Measurement: the Long and the Short of It Workbook

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 everything 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 different 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?"

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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 measurement 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.

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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 was brought to the United States. By 1830, two bronze yardsticks had been delivered and the U.S. Congress finally passed laws making the English pound and yard official measuring standards of the United States. It is believed that the only reason the English system was chosen over the metric system was that the U.S. Congress did not want to upset the English monarchy by installing a different system than the one being used in England at that time.

The English/Customary system of linear measurement uses the yard as its standard. All other measurements are either fractions or multiples of a yard. This is where the customary system of measurement begins to get complicated. Rather than establish a set pattern for determining larger and smaller units, the customary system divides units by three, twelve, thirty-six, halves, quarters, eighths, and so forth. Learning to use the customary system of measurement requires an understanding of different dimensions or fractions and their values.

THE METRIC SYSTEM The need for a single worldwide coordinated measurement system was recognized over 300 years ago. But it wasn't until 1790 that the National Assembly of France requested the French Academy of Sciences to "deduce an invariable standard for all the measures and all the weights." The Commission appointed by the Academy created a system that was simple and scientific. The unit of length was to be a portion of the earth's circumference. Measures for capacity (volume) and mass were to be derived from the unit of length, thus relating the basic units of the system to each other and to nature. Furthermore, the larger and smaller versions of each unit were to be created by multiplying or dividing the basic units by 10 and its pow- ers. Similar calculations in the metric system could be performed simply by shifting the decimal point. Thus, the metric system is a 10-base, or decimal, system.

The Commission assigned the name mètre (meter) to the unit of length. This name was derived from the Greek word metron, meaning a measure. The physical standard represent- ing the meter was to be constructed so that it would equal one ten-millionth of an imaginary line running from the North Pole to the Equator, that passed through Paris. Later, they made a master meter stick by marking that distance on a bar of metal made of platinum and iridi- um. It wasn't until after the French scientists had devised the system and made the standards that newer, more accurate measurements were taken that showed the original measurements were slightly off. Rather than change the system entirely, they decided to leave the standards as they were. After all, it wasn't important that the original measurement wasn't exactly one ten-millionth of the pole to equator distance. What was important was that everyone agreed that the distance that was marked on the master meter stick was the standard.

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Although the metric system was not accepted with enthusiasm at first, adoption by other nations occurred steadily after France made its use compulsory in 1840. Although the United States Congress did pass a law in 1866 allowing the use of the metric system, it did not insist that it be used. In 1875, an international treaty was signed by 17 countries, including the United States, to set up well-defined metric standards for length and mass. As a result of the treaty, physical metric standards were constructed and distributed to each nation that signed the treaty. Since 1893, the internationally agreed-to metric standards have served as the funda- mental measurement standards of the United States. Legally, all U.S. units of length are related to the meter. For instance, the yard is listed as being 0.9144 meters long.

The standardized character and decimal features of the metric system made it well suited to scientific and engineering work. Consequently, it is not surprising that the rapid spread of the system coincided with an age of rapid technological advancement. By the middle of the twen- tieth century, length measurements had become quite accurate and reliable, yet scientists con- tinued to search for new tools, new methods, and new standards that would advance their studies. In 1960 length measurements took a dramatic leap forward when a beam of light became the standard. No longer did all length measurements refer back to a metal bar that might possibly be lost, damaged, or stolen. The new standard would never be destroyed and could be reproduced in any laboratory anywhere in the world. For many years scientists strug- gled to find the best light source. After many discussions and tests it was decided that passing a current of electricity through the element Krypton-86 would be the best choice, since this particular element produces a pure light of only one wavelength. The length of one meter is equal to an established number of the wavelengths of this orange-red light.

Scientists finally had a standard that remained constant, and the world would no longer need to rely on a man-made piece of metal which was subject to the subtle erosion of time. But the krypton light has one serious drawback: it can only be used to measure lengths of up to about eight inches. Beyond that distance the interference pattern of the wavelength becomes indis- tinct. To measure longer distances it is necessary to make several measurements and add them together. In 1965 scientists began studying a new source of light called a laser. There is almost no limit to the length and accuracy of measurements that will be possible with the laser beam once a few problems are overcome.

