On a brief visit (an hour, say) The Magic Mathworks Travelling Circus can be used like any other hands-on science gallery: visitors tour the exhibition, study the captions, perform the experiments. This allows them to become familiar with the style and survey the contents. German teachers call such a session a Schnupperstunde.
If a longer or, better still, a second visit is possible, (the usual practice in our German schools), further possibilities open up. Best of all is the sequence: Schnupperstunde, maths lesson, second visit, since teachers can tailor the second session to the specific needs of their class.
If time is short, follow-up becomes all-important and there are sections on this site to help provide this:
The Virtual Circus for children (and teachers),
Heuristics for teachers.
But here are some suggestions appropriate to children in Grade 5/Year 6 and above if more time is available.
The Circus is primarily a three-dimensional experience and anything which reduces the time spent enjoying this should be discouraged. However, some modes of recording can be a help rather than a hindrance. Chief among them are those which make the children observe, e.g.:
- orthographic views from front, side and top of a Soma Cube, using squared paper,
- isometric views on the corresponding triangular paper,
- sketches of the soap films spanning skeleton polyhedra with pencil crayon on plain paper.
Now that cameras are routinely incorporated in mobile phones, the children can photograph what they have done. This does not aid observation at the time but does provide pictures which can be annotated, labelled and incorporated into electronic documents later: the observation is deferred, if you like.
The younger children can record a two-dimensional dissection or tiling by using the pieces themselves as templates and simply drawing round them. It’s hard to assess the value of this activity but one can say that it affords the children themselves great satisfaction.
The Leonardo (Dürer) Screen is present in its own right in the section ‘Transformations’. But of course there’s nothing to prevent the children using it to draw a model they have built under the heading ‘Polyhedra’. For a permanent record they should trace in thin pen or pencil what they have drawn on the screen with a thick dry-wipe pen. Since we added the section ‘2-D to 3-D’ to our repertoire (not listed in the inventories on this site), a refinement is possible: the children make their drawings in two colours with alternate eyes closed and view the result with anaglyptic spectacles.)
Older children can use protractors to determine the angles at vertices. Better still, where the geometry allows, they can measure some and deduce others. They can use rulers to measure a dimension on the original and the image to find the scale factor of an enlargement. (Younger children can use arbitrary units to do so, e.g. the length of a finger.) The children can measure and sum the lengths of rival solutions to the problem Motorway Networks. They can also determine dihedral angles in solids using the special Polydron protractor. (They can see without measurement that the sum of the dihedral angles for the regular tetrahedron and octahedron is a straight angle.)
Stations under the heading ‘Communication’ provide an exercise in the precise use of language orally. The general question of what to write down in the Circus is one the individual teacher needs to decide. Some teachers provide a pro forma with questions as prompts; others require a less structured record. The criterion is whether this documentation increases or decreases the child’s engagement with the station itself.
In calling The Magic Mathworks a ‘lab’ we are implying that it is a collection of apparatus for the visitor’s own experiments, that there is scope for activities not specified by the captions. Such activities may involve a different use for the materials at a single station, or the combination of materials from two different stations. We have already given examples of that. But we give them again here in a list of ways in which the stated tasks may be extended. Some of these suggestions are indeed made on the caption boards but are rarely taken up.
|Transformations||Perspective Drawing||Draw your model.|
|Transformations||Perspective Drawing||Draw your model in red with your left eye shut, green with your right eye shut. View the result with green (left) red (right) anaglyptic spectacles.|
|2-D to 3-D||Anaglyphs|
|Transformations||The Mira||Build in left- and right-handed versions – i.e. one with the ‘Polydron’ trademark inside, the other with it outside – and compare in the Mira.|
|Transformations||The Mira||Build the Soma Cube, or an object made with the Soma pieces, in left- and right-handed versions, and compare in the Mira.|
|Dissections||The Soma Cube|
|Transformations||The Profile Gauge||Build ‘pots’ with the Polydron Sphera and draw different cross-sections.|
|Transformations||Orthographic Projections||Draw the shadows cast by your chosen object from 2 perpendicular, focussed lamps on two perpendicular boards (or, more simply but less dramatically, use the same lamp and board and rotate the model). Use a single lamp and board to draw your friend’s profile.|
|Symmetry||Mirror Symmetry||Put Pattern Blocks in the 2-D kaleidoscope. Use more to make the complete design.|
|Symmetry||The Magic Mirror Cube||Use more Polydron to build what you see in the 3-D kaleidoscope.|
|Symmetry||The Magic Mirror Cube||Put a single cube in the mirror cube and see a cube-of-cubes.|
|Packing||Polyhedral Packing||Dissect the tetrahedron-octahedron packing in different ways, e.g. as a mixture of octahedra and cuboctahedra.|
|Packing||Polyhedra Packing 2||Make from card:
|Packing||Packing Spheres||Use the red Number-Building baseboard and balls. Model crystal line dislocations by off-setting one row of balls half a space.|
|Packing||Polyhedral Packing||Use the Number-Building balls in the Polyhedral Packing hoppers to perform the basic Number-Building experiments in inverted form.|
|Solids||Cross-sections||In parallel with work using the string models, use perspex solids partially filled with water to show the sections.|
|Solids||Cross-sections||Use Polydron to build the two parts of a regular tetrahedron or cube separated by a given cross-section.|
|Communication||Over the Phone||Use 3-D models (in Multilink or Polydron) in place of polygonal tiles.|
|Communication||The Feely Box||Use Polydron in place of Multilink to obtain more complicated 3-D shapes.|
|Heuristics||Safe Queens||Find more solutions in the 5 x 5 and 7 x 7 cases.|
|Heuristics||Nim||Start with different numbers of rows and matches.|
|Heuristics||Chomp||Start with a square block. Start with an n x 2 block.|