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Mathematics Investigation

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13 matches were used to make this one with four squares. Investigate the number of matches needed ... Square 1. Three. Two. One. Pattern. What Does This Mean? ... – PowerPoint PPT presentation

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Title: 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.
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