ACCURACY OR PRECISION Most people don't realize there is a difference between accuracy and precision. Accuracy tells how close the result is to the true value of a measurement. Precision tells how close to a true answer the tools and methods of the measurement will allow you to be. Even scientists using the most advanced equipment and techniques will admit there is no such thing as a perfect measurement—all measurement is approximate!

Before you decide how accurate or precise a measurement should be, you need to ask your- self why you want to make the measurement. Suppose you were trying to determine if a refrigerator would fit through a doorway in your house and you didn't have anything to measure with. You could take a piece of string and hold it up to the insides of the doorway. If you then held that same piece of string up to the refrigerator and had space left on each

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side you would be accurate enough to know it would fit. However, if you wanted to install a door in that same space, you would need to be more precise with your measurement to make sure the door would operate properly.

We have discussed the importance of expressing measurements in terms that are relative to the object you are measuring (two yards for a first down, instead of seventy-two inches). It is also equally important to use the proper measuring instrument. Different occupations use various tools to take measurements depending on the job being performed and the degree of accuracy needed. A carpenter using a tape measure to build a house would be extremely 1 th pleased if all measurements were within /16 of an inch. On the other hand, a machinist making pistons to fit the cylinders in an engine would need to make measurements much more precise than he could accomplish with the tape measure. He would need to use a 1 th micrometer (a device capable of measuring accurately to within /1000 of an inch) since even slight variations in the size of the pistons would be unacceptable. Surveyors, astronomers, scientists, carpenters, automotive technicians, and people in many other occupations use special instruments to make measurements as small as the width of an atom and as large as the distance to other galaxies.

CUSTOMARY MEASUREMENT UNITS In its simplest form, measuring is counting. Units are counted—whether they are yards or meters, inches or centimeters. Every measuring system must begin with a well-defined unit or set of units. Each unit is a fixed quantity and is usually part of a scale of units, large and small. The scale of units of length in the customary system includes inches, feet, yards, and miles. The table below shows the most widely used standards of linear measurement for the customary system. Customary Linear Measurements

12 inches == 1 foot 36 inches = 3 feet == 1 yard 5,280 feet = 1,760 yards == 1 mile

Since most of the measurements you will make using the customary system involve feet, inches, and fractions of inches, we will concentrate most of our attention on these units. When writing measurements, the ( ' ) mark is used to indicate feet and the ( " ) mark is used to indicate inches. Two feet is written as 2'. Six and one-half inches is written 1 as 6 /2".

Just as the foot is divided into twelve equal parts, the inch is also divided into smaller equal units called fractions, which comes from the Roman word fractus, meaning broken. In other words, the inch is broken into smaller units to allow us to measure more accurately and 1 1 1 1 measure things smaller than an inch. We get smaller fractional units ( /2", /4", /8", /16", etc.)

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by halving the inch, then halving the half-inch, and so on. Most rulers and tape measures are divided into sixteenths, or sometimes thirty-seconds of an inch. These are called fractional inch rulers. You can determine how the ruler you are using is divided by counting the num- 1 ber of lines in one inch. Throughout this manual we will only deal with measurements of /16" or larger, and all of the ruler diagrams will be divided into sixteenths. Let’s begin by defining what the various lines on a ruler indicate.

1 2 3 4 5

The longest vertical lines on any customary ruler indicate the inch marks.

1/2 1 1/2 2 1/2 3 1/2 4 1/2 5 1/2

Halfway between the inch marks are the next longest lines. They are used to indicate half-inches.

1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/2 1/2 1/2 1/2 1/2 1/2 1 2 3 4 5

The next longest lines indicate quarter-inches.

1/8 5/8 1/8 5/8 1/8 5/8 1/8 5/8 1/8 5/8 1/8 5/8 3/8 7/8 3/8 7/8 3/8 7/8 3/8 7/8 3/8 7/8 3/8 7/8 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/2 1/2 1/2 1/2 1/2 1/2 1 2 3 4 5

The next longest lines indicate eighth-inches.

