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Mathematical Activity Tiles Handbook
A guide to MATs for geometrical exploration
Related resources
Shape and space, tessellations, reflection, rotation angle and tiling patterns.
Shape and space, tessellations, reflection, rotation angle and tiling patterns.
The next generation of MATs: encouraging mathematical thinking and discussion.
2-D and 3-D possibilities opened up by cutting regular polygonal tiles.
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 Mathematical Activity Tiles Handbook - PDF
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Mathematical Activity Tiles Handbook
Mathematical Activity Tiles offer many opportunities for geometrical exploration. They do this with neither the delay involved in constructing nets nor the prescription implied by ready-made nets. They encourage an exploratory, 'prototype', way of working, facing the maker with choices and models he would not be likely to encounter otherwise.
The techniques involved are relatively easy to acquire, becoming refined through experience. Children of five years old have been capable of some satisfactory constructions and the model illustrated on the front was made by a nine year-old, who invented it and constructed it in the space of an hour.
He began with a flat design of ten pentagons around each hole, but found he could not continue this for long. After a pause for thought, he began to work in three dimensions! People of all ages seem to find themselves using rules, systems and codes in developing their models.
That some systems work, while others do not, raises questions about the natural constraints of 3D space and the MATs provide the medium for pursuing these. Both the systems and the questioning involve mathematical thinking. So do the classifying and seeking for relationships which follow the production of a range of polyhedra. These can readily move beyond those usually illustrated in standard references on mathematical models, which is releasing and challenging in a similar way to the effect of a geoboard on 2D geometry.
A range of starters and questions have been tried by myself and others over the past five years. Some of these are collected here and offered as a start to your collection.
