Research-based guidance and classroom activities for teachers of mathematics

# Ratio and proportional reasoning

 We have identified eight themes within the key idea of ratio and proportional reasoning: multiplicative relationships, managing relationships between several variables, ratios in mixtures, rates, proportional reasoning, scaling, division, and whole school approaches. Each theme page has links to relevant online activities and resources. A full list of all activities for ratio and proportional reasoning is on the right hand side of this page.
##### 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.

##### Activities and resources

Cooking numbers

Zin Obelisk

Ratios and dilutions

Product wars

Balancing 2

Oh! Harry!