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'Extending Great Squares' printed from http://nrich.maths.org/

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The activity is intended to extend Grrrreat Squares for those who need/want something much more challenging.

 
Choose one or more of the following five sets of pictures and explore them further for number patterns, area implications, trigonometrical facts and predictions.
 

$1$
 2
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$2$
 3
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$3$

 4
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$4$

 5
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$5$

 6