Title
The Non-Violence Commission (October Crowell)
Goals
1. Students will begin to explore the concept of apportionment as it applies to group decision making.
2. Students will work in small groups to decide on a fair apportionment of seats and be able to explain and justify how they arrived at their result.
Abstract
This activity can be used as an introductory activity to the concept of apportionment. Students are asked to decide in groups on a fair number of seats on a special district commission on non-violence that each high school should receive. The focus is on the differences in the methods used to apportion the seats based on the information given and the justification for the methods.
Problem Statement
The district superintendent has decided to form a commission of students to create a district non-violence policy. Each high school in the district will be give a certain number of seats. As a class, you need to decide how many seats each school will receive on the commission. Your decision should take into consideration the enrollment in each school as well as any other important information.
Instructor Suggestions
1. Discuss the Problem Statement (see above) with your students.
2. Distribute the "Non-Violence Commission" activity sheet (see attachment) and give the students time to read and review.
3. Break the class up into small groups and have them discuss how to allocate the seats on the commission. They should also be keeping record of how they arrived at their decision.
4. When the small groups are finished, have a spokesperson from each group share their seat apportionment and explain their method and reasoning involved in reaching their decision.
5. Discuss any class consensus or lack of class consensus for apportionment.
6. Discuss their methods as they relate to apportionment concepts.
Materials
"Non-Violence Commission" activity sheet, chalk or overhead projector.
Time
Activity Introduction (5 minutes), Group Work (20 minutes), Presentation and Discussion(20 minutes)
Mathematics Concepts
Discrete Mathematics Concepts
Apportionment, Hamilton Method, Jefferson Method, Webster Method, Hill Method
Related Mathematics Concepts
Ratio, Quota, Rounding, Arithmetic and Geometric Mean.
NCTM Standards Addressed
Problem Solving, Communication, Reasoning, Connections, Statistics, Discrete Mathematics.
Colorado Model Content Standards Addressed
Number Sense (1), Algebraic Techniques (2), Problem Solving Techniques (5), Linking Concepts and Procedures (6)
Curriculum Integration
This activity could be integrated into any traditional Algebra or Advanced Algebra class when the topics of statistics, specifically the mean, are examined. It can also be integrated at a Basic Math level when the topic of ratio is examined.
Further Investigation
This activity can be extended by discussing the need for more representation from a particular school based on its rate of violence or how the members of the commission will be chosen from each school.
Variations/Comments
References/Resources
Colorado State Content Standards. Colorado Department of Education
Crisler, N., Fisher, P., & Froelich, G. (1994). Discrete mathematics across the curriculum, K-12. Reston, VA: National Council of Teachers of Mathematics.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.