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The Meaning Of Fractions

Fractions can often be a source of frustration starting in elementary school. Many times this is because children have not previously been taught algorithms and procedures correctly. They may often confuse methods with others they have learned for whole numbers or have simply not practiced fractions enough to understand them fully. This is precisely why building and understanding the foundation of number sense has been shown to increase student achievement later on.

Parent Involvement

Parents looking to help their children with a better understanding of mathematics also need to develop a more sound understanding of the foundations. This is why we involve parents in our programs at Dropkick Math. Our trained instructors will help build a parent’s mathematics capacity so they can adequately support their child’s journey in elementary math. We believe that success is achieved by learning together.

Understanding Fractions

For students to really understand fractions, it is essential that they learn to view them as numbers. Specifically, numbers that represent different constructs based on the context. In the past, fractions education focused on the outcomes, memorizing procedures so that students could successfully operate with fractions. However, being a good mathematical thinker is no longer based on how quickly a child can produce an answer. It is more important that mathematical thinkers understand the process and have multiple pathways to a solution.

To become a good mathematical thinker, it is essential to understand the meaning of fractions. Fractions represent equal parts of a whole or of a collection.

Fraction of a whole: When a whole is divided into equal parts, each part is a fraction of the whole.

Fraction of a collection: Fractions can also represent parts of a set or a collection.

Fractions have two parts. The number on the top of the line is called the numerator and tells how many equal parts of the whole or collection are taken. The number below the line is called the denominator and shows the total divisible number of equal parts in a whole, or in a collection.

When explaining fractions to a child, some of the most common examples in real life are equal slices of pizza, fruit, cake, or a bar of chocolate. Children may also learn through these foods that when the parts of the whole are unevenly divided, they don’t form fractions.

Using examples of fractions in everyday life can help children understand and visualize the math concept. Some examples you can use for older children include: 

  • splitting a bill at a restaurant into halves, thirds, or quarters
  • working out price comparisons in the grocery store when something is half price
  • looking at a clock and teaching them about half an hour and a quarter past

When it comes to helping a child with their math homework, fractions are probably what you will struggle with the most. The best place to start when explaining fractions to a child is to offer a description such as, “a fraction is any part of a group, number, or whole.” Then, using real-life experiences, fractions can become a little less scary.

Math Anxiety

For children, the world of math can be filled with despair and anxiety if they struggle to understand the concept of fractions truly. Fractions are known to be one of the main contributors to math anxiety and can be one of the most significant barriers to your child’s success in math. However, this can be avoided with the help of Dropkick Math Academy. Our programs are designed specifically to work with children to overcome any learning gaps they may have. Our programs include working with adding and subtracting fractions with like and unlike denominators. Children will also work with multiplying and dividing fractions with whole numbers and gain the ability to add and subtract fractions using mental math.

As children advance through our program, they will connect fractions, percents, and decimals and use each form flexibly. They will strengthen their proportional reasoning skills and develop proficiency with fractions. By the end of our program, children will have developed a solid foundation for secondary mathematics involving linear relationships, radian measures, and trigonometry.

Get Back On Track

If your child is struggling with fractions or other math operations, Dropkick Math can help get them back on track! We focus on the critical gaps in learning where children often show difficulty and provide an exciting way for students to thrive in mathematics by applying newly discovered techniques. By focusing on the foundational concepts (number sense, operational sense, algebraic reasoning, and proportional reasoning), our engaging, innovative programs help students fully understand critical concepts that are the base fundamentals of mathematics.

We also address deficiencies through our innovative, research-based math learning techniques while correcting any underlying misconceptions about mathematics. All instructors are qualified Ontario Certified Teachers who can offer differentiated approaches, making it accessible for all learning needs.  

Show your child that math is fun by enrolling them in Dropkick Math Academy. Start with our FREE assessment today!

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Learn Math

Why Are Fractions So Hard?

Why Are Fractions So Hard?

Why Are Fractions So Hard?

When children start to have difficulty in math, it often begins when they are introduced to fractions. Before fractions, they may have only known counting numbers and the relationship between them and the set of objects they represent.

Once fractions are introduced, students may feel overwhelmed and unable to visualize what a fraction represents. This may lead to math anxiety and cause students to retreat and not want to continue learning.

Getting the help they need with fractions is vital for helping them stay on track with their peers. But, to understand how to help your child, you must understand why they struggle with fractions.  

Rushed Through Basics

Students start learning about fractions and making sense of them visually in Grade 3, but don’t start using fractions with operations until Grade 5 or higher. They are often rushed through the basics of fractions because at this stage in education, it is believed that these concepts should be “easy to grasp.”

Students start to work with concrete shapes to better understand adding and subtracting whole numbers from the start of school until Grade 2 and even Grade 3. So, they have years to let the brain develop an understanding and connection of the visual with the abstract symbols. However, students are expected to develop a similar understanding and ability to work with fractions within a few years. 

Not Taught in High School

Fractions as a topic are not taught in high school, so they are expected to have an adequate understanding of them by the time they get into Grade 9. This makes fractions one of the most important aspects for students to understand as they move through the junior and intermediate grades (Grade 4 – 8). They are also often used as an indicator of future mathematical ability.

Understanding Fractions

The problem with understanding fractions often comes once they start to learn about like and unlike denominators. Students begin to learn fractions with standard fraction addition, subtraction, multiplication, and division problems with like denominators (e.g., 3/5+4/5), but problems may start once unlike denominators (e.g., 3/5+2/3) arise. Research shows that 6th and 8th graders only tend to answer about 50% of items correctly when given unlike denominator questions.

This missing knowledge is especially unfortunate because fractions are foundational to many more advanced areas of mathematics and science. Fifth graders’ fraction knowledge predicts high school students’ algebra learning and overall math achievement, even after controlling for whole number knowledge, the students’ IQ, and their families’ education and income.

Often, the problem with fractions starts because students are not given the time to develop a sound understanding of what a fraction is. If they don’t fully understand what ¾ represents, they can’t be expected to work with it and learn how it relates to other numerical values.  

 Students need to visually see what a fraction represents to fully understand fractions. By looking at a representation of what ¾ looks like, they will begin to realize that ¾ is itself a symbol to represent the fraction. Developing brains need to see what it means in a concrete state before thinking of it using the ¾ symbol.

Once students get a solid understanding of what a fraction is, then they can start to manipulate it in their heads. Students must be able to use mental strategies that allow them to make sense of how they fit together and how to work with them in easy contexts first (eg., ¼ + 2/4 is ¾ OR 3  ¼ parts put together) to cement understanding before they can move to abstract ideas.

Develop a Thorough Understanding

 Help your child develop a concrete understanding of fractions with Dropkick Math. Our courses incorporate fractions to ensure that students understand how to compare, add, subtract, multiply, and divide fractions. Through visuals, your child will fully understand what fractions are and how they relate to each other.

Don’t let your child fall behind with their understanding of fractions. Our courses are designed to help you and your child better understand mathematics and pave the way for their achievements in high school. Get started today with our Free Early Indicators Quiz.