Fractions - First Steps

“Fractions”. The very word sounds hard and cold and it strikes terror into the heart of most primary school children! Let’s look at why the subject is so important and why it will pay great dividends to devote some quality parental time to it in the early years of a child’s life. At the same time, we will suggest some ways of making fractions more palatable to young children.

What is a Fraction?

The word is used in many situations to convey a small part or proportion of something. Synonyms for the use of the word in this context are fragment, snippet, segment, section and portion. In maths this is too airy-fairy and we need to drill down to a more precise mathematical meaning. We suggest keeping in mind the best definition we know, courtesy of the Oxford Dictionary:

Fraction (noun) - a numerical quantity that is not a whole number (e.g. ½, 0.5)

Bear in mind that 1, 58, 250 and 999 are all whole numbers. That’s not what we are talking about here – what we need to focus on (and get the children to focus on) is a PROPORTION of something bigger.

Why are Fractions So Important?

Fractions are to Maths what spelling is to English – they are fundamental building blocks to the whole of the subject. There is any amount of well-documented evidence to convince us that reading to young children is the best possible grounding that parents can give their children in English. Not so well-recognised is the fact that discussing fractions, and playing games that involve them, are probably the best ways to get children off to a flying start in mathematics.

Maths is all about the relationships of one number to another and these relationships are so often dependent upon fractions. Our challenge is to take the fear out of the topic so that the children move from an easily understood concept like a half (1/2) to the somewhat more challenging concept of E = MC2 !

Where to Begin?

Almost always the first fraction that children encounter is a “half”. Sharing a chocolate bar with your elder brother so that he has half and you have half is something you probably don’t want to do but it is a good introduction to the idea of a numeric relationship – he will have exactly the same amount as you!

Make the most of these very early encounters with the practicalities of fractions. When anything is divided into two equal parts, don’t call them parts or portions - make sure that you use the specific term “Half”.

The next step is to demonstrate the more complicated concept of a quarter. Divide a chocolate bar into two equal parts and then divide each of those into two equal parts. It is important that the child sees four portions of EQUAL size and knows that each of them is known as a quarter.

Halves and quarters are ideas that can be grasped very early on, even before counting to 10 becomes proficient. Look for real-life opportunities to demonstrate halves and quarters. Your child will become accustomed to looking at quantity relationships and thereby start to understand fractions long before they hear the dreaded word!

Moving On

With your help, your child will no doubt be learning to count, probably between the ages of 2 and 5 years old. When they are confident with numbers up to 10, you can introduce the concept of parts of the whole. Show the illustrations below to children and ask them to identify the fraction of the whole that is coloured. Get them to enunciate the fractions involved e.g. “Half”, “Quarter”, “Third”, “Five eighths”.

It is extremely important to be patient at this stage. As adults, we become familiar with fractions and the fact that they represent portions of the whole. We instantly visualize these and it is all too easy to forget just how difficult we found the concept when we were children.

Play with fractions in any and every way you can think of. Whenever a few articles are placed together, divide them into two sections and ask the children what proportion of the whole is involved in each of the two sections e.g. “a third” and “two thirds”. Use anything that happens to be to hand – pens, marbles, conkers, sweets, business cards, screws – the more things you use the better. By this means you will teach the child that proportions and fractions can be applied to almost anything.

Learning to Write Fractions

All of the work above has concentrated on conceptualising fractions and the next step is to learn to write them. Revisit the illustrations below and ask the child to write down the fraction. Explain that in the first example there are two boxes and a two therefore is the “bottom part” of the fraction. Only one of the boxes are coloured and a one goes in the top half of the fraction. Explain that 1 over 2 is the way we represent a “half”. Do the same for quarters and thirds.

Don’t Rush but Start Early

Have you ever tried to explain to a child why the word “knife” starts with a “k” but the “k” serves absolutely no useful purpose? If you have, you will be eternally grateful that maths contains no such unfathomable anomalies; it is absolutely logical and much easier to explain. BUT the concepts take some time to come to grips with. The sooner you start the process of teaching fractions the more likely it is that your child will start at the top of the class for maths and stay there.

For further reading you might like to try the authoritative article on Teaching Fractions with Understanding: Part-Whole Concept .

Fraction Quizzes

In view of the importance of fractions it will come as no surprise that they feature heavily throughout all curriculums on the Education Quizzes site. Here are some links to the most significant quizzes at each level.

And now for the quiz...

  1. Which of the options is NOT a synonym of 'fraction'?
    A fraction is a number that is NOT whole. For young children 'piece', 'part' or 'slice' might be terms they can relate to. For example a piece of a jigsaw, a part of a bicycle or a slice of cake are all fractions of the whole thing
  2. Why is it so important that children understand fractions?
    Unless a child is confident when using fractions they will struggle to learn other topics in Maths, such as ratios, percentages and algebra. We encounter fractions in our daily lives too - when planning a meal, sharing duties, decorating... the list is almost endless
  3. Which fraction will children first encounter?
    One half is the simplest of fractions and the easiest to work with. It is easy for a child to imagine two equal parts of something - especially if it is something the child wants their fair share of, like a cake!
  4. It is not always necessary to divide a whole object into pieces to demonstrate fractions. How else might one do it?
    There are many ways to illustrate the notion of fractions. The basic concept is that a fraction is a PROPORTION of something bigger - whether a few sweets from a whole packet, the coloured part of a circle or 10cm on a 30cm ruler
  5. What is the difference between four parts and four quarters?
    If an object is cut into four parts then each part MAY be a different size whereas four quarters MUST be the same size. It is important for a child to understand that each quarter is of EQUAL size. Again, get them to imagine a cake being cut into four pieces. They would be miffed if their sister got a larger piece than them!
  6. Which of the options would be a good tool to use when demonstrating fractions to your child?
    You can use almost anything to illustrate proportion and fractions to your child - in fact, the more the merrier as this will show them that fractions can be applied to everything. The opportunities are endless - "What fraction of the cows in the field are lying down?", "What proportion of the sweets are red?", "What fraction of the coins are 2ps?" ... etc.
  7. What is a 'numerator'?
    Younger children don't need to know this but older ones will - the number above the line is the numerator and the number below is the denominator
  8. What is the simplest best way to express 26?
    All four answers mean the same but 13 is correct because it is the simplest. As a child learns they will come to understand that 26, 412 and even 721 are all equal. Percentages will come too, as a result of learning fractions
  9. Which is more: 12 of 6 or 34 of 8?
    It's important that children learn to compare fractions. Working out this answer requires them to solve 2 problems (12 of 6 = 3 and 34 of 8 = 6) and then compare the answers. As you can see, knowing fractions helps with division - a very important function in Maths!
  10. A simple one to end the quiz (we hope!): in the last of the 10 pictures above, which fraction is shown?
    Did you get that right? It's a good idea to practise these examples as it will help to familiarise your child (and you!) with proportions and fractions. If you can make them confident with fractions even before they start school then their Maths career will be off to a good start!


Author: Colin King

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