lines of symmetry

a ppt is here

4d + 4u

4u: using 4 lengths of length 1 unit
4d: and 4 lengths of length (square root 2) 1 diagonal
create a closed shape

try to create shapes that have reflection or rotational symmetry (or both)

powerpoint: 4d + 4u

see also du

Talavera

originated in Spain
also found in Mexico

what symmetries do these have?

hole punching

the US and Canada dental admission test (DAT) has six categories of questions within the perceptual ability test (PAT)

a powerpoint with 10 questions (needs to be downloaded) explores 'hole punching' questions
with a view to students considering, eventually, how they might advise people taking the test

the six categories:

• angle ranking (put shown angles in order of size)
• keyholes/apertures (3D visualisation: which 'solid' will fit through all of the shown 'keyholes')
• painted faces on cube constructions - when all the outside faces are painted
• view recognition (decide which of the 'solids' fit the given plan and elevations)
• nets (which is the net of the solid)
• hole punching

the hole punching tasks involve paper folding and reflection symmetry:

bead patterns

continue and complete a pattern:

see frieze patterns

pattern experiments

Lucy Walker's pattern experiments

quartering a 5 by 5 grid

hopefully being systematic, using some logic/reasoning, students can look to find all the ways to
quarter a 5 by 5 dotty grid with
(i) rotational symmetry order 4
(ii) rotational symmetry order 2
(iii) one line of symmetry

they could also find all 13 ways to half a 4 by 4 grid

the powerpoint for this

Korean symbol symmetry

mostly from Chloe Koo
what symmetries do these symbols have?

designing tessellations

an argument for spending more time on tessellating in the curriculum is that an analysis can lead to an appreciation of transformations, angle facts and symmetry properties

Jinny Beyer is well known for her long term work with quilting

in her book, 'designing tessellations, the secrets of interlocking patterns' she offers some analysis of e.g. how a square might be adapted by cutting and fitting to create several different designs using this basic principle:

students could create their own versions
or
try to reproduce one of the twenty that Jinny identifies in her book

papercutting

Poland: Wycinanki
Ukraine: Vytynanky