Mathematics Investigation

1
Mathematics Investigation

• Matches

2
The Question?

• Polyominoes are made up of a number of squares
  connected by common sides. 13 matches were used
  to make this one with four squares. Investigate
  the number of matches needed to make others.

3
What First?
First I made a single line of squares
to determine if there was a pattern involved
in the investigation.
4
Pattern One
Difference
3
3
3
3
3
The difference each time was three
A formula was produced to explain the pattern
5
The Formula

• Formula 3n1
• n number of squares.
• Question? Did the pattern change if the shape of
  the polyominoe changed?
• I then arranged the squares as follows

6
Pattern Two
Difference
3
2
3
2
3
The formula that I had produced for the first
pattern did not match the second pattern.
7
Did This Pattern Have A Formula?

• NO! The pattern was changing continuously and a
  formula could not be established.
• Question? Was this pattern a one off or did the
  shape of the polyominoe play a part in the number
  of matches needed?
• I then began to create a new polyominoe.

8
Pattern Three
Difference
3
3
3
3
3
9
Comparing The Patterns!
10
What Does This Mean?

• The formula 3n1 used for the first pattern works
  with the third.
• Pattern two cannot be placed into a formula.
• Changing the shape of the polyominoe changes the
  pattern on some occassions but not on others.
• A formula can be used to work out the number of
  matchsticks needed to construct a polyominoe.

11
What Has This Taught Us?

• This PowerPoint will be placed in my e-portfolio
  in the Curriculum Knowledge page as through
  this investigation I have realised
• That investigations are not simply about finding
  an answer
• Not everything is about the answer sometimes the
  process is more important.
• Investigations open up even more questions than
  the one that has been asked.