In the process of working with some groups of teachers on using questions to promote mathematical thinking, the following table was developed. It provides examples of generic questions that can be used to guide children through a mathematical investigation, and at the same time prompt higher levels of thinking.
Investigate sequences given by $a_n = \frac{1+a_{n-1}}{a_{n-2}}$ for different choices of the first two terms. Make a conjecture about the behaviour of these sequences. Can you prove your conjecture?
Bernard Bagnall recommends some primary school problems which use numbers from the environment around us, from clocks to house numbers.
Explore the shape of a square after it is transformed by the action of a matrix.
This problem explores the shapes and symmetries in some national flags.
