M4N6 (a); M5N4 (b) & (c) - Equivalent Fractions (1)

M4N6. Students will further develop their understanding of the meaning of common fractions and use them in computations.
a. Understand representations of simple equivalent fractions.
M5N4. Students will continue to develop their understanding of the meaning of common fractions and compute with them.
b. Understand the value of a fraction is not changed when both its numerator and denominator are multiplied or divided by the same number because it is the same as multiplying or dividing by one.
c. Find equivalent fractions and simplify fractions.

In an earlier post, I discussed different meaning of fractions. The fact that fractions may be interpreted in many different ways is a major reason why fraction is so difficult to teach and learn. Another major difference between fractions and whole numbers is the fact that fractions that look different can represent the same number – we call those fractions “equivalent fractions.” In the Georgia Performance Standards for school mathematics, the idea of equivalent fractions first appear in Grade 4, M4N6 (a). However, it should be noted that the goal in Grade 4 is that students become aware of the fact that two fractions that look different may represent the same number. Students are to understand this idea and be able to demonstrate their understanding by representing those fractions to show their equivalence. Understanding how to create equivalent fractions by multiplying (or dividing) both the numerator and the denominator by the same number is a Grade 5 standard, M5N4 (b) and (c). Consequently, answering problems involving fractions with the simplest form should NOT be a focus in Grade 4. Thus, for example, if students calculate 3/4 – 1/4 in Grade 4, the answer should be written as 2/4, not 1/2. Clearly, some students will understand that 2/4 and 1/2 are the same based on their study of equivalent fractions. Therefore, if they do present their answers in the simplest form, that is ok. However, we should not penalize students who do not present their solutions in the simplest form. That emphasis should begin only after students understand the procedure for creating equivalent fractions.