Piaget has charted the cognitive development of preadolescents, and his research indicates that even at the age of 12, most children deal only with symbols that are closely tied to their perceptions. For example, the symbolic representation of 1/6+2/3=5/6 has meaning for most elementary school children only if they can relate it directly to concrete or pictorial representations.
- Obtaining Common Denominators: If each part of the 5/6 bar is split into 2 equal parts and the 1/4 bar is split into 3 equal parts, both bars will have 12 parts of the same size. These new bars show that 5/6 + 1/4 = 13/12 (Improper) that changed into 1 1/12 (Mixed Number) and then, 5/6 - 1/4 = 7/12
Subtraction of same fraction numbers
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Multiplication: To determine 1/3 x 4/5, split each shaded part of the 4/5 bar into 3 equal parts. One of these split parts is 1/15 of the whole bar, and 4 of these split parts is 4/15 of the whole bar.
(You can think of this as having 4/5 of an amount and taking 1/3 of each fifth).
Division: Using the measurement approach to division, we can write 1/2 / 1/6 = 3, becuase the shaded portion in the picture below of the 1/6 bar can be measured off (or fits into) exactly 3 times on the shaded part of the 1/2 bar.
Similarly, 5/6 / 1/3 = 2 1/2 because the shaded portion of the 1/3 bar can be measured off (or fits into) 2 1/2 times on the shaded part of the 5/6 bar.
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