7 by 7.
Then you – 1 so you go back down two the grid size which is 6 by 2. Then you times 6 by 6 which equals 36. With this answer you then time it by the actual grid size which is 9. After that you come up with 324.
I am now going to test my predation, by doing the same thing as I did for the other number grids.
6 by 6 grids
- 1x51=51
6x46=276
276-51=225
- 4x54=216
9x49=441
441-216=225
- 28x78=2184
33x73=2409
2409-2184=225
- 31x81=2511
36x76=2736
2736-2511=225
I predict that the 6 by 6 would equal 225 and I got it right by using the formula that I had worked out to predict the answer for the 6 by 6 grids.
7 by 7 grids
- 1x61=61
7x55=385
385-61=324
- 3x63=189
9x57=513
513-189=324
- 19x79=1501
25x73=1825
1825-1501=324
- 21x81=1701
27x75=2025
2025-1701=324
I also predicted that the 7 by 7 would equal 324 and I got it right by using the formula that I had worked out to predict the answer for the 7 by 7 grids.
Conclusion
I thought that this course work went well because I wrote a lot of pages. In this course work I found out the formula to working out the number grids and that there were patterns that helped me work out the answer. I would apply the same formula to bigger grids like 11 by 11.