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# Pure Investigations

These two books from the Shell centre focus on the pure investigations. The pure investigation tasks are, perhaps, rather different from the other two main types of extended task, those of a practical nature and those of an applied nature, in the sense that they allow students to seek out the pattern and beauty of mathematics without being constrained by real life. The common element amongst all the items within this cluster is the idea that they may be used to stimulate generalisations or optimisations according to the individual need and ability of each student.

Making the most of It
The lead task is Barriers, a pure mathematical investigation and is one of a family of similar ideas looking at things, such as the minimum number of barriers required to fence off given areas, or the maximum area which can be fenced off using a specified number of barriers Tasks such as these are generally classified as optimisation problems. Barriers was intended to be used as a pure mathematical investigation during which students try to discover rules and generalisations.

The alternative tasks are:
*Cross numbers
*Border tiles
*Dominoes
*Stars
*Joining dots
*Crossings

Looking deeper
The lead task is Connect 4. The most fruitful area for developing this task seemed to be within general pure investigative mathematics. However, the work could well be carried into a more probability or permutations and combinations based study.

The alternative tasks are:
*Stamps
*Triangles galore
*Drawing squares
*Shape it up
*Dotty polygons
*Chaining

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