## Monday, March 8, 2010

### M3N5 - What are decimal fractions?

M3N5. Students will understand the meaning of decimal fractions and common fractions in simple cases and apply them in problem-solving situations.

When the GPS was first released, some people wondered what the phrase found in this standard, "decimal fractions," meant. If you research the Internet, you will find that "decimal fractions" are fractions with powers of 10 as denominators. This interpretation was emphasized in the 2008 revision of the GPS. Thus, M3N5(b) states, "Understand that a decimal fraction (i.e. 3/10) can be written as a decimal (i.e. 0.3)." The corresponding standards in the original GPS, M3N5(c), stated, Understand a one place decimal fraction represents tenths, i.e., 0.3 = 3/10."

However, I believe this was an unnecessary change which actually made the revised GPS a bit incoherent. It seems clear that the phrase, "decimal fractions," in the original GPS was used to mean "decimal numbers." Although the phrase "decimal fractions" isn't commonly used in the existing literature, when it is used, it typically means decimal numbers - or fractional quantities expressed in decimal format. Clearly, it is important for students to understand the equivalence of 3/10 and 0.3, but separating out fractions with powers of 10 as denominator seems to make a little sense mathematically. Furthermore, there are other statements in the GPS where this interpretation of "decimal fractions" creates some problems.

For example, the first sentence describing Grade 3 Number and Operations states, "Students will use decimal fractions and common fractions to represent parts of a whole." By examining the actual standards, we notice that students are also introduced to decimal numbers in Grade 3, but if we interpret "decimal fractions" as fractions with powers of 10 as denominators, then there is no reference to decimal numbers in the description of the standard. Similarly, the description of Grade 4 Number and Operations states, " Students will further develop their understanding of addition and subtraction of decimal fractions and common fractions with like denominators." However, students are to learn addition and subtraction of decimal numbers, M4N5.

In fact, everywhere except in M3N5, the GPS makes much better sense if we interpret "decimal fractions" to mean "decimal numbers." This is a great example how a simple phrase plays an important role in interpreting the standards. I really wish the state DOE will actually publish a document that will further elaborate what they meant.