Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?
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?
A napkin is folded so that a corner coincides with the midpoint of an opposite edge. Investigate the three triangles formed.
Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?
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 explain the surprising results Jo found when she calculated the difference between square numbers?
In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?
