rotation questions

these are based on KS2 SAT past paper questions

a ppt is here

transformations, combined reflections

a ppt is here

rotation 90 clockwise

rotation 270 anticlockwise

plus three other options

non-commutative

but a neat symmetry

rabbit rotations

what angles do the rabbits turn through?
powerpoint: rabbit rotation angles

not just rabbits
powerpoint: rotating things
(makes me feel giddy...)

windmills, order 4 and order 3

creating shapes with rotational symmetry

intended to be done (initially attempted) without tracing paper

powerpoint: windmills

maths jigsaw

the shapes fit together to make a square (on the 5 by 5 dotty grid)

I'm fairly confident that you just need to rotate some of the shapes (mentally or otherwise) to fit them together i.e. you do not need to reflect/flip them

a related task:
fill up a 7 by 7 grid with the shapes indicated
the whole area should be covered

students could be asked to find alternatives

some of the questions have a few possibilities
e.g. for question 5 (there may well be more...) :

180 degree rotations

if you download the powerpoint here the rotations are animated

rotate 180 about 1

rotate this (image) shape 180 about 2

rotate about another point 3

through 180 to end in the position shown above

students could produce their own examples

what do students notice if they connect together the four centres of rotation?

consider the effect of two 180 degree rotations about different centres

two rotations through 180 degrees seems to be a translation

what relationship is there between the translation vector and the two centres of enlargement?



a reason for this, approached vectorially:

turning

different rotation centres