Index

Discrete Mathematics Project

Matrices Activity

Title

Goals

1. Students will use matrix operations to solve a real life application.

2. Students will be able to sort given information into matrix form.

Abstract

This activity is presented as a practical application of the use of matrix multiplication. It is envisioned to be presented after students have been introduced to the matrix perations of addition and multiplication.

Problem Statement

Remind students that they are overwhelmed with advertising everyday in a multitude of places. It is important for them to know that advertising is a multi-billion dollar industry. Also, advertising often offers high paying careers. This activity shows the inner workings of one aspect of this industry.

Instructor Suggestions

1. Begin the activity by reviewing examples of matrix multiplication. Include checking the size of the matrix and whether or not is possible to multiply. Look also at the failure of the commutative property with matrix multiplication.

2. Distribute the worksheets and read the introduction to the problem. Discuss what the goals of an advertising campaign might be. Also, discuss market share.

3. The difficulty of the problem is in the set up of the matrix. Allow the students to try this on their own. Then go over the results as a class.

4. Multiply the matrices. Use graphing calculators if desired. Then interpret the results.

Materials

"Advertising Campaign" worksheets, dry erase board

Time

Review of matrix multiplication (10 minutes), Introduction of the problem (5 minutes), Individual work to set up matrix (5 minutes), Large group discussion of matrix (10 minutes), Large group solution of problem (10 minutes)

Mathematics Concepts

Discrete Mathematics Concepts:

Matrix dimensions, elements, multiplication

Related Mathematics Concepts:

Percentages

Problem Solving, Reasoning, Communication, Connections, Algebra, Discrete Math

Number Sense (1), Algebraic Methods (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity fits well into the initial discussion of matrices in an Algebra I class. It provides a concrete application to matrix multiplication.

Further Investigation

Activities involving applications of advertising could be continued. For example, the advertising industries' manipulation of the truth of the major and/or minor premise in an argument, and how it effects the conclusions that you draw about their products.