Geomagic Square puzzles (1 and 2)

These are the first two of a set of original mathematical puzzles that appear to be solely spatial, but that are related to, and can be created from, numerical 'Magic Squares'. A variety of other similar puzzles will be published soon. Each puzzle is presented on a single page, as is a solution of it. Another page provides, for the first puzzle only, a set of shapes for pupils to cut-out and manipulate. A solution of a third puzzle is included on the introductory page. The last page offers examples of the kinds of mathematical question that pupils can ask themselves in order to 'spark-off' productive chains of reasoning. In learning how appropriate questioning enables them to persevere to solutions, pupils have opportunities to develop, and to appreciate, their natural reasoning abilities. They may also become more aware of how geometric intuition can support insights that are confirmed through reasoning. Some implications that they 'see' and use will be derived from existing geometrical and numerical knowledge, and that knowledge is likely thereby to be deepened , and possibly extended.