Research-based guidance and classroom activities for teachers of mathematics

Proportional reasoning

Proportional reasoning is a theme within ratio and proportional reasoning. Links to relevant activities and resources are on the right hand side of this page. 

Proportional reasoning involves comparing ratios within or between objects, and understanding that scaling one object while maintaining the ratios involves four variables.When a/b = c/d an increase in a can be compensated by decreasing d, or increasing b, or increasing c. Deciding which quantities to increase or decrease, and whether to achieve this by multiplying or dividing, requires a strong grasp of non-integer arithmetic and the meaning of multiplying as scaling.