Discrete Mathematics Project

Counting Techniques Activity


Social Security Numbers (Kim Kendrick)


(1) Students will continue to explore the concept of permutations and combinations and apply the Fundamental Counting Property to solve a real world problem.

(2) Students will compare solutions as conditions vary within the problem and be able to justify their solutions in sentence format.

(3) Students will integrate their knowledge of population and growth to extend and expand the assignment.


This activity requires students to have a basic knowledge of how to select and arrange objects. The main focus is on the numbers used in the United Stated in our Social Security system. The students will have to determine total possible arrangements, and then extend the lesson. This extension requires the use of a library. Your students should have appropriate understanding of how to research and locate reference materials. They will have to draw conclusions and make predictions based on the research.

Problem Statement

Every citizen in the United States is given a distinct social security number. This number is used in many ways to identify each and every one of us. In fact, in this school, your social security number is also your student number. Imagine what would happen if two of you had the same number. It would be impossible for the school to keep track of exactly WHO you are, what you have accomplished, and your general student progress. It is absolutely essential that no two social security numbers are the same for these types of reasons. In this assignment you will investigate the number of ID's available in our current system. In the second part you will be required to use the library and certain skills from your social studies classes in order to further investigate our current system. This will be a lengthy assignment, but you will be given the next week to complete it to the best of your ability.

Instructor Suggestions

(1) Set the stage by discussing the "Problem Statement" (see above) with the class.

(2) Distribute the "Social Security Number" activity sheet (see attachment) and allow the students to individually read the activity.

(3) When all of the students are finished reading, have them complete the first part of assignment individually.

(4) After all of the students have finished, have them form small groups to discuss a possible plan or starting point.

(5) Take students to the library so that they can research and gather data.

(6) Allow the students to work on this activity over the course of a week, providing time in class to answer questions and guide them.


"Social Security Number" activity sheet

chalk board



Introduction of problem statement (5 minutes), Individual work (20 minutes), Small group work (10-15 minutes), Library (20 minutes), Completion of project (1 week), Class time every day (15 minutes maximum)

Mathematics Concepts

Discrete Mathematics Concepts:

Counting techniques (permutations and combinations)

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Connections (within mathematics and across disciplines), Arrangements, Discrete Mathematics.

Colorado Model Content Standards Addressed

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

Curriculum Integration

This activity will be used in the first year of the Integrated Math Program as a separate module. It could also be used in a traditional Algebra I class when discussing series or in an Algebra II class when discussing probability.


This lesson could be integrated into a social studies unit when studying population growth. The students should have a basic understanding of research techniques, population growth, interpreting data tables, and preparing data tables to successfully complete this activity.


Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete Mathematics Through Applications. New York: W.H. Freeman and Company.

Last updated January 16, 1997