Research-based guidance and classroom activities for teachers of mathematics

Reasoning about uncertainty

We have identified six themes within the key idea of reasoning about uncertainty: intuitions, misconceptions, simulations, modelling, distribution, and risk

Each theme page has links to relevant online activities and resources. A full list of all activities for reasoning about uncertainty is on the right hand side of this page.

What creates uncertainty?

Lack of information creates uncertainty. In some circumstances, such as card games or sport, this uncertainty can be compelling for both players and spectators. By reasoning about uncertainty, a player can adopt a strategic approach that will improve his or her success rate in the long term, even if it appears ‘unlucky’ in the short term.


Reasoning about uncertainty can play an important role in the decision-making process. For example, weather forecasters tell us how likely it is to rain, and doctors explain the likelihood of experiencing side effects when they prescribe medication. In these situations, decisions are made based on an understanding of both the chances of a particular outcome occurring, and of the costs and benefits associated should it happen.

In order to reason about uncertainty, we need to know when it might be appropriate to apply a random model. Often, a situation might not be recognised as being open to a random analysis. For example a player in a game might interpret their success or failure as essentially a matter of luck, but this approach is unlikely to be successful in the long run.

The Law of Large Numbers

The notion that uncertain events, if repeated sufficiently often, become predictable, referred to as the Law of Large Numbers, is a key understanding in reasoning about uncertainty.