Translations

problem
Combining transformations

Age

11 to 14

Challenge level

Does changing the order of transformations always/sometimes/never produce the same transformation?
problem
Decoding transformations

Age

11 to 14

Challenge level

See the effects of some combined transformations on a shape. Can you describe what the individual transformations do?
problem
Footprints

Age

16 to 18

Challenge level

Make a footprint pattern using only reflections.
problem
Symmetric trace

Age

14 to 16

Challenge level

Points off a rolling wheel make traces. What makes those traces have symmetry?
problem
Central distance

Age

11 to 14

Challenge level

Weekly Problem 1 - 2006
The diagram shows two circles enclosed in a rectangle. What is the distance between the centres of the circles?
problem
Pink and white

Age

14 to 16

Challenge level

The white square slides once around the pink square. Through what distance does the point P on the white square move?
problem
Patchwork quilt

Age

7 to 14

Challenge level

Squares of the type shown are sewn together to make a quilt. How many different quilts can be made?
problem
Transformation tease

Age

7 to 11

Challenge level

What are the coordinates of this shape after it has been transformed in the ways described? Compare these with the original coordinates. What do you notice about the numbers?
problem
Is there a theorem?

Age

11 to 14

Challenge level

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?
page
Topkapi palace

These images are taken from the Topkapi Palace in Istanbul, Turkey. Can you work out the basic unit that makes up each pattern? Can you continue the pattern? Can you see any similarities and differences in the designs?