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Magic Penny Learning Notes: PatagoniaMath
"VamosPatagonia" - "Go-Patagonia"
Checkers Games and Pattern Recognition
A "2"group square array to which no further similar group can be added without it touching an existing group. Is there a simpler pattern with the same properties?
A "7-rose" group hexagonal array to which no further similar groupcan be added without it touching an existing group. Is there a simpler pattern with the same properties?
Suitability: adaptable for any age
- pattern recognition
- interest in math, geometry, art and design
- strategic planning
- group cooperation and management
any hexagonal close packed and/or square array of 169 circular cells, which can be individually distiguished by colouring/marking them directly, or, by filling or empting them of objects
eg drawn, printed or otherwise constructed grids/ arrays;
boards (eg of wood, plastic or metal) with holes into which exactly 169 pegs with ends of similar or different colours can be placed;
magicpenny square and hexagonal math frames in which exactly 169 objects of similar circular crosssection such as similar coins, cans, circular, chips or counters, can be placed or removed.
make patterns of different sized groups of cells of different shapes, within the 169 hexagon or square array,
so that no group touches another of the same colour and can therefore be distinguished individually
eg groups of 2in a straight line, 3 in a straight line or triangle, 4 in a rhombus or square, 7 in a rose, 28 in a triangle
apply different constraints (possible or impossible)
- all the groups must be of the same size
- all the groups must be of the same shape
- all the groups must be of the same colour
- all the corners of the hexagon or square must be occupied
- the pattern must have a line of symmetry. Practice Squares Hexagons
undertake different challenges
- what is the arrangement that allows the largest number of groups of cells of a particular size and shape to be exhibited?
- what is the smallest arrangement that prevents any further similar groups of cells to be exhibited?
- what is the largest number of different situations that a particular group (eg a 4-rhombus, 7-rose, or a 9-square), can be placed?
- how quickly can a particular pattern be made?
- how quicky can a particular hexagonal pattern of objects be transferred to a particular square pattern or vice versa
individual/ teams cooperate or compete
against the clock or against each other
eg by strategically filling particular cells so reducing the competitors number of arrangement options until eventually the competitor cannot exhibit another individual group;
attempting to transfer a particular hexagonal frame pattern into a particular square frame pattern as quickly as possible.
Based on: - the Golden Hexagon of Patagonia
License/Copyright: Magic Penny Trust
© Magic Penny Trust, 2001