# Ratio and proportional reasoning

We have identified eight Each theme page has links to |

##### Fundamental concept

The fundamental concept behind ratio and proportional reasoning is the multiplicative relationship in which quantities, whether discrete or continuous, are compared using scalar multipliers. For students who may only have a ‘repeated addition’ sense of multiplication, understanding ratio wherever it turns up can be hard.

Understanding these ideas can be ‘make or break’ learners of mathematics, so there is a huge body of research about how people might learn it better. Proportionality appears everywhere in the curriculum and in other contexts, but explicit teaching often treats it in a few standard unconnected ways. When the concept appears in measures, trigonometry, or gradients, it is often treated implicitly.

##### Repeated and varied experiences

Students learn ratio and proportional reasoning through repeated and varied experiences, over time, so that multiple uses of the words and the associated ideas and methods are met, used, and connected.