35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 1 Measurement The Long and the Short of It Workbook 1 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 3 Measurement The Long and the Short of It Workbook Shopware 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 4 For additional copies, call or send orders to: SHOPWARE 2572 Brunswick Pike, Lawrenceville, NJ 08648 Phone: 1-800-487-3392; 609-671-1000; Fax: 1-800-900-5172 Email to: [email protected] © 2007. All rights reserved. No part of this book may be reproduced in any form or by any means, or stored in a database or retrieval system, without prior written permission of the publisher except in the case of brief quotations embodied in critical articles or reviews. 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 5 Table of Contents Introduction ............................................................................................................. page 1 The History of Linear Measurement .......................................................................... page 2 The English or Customary System ............................................................................ page 2 The Metric System ................................................................................................... page 3 Accuracy or Precision ............................................................................................... page 4 Customary Measurement Units ................................................................................ page 5 Metric Measurement Units ...................................................................................... page 8 Conclusion .............................................................................................................. page 10 Tables of Linear Measurements ................................................................................ page 11 Table of Equivalents ................................................................................................. page 11 Conversion Table ...................................................................................................... page 11 Worksheets Part 1..................................................................................................... page 12 Answer Key ..............................................................................................................page 25 Worksheets Part 2 .................................................................................................... page 27 Answer Key ..............................................................................................................page 34 For Discussion .......................................................................................................... page 35 35899 Measurement WORKBOOK 5/6/08 12:45 PM Page 6 INTRODUCTION From the moment you were born, one of the first things known about you was how much you weighed and how long you were. Since that time, measurement has affected almost every- thing you do. The glass of milk you had this morning probably came from a gallon or quart container. The tomatoes your mother picked up at the supermarket were bought by the pound. The clothes and shoes you are wearing were made a certain size, or they would be so tight you couldn't breathe or so loose that they would fall off of you. All of these are specific types of measurement. And whether you realize it or not, you are measuring at this very moment! Your eyes must measure the distance to this page and send the proper signals to your brain in order for you to read. I think you understand how important measurement is to all of us. However, measurement is useless unless you are able to communicate your findings to other people. If I tell you that it is three miles to the nearest gas station, you would have some idea of how far that is. But if I told you it was fourteen goombas from here to the next town, would you have any clue what I was talking about? Probably not. That is where units of measure come in. Units of measure provide you with a way to express whatever it is that you're measuring in relation to commonly recognized standards. Standards are agreed-upon specifications to which other things can be compared. Let's look at this from a different perspective. Suppose a friend was giving you directions to his home and he told you to go down Main Street about 10,560 feet and take a left. Without using a conversion chart you may not understand that he meant for you to go about two miles before you turned. Although you could say that your football team needed seventy-two inches for a first down and be correct, you would probably say they needed two yards. The point is not only do you need to express measurements in recognized standards, you also need to keep your expressions in terms that are easily communicated and understood. Ancient civilizations invented the first systems of measuring in order to build structures, divide land, and trade farming goods on a relatively equal and fair basis. These primitive systems served their purposes but were extremely inefficient due to inconsistencies in the standards that were used. Today, modern measurement techniques allow you to calculate distance, time, mass, area, volume, weight, and force. Various formulas and tables have been devised to help you put a number on almost everything in the universe. Rather than try to explain all the dif- ferent ways to calculate measurements, the purpose of this manual is to give you a basic understanding of linear measurement. Linear measurement simply means calculating the length of a line. It is used to measure the distance from point A to point B. It answers the question "How far?" 1 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 7 THE HISTORY OF LINEAR MEASUREMENT Even early civilizations needed some way to know how far, how big, or how long. Understandably, humans first turned to parts of the body to use as measuring instruments. Early Babylonian and Egyptian records indicate that length was first measured with the finger, hand, forearm, and foot. The width of a man's thumb equaled one inch. Three grains of barley placed end to end made one finger, or digit. Four digits equaled one hand—the unit we still use to measure the height of a horse. The distance from the tip of the middle finger to the elbow was one cubit. Two cubits equaled one arm, and one arm, measured from the fingertips to the chin, was one yard. Two arms (or yards) made one fathom—a unit still used to measure depths of the ocean. The “foot” measurement unit still used today was originally the length of an adult human foot. Using the human body as a measuring stick proved to be very unreliable, and it is easy to see why. Very few human bodies are exactly the same proportion. Look around the room where you're sitting. How many different sizes of hands, feet, and arms do you see? Whose body are you going to use for a standard form of measurement? The ancient Egyptians decided that the person in power at that time would be used as the official standard—but the standard changed each time a new king or queen held the throne. Another problem was that the king or queen could change the standard to suit their specific needs any time they wished. To add to the confusion, people soon came to realize that neighboring villages might have chosen a completely different set of standards for their measurements. As societies evolved, measurement units became more complex. The invention of numbering systems and the science of mathematics made it possible to create whole systems of measure- ment units suited to trade and commerce, land division, taxation, or scientific research. For these more sophisticated uses, it was necessary not only to measure more complex things, but measure accurately time after time and in different locations. THE ENGLISH OR CUSTOMARY SYSTEM The measurement system commonly used in the United States today is nearly the same as that brought from England by the original colonists. These measures originated from a variety of cultures including Babylonian, Egyptian, Roman, Anglo-Saxon, and Norman-French. Many of these units were extremely loose and arbitrary and created a great deal of confusion. For instance, the inch, the smallest length unit in the English system of measurement, started out as the width of a man's thumb. Since there are about twelve thumb-widths in a foot, the English called each one an unch, which comes from the Roman word for one-twelfth, uncia. In time, unch became inch. The English units were well suited to commerce and trade because they had been developed and refined to meet commercial needs. Through coloniza- tion and dominance of world commerce during the 17th, 18th, and 19th centuries, the English system of measurement spread and was established in many parts of the world, including the American colonies. 2 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 8 It wasn't until the late 1700s that standards of measurement became an important issue. George Washington's first message to Congress in 1790 expressed the importance of “creat- ing uniformity in standards of currency, weights and measures in use in the United States.” Thomas Jefferson, then Secretary of State, suggested adopting either the English system— with units of yard, pound, and gallon—or the French metric system—with units of meter, gram, and liter. Congress was unsure of which system to choose and ignored the matter for several years. It wasn't until 1827 that a brass duplicate of the English pound weight