Being resourceful

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?

What is the largest number which, when divided into these five numbers in turn, leaves the same remainder each time?

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

A mother wants to share some money by giving each child in turn a lump sum plus a fraction of the remainder. How can she do this to share the money out equally?

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at each price?

Can you make sense of information about trees in order to maximise the profits of a forestry company?