Operational Sense

As children grow and learn, they are tasked with understanding basic mathematical concepts that will help them succeed in later years. One of the most crucial skills to master is operational sense, or the ability to make sense of and utilize addition, subtraction, multiplication, and division.

This understanding goes beyond simply memorizing facts and figures; it involves applying those rules in real-world situations and problem-solving scenarios. When children develop operational sense, they can confidently tackle mathematical challenges and build a foundation for success in future learning endeavours.

Operational sense starts for students in primary grades where they use counting strategies, combining and partitioning numbers to learn addition and subtraction. In junior grades, students learn the development of operational sense, focusing on multiplication and division. At this level, teachers need to use meaningful contexts to help students gain an understanding of the operations. When a child is able to develop a strong understanding of the operations, they can recognize the relationships among them, and develop systems for computing numbers.

Student Learning

Using operations and performing calculations depends on an understanding of part-whole relationships. When students can successfully work with a variety of computational strategies, they demonstrate operational sense.

Other characteristics of
student learning

Using algorithms and strategies that make sense to them

Understanding the relationships between the operations

Developing a range of strategies and algorithms, including those of their own making

Determining an appropriate method of computation for the context and numbers involved in the problem

Two central instructional components in teaching operational sense are problem-solving and modelling. By breaking down problems into manageable parts, students can better understand how to approach and solve them.

Similarly, modelling allows students to create visual representations of mathematical concepts, helping to solidify their understanding. Through the use of these teaching techniques, students can develop a strong foundation in operational sense, empowering them to tackle more complex mathematical challenges with confidence.

Making Learning Fun
Operational sense can be a tricky concept for children to grasp

But it is an essential skill to develop. Research has shown that meaningful and exciting activities can help children understand operational concepts faster. By making the learning experience fun, children can stay engaged and motivated, which can ultimately accelerate the development process.

Simple activities like counting, sorting objects, and measuring quantities can help children understand operational sense at a faster pace. As educators and parents, it’s important to recognize that every child learns differently, and it’s up to us to find the best methods for each child. With patience, encouragement, and engaging activities, children will develop an operational sense in no time.

At Dropkick Math Academy, we believe in using fun and engaging games to teach children operational sense. Children can begin to use operations and perform calculations by understanding part-whole relationships. So, we use carefully designed games to help children understand these relationships.

One of our most popular programs that can help children improve their operational sense is Operations, Decimals and Space.

This module takes place on

This module takes place on

Students will practice their math operations throughout this battle, including adding, subtracting, multiplying and dividing. By providing support in learning the building blocks of mathematics and engaging in a fun and interactive learning environment, your child will begin to thrive.

Relationships in

Performing Computations

Relationships are an essential part of understanding operations. When students understand these relationships, they are able to use alternative ways of computing with numbers.

For example, addition and subtraction are related as inverse operations, which students can learn to help compute problems.

Students who understand the relationships between operations learn how numbers can be composed or decomposed. Understanding that a whole number can be broken into parts helps students develop their own strategies for addition and subtraction.

Students with a strong grasp of relationships know the base ten relations in the number system. This knowledge empowers them to utilize this structure to evaluate numbers based on their size, carry out calculations with greater accuracy, and compare numerical concepts. In particular, they can skillfully apply methods of comparing and ordering numbers while also considering their respective values within both whole and decimal number systems.

By knowing how to utilize these relationships, students can have effective communication within mathematical systems and encourage greater interdisciplinary dialogues, which may ultimately inform the broader collective understanding of numerical relationships.

Students can successfully say that they understand operations sense by understanding relationships, composing and decomposing numbers and relating fractions to benchmarks.

Is Your Child Struggling?

For students struggling with math, extra help can make all the difference. 

At Dropkick Math Academy, we understand the importance of quality tutoring, which is why we use certified Ontario teachers to lead our group tutoring programs. Our teachers are experts in their field and are equipped with the tools and strategies needed to help students of all levels succeed.

We believe every child deserves the opportunity to excel in math and strive to make that a reality for all our students. Let us help your child unlock their full potential and improve their math skills today.

To get started with our program today, simply fill out our Free Early Indicators Assessment. From there, we can help place your child in our program and get them started on building their math confidence and developing their skills for the future.


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.