Chance
The Chance construct describes a progression of understandings about uncertainty and its measure. There are three anchoring ideas that are elaborated as students learn about chance. The first is that a measure of uncertainty, probability, relies on thinking about a repeated process where the outcome(s) cannot be known in advance with certainty. The second is that probability can be estimated by thinking about the structure of the process generating the uncertain outcomes -- a theoretical probability. The third is that probability can also be estimated by observing the outcomes of the process as it is repeated — an empirical probability.
Levels
1 Hold an informal view of chance.
2 Develop the concept of trial.
3 Quantify chance as probability and relate it to the structure of a simple event.
4 Empirically examine the relationship between observations and all possible outcomes of repeated events.
5 Develop sample space for aggregate events.
6 Coordinate sample space, probability, and relative frequency for aggregate events.