This investigation brings out patterns in numbers, shapes and factors as
well as often making a very satisfactory 'finished product'.
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Although it is quite possible for pupils to draw all the circles and make
marks evenly spaced round it makes for a much better start to give them a
sheet of circles like those below appropriately marked first in 12s and
then in 10s. (There really is no need to put on the numbers although some
pupils may like to do this at first.)
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There are many patterns both in shapes and numbers in this investigation.
Pupils will be able to make some rules quite soon, and then abstract from
these. Predictions should be encouraged! Factors, numbers that have a
common factor and numbers that are mutually prime should emerge.
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Using circles marked with certain numbers of dots produce some beautiful
stars. These can be incorporated into Christmas and Divali decorations! See
if the pupils can find them.
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The investigation can be extended by working with quite large numbers and
predicting shapes that would come. Numbers that have a common factor
produce the most interesting and least predictable results and are often
worth drawing out.
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