Advertising Campaign (Dan Snook)
1. Students will use matrix operations to solve a real life application.
2. Students will be able to sort given information into matrix form.
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.
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.
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.
"Advertising Campaign" worksheets, dry erase board
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)
Discrete Mathematics Concepts:
Matrix dimensions, elements, multiplication
Related Mathematics Concepts:
NCTM Standards Addressed
Problem Solving, Reasoning, Communication, Connections, Algebra, Discrete Math
Colorado and District Standards Addressed
Number Sense (1), Algebraic Methods (2), Data Collection and Analysis (3), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
This activity fits well into the initial discussion of matrices in an Algebra I class. It provides a concrete application to matrix multiplication.
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.
This is a good activity to use while teaching matrix operations. Multiplying matrices is a difficult problem for students at first. Having mastered the procedure, this activity shows a use for the technique.
Colorado Model Mathematics Standards Task Force. (1995) Colorado model content standards for mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author: