Visualising and representing

problem
Threesomes

Age

11 to 14

Challenge level

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?
problem
Reflecting squarely

Age

11 to 14

Challenge level

In how many ways can you fit all three pieces together to make shapes with line symmetry?
problem
Diagrams

Age

7 to 11

Challenge level

A group activity using visualisation of squares and triangles.
problem
Remainders

Age

7 to 14

Challenge level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?
problem
LOGO challenge - triangles-squares-stars

Age

11 to 16

Challenge level

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.
problem
LOGO challenge - circles as animals

Age

11 to 16

Challenge level

See if you can anticipate successive 'generations' of the two animals shown here.
problem
Frogs

Age

11 to 14

Challenge level

How many moves does it take to swap over some red and blue frogs? Do you have a method?
problem
Think of two numbers

Age

11 to 14

Challenge level

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
problem
Cubist cuts

Age

11 to 14

Challenge level

A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
problem
Triangles to tetrahedra

Age

11 to 14

Challenge level

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?