WHOLES AND PARTS: THE BIRTH OF FRACTIONS

Feb 18, 2023 | Red Deer

This blog is a part of our series: Wholes and Parts; and as promised in our blog WHOLES AND PARTS: THE CONCEPT THAT YOUR CHILD NEEDS TO HAVE FOR SUCCESS, we will now explain about The Birth of Fractions, because “fractions” is a natural extension of seeing wholes and parts.

The Birth of Fractions

When a whole is divided (fractured) into a number of equal parts, we have what are called fractions. When a person encounters the word “fraction,” the images “part of a whole” and “equal parts” must come to mind. The notion that a fraction results from the equal division of a whole must be second nature and deeply embedded in the child’s consciousness, and the earlier in life the better.

Mathnasium has its own unique method to teach a child, age four and up, the basic concepts of fractions.

How Mathnasium Teach “Two Parts the Same”

We start by teaching children about the fraction one-half (1/2). But before introducing the concept of halving, they need to understand the concept of doubling and master it. All the basic principles that apply to all fractions are embodied in the study of half. Once the idea of half is learned thoroughly, its attributes can easily be applied to all the other fractions.

The process of learning about half immediately exposes students to many facets of the mathematics curriculum that other programs do not present until much later, after both common fractions and decimal fractions have been mastered.

In fact, children can begin problem solving years earlier than is currently taught in most school systems. Kids can handle it, if the problems are appropriate.

Introducing the concept of “two parts the same”

Children often call any division into two pieces “half,” whether the pieces are the same (equal) or not. If the cut is not equal, we correct the child and say, “you have two pieces, two parts, but you do not have half. The two parts must be the same to have halves.” We make sure that each student has a clear understanding that half means (two) equal pieces.

Then when a student understands the basic concept of “two parts the same” they can move to the next stage: halving using basic numbers. Using visualization of balancing like this would really help them – both for younger kids with basic numbers and older kids with more complex numbers:

When the child knows and can communicate what half means, the child is ready to apply this knowledge to the solution of a wide range of problems. We ask the halving exercise verbally, so that they perform calculation mentally, to the maximum extent possible. Why mental math is essential? Please read YOUR CHILD CANNOT DO MENTAL MATH? BETTER START NOW for the explanation.

Yes, you’d better believe that kids can handle it, don’t underestimate their potential. This five-years-old kindergartener is on the right path for her long-term math success by starting early. Having a strong math understanding since young – not only it means avoiding problems before they start – but more importantly it will make a child’s math learning a bliss and enjoyable.

When she is ready, we will help her with halving even numbers up to 24, and halving the odd numbers. Patiently introducing kids to the Wholes & Parts concept, and especially the concept of halving and doubling with the right method, will make students understand a very important mathematical image: All wholes can be broken-down into parts.

There is no need at this point to attach the name “fraction” to this idea. The vocabulary will come later, at the right time. Next time, we will explain the Reverse Question as a crucial factor to build understanding of the Wholes & Parts concept.

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