What do you do when your young child starts asking about dividing things into equal pieces? Do you embark on a formal course in fractions, or tell him to wait until he’s older?
Introduce fractions casually
Fractions are not actually a hard concept; however they can seem difficult when symbols and numbers are introduced and rules explained, before the child has the concept firmly established. Most children of about 4 are quite ready to understand visible, concrete examples of fractions such as dividing up an apple or a cake into equal portions to share. So use the correct terms (‘half’, ‘two-thirds’ etc) in conversation naturally, and your child will gain a valuable overview of the way fractions are used in real life.
As soon as a child expresses interest in knowing more, answer his questions as they come up, and perhaps show him different ways to divide things between different numbers of people. Do, however, resist showing him how to write fractions unless he actually asks. Much of the phobia about mathematics comes from introducing symbols before a child has truly grasped the relevant concepts.
Fractions in everyday life
One of my sons spontaneously remarked, at around that age, ‘Oh, so two quarters is the same as a half,’ when I had been cutting up some apples. I resisted the urge to leap into explanations about fractions; I just talked about them with him when appropriate. But when he later learned more formally about fractions (he was at school for some years) he already had the concept in his brain and found the topic easy. Other children, who hadn’t seen apples being divided different ways (or hadn’t discussed them with their parents) struggled enormously with what seemed to them a new torture consisting of numbers and symbols to be manipulated in increasingly mysterious ways.
If your child wants to play around with fractions in a non-threatening way, there are visual demonstrations of fractions in different concepts at BBC Skillswise: fractions activity.
Lego bricks and basic arithmetic
Lego bricks are an excellent mathematical resource. Not that I ever used them as a direct teaching tool but I would sometimes sit with my children as they built walls, and enjoyed seeing them ‘discover’ things about fractions, odd and even numbers, multiplication and so on. I would answer their questions as appropriate, while not attempting to ‘teach’ anything. When a child sees that three four-bricks take up the same space as four three-bricks, he probably has no trouble with the same concept in multiplication later on. He will, moreover, understand intuitively that twelve can be divided into three fours, or four threes.
Once he has a fairly solid idea of simple fractions, explain that we use the same words when dividing several items or people into groups. There are some children who can understand about dividing a single cake into thirds or fifths, but have difficulty extrapolating this when thinking about sharing a packet of cookies between five people. A fifth of twenty-five is five, and this is so obvious to adults that we sometimes miss the necessary leap of understanding. I have seen children look at a question like ‘find a fifth of twenty-five apples’ who will think of dividing each apple into fifths, and then adding them up. Clearly this will lead to the correct result, if no mistakes are made, but is far more complicated than simply sharing into five groups.
If this link is made when the child is ready to learn – whatever age this might be – then the whole topic of fractions, and fractional notation, will be a useful shorthand later on for something the child already understands. See my article Writing Fractions for how to introduce simple fractional notation. This is how it should be. If the concept isn’t already grasped, fractions may become the beginning of a maths phobia which can last a lifetime.
The big advantage with home education is that the child can learn at his own rate, and parents can ensure that concrete understanding and concepts are fully in place before symbolic notation and ‘rules’ are ever introduced. As a child needs to understand language before learning to read, he needs to understand mathematical language before learning to read mathematical notation.
For more articles about teaching basic maths without workbooks or drill, see: