Fractions are often a source of great confusion among students. However, if they are taught in a systematic and real-life manner, students can understand and use them much more quickly and efficiently than they ever dreamed.
Fractions have been with us for many years. In fact, 4,000 years ago, the Babylonians were among the first recorded civilizations to use fractions to represent the parts of a whole.
For example, we find evidence that they divided a day into 24 hours, each hour into 60 minutes, and each minute into 60 seconds. They would write, “10h, 30m, 45s” as “10, 30/60, 45/3600.”
" ... have some fun with fractions by engaging your children in activities that use fractional concepts, such as cooking, measuring, mixing liquids, building and constructing."
However the word, “fraction,” actually comes from the Latin “fractio” which means “to break,” because when necessary the ancient Romans used to break up standardized weights into smaller units. The actual mathematical use of fractions as we know them today was implemented in the 17th century in Europe.
One of Mathnasium’s key concepts is the idea that mathematics is the study of “wholes and parts.” In other words, “a whole” is equal to “a part + a part + a part, etc.” We find that even young children understand fractional concepts when we ask them about sharing half a cookie or eating a quarter of the pizza. Yet many students “fear” fractions because they don’t understand the meaning and use of the symbols that represent fractions, such as 1/2 or 1/4.
There are two easy ways to begin acquainting young children with fractions.
One is to divide whole objects into equal parts. For example, show your child one large cookie and ask him/her to split it up so that each of two friends, three friends, or four friends gets a fair, or equal share. Ask, “In how many pieces will I have to break up this cookie? Do you think your friends would each like a same-sized piece or a different-sized piece?”
The second way to introduce fractional concepts is to divide groups of objects such as jellybeans, raisins, or beads into equal piles. From this technique your child learns that a “whole” can actually be a group comprised of the sum of all its parts.
You can have older children make more meaningful comparisons. For example ask, “How do you split three pizzas among four friends? Does each friend get more or less than half a pizza?”
What's the common denominator?
Too often, in learning fractions, children hear the words, “numerator” and “denominator,” without first understanding what each means. Besides hearing that they are the top and bottom numbers of a fraction, children can more easily remember these terms if they have a mental “hook.”
We tell our students that the denominator is “de name (‘nom’ in Latin) of de fraction.” In other words, it refers to the number of equally-sized parts in the whole, such as the number of slices a pizza is cut into before anyone eats any.
Likewise, the numerator tells us the number of pieces of pizza remaining after some slices have been eaten.
We also teach the “Law of Sameness” which states that it is only possible to add and subtract things of the same kind, things with the same name (denomination). It is true that 2 apples + 3 apples = 5 apples; and 2 bananas + 3 bananas = 5 bananas, but 2 apples + 3 bananas DON’T= 5 banapples! Rather, they = 5 pieces of fruit (a common denomination).
Hence, when adding and subtracting fractions, one must change the name (denominator) of the fraction to a common one before adding or subtracting.
Therefore, children easily see that you can add 2/7 + 3/7 = 5/7, but in order to add 1/5 + 2/7 =? they must first change the “name” of the fractions so that they are the same. When they change the name to 35ths, then the addition can be performed.
By having children first conceptualize the concept of Whole = Part + Part, etc., and the Law of Sameness, they can better develop a solid foundation for understanding more complex fractional concepts such as proportion, ratio, probability, and percentage.
We recommend that you have some fun with fractions by engaging your children in activities that use fractional concepts, such as cooking, measuring, mixing liquids, building and constructing.
Children learn math concepts much more easily when they learn to apply these concepts in everyday life.
– Dan Gehlbach of Urbandale is the owner and center eirector for Mathnasium of West Des Moines