Matchstick Staircase Investigation
Introduction
This investigation is based on the 'number sequence' and I am going to
make further more matchstick staircases for this investigation.
Investigation to find out the number of matchsticks on the perimeter
in a matchstick staircase using the GENERAL RULE.
I have drawn 6 matchstick staircases on the graph paper and I am going
to put the number of matchsticks on the base, number of matchsticks on
the perimeter, total number of matchsticks in a table based on the 6
matchstick staircases.
Table to show the number of matchsticks on the base, on the perimeter
and the total number of matchsticks.
Number of matchsticks on the base
Number of matchsticks on the perimeter
Total number of matchsticks
1
4
4
2
8
10
3
12
18
4
16
28
5
20
40
6
24
54
And I'm going to make another table to find out the difference on
perimeter from the number of matchsticks on the perimeter.
Number of matchsticks on base
1
2
3
4
5
6
Number of matchsticks on perimeter
4 8 12 16 20 24
4 4 4 4 4
Perimeter difference
From this table I'm going to make a general rule, in terms of letters.
Number of matchsticks on perimeter = P
Number of base = b
Perimeter difference = 4 (always)
When the perimeter difference is always the same therefore the general
rule will be linear pattern:
P = 4b
Prediction:
===========
I predict that, I can find the number of matchsticks on the perimeter
using this general rule, P = 4b
Example 1:
Number of matchsticks on base = 9
Perimeter difference = 4
Therefore:
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