Chapter 0. Introduction

How to Solve Word Problems Programmatically

0. Introduction


0.1	Overcoming Fear
0.2	Components of Meaning
0.3	Organizing Measurements and Relationships
0.4	Programmable Steps of Modeling
0.5	About the Author

0.1

Overcoming Fear

Afraid?

Do you fear word problems?

You're not swimming alone; many people experience fear when approaching math word problems. This book attacks that fear head on. It will help you achieve the following objectives:

Objectives

View mathematics as a language of measurement

Expand mathematical vocabulary

Apply math in real-world problems effectively

Understand product specifications (5 dB, 2.6 GHz, 10 Ohm, 15 Amps, 9 Volts, 2.5 Watts, etc.)

Develop a deeper appreciation for the interaction between math, business, and science

Improve math and science test scores (High School Proficiency, SAT, ACT, GRE, etc.)

Enhance critical thinking and problem solving skills

Increase confidence in learning and teaching math and science

Fear often comes from not knowing the meaning of things like unexpected movements in a dark room. This book will throw new light into the darker spaces of your math background by giving you meaning and perspective. It is a valuable supplement to textbooks in math and science that require a working knowledge of algebra. It can also help you prepare for exams that require an algebra background.

0.2

Components of Meaning

[unit~Dimension(Thing)]

First we will carefully define "meaning" associated with quantities in word problems using three components: units, dimensions and things. Then using algebraic expressions of these components, we will learn how to build math and science equations as easily as assembling jigsaw puzzle pieces using their shapes and colors.

0.3

Organizing Measurements and Relationships

Qty	Value	Meaning	Relationship
q1
q2
q3
q4
q5
…

This "meaning table" organize in a consistent way our thought processes when solving word problems. It will help us to focus our attention on defining quantities and relationships separate from the algebraic manipulation of mathematical expressions. This important paradigm shift will give you the ability to solve complex problems by breaking them down into their natural meaningful relationships.

0.4

Programmable Steps of Modeling

Identify

Measure

Relate

Formulate

Solve

Steps of Unified Math®

We organize this book around five steps of modeling with three chapters each. These steps along with the components of meaning and the meaning table lead to a systematic solution process.

What does this mean for you? Once you understand how to (1) identify things and their dimensions in a given problem, (2) measure those dimensions, and (3) relate those quantities, you can then follow programmable rules to formulate and solve the problems. This will significantly increase your critical thinking and problem solving skills. You will realize that mathematical rules are the easy part since they are completely deterministic; the challenge lies in determining meaning.

Our patent-pending "meaning calculators" (a generation of calculators beyond graphing calculators) take advantage of this opportunity of programmability and will provide you with tools to focus on the meaning while formulating and solving problems. Then you learn the abstract principles of mathematics in their natural context.

0.5

About the Author

Dr. Ranel E. Erickson received his doctorate degree from Stanford University in Operations Research, a field that develops and applies mathematical models to complex quantitative business problems. After helping many students formulate and solve word problems in his quantitative management and computer related courses at the University of Nevada, Las Vegas (UNLV) he has developed and patented systematic methods of formulating and solving word problems, collectively called Unified Math®.

Dr. Ranel E. Erickson

The Author

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