Compound transformations

problem
Counting triangles

Age

11 to 14

Challenge level

Triangles are formed by joining the vertices of a skeletal cube. How many different types of triangle are there? How many triangles altogether?
problem
Transformations tables

Age

7 to 11

Challenge level

These grids are filled according to some rules - can you complete them?
problem
Rots and refs

Age

16 to 18

Challenge level

Follow hints using a little coordinate geometry, plane geometry and trig to see how matrices are used to work on transformations of the plane.
problem
Squares, squares and more squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
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
Triangular tantaliser

Age

11 to 14

Challenge level

Draw all the possible distinct triangles on a 4 x 4 dotty grid. Convince me that you have all possible triangles.
problem
Flight of the Flibbins

Age

11 to 14

Challenge level

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to the new planet?
problem
Matching frieze patterns

Age

11 to 14

Challenge level

Sort the frieze patterns into seven pairs according to the way in which the motif is repeated.
problem
Footprints

Age

16 to 18

Challenge level

Make a footprint pattern using only reflections.
problem
Combining transformations

Age

11 to 14

Challenge level

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