square symmetries (i)

these resources link with the fine task 'attractive tablecloths' developed by Charlie Gilderdale for Nrich

initially you could ask students to place 8 crosses on a 4 by 4 grid so that there is a symmetrical pattern for the overall square




















students could be asked to produce e.g. three patterns using 8 crosses so that the whole square has just rotational symmetry, order 2 etc.

can they produce a pattern with just two lines of symmetry (i.e. not with rotational symmetry)?

can they produce a pattern just with rotational symmetry, order 4 (i.e. not with any lines of symmetry)?



describe the symmetries of these patterns for the whole 4 by 4 square

describe the symmetries of these patterns for the whole 5 by 5 square













the NRICH tasks develop this work to consider the maximum numbers of colours that can be used for patterns with various symmetries and for squares of different sizes - a clever link to well known sequences

NRICH provide a set of interactivities for 5 by 5 grids, that can be made whole screen

but... these use flash and may well be blocked in most (all) browsers
[flash player is due to be discontinued in 2020]

one line of symmetry
just rotational symmetry, order 4
two lines of symmetry, rotational symmetry, order 2
two diagonal lines and rotational symmetry, order 2
four lines of symmetry, rotational symmetry, order 4

even sized grids