Are Hershels examples correct? Does his procedure always work?
Explain your reasoning. Small groups of students can generate other examples to test whether Hershel’s procedure works. A key step in the problem is considering various pairs of fractions and a wide array of possibilities for the “new” numerator and denominator. Assessment should focus on whether students can generate examples that fit Hershel’s model and on their cleverness in selecting those examples. If they continually choose examples in which the numerators and denominators differ by 2, they might incorrectly conclude that the procedure works. The identification of a fraction that doesn’t work, such as 3/8 in example b, is a valid response. A more insightful response is to consider what the procedure means when it is applied to fractions like 1/3 and 2/4. Grades 9-12 1. Give reasons for the steps in a procedure.
