Compound transformations

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

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

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

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

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

Squaring the rectangle

Age

14 to 18

Challenge level

Can you find a way to turn a rectangle into a square?
problem

Screwed-up

Age

11 to 14

Challenge level

A cylindrical helix is just a spiral on a cylinder, like an ordinary spring or the thread on a bolt. If I turn a left-handed helix over (top to bottom) does it become a right handed helix?
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

Sine problem

Age

16 to 18

Challenge level

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
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?