Math Series Measurement Measuring Lengths and Distances Copyright 2019 Oklahoma Department of Career and Technology Education Resource Center for CareerTech Advancement All rights reserved. Printed in the United States of America by the Oklahoma Department of Career and Technology Education Stillwater, OK 74074-4364 This publication, or parts thereof, may not be reproduced in any form photographic, electrostatic, mechanical, or any other methods for any use including information storage and retrieval, without written permission from the publisher. Use of commercial products in these instructional materials does not imply endorsement by the Oklahoma Department of Career and Technology Education. Web site addresses were accurate and all content on referenced web sites was appropriate during the development and production of this product. However, web sites sometimes change; the Resource Center takes no responsibility for a site’s content. The inclusion of a website does not constitute an endorsement of that site’s other pages, products, or owners. You are encouraged to verify all web sites prior to use. The Oklahoma Department of Career and Technology Education does not discriminate on the basis of race, color, national origin, sex/gender, age, disability, or veteran status. Permission granted to download and print this publication for non-commercial use in a classroom or training setting. Measuring Lengths and Distances How tall are you? How wide is your bedroom? For example: a STEEL TAPE allows carpenters to measure How far is your workplace from your home? regular and irregular shapes; surveyors may use surveying These are just a few examples of lengths and tapes that are very long, including 300- and 500-foot distances that people measure every day. lengths; You may wonder why it is important to understand these measurements. Suppose you want to paint your living room. How much paint will you need? In order to determine this, you must know the height and width of your living room walls. Suppose you want to ride your bike to work instead of driving or taking the bus. ‘ How long will it take you to get there? Knowing the distance from your home to your workplace will help you make that calculation. MICROMETERS allow automotive service technicians to make extremely accurate inside and outside You use different tools to measure lengths and measurements; and distances every day. You are probably already familiar with rulers and yardsticks. (This unit will give you more practice in reading rulers.) You have probably watched, or participated in, sporting events such as swimming and track and field, where distances are measured in meters. In addition to these, the odometer in your vehicle indicates the distance traveled by the vehicle. A pedometer measures the number of steps you take as you walk. Other tools are used to measure length and distance on the job. DIAMETER TAPE, TREE CALIPERS, and DIAMETER STICKS all help foresters and others measure the diameter of a tree. SPECIFIC OBJECTIVES 1. Identify the units used to measure lengths and distances. 2. State the abbreviations of units used to measure lengths and distances. 3. Identify the divisions of a ruler. 4. Explain how to read a ruler. 5. State the steps for measuring an object with a ruler. 6. Determine lengths by using a ruler. (Assignment Sheet 1) 7. Explain how to read a metric ruler. 8. State the steps for measuring an object with a metric ruler. 9. Determine lengths by using a metric ruler. (Assignment Sheet 2) 10. Convert units of length and distance between the metric and English systems. (Assignment Sheet 3) 11. Explain how to convert units of length and distance between larger and smaller units. 12. Convert units of measurement. (Assignment Sheet 4) 13. State principles for adding and subtracting units of length and distance. 14. Calculate measurements of length and distance using addition and subtraction. (Assignment Sheet 5) Focus Assignment List three (3) things throughout your house that you would like to measure. Next to each item, write down what you estimate the length (or height) to be. Determine the actual measurement and compare that to your estimate. objective 1 IDENTIFY THE UNITS USED TO MEASURE LENGTHS AND DISTANCES. words you should know DISTANCE measurement of the space between two places or objects LENGTH measurement of the size of an object MEASURE to determine the size or quantity by comparing with a fixed unit or with an object of known size UNIT a standard measurement of physical quantities that need clear definitions to be useful • ENGLISH UNITS Did You Know? 12 inches = 1 foot 3 feet = 1 yard The English system of units—also known as the U.S. customary units or standard units—is a system of non-metric units of 1,760 yards = 1 mile measurement used in the United States. It is sometimes used alongside the metric system of units. The Imperial system of METRIC UNITS units is a collection of English units first defined in the Weights • 1,000 millimeters = 1 meter and Measures Act of 1824. Imperial units were used in the United Kingdom and its colonies, but were not used in the 100 centimeters = 1 meter United States. Both the Imperial and English systems use similar 10 decimeters = 1 meter naming “rules” and, in some cases, even use the same measures. 