Compound transformations

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
Friezes using Logo

Age

11 to 14

Challenge level

Experimenting with variables and friezes.
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
Simplifying transformations

Age

11 to 14

Challenge level

How many different transformations can you find made up from combinations of R, S and their inverses? Can you be sure that you have found them all?
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?
problem
Transforming the letters

Age

7 to 11

Challenge level

What happens to these capital letters when they are rotated through one half turn, or flipped sideways and from top to bottom?