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Borders Maths Investigation
1) Investigate the different patterns of development



Order of squares going down
1 + 3 + 1 = 5
1 + 3 + 5 + 3 + 1 = 13
New additions. In each case 2 has been added.
1 + 3 +5 7 + 5 + 3 + 1 = 25
Like the previous pattern there are
Additions with 2 being added on.
For the next pattern I predict that the total number of squares will be 41, using the following pattern:
1 + 3 + 5 + 7 + 9 + 7 + 5 + 3 + 1 = 41
I am now going to check to test my prediction.
Number of squares = 25 + 16 = 41
My prediction was correct. As well as finding a correct method of finding the next pattern I noticed that to find the number of dark squares on the next pattern you use the total number for the previous pattern.
Pattern Dark squares White squares
1 1 4 1 + 4 = 5
2 5 8 5 + 8 = 13
3 13 12 13 + 12 = 25
4 25 16 25 + 16 = 41
WHY?
This happens because you are simply adding on to this. This could be a useful fact in searching for a formula.
I am......

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