It’s not uncommon to hear a grade 5 student said, “there’s no such thing as half of five!” For students who do not grasp the value of 0 and 1 and the numbers in between, the concept of fractions is not yet familiar to them. End even when we tell them the concept of ½ or half, many kids initially use it very awkwardly like “I don’t know what to call this number” or they write 1 ½ when what they mean is one half or a half, and not one and a half.

When a person encounters the word “fraction”, the images of “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 imbedded in the child’s consciousness, and the earlier in life the better.

At Mathnasium, we teach basic halving to students since they are in kindergarten, then expand to halving bigger numbers, halving of both even and odd numbers starting in grade 1. Before learning halving, a student should know double facts, since halving is just the opposite of doubling.

• Why your child should know Double Facts - while they were young
• How to introduce Fractions to your child

Half

Half is the primal fraction, the first occurrence of a whole being broken-down into equal parts; in this case, “two parts the same.” It is the easiest fraction to demonstrate, and is therefore the easiest to understand.

To write half as “½” is better than 0.5 (especially for younger kids) because they can see the relationships between the two numbers directly and that it is the result from an equal division.   

The way in which half behaves when added, subtracted, multiplied, and divided serves as a model for the actions of all the other fractions.

By learning all about half first, the study of the other fractions becomes an extension of known ideas instead of a constant process of attempting to reinvent the wheel.

Exploring Half

Instead of first introducing halves, then thirds, then fourths in rapid succession, dwell upon the fraction half and explore it for a while from a variety of perspectives:

• “All numbers can be split in half.”

• “Half of an even number is a whole number.”

• “Half of an odd number is a whole number and the fraction 1/2.”

• “A half plus a half equals a whole.”

• “A whole, take away a half, equals a half.”

Expanding to other fractions

Once these basic concepts are in place, other fractions can be introduced as natural extensions of these patterns.

The most immediate of these extensions is the idea that a fourth (a quarter) is “half of ½.” Eighths follow naturally as “half of a–half–of– ½.” After thirds have been explored, sixths can be developed as “half of 1/3.”

Before students wrestle with these other fractions, they should be able to verbally (orally) explain how to do the following:

• “How much is half of 6?”

• “How much is half of 3?”

• “Half of what number is 5?”

• “Half of what number is 4 ½?”

• “How much is half of 25?”

• “How much is half 99?”

• “How much is 7 take away 2 ½?”

• “If you cut something in half, and then cut each half in half, how many pieces will you have?”

• “How much is 2 ½ plus 2 ½?”

• “How much is 1 ½, three times?”

• “How many halves are there in three wholes?”

• “ 2 ½ plus what number equals 4?”

• “What number, four times, makes 10?”

It is worthwhile to describe the “family of half” (halves, fourths, sixths, eighths...). The critical concepts of this “family” are:

1) The denominator (the name of the fraction) is a multiple of the original denominator, in this case 2.

2) These fractions are the only ones into which a half can be subdivided using whole number divisors. (It is not possible to cut a pie that has already been cut in half into 3 equal size whole pieces. If you try it, somebody’s going to get two sixths instead of one third.)

This kind of focus on the nature of related fractions, and the ways in which they relate, will be very useful later when studying equivalent fractions and doing computations involving fractions.

Illustration

This is an illustration of how to solve half of 5 3/4 when a student really grasps the concept of halving - and the natural extension of halving.  

Does your child need extra support in math? Mathnasium of Red Deer is your neighbourhood’s math-only learning centre, and we are here to unlock your child’s potential and set them on a path to lifetime success. Our centre director, Riwan, and the whole team, would be happy to meet you! We are conveniently located in the shopping destination area in Red Deer: 5250 22nd St, Unit 30 B – at the Gaetz Avenue Crossing shopping centre, in the same area as Chapters Indigo/Starbucks, Michael Arts, Petland and Ashley, and the phone number is 403-872 MATH (6284). 

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