Proportional Reasoning

The Dynamics of Proportional Reasoning – Uncovering Crucial Connections!

Proportional reasoning is an incredibly valuable math concept that is one of the four pillars of mathematics. It requires students to grasp relative size and ratio and proportional relationships between sets of numbers or objects. It also enables children to understand and make proportional judgments in various situations, which are integral to success in mathematics. 

When proportional reasoning is understood correctly, children can quickly break down complex mathematical problems into simpler parts, helping them form a strong foundation within mathematics and build a deeper comprehension essential for future math challenges. 

However, if a child is struggling in math, they may be missing the basic foundation, including proportional reasoning. As one of the leading math programs in Toronto, Dropkick Math Academy works with students to help repair any misunderstandings or gaps in learning. 

Does Your Child Enjoy Learning About Proportional Reasoning?

If your child enjoys spending time rationalizing and solving puzzles, chances are they enjoy learning about proportional reasoning. As one of the four pillars of math, proportional reasoning offers children the perfect combination of challenges, whether they want to test their problem-solving skills or just strengthen those mental muscles. 

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.  

The Relationships

Relationships are a key component in mathematics, especially in proportional reasoning, as it relies heavily on comparing quantities and values. These relationships are evident through the study of ratios, rates and rational numbers. 

An example of how relationships work in proportional reasoning is shown when comparing values in a ratio. When children start to understand relationships, they will better understand the concept of the mathematical equation and how to solve it. 

Developing Proportional Reasoning

Students developing proportional reasoning can generally distinguish between additive and multiplicative relationships. They are able to solve problems involving proportional reasoning and can compare ratios. Students should learn proportional reasoning over several years, beginning in younger grades alongside the development of their rational number sense. 

For children who may be struggling with proportional reasoning, Dropkick Math Academy can help! Proportional reasoning is a fundamental component of mathematics and an invaluable asset for students of all ages. This skill can help students tackle any subject that requires arithmetic or mathematical understanding

Students of all academic levels must be equipped with proportional reasoning competencies to successfully get through school and have basic skills beyond their academic years. Employers in various fields may also appreciate workers who possess proportional reasoning abilities, so mastering this important concept should never be overlooked or belittled.

The Four Pillars Of Math

As experienced Ontario teachers, we have seen a lack of confidence and understanding from our students in mathematics over the years. Upon further review, we recognized four key areas that children struggled with when mastering math – Number Sense, Operational Sense, Proportional Reasoning and Algebraic Reasoning. 

We now understand that if students do not possess a strong base in these four pillars of math, they risk struggling to keep up in the classroom setting. Our goal is to improve our students’ foundational skills by incorporating the basic fundamentals in each of our programs to enrich math education for all.

Our Programs

Seeking relationships between mathematical concepts is a key component of learning, particularly when it comes to children. Understanding relationships between the different elements of mathematics can help children learn more efficiently and set them up for greater success beyond basic arithmetic. However, forcing children to uncover relationships before they understand the basics can be detrimental as it can disconnect them from math, causing them to shut down and be unwilling to engage in learning at all. 

Ultimately, introducing relationships into a child’s mathematics learning requires careful and thoughtful implementation; too little and their instruction could suffer, but too much will cause them to become disinterested. This is why we leave the stuffy textbooks behind and make learning fun

At Dropkick Math, our small-class math tutoring approach allows us to tailor lessons to the student’s needs and learning styles. So, whether your child is struggling with algebra or decimals and fractions, our team is here to provide the math learning techniques needed to support and guide your child every step of the way. Trust us for expert math help from caring professionals.

If your child is struggling with mathematics, it is essential to understand where they need extra help. An online math tutor like Dropkick Math Academy can help your child catch up and boost their confidence which will last for years to come. Get started with our program today by filling out our Free Early Indicators Check-In. 

Proportional Reasoning

How Proportional Reasoning Is Used In Everyday Life

As a parent, you might wonder what mathematical concepts your child is learning in school and how they will be used in everyday life. Today, we’re going to take a look at proportional reasoning and how it’s used daily.

Proportional reasoning is the ability to understand that two quantities are in proportion if they change at the same rate. For example, if we know that there are 2 apples for every 3 oranges, then we can also say that there are 6 apples for every 9 oranges. This is because both ratios are equivalent (2:3 = 6:9). This math concept is just one of the four pillars (number sense, operational sense, proportional reasoning, algebraic reasoning) that we focus on at Dropkick Math tutoring company. 

Understanding The World Around Us

Too often, children see math as a dull and difficult subject that has no relevance to their lives. However, they are more inclined to want to learn when they understand why math is important in everyday life. After all, math is more than just a set of arbitrary rules. It helps us to understand the world around us and make sense of the patterns we see. 

In fact, math is a vital tool in many different fields, from medicine and engineering to finance and architecture. By showing children how math is used in the real world, we can help them to see its value and appreciate its importance. Only then will they be motivated to learn math and develop the skills they need for success in school and beyond.

What Are Some Examples Of Proportional Reasoning?

When we speak about proportional reasoning, it is essential to help children understand how it can be used in everyday life. If your child is struggling with math concepts, let them know that they have probably already been using proportional reasoning without even knowing it! If they hear that they already know how to do something, it can help boost their confidence and willingness to learn more. 

Some examples of everyday proportional reasoning include:

-When we’re trying to figure out how much shampoo to use, we usually start with a small amount and then add more if we need it. This is because we know that the amount of shampoo is directly proportional to the amount of hair we have.

-When we’re cooking, we often need to double or halve recipes depending on how many people we’re feeding. This requires us to understand that the ingredients are proportional to the number of people we’re serving.

-When we’re driving, we need to constantly adjust our speed based on the flow of traffic. We know that if the traffic is moving faster, we need to speed up; if it’s moving slower, we need to slow down. This is because our speed is directly proportional to the speed of traffic around us.

Why Is Proportional Reasoning Important?

As you can see, proportional reasoning is a useful skill that we use all the time without even realizing it! So next time your child does something where they need to make a quick calculation, let them know that they are using their proportional reasoning skills. 

Proportional reasoning is a skill that allows us to interpret graphs and charts accurately, make comparisons between quantities, and solve problems efficiently. In fact, many algebraic equations can even be solved using proportional reasoning skills. Without these abilities, it would be nearly impossible to navigate daily life tasks effectively. Proportional reasoning is a vital skill that should be developed and honed throughout our education and career.

Building Upon Math Concepts

Mathematics is often considered a series of isolated concepts, each to be memorized and applied to specific problems. However, this view overlooks the fact that mathematics constantly evolves and builds upon itself. One concept can lead to the discovery or development of another, leading to a deeper understanding of the underlying principles at play. 

For example, students who are developing proportional reasoning skills can also improve overall mathematical thinking and problem-solving abilities. Building upon previous concepts is central to the very nature of mathematics and helps explain its power as a problem-solving tool. Without this foundation, Mathematics would not be nearly as effective or versatile. So next time your child struggles with a complex math problem, remember that it may just be laying the groundwork for an even greater discovery in the future. Encourage them to work through the problems using proportional reasoning and demonstrate the equation in a real-life situation to make it more relatable to them. 

About The Four Pillars Of Math

At Dropkick Math Academy, we focus our curriculum on the four pillars of math. As one of the main pillars, we believe that the ability to reason and think proportionally is critical 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.

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 certified Ontario teachers can help your child with any gaps in education and help them catch up with their learning. 

Finding A Reputable Tutoring Company

When it comes to online math help, it can be difficult to find reliable and professional help. Many websites offer generic, automated solutions that can’t address individual student needs. But here at Dropkick Math, we have a team of dedicated math teachers who genuinely care about the success of our students. Our one-on-one approach allows us to tailor each lesson to the student’s specific needs and learning style. In addition, our teachers are all highly trained and passionate about math education. So, whether your child is struggling with algebra or decimals and fractions, our team is here to provide personalized support and guidance every step of the way. Trust us for expert math help from caring professionals.

Learn more about our math tutoring today by visiting our website.

Pillars of Math

What Are The Four Pillars Of Math?

The Four Pillars of Math are four concepts that are essential for students to understand in order to be successful in math. These pillars are: number sense, operational sense, proportional reasoning, and algebraic reasoning. By mastering these four fundamental concepts,  students will be able to solve any problem they encounter in math. In addition, the four pillars of math provide a strong foundation for students to build upon as they move on to more advanced concepts.

