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High School Mathematics And Its Applications (HiMAP)

HiMAP Modules are the perfect companion to any high school text. Each Module is a self contained modeling problem that includes exercises, activities, and where appropriate, assessment problems. HiMAP Modules cover a broad range of application areas, and topics in both discrete and continuous mathematics. With dozens of modules in print, for courses from pre algebra to pre calculus, there is a module for almost any subject, interest, and mathematics ability.

Each of these modules is available, free of charge, to COMAP members for use in the classroom. Photocopying is permitted for use only within a single class of students or teachers. The material may not be sold or modified in any way without written permission from COMAP.

COMAP members can download and use any of these units:

Loads of Codes, by Joseph Malkevitch and Gary Froelich
This unit explores the mathematics of protecting and communicating information, through cryptography and digital data storage.

Drawing Pictures With One Line, by Darrah Chavey
This unit uses Euler's Theorem and the fascinating one-line drawings of the Malekula people in the South Pacific to demonstrate the many applications of circuit design.

Optimality Pays: An Introduction to Linear Programming, by Jeganathan Sriskandaraajah
This module provides a history of linear programming and covers several business-management concepts including assignment, transportation, and traveling-salesperson problems.

Fair Voting - Weighted Votes for Unequal Constituencies, by William F. Lucas
Students are challenged to use the mathematics of weighted voting to wrestle with important social issues such as how power can be measured quantitatively, and how power is divided in our government.

Codes Galore, by Joseph Malkevitch, Gary Froelich, and Daniel Froelich
Students use the recently developed mathematics of codes used to hide and compress data.

The Abacus: Its History and Applications, by Frances Rosebell Metallo
Critical mathematics concepts such as using word names, standard notation, and place value are brought to life when students actually build a working abacus.

Explore Sorts, by Rochelle Wilson Meyer
Sorting algorithms are used by virtually every computer program. This module  examines several sorting algorithms and give an analysis of their efficiency.

A Uniform Approach to Rate and Ratio Problems, by James R. Rogers
A technique for solving rate and ratio problems, the Universal Rate Formula, is applied to a variety of mathematical situations ranging from fundamental multiplication to differential calculus.

Decision Making & Math Models, by G.Surya Kumar
This unit discusses the mathematical models that help solve three common management problems. The unit works well with introductory pre-calculus or trigonometry students.

The Mathematician's Coloring Book, by Richard L. Francis
The four-color theorem is introduced through maps, pictures, and worksheets, which explore the branch of mathematics that uses colors to divide, discern, and qualify items as diverse as territories and vegetables.

Spheres and Satellites, by William B. Martin
Students use graphing calculators to discover amazing geometric facts about our backyards, our world, and beyond.

Applications of Geometrical Probability, by Fred C. Djang
Students are encouraged to experiment and estimate when analyzing probability problems, and use their estimates to develop diagrams that simplify a complex real-world problem.

A Mathematical Look at the Calendar, by Richard L. Francis
This unit demonstrates mathematical techniques for finding the day of the week on a given date, finding mathematical patterns in the calendar, and using these patterns to develop algorithms.

Fair Divisions: Getting Your Fair Share, by Sandi Bennett; Duane DeTemple; Michael Dirks; Bob Newell; Jack M. Robertson; Bob Tyus
Demonstrates how mathematics can be used to divide objects fairly, such as the equitable distribution of an item that is not divisible (e.g., a hose from an estate).

The Apportionment Problem: The Search for the Perfect Democracy
, by Sandi Bennett; Duane DeTemple; Michael Dirks; Bob Newell; Jack M. Robertson; Bob Tyus
A look at the apportionment of the House of Representatives, and how many representatives from each state are sent to Congress.

Student Generations, by Stephen I. Brown
Introduces functions and strategies (heuristics) to generate and solve their own problems.

Problem Solving Using Graphs, by Margaret B. Cozzens and Richard D. Porter
This examination of graph theory introduces techniques such as minimum-cost spanning tress, shortest-route algorithms, and Euler circuits as tools that can solve real problems.

Using Percent, by Jo Anne S. Growney
This comprehensive unit emphasizes that understanding percentages is essential for survival in today's world of complicated consumer issues and misleading headlines.

Symmetry, Rigid Motion, and Patterns, by Donald Crowe
Students examine patterns in wallpaper and ancient artifacts to discover the fascinating applications of basic aspects of plane geometry to archaeology, anthropology, and design.

The Mathematics of Conflict, by Frank C. Zagare
Students see how decision mathematics can be used to understand conflict and give us a new historical perspective.

Recurrence Relations - "Counting Backwards", by Margaret Cozzens and Richard Porter
Introduce students to difference equations by showing their unique application to computer science.

The Mathematical Theory of Elections, by Joseph Malkevitch
This module illustrates how mathematics can design and analyze election and ranking methods. Preference schedules, fairness criteria, and weighted voting all demonstrate that how votes are counted can affect the outcome of an election.