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Published byTyler Ward Modified over 8 years ago

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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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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 50 100 by 100 n by n 2 red sides = ? 1 red side = ? 0 red sides = ?

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Generalising from Diagram 20 by 30 50 by 40 90 by 50 a by b 2 red sides = ? 1 red side = ? 0 red sides = ?

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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!

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