transformations, combined reflections

a ppt is here

rotation 90 clockwise

rotation 270 anticlockwise

plus three other options

non-commutative

but a neat symmetry

grid reflections

based on KS2 SATs in England

a ppt is here

wordly reflections

reflecting diagonally

generalising reflections in x = 3

three pieces

these are five of Geoff Giles' line symmetry puzzles (once upon a time available from DIME materials)

find all the ways you can find to fit the three pieces together so that there is at least one line of symmetry for the overall outline of the combined shape

my preference is to establish a rule that edges must meet whole edges

question (2) has several other solutions but with the same outline as one of the others

(with the single and the double pieces swapped over) 

many thanks to the Puntmat team (and students) who have provided additional solutions

(1) 14 solutions to this, with  20 if half square meeting is allowed

 (2) 10 solutions

(3) 5 solutions 

(4) 4 solutions

(5) 9 solutions (8 different outlines)

[ nrich1840 ]

where does the yellow rectangle need to be placed?















below are Puntmat's 14 solutions for puzzle (1)

and another 6 if you allow 'half square' joins

a powerpoint

symmetry patterns

still pools

add one square

the extra square must join along the whole of one edge

not just a corner

three, two, one

2 ways with one dot
3 ways with two dots
4 ways with three dots
then the 'opposites'

two reflections

reflect this shape in one of the four lines (a, b, c or d)

then reflect the two shapes in another line
















adopting the convention for combined functions, the example below is
ba ('a' first then 'b'):

students should be able to find a total of eight different resulting shapes