## Tuesday, December 18, 2007

### M6N1 f - Percents (1)

M6N1. Students will understand the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts to solve problems.
f. Use fractions, decimals, and percents interchangeably.

Since I discussed ideas related to fractions and decimals, let me discuss another standard that deals with those ideas, M6N1f. As most of you are aware, the Georgia Performance Standards were heavily influenced by the 1989 Japanese Course of Study. There are many GPS statements that are identical to what you would find in the Japanese standards. However, this is one statement you will NOT find in the Japanese standards. Since a standard like this is probably very familiar to many of us, that might come as a surprise. Why doesn’t the Japanese standards expect students to be able to use “fractions, decimals and percents interchangeably”?

Before answering that question, let’s consider why fractions, decimals and percents might be used interchangeably. Some people claim that percent is just another representation of rational numbers. After all, “percents” means “out of 100.” Therefore, just like decimal numbers are based on powers of 10, percents are based on a particular power of 10, namely 100. Thus, 32% means 32 out of 100. M5N5a does state that students should be able to “model percent on 10 by 10 grids.” Thus, 32% may be represented by shading in 32 small squares on a 10 by 10 grids. Of course, the same model may be used to model a decimal number, 0.32, or a fraction 32/100. So, since percent is another way to represent rational numbers, decimals, fractions and percents are interchangeable.

However, if percents, fractions, and decimals are interchangeable, then we should be able to make statements like,
• I bought a 50% gallon of milk.
• The next exit is 75% mile away.
• My son is 350% year old.
These statements sound rather absurd, but why is it? If fractions, decimals, and percents are truly interchangeable, shouldn’t these statements make perfect sense? Or, consider these cases:

Jenny made 7 out of 10 (70%) free throws during the first half of a game. In the second half, she made 8 out of 10 (80%) free throws.
So, did Jenny make 70+80 = 150% of free throws in the game?
Can we express this situation as 7/10 + 8/10 = 15/20?

These situations suggest that there are some significant differences between percents and fractions/decimals, and they are not interchangeable all the time. So, when can we use these three interchangeably and why can we not? To answer this question, we must first understand what percents mean – they are not just another representation of rational numbers.

Dalila said...

Hi,
I came across your blog by chance. I will be teaching a Thematic Unit on Japan in a couple of weeks. I am very interested in your interpretation of the GPS.