The Foundation Of Our Program

At Dropkick Math Academy, the foundation of our math tutoring program focuses on the four pillars of math. These four pillars are essential building blocks for understanding higher-level math concepts. We focus on one or more of these pillars throughout our program in each module. For example, in our first module, Operations, Whole Numbers, and Pirates, we focus heavily on developing a conceptual understanding of both number and operational sense. Without a strong understanding of these operations, it would be impossible to move on to more complex topics like algebra. However, we also touch on the other three pillars in this module. For instance, we use proportional reasoning to explore place value. By the end of the module, students have a well-rounded foundation in arithmetic and are prepared to move on to more advanced modules.

The Four Pillars Of Math

Let’s take a closer look at each of the four pillars:

Number Sense

Number sense is understanding the quantity represented by a number. It is not the same as numeracy, which is the ability to do calculations. Number sense develops gradually. For example, a baby starts by recognizing that they see one person or two people. By the time they start school, they can count up to 20 or more. They learn what numbers mean in terms of amounts and quantities. This knowledge forms the foundation for learning more complex math concepts later on. 

Fractions are an excellent example of a concept that builds on number sense. In order to understand fractions, students need to be able to visualize the quantity represented by a number. For example, if there are four pieces of candy and I eat two of them, then I have eaten half of the candy. Fractions are a way of representing numbers that are not whole numbers, and understanding fractions requires a strong foundation in number sense. 

Operational Sense

Operational sense is a critical math concept that refers to a child’s ability to make sense of addition, subtraction, multiplication, and division and use them in problem-solving situations. 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. This understanding helps to form the basis for the four pillars of math.

Operational sense is not just about being able to do the computations but about understanding when and how to use them. For example, a child who knows that addition can be used to find out how many objects are in a group but does not understand that it can also be used to put together two groups of objects has not yet developed operational sense. Operational sense is a critical foundation for success in math, and children who develop a strong understanding of the operations are well on their way to becoming math problem-solvers.

Proportional Reasoning

Proportional reasoning is a unifying theme in mathematics and is often considered the foundation of abstract mathematical understanding. All four pillars connect to proportional reasoning. For example, in whole numbers, students learn about place value which is based on 10s. In decimals, place value is based on 10s with an added number after the decimal point. In fractions, there are different parts of a whole, and students use visual representations to help understand the relationships between those parts. Lastly, in percentages, there are hundredths and relationships are represented out of 100. 

By making connections to prior learning, students see that proportional reasoning is everywhere in mathematics! Proportional reasoning is not just a process but rather it’s a way of looking at the world and solving problems. In essence, proportional reasoning is the consideration of numbers in relative terms compared to absolute terms.

Algebraic Reasoning

Patterns are all around us. They can be found in the seasons, the way leaves grow on a tree, and the numbers we use every day. Understanding patterns is an essential mathematical skill that helps us to make sense of the world around us. 

Algebraic reasoning is a way of thinking that uses mathematics to solve problems and understand relationships. It is an essential skill that is introduced in the early years of learning and continues to play an increasingly important role through grades 4 to 9.

Algebraic reasoning can be used to solve problems in a variety of ways, including by using algebraic equations, graphing, and creating tables and charts. It is a powerful tool that can help us to understand complex ideas and make predictions about the future. By understanding algebraic reasoning, we can better understand the world around us and our place within it.

Learning Skills

The approach used in Dropkick Math Academy teaches children certain skills along with the four pillars to set them up for success in their future education. These include:

Concepts – Concepts are the building blocks of math. If students don’t understand the basic concepts, they’ll struggle to progress. That’s why we focus on teaching concepts in a way that is clear and easy to understand. We want students to really grasp the material so they can build on it later.

Fluency – Fluency is about being able to do math accurately. It’s important for students to be able to recall math facts and equations quickly so they can focus on solving problems. We use a variety of techniques to help students improve their fluency, including games and practice with real-world applications.

Problem-solving – Problem-solving is an essential skill for all students, not just those interested in math or science. Breaking down a problem and finding a solution is a valuable life skill that will serve students well no matter what path they choose. We encourage students to approach problem-solving with confidence and to persevere when they find themselves stuck.

