Borders Maths Investigation - page 1
Keywords: Borders Maths Investigation
By Grant867 on 07/12/2008
Level: GCSE Key Stage 4 (Years 10-11)
Page Number: 1 of 3 pages: 1 2 3
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 now going to investigate any differences between the totals.
First of all I will need to find some more totals, as the amount I have will not be conclusive. To find these without drawing any more diagrams I will use my knowledge of the structure (e.g. 1 + 3 + 1).
New orders
Pattern
Previous total
New additions
New totals
5
41
11 + 9 = 20
61 (20 + 41 = 61)
6
61
13 + 11 =24
85 (61 + 24 =85)
7
85
15 + 13 = 28
113
8
113
17 + 15 =32
145
9
145
19 + 17 = 36
181
10
181
21 + 19 =40
221
(These are white squares)
Differences
Total
5 13 25 41 61 85 113 145 181 221
1st difference
8 12 16 20 24 28 32 36 40
2nd difference
4 4 4 4 4 4 4 4
This shows a main difference of 4. I think this will influence the formula. I think this will mainly be in the form of a multiple of 4.
The first formula I will try to find is the formula for the
Last 5 comments…
There have been no comments posted for this article, but you need to register if you want to be the first!