This activity lends itself well to the use of Cuisenaire
 
Rods.   It is then useful to supply centimetre squared paper
 
for the calculation of the inner area of the rectangles.  
 
It provides a good opportunity for these able pupile to try
 
to put ideas into words, particularly when you ask about
 
situations where the areas are different by 1.
 

 
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Some children get hooked onto the idea of creating the
 
nearest things to a square each time so as to get the
 
largest area.
 

 
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Others tend to just lengthen the rectangle each time and
 
therefore lose out when they come to using 8 blocks to
 
surround the largest area - this time in the shape of a
 
square.
 

 
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If you have a large group of children doing this activity
 
then it is very useful to have them working with different
 
lengths of rods.   This allow an interesting comparison
 
between those who used [for example] the 4 rods with those
 
who used the 5 rods and the 6 rods.   A large table of
 
results leads usually to interesting discussions.
 

 
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Please send in any reports of the kinds of discussions that
 
occurred.
 

 
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