Many middle grade children have their first significant math crisis when they are formally introduced to fractions. The anxiety grows with advancing age with very few exceptions who may get proper guidance. In earlier grades children are taught the operations on whole numbers using discrete objects, like buttons, leaves, flowers, marbles etc. Strangely fractions and the operations on them are taught using written work alone.
It would be better to teaching fractions allowing individualized concrete experiences rather than using symbolic level.
An effective way of providing concrete experiences in fractions is to have each child develop his/her “Fraction Kit”.
As discussed earlier we can make children learn all concepts related to fractions using geometrical figures and discrete objects like coins, beads, plastic squares etc.
To teach fractions using geometrical figures we can use a copy of the fraction wall given below.
Children should be given fraction walls of different sizes. They should paste this wall on a cardboard. After allowing some time for fixing the wall firmly to the cardboard, children should cut out the portions demarcated by the horizontal and vertical lines, using scissors. In all they will have 55 different pieces cut from the cardboard. If they have not mixed these pieces let them jumble them, before starting any activity.
The first thing they may do is to find out what fraction of the biggest strip (top row of the wall) is each of the smaller pieces. Smarter children usually intuitively sort out pieces of equal lengths and by arranging them on the biggest strip, which is a whole, find out how many of the smaller strips together cover the “whole strip”. From this information they can easily and correctly identify and write the fraction name that goes with each piece. You may ask children to color strips of equal lengths using one particular color. Thus, the whole class will have one color, say yellow for the fraction “half”. Fraction half with one child can be bigger than that with other children in the class, as each child may have used the “whole” with different dimensions.
The second activity they can have is to select one piece of each type of fraction. Thus, they will have one “whole”, one “half”, one “thirds” and so on. They can arrange them one below the other, in decreasing order of size. Let them note down in their notebook the fractions one after the other in the decreasing order. Ask them to jumble these pieces again. However, this time they have to arrange these pieces one below the other in the increasing order of the size. Let them note down in their notebook the fractions in the ascending order. The teacher can quickly check correctness of their activity by looking at the order of colors. For example, yellow which is “half” will be second if fractions are arranged in decreasing order. This is the advantage of using one color uniformly for a given fraction.
While completing both the activities discussed above children are basically comparing different fractions and identifying their names. However, they also do additions of fractions to identifying fraction-name for the piece. Teachers can think of many other activities, allowing familiarity with different fractions and their relative sizes.
Children in higher grades can be taught to divide a line into as many parts as they like. Then they can choose strips of the length they prefer, and divide them further into equal number of two, three, and so on number of pieces, which could be used to prepare a fraction wall.