# Proportional reasoning

Proportional reasoning is a powerful and essential concept that lays the foundation for a range of mathematical topics, from basic arithmetic to more complex areas of mathematics. It involves understanding proportional relationships between different quantities, determining the amount one variable changes when another variable changes, and recognizing patterns in proportional relationships.

By fostering an understanding of proportional reasoning, students are able to make connections between various mathematical principles and see the relationship between abstract ideas and real-world applications. Proportional reasoning is thus seen as an integral component of mathematical learning and provides a framework for developing and deepening Mathematical thinking.

Although proportional reasoning is often considered the foundation of abstract mathematical understanding, 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.  When Do Students Start Learning

Proportional Reasoning?

Early in math learning, students use proportional reasoning when, for example, they think of 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. In learning, students will continue to use proportional reasoning when thinking about percentages, the slope of lines and rates of change.

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.  Why Is It Important?

It is seen throughout math, from the very basic to the more complex topics such as algebra and geometry. Proportional reasoning helps to understand that numbers and equations represent real-world scenarios and can be manipulated to discover patterns, solve problems, and even make predictions.

By mastering proportional reasoning, students can think abstractly, helping them explore deeper meaning within mathematical relationships and ideas. Moreover, proportional reasoning is a unifying theme in mathematics – meaning with a strong foundation in proportional thinking, students are ready to tackle more sophisticated concepts confidently.

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 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. However, parents need to be aware that while some students may have memorized how to solve a proportion problem, this does not mean they can think proportionally.

By mastering proportional reasoning, students can think abstractly, helping them explore deeper meaning within mathematical relationships and ideas. Moreover, proportional reasoning is a unifying theme in mathematics – meaning with a strong foundation in proportional thinking, students are ready to tackle more sophisticated concepts confidently.

Student Learning

Proportional reasoning is an important step in the sequence of student development. Students who can successfully distinguish between additive and multiplicative relationships can typically apply proportional reasoning more effectively in various other areas.

Additive relationships involve proportional changes that result in a person or items getting an additional part; for example, adding eight candy bars to a pile would indicate an additive relationship. On the other hand, multiplicative relationships show proportional changes that yield more than the original amount; a proportional increase of two candy bars would result in three times as many candy bars instead of just two.

Proportional reasoning is an important step in the sequence of student development. Students who can successfully distinguish between additive and multiplicative relationships can typically apply proportional reasoning more effectively in various other areas. Proportional Reasoning? Proportional reasoning is an important step in the sequence of student development. Students who can successfully distinguish between additive and multiplicative relationships can typically apply proportional reasoning more effectively in various other areas.

With proportional reasoning paving the way toward understanding fundamental mathematical concepts, it’s no wonder why children must get a firm grasp on the subject. Children can power up their equation-solving abilities by fully understanding how deep relationships work in proportional reasoning. 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. Our programs offer a FREE assessment to learn where your child may be experiencing gaps in learning.

Once we know where their misunderstanding occurs, we will place them in the appropriate program. All of our programs are centred around the four pillars of math (number sense, operations sense, proportional reasoning, and algebraic reasoning) to help students understand the fundamentals of mathematics. The pandemic has undoubtedly disrupted the learning trajectories of many children worldwide, leaving them behind in traditional education practices. Our classes are staffed by certified Ontario teachers who know that children have experienced a disruption in their learning and may be missing fundamentals.

This can include proportional reasoning, which is a critical aspect of mathematics. Our educators understand this gap and how difficult it is for young learners to keep up in today’s environment. We are here to provide supportive, expert-led classes so children can get back on track with their math skills and be ready for success in school and beyond.

Get your child started today with our FREE Early Indicators Assessment and give them back the confidence in mathematics that will last them a lifetime!

## FAQ's 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.