Mastering The Four Pillars

The Dropkick Math team is committed to helping students master the Four Pillars of Math. We believe that this is the best way to set students up for success in their math education. We have created a variety of resources, such as articles, videos, and games, that all focus on helping students understand and master these four concepts and better understand math operations. Visit our website today to start exploring these resources and learn more about our math help services. By taking our FREE assessment, your child can begin to build a strong foundation in math!

Learn Math

Why Spatial Reasoning Is So Important For Mathematics

Do you remember the first time you solved a puzzle? The satisfaction of completing it and finally understanding how all the pieces fit together was an amazing feeling. As parents, we want to give our children the best opportunities for success in life, and part of that includes helping them develop strong problem-solving skills such as those that accomplish finishing a puzzle. 

One skill that is essential for mathematical success is spatial reasoning. Developing this ability at an early age can set your child up for future academic achievement and it can even predict students’ later success in higher levels of mathematics, such as proportional thinking and algebraic reasoning. Keep reading to learn more about why spatial reasoning is so important for children’s mathematics and what you can do to help them excel in this area. 

What Is Spatial Reasoning?

The ability to reason spatially is a fundamental human skill that allows us to make sense of the world around us. Spatial reasoning skills are used when we navigate our environment, manipulate objects, or even daydream. Although we are often not consciously aware of it, spatial reasoning is essential for everyday life.

There are many different types of spatial reasoning tasks, but they all involve mental manipulation of 2-dimensional or 3-dimensional images. For example, a common spatial reasoning task is mental rotation, which requires imagining how an object would look if it were rotated in space. Another type of spatial reasoning task is mental folding, which involves folding a 2-dimensional image in your mind to visualize a 3-dimensional object.

Spatial reasoning skills develop throughout childhood and continue to improve into adulthood. However, some people are naturally better at spatial reasoning than others. One’s ability to reason spatially can also be affected by factors such as fatigue, stress, and boredom. Spatial reasoning skills can be improved with practice, so there’s no need to worry if your child doesn’t seem naturally gifted in this area. With a little bit of practice, anyone can become better at spatial reasoning.

Math Is More Than Numbers

When most people think of math, they think of numbers. However, math is so much more than that. It encompasses spatial reasoning, pattern recognition, and other important skills. For kids, this can be a lot to take in. They may get bored quickly if they think math is just about numbers. However, when they are exposed to spatial reasoning tasks and toys, they suddenly become interested in learning more. They may even choose to play with math materials during their free time. 

Spatial reasoning is a key part of math education and it can be very engaging for kids. By exposing them to spatial reasoning tasks and toys, we can help them develop a love for math.

Mathematical Abilities

A recent study has found that spatial reasoning skills in early childhood can predict mathematical abilities later in life. The study followed a group of children from ages 6 to 8, and found that those with strong spatial reasoning skills at age 6 were more likely to perform well on mathematical tasks at age 8. This relationship was especially strong for tasks involving the linear number line. 

The findings suggest that spatial reasoning skills play an essential role in the development of mathematical abilities. Furthermore, they indicate that intervening to improve spatial reasoning skills in early childhood could positively impact later math achievement. The study provides new insights into the importance of spatial reasoning skills and highlights the need for further research on ways to support the development of these skills in young children.

Standardized Testing

In Ontario, students take a standardized test in Grade 3 called the EQAO that determines if they are on grade level. Many teachers notice that in grade 2 students often struggle with tasks that involve spatial sense, indicating that it should be included more in math education in the early elementary classroom. But it shouldn’t just fall on teachers to help children understand spatial reasoning. There are many activities that parents can offer their children to help advance their understanding of spatial reasoning.   

How To Be Proactive

Spatial reasoning is a critical skill set for many STEM fields, and strong spatial reasoning skills have been linked to success in mathematics. As I previously mentioned, spatial reasoning skills are often not formally taught in schools which means that children could fall behind. However, parents can be proactive by helping their children develop strong spatial reasoning skills from an early age. This can be done by encouraging spatial talk in children. 

Through spatial talk, children learn to use language to describe spatial relationships and solve problems. For example, a parent might ask a child to put away their toys by saying, “Please put the red block on top of the blue cube.” Parents can also provide opportunities for spatial play, such as puzzles, building blocks, and drawing. By encouraging spatial talk and providing opportunities for spatial play, parents can help their children develop strong spatial reasoning skills that will set them up for success in school and beyond.

