Discrete Mathematics Project

Counting Techniques Activity


Choose Your Dream Machine (Greta Lawlor)


1) Students will explore the concept of the addition and multiplication principles.

2) Students will work in groups to solve problems using the addition and multiplication principles separately and then together in one problem.

3) Students will be able to communicate and justify their solutions.


The students are asked to determine the number of choices available in choosing options on a vehicle. The first question uses the addition principle, the second the multiplication principle and the third uses both. This problem could be used to explore the counting principles or for practice after the principles have been discusses.

Problem Statement

Each student will have the opportunity to choose a car or will dream about choosing a car that has all the "extras" they just have to have. This problem presents the counting principles in a context the students will connect with. This activity will point out just how many choices are available when choosing several types of options.

Instructor Suggestions

1) Hand out the activity "Choose Your Dream Machine" for the students to work on before you discuss the counting principles. Give them transparencies and markers to present with.

2) Have the students work together in groups on developing a strategy to decide how many choices they have for each question. As the students begin to finish problem number one, interrupt them and have one or two groups that are on the right track present. Then turn them loose on questions three and four.

3) Have each of the solutions presented. If no group comes up with the principles, they can be discusses by way of a simpler problem and then let the students reconsider, or the teacher may show the students how to use the principles directly to solve the problem.

4) Once the students have presented solutions with the counting principles, be sure to give the students the vocabulary that accompanies the solution.


"Choose Your Dream Machine" activity sheet, transparencies, markers.


Introduction and instructions (5 minutes), group work and initial presentation of question 1 (15 minutes), finish problems 2 and 3 and presentations (25 minutes.)

Mathematics Concepts

Discrete Math Concepts

Addition Principle, Multiplication Principle

Related Mathematics Concepts

Sets, counting techniques

NCTM Standards Addressed

Problem Solving, Communication, Reasoning, Discrete Mathematics

Colorado Model Content Standards

Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)

Curriculum Integration

This activity would be a good lead into permutations and combinations in an Algebra class or a Probability and Statistics class.

Further Investigations

This problem could be extended to use the pigeon-hole principle. If students obtained pamphlets on their favorite cars, they could determine how many different ways that car

could be offered.


This activity can be used as an exploratory activity or as an assessment activity, depending on how much direction and questioning the teacher decides to do.


Dossey, John A., & Otto, Albert D. et. al., Discrete Mathematics. Scott, Foresman and Company. Glenview, Illinois: 1972.

Last updated January 15, 1997