The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Can you decide whose drink has the strongest blackcurrant flavour from these pictures?

Can you work out the height of Baby Bear's chair and whose bed is whose if all the things the three bears have are in the same proportions?

Use the ratio of cashew nuts to peanuts to find out how many peanuts Rachel has. What would the ratio be if Rachel and Marianne mixed their bags?

Use the Cuisenaire rods environment to investigate ratio. Can you find pairs of rods in the ratio 3:2? How about 9:6?

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

A decorator can buy pink paint from two manufacturers. What is the least number he would need of each type in order to produce different shades of pink.

Is it always possible to combine two paints made up in the ratios 1:x and 1:y and turn them into paint made up in the ratio a:b ? Can you find an efficent way of doing this?

There are two sets of numbers. The second is the result of the first after an increase by a constant percentage. How can you find that percentage if one set of numbers is in code?

What angle is needed for a ball to do a circuit of the billiard table and then pass through its original position?

A finite area inside and infinite skin! You can paint the interior of this fractal with a small tin of paint but you could never get enough paint to paint the edge.

What is the total area of the triangles remaining in the nth stage of constructing a Sierpinski Triangle? Work out the dimension of this fractal.

Make a poster using equilateral triangles with sides 27, 9, 3 and 1 units assembled as stage 3 of the Von Koch fractal. Investigate areas & lengths when you repeat a process infinitely often.

Jessica and Emily found many different places to hang the weights so that the scales balanced. Do you think they have found them all?

Jake sent in a very full solution to the Balancing 3 problem. He identifies a very useful measure to solve this problem.

Some excellent use of algebraic interpretation by Joan, Jia and Jeremy in the Inside Outside problem.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

The harmonic triangle is built from fractions with unit numerators using a rule very similar to Pascal's triangle.