Finding position-to-term rules

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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Finding position-to-term rules
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Find position-to-term rules for these sequences
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Squares investigation
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Squares investigation

• Imagine a 3 x 3 square

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Squares investigation

• Imagine a 3 x 3 square
• Colour the outside red

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Squares investigation

• Imagine a 3 x 3 square
• Colour the outside red

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Squares investigation

• How many of the small squares have
• 0 red sides?
• 1 red side?
• 2 red sides?
• 3 red sides?
• 4 red sides?

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Squares investigation

• Now change the size of the starting square to
• 2 x 2 ?
• 4 x 4 ?
• etc

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Squares investigation

• How many of the small squares now have
• 0 red sides?
• 1 red side?
• 2 red sides?
• 3 red sides?
• 4 red sides?
• INVESTIGATE!

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Generalising from Diagrams








8 by 8
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Generalising from Diagrams








20 by 20
50 by 50
2 red sides ? 1 red side ? 0 red sides ?
100 by 100
n by n
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Generalising from Diagram






20 by 30
2 red sides ? 1 red side ? 0 red sides ?
50 by 40
90 by 50
a by b
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Squares investigation

• Put your results into a table! (If you need to)
• Work methodically!
• Spot patterns!
• Try to find some general rules!