## Lesson: Factors and Fractions

Developing the Concept

Students will remember concepts more readily when they are connected to other concepts. The GCF and LCM are the underlying concepts for finding equivalent fractions and adding and subtracting fractions, which students will do later.

**Materials:** paper and pencil

**Preparation:** none

**Prerequisite Skills and Background:** Students should know what prime and composite numbers are and how to find the prime factorization of a number. Students should also have a fundamental understanding of fractions.

**Wrap-Up and Assessment Hints**

An excellent way to deepen your students' understanding of the LCM is to create an open-ended request, such as “Find three pairs of numbers whose LCM is 20.” There are many solutions to this problem including the following: 1 and 20, 4 and 5, 10 and 4, and 20 and 5. In order for students to find solutions to the problem, they will have to be sure that at most one factor of 5 appears in one of the numbers and that 4 is a factor of one of the numbers, since 20 = 2² x 5.

Similarly, to deepen your students' understanding of the GCF, create an open-ended request, such as “Find three pairs of numbers whose GCF is 12.” Once again, there are many solutions to this problem, including the following: 12 and 36, 36 and 24, and 36 and 60. Students should realize that all the number pairs are multiples of the GCF (12) but have no other common factor.