Learning and assessment framework for multiplicative thinking

The Learning and Assessment Framework for Multiplicative Thinking (LAF) was developed on the basis of research conducted through Scaffolding Numeracy in the Middle Years (SNMY) project.

A learning and assessment framework is generally understood to be a hierarchy of key ideas and strategies related to the development of an important aspect of the mathematics curriculum that is expressed in way that is accessible and useful to teachers. To date, these have tended to be developed for the Early Years in fairly independent ‘domains’.

The LAF attempts to bring together all of the key ideas, strategies and representations of multiplication and division needed to work flexibly and confidently with whole numbers, fractions, decimals and percent across a wide range of contexts.

The LAF is organised in terms of 8 zones from initial explorations with concrete materials through to the confident use of a wide variety of multiplicative structures and symbolic forms.

It is linked to the rich assessment tasks used to evaluate multiplicative thinking and contains explicit advice on teaching implications. It also reflects the growth of problem-solving skills and higher-order cognitive thinking.

Multiplicative thinking

A definition of multiplicative thinking that includes examples of how students develop multiplicative thinking and construct and coordinate multiplicative situations.

The eight zones

Compare the key characteristics of all eight zones of the LAF. Your students may be located across several zones in the LAF, so you may need to familiarise yourself with several areas of the framework.


Select a zone below to view information about the key characteristics, teaching implications and learning plans associated with a specific zone of the LAF: