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.

2 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. For permission requests, write to the publisher, addressed Attention: Permissions Coordinator, at the address above. Ordering Information: Quantity sales.

3 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) 835-1718. 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.

4 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.

5 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. 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.

6 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 as 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. He told me, Then just make a guess, any guess.

7 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.

8 But I learned a valuable lesson (at least in math not about females) that lasted a lifetime! 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.

9 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. iii In college, I had a double major: engineering and computer science. 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).

10 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.