Proportional Reasoning

Proportional reasoning is a unifying theme in mathematics and is often considered the foundation to abstract mathematical understanding. Yet, it is estimated that over ½ of the adult population are not proportional thinkers. Many believe this is a direct result of experiencing procedural methods in schooling instead of developing conceptual understanding. 

Early in math learning, students use proportional reasoning when, for example, they think of an 8 as two fours or four twos rather than a whole number. Later in education, they may use proportional reasoning to think of how a speed of 50km/h is the same speed as 25km/30 min. Continuing on in learning, students will continue to use proportional reasoning when thinking about percents, slopes of lines and rates of change.  

In essence, proportional reasoning is the consideration of numbers in relative terms compared to absolute terms. The formal work on proportional reasoning is typically completed in Grades 9 or 10, but students may continue to use it in trigonometry or scale diagrams. 

Relationships in Mathematics

Relationships are a key component in mathematics, and proportional reasoning relies heavily on comparisons of quantities and values. It is a complex concept to define but is sometimes perceived as only being the study of ratios, rates, and rational numbers. It is common in fractions, decimals, and percents, but can be included through all strands of mathematics. It is known as the ability to think about and compare values in a ratio, but also the relationship between two or more ratios.

Why Is It Important?

Students who are not as interested in mathematics may be surprised to know that proportional reasoning can be helpful in other subject areas such as science, music, and geography. It is also evident in everyday activities. On a daily basis, people use proportional reasoning to calculate taxes, investments, best deals at the stores, or even to adjust recipes. 

The ability to reason and think proportionally is a critical factor in developing an individual’s ability to understand mathematics. While students may have memorized how to solve a proportion problem, this does not mean they can think proportionally.

Student Learning

Students who are developing proportional reasoning can generally distinguish between additive relationships and multiplicative relationships. They are able to solve problems involving proportional reasoning and can compare ratios. 

As one of the essential understandings of mathematics, all students must acquire good proportional reasoning skills to take them through school and later in life. If your child is struggling with mathematics, it is essential to understand where they need extra help. Get started with our program today by filling out our Free Early Indicators Check-In. 


Proportional reasoning is the ability to see relationships between quantities and to reason about those relationships. It is often considered the foundation of abstract mathematical understanding, as it allows students to build on their knowledge of quantities and how they relate to each other.

The oil for your car comes in three sizes – a little 50-ounce bottle on sale for $7.99, a medium 100-ounce bottle for $13.99, and a big 150-ounce bottle on sale for $17.99. So, which one should you purchase to get the best deal? 

By using proportional reasoning, we can compare the price per ounce and determine the most cost-effective. The phrase “price per ounce” tells us exactly which ratios we should compare – the price divided by ounces. 

Little bottle: $7.99/50 ounces is about $0.16 per ounce. Medium bottle: $13.99/100 ounces is about $0.14 per ounce. Big bottle: $17.99/150 ounces is about $0.12 per ounce. Therefore, the big bottle is the best deal.

Proportional reasoning is a way of thinking about mathematics in terms of proportions. This way of thinking allows us to see relationships between quantities and to understand how changes in one quantity can affect the other. For example, we can use proportional reasoning to figure out how much more or less something costs with a price increase or decrease.