Pre-Algebra: A practical step-by-step approach

1 Pre-Algebra: A practical step-by-step approach Gary S. Goldman, PhD Dedicated to my 5th grade math teacher Mr. Hivesly Author: Gary S. Goldman, Title: Pre-Algebra: A practical step-by-step approach Editor: Preston R. Meltzer, BA, Educator (35 years experience), Life-time Teaching Credential Copyright 2012, 2013, 2019 Gary S. Goldman Publisher: Pearblossom Academy, Inc., 1882 Mill Creek Ln SW, Bogue Chitto, MS 39629 Email: Phone: 800-309-3569 FOURTH EDITION ALL RIGHTS RESERVED. This book (or ebook) contains material protected under International and Federal Copyright Laws and Treaties. Any unauthorized reprint or use of this material is prohibited. No part of this book or ebook (electronic book) may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system without express written permission from the author / publisher.

2 For permission requests, write to the publisher, addressed Attention: Permissions Coordinator, at the address above. Ordering Information: Quantity sales. Special discounts are available on quantity purchases by corporations, associations, and educational institutions. For details, contact the publisher at the address above. Please contact Pearblossom Academy, Inc.: Tel: (800) 309-3569; Fax: (601) 835-1718iii About the Author I am 59 years old, but I still recall an event from 1964 that had a significant impact on my life. I was 10-years-old in 5th grade at Gardenhill Elementary School located in La Mirada, California. Two individuals in that grade especially influenced me back then: (1) my friend Jill Hagan, who slapped me in the face when I failed to vote for her as class president; and (2) my classroom teacher, Mr.

3 Hivesly, who contributed greatly to my comprehension of math concepts. On the day that I received the slap (which occurred during recess), all students in Mr. Hivesly s classroom had voted for class president and had taken a math test that involved problems on simple division. Several days later, these tests had now all been graded. Students were in anticipation as the teacher returned each test paper with the letter grade shown prominently as a large letter at the top of the test page. I missed virtually every problem and could not stop focusing on the large F at the top of my test. I was near to tears, but was too embarrassed to cry in front of my classmates so I was unusually quiet for the remainder of class trying to maintain a normal composure without any tears.

4 For me, time seemed to be dragging on, until finally the bell rang all students were formally dismissed by the teacher. I purposely was slow in organizing my homework and to carry home making certain that all students had exited the class when I finally approached my teacher. I think at this point, I did have tears in my eyes as I politely asked, Mr. Hivesly, I just don t understand how to divide. Mr. Hivesly discerned my tears (though I tried to fight them back by wiping my eyes as they teared up). He patiently took the time right then to show me an example problem on the blackboard: 43 divided by 8. I wiped back my tears and tried to focus a s he took the chalk in his hands and kindly asked, How many times does 8 go into 43? I told him, I just don t know I don t understand how to divide.

5 He told me, Then just make a guess, any guess. I said, How about 2? He said, Well, 2 times 8 is 16, that s too low, we re trying to get to 43, without going over that number. So guess again. I said, How about 4? Mr. Hivesly said, Well, 4 times 8 is 32 you re getting closer! I said, Try 5. He said, 5 times 8 is 40. Now, 43 minus 40 is 3, so the answer is 5 remainder 3. I said, I think I am starting to understand, can we do another problem ? Mr. Hivesly proceeded to show me two more division problems before I thanked him, dismissed myself, then walked home (without my friend Jill) arriving just 10 minutes later than usual. But I learned a valuable lesson (at least in math not about females) that lasted a lifetime!

6 From that point on, I not only understood division; but I learned other math concepts often as quickly as they were presented to me. For the remainder of 5th grade, continuing through college, where I took Calculus, Vector Analysis, and other math courses, I always earned an A . In fact, in an advanced course called Fourier Series and Laplace Transforms, I actually never missed a single test problem math came easy to me. And in this book, I will try to make math easy for you! It is not uncommon for a student in a math class to ask such questions as: Why is this important? What benefit could this possibly have? Where possible, in this book, math concepts will be put to use in real world problems and realistic applications. iv In college, I had a double major: engineering and computer science.

7 I received two Bachelor of Science degrees. Later, I received a (or doctorate) degree in Computer Science. In my employment, I developed the first microcomputer-based CAD (Computer Aided Drafting) System (prior to today s widely known AutoCAD system). I also patented a Power Wheel an efficient motor in a wheel for electric cars. The CAD applications software allowed a user to create various engineering drawings. Writing that software required mastery of basic mathe-matics, algebra, geometry, and trigonometry. Later work involved some statistical methods and modeling of disease trends within a community. Math, to me, was not just variables and equations, it was a way to analyze and model real world applications. While some persons are satisfied recording data and tabulating figures, I have always been interested in understanding the underlying reasons for any trends or patterns that exist among the numbers.

8 Over the past 40+ years I have acquired real-world experience as a (1) designer and tester of electronic modules for Hughes Ground Systems, Fullerton, (2) contractor with a Class B General Contractor's License, (3) senior systems analyst in the Computer Aided Drafting (CAD) department at Holmes & Narver, Inc. (in Orange, CA), (4) computer consultant to CSUF faculty, staff, and students, (5) vice-president of Systems Development for Cascade Graphics Development (in Irvine, CA) producing the first microcomputer-based CAD system, (6) research analyst for the varicella surveillance project funded by the CDC, responsible for authoring medical journal papers on capture-recapture methods, varicella and herpes zoster, and other epidemiological subjects, (7) inventor of the Power-Wheel ( Patent) a highly efficient electric motor for vehicular transportation, (8)

9 Independent computer consultant working on a variety of projects ranging from the automation of the design of vertical cylindrical heaters to earth retainer walls with traffic loads (involving heuristic programming) and (9) substitute teacher for all subjects and all grades in three local school districts. This real-world work experience combined with the answering of student math questions during the past twenty years as founder and director of Pearblossom Private School, Inc. has contributed to my ability to understand the math difficulties that students frequently encounter and direct students to a straightforward, practical , step-by-step procedure for solving problems. It is highly recommended that you, the student, do every single exercise in this book.

10 The repetition and variety of problems well help to re-enforce the concepts in each section so that you gain self-confidence and competency. I have always maintained that if a student received a poor grade in math, this was more a reflection on the qualities of the teacher rather than the ability of the student. This course will provide you with algebra fundamentals that will help you to score well on most college entrance exams (such as ) or placement tests. But it may also impact your ability to think logically and apply math concepts in other endeavors. It is recommended that you NOT utilize a calculator for most problems in this book. As a prerequisite for this course, you should already be adept at reciting multiplication tables from memory and knowing the basic computational skills associated with addition, subtraction, multiplication, and division, as well as some basics working with fractions and decimals.