Rich learning tasks embedded within a familiar context allow students to work like mathematicians while making sense of the mathematics. This article demonstrates how 11-12 year-old students were able to employ all of the proficiency strands while demonstrating a deep understanding of some of the "big ideas" of probabilistic thinking.

The multiplicative principle is the tool allowing the counting of groups that can be described by a sequence of events. An event is a subset of sample space, i.e. a collection of possible outcomes, which may be equal to or smaller than the sample space as a whole. It is important that students understand this basic principle early on and know how…

Examines hypotheses and strategies used by children at the kindergarten, second-, fourth- and sixth-grade levels in making proportional judgements. The task involved 36 trials in which the child had to choose between two groups to obtain a target-color "chip." Results generally conformed to the developmental sequence proposed by Piaget…