10 meters = 1 dekameter However, it is important to recognize them as two separate and different systems of measurement. 100 meters = 1 hectometer 1,000 meters = 1 kilometer The International System of units—often called SI, which stands for the French translation of the term, Système International --> NOTE: To convert from one metric measurement to d’Unités—is also called the metric system in the United States. another, all you have to do is multiply or divide by units Every country in the world, except the United States, uses the SI system in daily life. Almost every country—including the United of 10. See Supplement 2. States—uses the SI system in the scientific field. Resource Center for CareerTech Advancement Page 4 objective 2 STATE THE ABBREVIATIONS OF UNITS USED TO MEASURE LENGTHS AND DISTANCES. ENGLISH UNITS • in. = inch(es) ft. = foot/feet yd. = yard(s) mi. = mile(s) METRIC UNITS • mm = millimeter(s) cm = centimeter(s) dm = decimeter(s) m = meter(s) dkm = dekameter(s) hm = hectometer(s) km = kilometer(s) Did You Know? The earliest system of units was based on parts of the body. 1500 B.C., which equaled about 13 inches. The Romans and The problem with this system was that measurements varied Greeks also used the human foot as measurement, which from one person to another. The Egyptians used the width equaled about 11.7 inches. Inches were first introduced by of a man’s middle finger (called a digit) and the distance the Romans, who divided one foot into 12 units that equaled across his palm (called a palm). The Greeks used the length the width of a man’s thumb. A mile originally equaled 1,000 of a finger, which was 0.8 inches. The hand, which equals 4 paces of a Roman soldier (where one pace equaled two inches, is still used today to measure the height of horses. strides). It was approximately 1,591 yards. The measurement of a yard was introduced by traders to measure cloth and From ancient Egypt, a cubit was the distance from a person’s equaled the length of the stretched out cloth between elbow to the tip of his or her outstretched finger; it equaled the chin and fingertip. In the 12th century, King Henry I of about 19.5 inches. To avoid confusion, a standard cubit England defined a yard as the distance between his nose and was formed from black granite and called the Royal Cubit. the tip of his middle finger. In 1305 the yard was changed to It measured 20.4 inches, and all other cubit sticks were equal 3 feet. measured against this one. The Babylonians were the first to use the human foot as a unit of measurement in about Resource Center for CareerTech Advancement Page 5 objective 3 IDENTIFY THE DIVISIONS OF A RULER. • 1 INCH Figure 1 --> NOTE: Each inch is marked with a vertical line and a number. 1 • /2 INCH Figure 2 --> NOTE: Each inch is divided into 2 equal sections. These sections are called fractions. Each section equals ½ inch. The bottom number of the fraction tells you how many units there are per inch. In this case, there are two units per inch. Resource Center for CareerTech Advancement Page 6 1 • /4 INCH Figure 3 -- > NOTE: Each inch is divided into 4 equal sections. Each section equals ¼ inch. 1 • /8 INCH Figure 4 --> NOTE: Each inch is divided into 8 equal sections. Each section equals ¹⁄₈ inch. 1 • /16 INCH Figure 5 --> NOTE: Each inch is divided into 16 equal sections. Each section equals ¹⁄₁₆ inch. This is the most accurate type of ruler that measures inches. Resource Center for CareerTech Advancement Page 7 objective 4 EXPLAIN HOW TO READ A RULER. The figure below illustrates a ruler that measures ⁄¹₁₆ of an inch. You can also use this ruler to read ¹⁄₈ of an inch, ¼ of an inch, and ½ of an inch. As the fraction becomes smaller, the lines become shorter. Figure 6 • Reading inches—Each inch is marked by a numbered line. These lines are the longest. • Reading ½ inch—The second longest lines indicate the ½ inch marks. • Reading ¼ inch—The third longest lines indicate the ¼ inch marks. • Reading ¹⁄₈ inch—The fourth longest lines indicate the ¹⁄₈ inch marks. • Reading ¹⁄₁₆ inch—The shortest lines indicate the ¹⁄₁₆ inch marks. Resource Center for CareerTech Advancement Page 8 objective 5 STATE THE STEPS FOR MEASURING AN OBJECT WITH A RULER.