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## How Proportional Reasoning Can Simplify Division Problems

If your child struggles with division problems, don’t worry – they are not alone. But there is a solution: proportional reasoning. Proportional reasoning can simplify division problems and help better understand math concepts. In this blog post, we’ll discuss what proportional reasoning is, how it can help with division problems, and give some examples. We’ll also explain how we use it regularly in our math help services. So read on to learn more!

## What Is Proportional Reasoning?

Proportional reasoning is perhaps best described as seeing relationships between numbers and understanding how those relationships can be applied in different situations. In many ways, proportional reasoning is the foundation of mathematics, providing a way to see the world in terms of numbers and to understand proportions and how those numbers work together. By understanding proportional reasoning, we can begin to see mathematics as a tool for solving problems and making predictions rather than simply a set of rules to be memorized. As we develop our proportional reasoning skills, we open up a world of possibilities for mathematical understanding.

## Why Is Division So Challenging?

Division is one of the most fundamental operations in mathematics, and it can be one of the most challenging for children to learn. There are a number of reasons why division can be difficult for kids. First, division often requires children to think in terms of fractions and decimals, which can be confusing. Second, division problems can often be lengthy and complicated, making them difficult to solve. Finally, division often requires a high level of abstraction, which can be difficult for young minds to grasp.

Division can also be difficult for children as it is not always taught in a concrete way. For example, many children are first introduced to division by being asked to divide objects into groups. However, this can be difficult to visualize, so children may have difficulty understanding the concept. If children have difficulty with math in general, division (and other math operations), it may be even more challenging, and they may need a math tutor

However, most children can learn to divide effectively with patience and practice. By understanding division’s challenges, parents and teachers can help kids overcome these difficulties and develop a strong foundation in mathematics.

## How To Use Proportional Reasoning In Division

As adults, we can talk about how relationships are a key component in mathematics, and proportional reasoning relies heavily on comparisons of quantities and values. However, when helping children with math, giving the formal definition of proportional reasoning may cause their eyes to roll to the back of their heads. So, always remember to try and leave the stuffy mathematical definitions to the textbooks. Here at Dropkick Academy, we think learning should be fun. So, let’s take a look at how to help children learn division through proportional reasoning in an entertaining way.

In grade 7, students learn that a fraction can represent division. Just like we can simplify a fraction, we can simplify a division problem by using proportional reasoning to look at common factors.

When the dividend and divisor have a common factor, the problem can be simplified. Let’s look at a division problem and see how proportional reasoning can help simplify the process.

## 12 ÷ 4 = ?

If a child is given the question 12 ÷ 4 it may give them anxiety because it is a larger number. However, this can be simplified. Using math manipulatives, show them how to divide 12 pieces into 4 groups of 3 to get the answer.

Next, you will want to show them how to simplify the problem by finding a common factor between the dividend and the divisor. In this case, the number 2 is a common factor. So, divide the problem by two, changing it to 6 ÷ 2. Is the answer still 3? Yes! Because both amounts were reduced at the same rate, it didn’t change the outcome. It just simplified the problem.

Now, go one step further and show them how 2 is also a common factor of 6 ÷ 2. So, the problem can now become 3 ÷ 1. The answer is once again 3!

When children face a challenging division problem with larger numbers, they can now check to see if it can be simplified by thinking about proportional reasoning

Another way to look at this is by thinking how 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).

## Math Manipulatives

By using math manipulatives to help children visualize each group’s proportions, they can better understand the concept at hand. Math manipulatives can also make learning more fun by creating a tactile way of learning.

Manipulatives allow children to feel, touch and visualize what they can’t yet create on their own. They can enable children to receive immediate feedback about whether their idea makes sense. Using tools, a child can move hands-on objects to investigate and explore a math concept that may be challenging.

Understanding the fundamentals behind the mathematical foundation is critical for a child’s fluency and math development. Using both manipulatives and representations, children can build a deeper understanding of the four pillars of math (number sense, operational sense, algebraic reasoning, and proportional reasoning).

At Dropkick Math Academy, we believe using math manipulatives is an excellent way of learning. In fact, we even include them in some of our battle kits for our students to use in our programs!

## Proportional Reasoning At Dropkick Math

As one of the leading math services in Ontario, our certified teachers support learning by focusing on the four pillars to give students an understanding of the root of mathematics. Our one-on-one math tutoring approach allows us to tailor each lesson to the student’s specific needs and learning style.

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.

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# Is Your Child A Proportional Thinker?

When your child comes to you for math help, you may think they are speaking an entirely different language. The way that math operations are now taught have most likely changed since you were in school and appear completely different. Not only is the representation different, but the way your child speaks about math may also be different.

We recognize these barriers between parent and child when discussing mathematics, which is why at Dropkick Math, we believe it is so important to educate the child and the parent. When you get involved and upgrade your education on the foundation of math, you can better help your child in their studies.

## The Four Pillars

We focus our programs on the four pillars of math (number sense, operational sense, algebraic reasoning, proportional reasoning). It is vital that every student fully understands each of these four pillars as the foundational concepts because one weak pillar can significantly impact future success.

Proportional reasoning is often considered the foundation to abstract mathematical understanding as it is a unifying theme throughout mathematics. However, it is estimated that over half of the adult population are not proportional thinkers. So how can you tell if your child is a proportional thinker?

If your child can generally distinguish between additive relationships, (e.g., 8 is 6 more than 2) and multiplicative relationships, (e.g., 8 is 4 times as much as 2) they may be a proportional thinker. If they are able to compare ratios, they also may be a proportional thinker. Overall if your child can describe relationships between two or more things and see groups of items in various ways, they may be a proportional thinker.

## Proportional Thinking Education

It is vital for all children to acquire good proportional reasoning skills to take them through school and later in life. The importance of proportional reasoning for students is often focused in junior and intermediate grades. Still, many educators believe it is vital to grasp these skills in kindergarten and primary grades when students begin grouping, unitizing, (e.g., one dime is a unit of 10 pennies) and sharing.

Students begin to use proportional reasoning early in math education. They often start by thinking of groups of numbers rather than whole numbers. For example, they may think of 10 as two groups of 5. Later on in education, proportional reasoning is used slightly differently. An example of this may be thinking how a speed of 50/km an hour is the same speed as 25/km per 30 minutes. Continuing in their education, students will use proportional reasoning when learning about percents, rates of change, and slopes of lines.

## How Is Proportional Reasoning Used?

But proportional reasoning isn’t just used for mathematics. Many may be surprised to know that proportional reasoning can be helpful in other subject areas such as music, geography, and science. On a daily basis, people also use proportional reasoning to calculate taxes, find the best deals at a store, or adjust recipes.

From these examples, it is easy to see how thinking proportionally is critical in developing a child’s understanding of mathematics. But young children don’t think proportionately naturally. Proportional thinking must be developed as a foundational skill of our most basic math concepts, which is why many parents explore math tutoring for their children.

As one of the four main pillars of mathematics, our programs help students learn proportional reasoning and fill in any underlying misconceptions they may have. Our math help services are built to suit each child, offering differentiated approaches, making it accessible for all learning needs.