Spatial reasoning can be taught through each of the four pillars of math (number sense, operational sense, algebraic reasoning, and proportional reasoning). When thinking of math concepts, parents should try and view them through a spatial and geometry lens. For example, when a child is learning about number sense, they can be encouraged to gesture with their hands, or they can visualize the number line. 

If your child is struggling with spatial reasoning or any other math concept, Dropkick Math Academy can help. So, before you start searching for “math tutor near me” learn about our programs or get in contact if you have any questions. Our team of Ontario certified teachers understands the gaps in education that can often occur and can address them while boosting your child’s confidence in mathematics. 

Get started today by having your child complete our FREE assessment

Pillars of Math

What Are The STEM Majors?

What Are The STEM Majors?

What Are The STEM Majors

When your child looks to their future, what do they see? If they see themselves in a career that requires math and science skills, they will most likely focus on a STEM major in higher education. A STEM major is a field of study in Science, Technology, Engineering, and Math. These programs are designed to give students the skills they need to succeed in high-demand fields. In this blog post, we will discuss math concepts that are important for students who want to pursue a STEM major in university. We will also talk about how our math intervention program can help prepare your child for success!

The Buzz Around STEM

Recently in elementary education, there has been a buzz around science, technology, engineering, and mathematics. It is well known that our country needs to produce students skilled in the STEM fields to fill jobs and continue our country’s tradition of innovation. However, understanding that we need more children to get excited about stem majors and actually growing the number who go into that field are very different matters.

The STEM majors list includes:

  • Astronomy
  • Biology
  • Chemistry
  • Computer science
  • Engineering
  • Earth sciences
  • Health Sciences
  • Information technology
  • Mathematics
  • Physics

There are numerous branches of study within these individual disciplines leading to various career paths. 

Skills Built From An Early Age

Evidence is mounting to show that STEM skills built from early learning can help students to develop the habits and knowledge that will last them a lifetime of understanding and proficiency. Children naturally learn by exploring, asking questions, and discussing their findings, so it is important to encourage STEM learning early in school.

Early childhood education teachers are currently trying innovative new models to include more STEM education in their classrooms. In elementary school, creative teachers have managed to find STEM-related activities so that children can develop their math, science and technology skills.

In early education, children have the gift for exploration and experimentation already in place. When those natural impulses are matched with math concepts, students can gain a solid foundation to help them move forward throughout school. At Dropkick Math, we offer innovative, online, engaging activities and hands-on offline games to guide students’ exploration while building a solid foundation in mathematical skills.

Math Foundation

It is never too early to get your child interested in a chosen career path. But if that career choice includes math and your child struggles with the subject, our program may be able to help. If you have been wondering, “Is there a math tutor near me?” Dropkick Math can offer a solution. Our programs differ from a traditional math tutor in many ways, including providing your child with the foundation of mathematics in a fun and engaging way. 

The Transfer Of Knowledge

Evidence suggests that basic addition and subtraction math concepts can be used to build upon later in education to accomplish more complicated skills. The “transfer of learning” can often help a child understand a different principle. Transfer of learning has been demonstrated repeatedly in early education studies. For example, early understanding of a mathematical skill can set the stage to incorporate that knowledge later as math processes expand into more complex questions. This is one reason why it is important for children to understand the basic principles of math at an early age. Dropkick Math can help students build on these skills at an early age to help with their math comprehension and overall academic performance throughout their learning years.

The Four Pillars Of Math

At Dropkick Math, we offer fun and engaging programs that involve the parent/caregiver while learning the four pillars of math. The four pillars of math include algebraic reasoning, proportional reasoning, operational sense, and number sense. The approach we use provides alternative studies that allow for conceptual understanding. We recognize common areas of difficulty in mathematics that students may have, and provide instructional practices for addressing these areas of difficulty.

Your child will need to excel in mathematics to continue to a STEM major. But we know that a weak pillar can significantly impact future math success. The gap in learning caused by the pandemic has also affected some children in math. So, we have built our programs so that your child gains a conceptual understanding of mathematics and can get caught up with any missed learning caused by COVID. Contact us today to learn more about our programs and how they can help your child stay on track with their education for the future.