Explaining, convincing and proving

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.

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 produce convincing arguments that a selection of statements about numbers are true?

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

Can you express every recurring decimal as a fraction?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?