#### Type:

Graphic Organizer/Worksheet

#### Description:

This folder collects problem sets in fractions that are more challenging then the ones found in most textbooks. Most will require students to think about factorizations of numbers and what it means to be prime, rather than simply being a lesson in guessing and LCD.

#### Subjects:

• Mathematics > General
• Mathematics > Algebra

#### Education Levels:

• Higher Education

English

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Joan Cordova
August 11, 2011

1) The first sentence under Some things to remember: "A number x is a factor of y if y = xm for some m." Although this statement is satisfying to people who already understand algebra, it probably will cause confusion rather than impart information to our prealgebra students. It might be better to avoid variables when first describing ideas to prealgebra students. (Please check your spelling of "divisible.")

2) Table 2 has several instances of a nonstandard notation involving operations with negative numbers. For example, instead of -7/47 - -1/3, the standard would be either to put parentheses around the second fraction -7/47 - (-1/3), or to use a symbol for negation that is distinct from the subtraction symbol, typically accomplished by using an en dash that is elevated above the midline of the number, or by putting the negative symbol in the numerator of the fraction.

3) Many educators prefer expressions like "remove factors of 1" or "factor out common factors" which is mathematically correct rather than "cancel common factors" which leaves room for interpretation. Cancel is one of the words NCTM has noted is used differently by different instructors.

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