Discrete Mathematics Project

Counting Techniques Activity


You Make The Call (John Long)


Students should use the addition and multiplication principles in order to solve the problems.


This activity, which is set in the context of finding how many phone numbers can be made, explores the addition and multiplication principles of probability. This activity is envisioned to be implemented after students have been introduced to this principle.

Problem Statement

Remind students that just recently 2 new area codes were added to Colorado's phone system. As a matter of fact, communities add new prefixes to their phone numbers all the time. These problem will investigate the number of new phone numbers that are made by adding new prefixes.

Instructors Suggestions

(1) Set the stage by discussing the "Problem Statement"

(2) Divide the student into small groups and allow them to work through the activity sheet.

(3) Discuss the solutions in a large group.


Activity Sheet


Introduction (5 min.), activity (20 min.), discussion (10 min.).

Mathematics Concepts

Discrete Mathematics Concepts

Counting and Probability, Addition and Multiplication principals.

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Connections, Discrete Mathematics, Probability

Colorado Model Content Standards Addressed

Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity should be introduced in a probability section of a course at any level of mathematics. This activity is envisioned to be done after introducing addition or multiplication principals.

Further Investigation

Find out the number of prefixes on your town phone numbers. How many different number can be made using those? How were phone number made 50 years ago?



Last updated January 16, 1997