The process of investigating some of the properties of diagonals and other geometric concepts with a group of 11-year-old girls is presented. Possible changes that could have been made in the lesson are discussed, and examples of individual student work are provided. (MP)

Several methods of numerical mappings other than the usual cartesian coordinate system are considered. Some examples using parallel axes representation, which are seen to lead to aesthetically pleasing or interesting configurations, are presented. Exercises with alternative representations can stimulate pupil imagination and exploration in…

The number of triangles having a fixed length of longest side is investigated. (SD)

Two students (aged 10) and a teacher described their exploratory approach to problems involved in sliding blocks games. (SD)

Details of a class exploration of graphs that drew upon knowledge about the behavior of particular kinds of functions and applied them in a new context are provided. (MP)

The problem of finding the maximum number of right angles a polygon can have, given the number of sides, is discussed in detail. (MP)