Compound transformations

problem

Squares, Squares and More Squares

Age

11 to 14

Challenge level

1 out of 3

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

2 out of 3

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

2 out of 3

Make a footprint pattern using only reflections.
problem

2001 Spatial Oddity

Age

11 to 14

Challenge level

3 out of 3

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

3 out of 3

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

Reflect Again

Age

16 to 18

Challenge level

3 out of 3

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

1 out of 3

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

1 out of 3

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

1 out of 3

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

1 out of 3

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