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We need to provide some more examples of non-congruent partitioning, where the child has to carefully check if the given pieces fit on each other perfectly. Ask them to check if the two pieces with similar shape but different in size can make a whole. Such an experience is necessary to understand the basic requirement to work on fractions, that is congruency of parts. To provide this experience use squared cardboard pieces of different size. Then cut them into half and mix all these pieces together. Ask children to make whole squares by selecting congruent pieces. Such models are shown below:
Similar experiences should be given using paper strips of different widths and lengths and cutting them into halves. Through different kinds of experiences children will know that when we talk about one-half it is with respect to some definite whole. The children should see that if a square is divided into two pieces and these pieces are just the same size, each piece is one-half of the whole square. The two basic ideas involved in the understanding of one-half are that there must be just two pieces and these must be equal in size. (Later, when children are taught the idea of one-half in connection with the group of objects they will learn that one-half may be represented with more than one piece.) It has been found that associated with these two basic ideas there are two incorrect ideas, which children acquire from their out-of-school experiences. Special efforts are required on part of the teacher to identify if there are any such misconceptions in children's mind and proper experiences should be provided to overcome them. The first misunderstanding is that an object may yield more than two halves. They think that if the pizza is divided into four parts, each part is one-half. For many young children, "one-half" means simply a part, not necessarily two equal parts. The second misconception is that an object may be divided into halves even though the two pieces are not equal in size. When children divide a cookie by breaking it, they usually get two uneven portions. So they talk about "the biggest half" and "the littlest half". These ideas need to be corrected as early as possible using cardboard models like those in Figure 1. Teacher can check if children talk about one-half only in the context of a particular whole After teaching the idea of one-half we can teach the idea of one-fourth and then the idea of one-third. Because one-fourth occurs earlier and more frequently in children's experiences than does one-third. Another fact is that children can easily cut halves to get one-fourths. Thirds are much more difficult to make and teacher has to provide help.
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The copyright of the article Introducing Fractional Numbers (II) in Math for Kids is owned by Vidya Narayan Wadadekar . Permission to republish Introducing Fractional Numbers (II) in print or online must be granted by the author in writing.
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