Stair Shape on a 10x10 Number Grid
Introduction
For this investigation I will be investigating the relationship
between no. total and stair no. on a 10x10 number grid. I will also be
comparing results when the stairs are moved around the grid, finding
patterns that may occur.
Method
A diagram of the stair shape is shown below. There are three numbers
on the bottom layer, two on the second and one on the top, starting
from left. The stair no. will be identified by the number in the
bottom left hand corner of the stair. The grid starts from one in the
bottom left hand corner and ascends to 100 in the top right. This is
done so the stairs are in an up-right position rather than up side
down. As shown below.
I began by planning the first set of stairs…
I shaded in no.s 1,2, 3, 4 and 5 to make the outline of the stair case
clear. The no. in the bottom left hand corner is1, therefore this
stair will be known as stair shape no. 1…
Then, to work out the total no. I added up all the numbers in the
stair shape, using a calculator, to ensure the results are accurate…
The answer = 50
Therefore;
Stair no. = 1 Stair total = 50
I proceeded to apply this method to the next few stair no.s
To be able to compare the relationship between stair no. and total
horizontally across the grid, I am going to chose the next four stair
no.s to the right of 1.i.e stair no.s 1-5.This will make the formulae
easier to work out.I found the following results;
Stair no.
1
2
3
4
5
Stair total
50
56
62
68
72 74
+6 +6 +6 +4? +6
For stair no.5 the total did not follow the pattern.I will check it's
total for a second time…
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