**The Primary and Junior Programs, in greater detail**

The Primary and Junior Programs were developed a number of years ago by Dr Hoffman. The Primary Program is for mainly Year 6 students and the Junior Program is for mainly Year 7 students. Each program focuses on

**systematic approaches to problem solving**. This is done in the context of problems that involve systematic counting (combinatorics), chance (random) processes, geometric relationships, and prime factorisation. A consistent theme is that a problem may have no solutions, one solution, several solutions or many solutions. Solving a problem means finding all solutions, not merely one of them (if there is more than one).

In the Primary and Junior Programs, the problems are explored over an extended period, typically several months. First a simple version of the problem is examined, then a simple extension, then more complex extensions. Each problem is explored to sufficient depth for students to appreciate the solution strategy involved and the process by which it is obtained. The problems span the range of arithmetic, geometric and symbolic contexts.

Another significant strand in the programs is concerned with chance processes. Students in the Junior Program explore chance processes in Problem 6 below. The problem, Famous Footballers, is an adaptation of a problem given by the German mathematician, Arthur Engel.

The nature of the programs is probably best illustrated by some examples of the problems tackled by students. The solutions to the problems, together with some discussion, are given after the problems. The reader is urged to attempt the problems before examining the solutions to problems 1 to 2 here and problems 3 to 6 here.