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Mathematics Investigation

- Matches

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.

What First?

First I made a single line of squares

to determine if there was a pattern involved

in the investigation.

Pattern One

Difference

3

3

3

3

3

The difference each time was three

A formula was produced to explain the pattern

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

Pattern Two

Difference

3

2

3

2

3

The formula that I had produced for the first

pattern did not match the second pattern.

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.

Pattern Three

Difference

3

3

3

3

3

Comparing The Patterns!

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.

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.