# Activities

• • • ##### Subject Area

• Math: PreAlgebra: Number Sense and Operations
• Math: Middle Grades Math: Number Sense

• ##### Author 6-8

60 Minutes

• ##### Device
• TI-73 Explorer™
• ##### Other Materials
This is Activity 4 from the EXPLORATIONS Book:
Discovering Mathematics with the TI-73: Activities for Grades 7 And 8

Oliver's Method

#### Activity Overview

Students discover a relationship between the Greatest Common Factor (GCF) and the Least Common Multiple (LCM) of two numbers. Students will find and justify the relationship that the product of two numbers is equal to the product of the LCM and the GCF.

#### Before the Activity

• See the attached PDF file for detailed instructions for this activity
• Print pages 33 - 36 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Use the LCM function on the calculator to find the least common multiple (LCM) of the 2 numbers
• Use the GCD function on the calculator to find the greatest common divisor (GCD) of the same 2 numbers
• Test Oliver's Method by writing the two numbers as a fraction
• Simplify the fraction
• Multiply the original fraction by the reciprocal of the simplified fraction to get the LCM
• Create a list of two numbers, their GCD, their LCM, and their product
• Observe that the product of the two numbers equals the product of the GCD and the LCM of the two numbers
• #### After the Activity

Students will complete the Worksheet and analyze the results.

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary