Proportions and Ratio in MYP Year 5 Maths

Ratio and Proportion in MYP Year 5

Proportional reasoning is one of the most widely applied mathematical skills — it connects number to geometry, statistics, and real-world problem solving. In MYP Year 5, students formalise their understanding of ratio and both types of proportion: direct and inverse.

Ratio

A ratio compares two or more quantities. Students must be able to simplify ratios, divide quantities in a given ratio, and work with ratios expressed in different forms (e.g. 3:5 and 0.6). Problems may involve scaling — for example, adjusting recipe quantities or map distances.

Direct Proportion

Two quantities are in direct proportion if increasing one increases the other at a constant rate. This is written as y ∝ x, or y = kx where k is the constant of proportionality. Students identify direct proportion from tables, graphs (straight lines through the origin), and equations.

Inverse Proportion

Two quantities are in inverse proportion if increasing one decreases the other such that their product remains constant: y = k/x. Graphs of inverse proportion are hyperbolas, not straight lines. Common real-world examples include speed and time at a fixed distance, or workforce and time to complete a task.

Problem-Solving in Context

MYP Criterion D tasks often present proportional reasoning within genuine real-world scenarios — currency exchange, fuel efficiency, population density. Students are expected to identify the type of proportion, set up the equation, solve, and interpret the answer in context.

Mistakes to Watch For

• Confusing direct and inverse proportion — particularly when tables show one increasing and the other decreasing
• Assuming all relationships that increase together are directly proportional (they may be linear but not through the origin)
• Failing to define or use the constant k explicitly in written solutions