However, making good sense of fractions should also be achieved through experiences with discrete objects. In a real situation, fractions provide an easy way to describe the portions of discrete objects as a part of the given set or whole we are referring to.
For example, a child may have solved three problems correctly out of the five solved by him. Whereas, another child might have solved six problems correctly, but out of the ten he attempted. How to compare these two children's performances? Fractions will make this problem easier to solve. Compare the portion of the right problems against the attempted problems. The first child has solved 3/5th problems correctly and the other child has solved 6/10th problems correctly. Later, when children learn about equivalent fractions, they will know that 6/10th is another name for the fraction 3/5th. Therefore, problem solving ability of both the children above is comparable.
The example given above shows how it is important to understand fractions in the context of discrete objects.
Hand a group of discrete objects like counters, pennies, marbles, beads, beans, matchsticks, etc., to the child. Let the child try to distribute the given objects equally into as many different number of groups as possible. This activity is the one they are familiar with. Let them note their observations into a chart of the type given below:
The chart above is prepared for a set of 24 objects. Let the child first divide the given set of objects into two equal parts and note down the number of objects in each part. After this, the child will note down the number of objects we get when we take multiples of such parts. The child manages it simply by carrying out the multiplication required and notes down the number in the appropriate column.
Next, let the child divides the given set of objects into an increasingly larger number of parts. Each time, the child should note down the number of objects in each part. The child then carries out multiplication to find out the number of objects we would get in multiples of each part and keeps record of the answers obtained in the respective columns.
Let children prepare some more such fraction charts using different numbers of objects, like: 12, 30, 48, etc.
The chart does not allow us all the possible fractions, as we cannot divide a single object like a bead or a counter. For example, in the case of the chart for a group of 24 objects, we could not try fractions like: one-fifth, one-seventh, one-ninth, etc. Therefore, we need to give children a number of objects, which will allow one-fifth or one-seventh of the whole, easily. A group of 70 objects is a good one to get five or seven groups of equal number of objects. The chart below is prepared for a group of 70 objects.
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