Compound transformations

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

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

2001 Spatial Oddity

Age

11 to 14

Challenge level

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
problem

Trees and Friezes

Age

11 to 14

Challenge level

This problem is based on the idea of building patterns using transformations.
problem

Reflect Again

Age

16 to 18

Challenge level

Follow hints to investigate the matrix which gives a reflection of the plane in the line y=tanx. Show that the combination of two reflections in intersecting lines is a rotation.
problem

Cutting Corners

Age

7 to 11

Challenge level

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?
problem

Cut and Make

Age

7 to 11

Challenge level

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
problem

Square to L

Age

7 to 11

Challenge level

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
problem

Midpoint Triangle

Age

7 to 11

Challenge level

Can you cut up a square in the way shown and make the pieces into a triangle?