1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/2 1/2 1/2 1/2 1/2 1/2 1 2 3 4 5

The next longest lines indicate sixteenth-inches.

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When you begin to measure, it is critical to align the left edge of your ruler with the edge of the object you want to measure. If the object’s length is longer than one inch, simply read the closest inch mark to the left, and then the fractional inch mark.

What is the length of this line?

1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/2 1/2 1/2 1/2 1/2 1/2 1 2 3 4 5

1 2 /2" is the correct measurement.

What is the length of this line?

1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/4 3/4 1/2 1/2 1/2 1/2 1/2 1/2 1 2 3 4 5

3 1 /4" is the correct measurement.

Use a six- or twelve-inch ruler to measure the following lines. Write your measurement in the space provided, and remember to include the (") sign to indicate inches.

A. ______

B. ______

C. ______

D. ______

E. ______

" " " " " ) / = E 5 = D / 3 = C / 1 = B / 4 = (A

8 8 16 4

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METRIC MEASUREMENT UNITS Although at first glance the metric system of measurement looks complicated with all its prefixes and factors of ten, in reality it is quite simple. All linear measurements are based on the meter. Larger and smaller units are formed by dividing or multiplying the meter by ten or factors of ten. For example, the prefix centi means hundredth part, and centimeter is one-hundredth of a meter. The prefix milli means thousandth part, and millimeter is one- thousandth of a meter. On the other side of the scale, the prefix kilo means one thousand, and one kilometer is one thousand meters. Addition, subtraction, multiplication, and division of metric measurements are easily performed since all measurements can be converted from one unit to the next by simply moving the decimal point. The table on page 11 shows the most common metric measurements and their values.

Rather than trying to memorize all the metric prefixes and their values, you should get along fine by remembering four basic units: millimeters, centimeters, meters, and kilometers. When writing metric measurements the following symbols are used:

mm = millimeters cm = centimeters m = meters km = kilometers

Since most of the measurements you will need to be able to perform will involve millimeters and centimeters, all of the exercises will concentrate on these two units. Metric rulers are divided into centimeters and millimeters, allowing you to measure small distances fairly accurately. Let's look at what the lines on a metric ruler indicate.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

The longest lines on any metric ruler indicate centimeters.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

The short lines indicate millimeters. Halfway between any two centimeter marks is a line that is longer than those used to indicate millimeters, but shorter than centimeter lines. It is used to indicate a distance of five millimeters—very helpful when you are measuring short distances.

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Before we begin to do some practice measuring, you need to understand that you must keep your measurements in like units. When using the customary system, you could list a single 1 1 measurement in different units (2' 4 /2"; that is, 2 feet and 4 /2 inches). Although you can express any metric measurement in either centimeters or millimeters, don't begin listing measurements in centimeters and then switch to millimeters. Let's look at some examples.

Can you tell how long this line is?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

It is longer than 7 centimeters, yet shorter than 8 centimeters. You cannot say this line is 7 cm 4 mm long. There are two ways you can express this measurement. If you are expressing it in centimeters you would say it is 7.4 cm. Since you know there are 10 millimeters in each centimeter you could also say the measurement is 74 mm. Either way is correct, but you must stay consistent with any other measurements you will be making.

Use the following lines to do some practice measuring. In the space at the left, write the measurement in centimeters. Use the space at the right to write the measurement in millimeters. Remember to include cm or mm to indicate centimeters or millimeters.

A. ______

B. ______

C. ______

D. ______

E. ______(A = 4.5 cm; 45 mm B = 6.1 cm; 61 mm C = 9 cm; 90 mm D = .8 cm; 8 mm E = 5.3 cm; 53 mm) 53 cm; 5.3 = E mm 8 cm; .8 = D mm 90 cm; 9 = C mm 61 cm; 6.1 = B mm 45 cm; 4.5 = (A

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CONCLUSION One of the great things about measurement is that it is a truly universal language. A centimeter in Japan is the same as a centimeter in New York. A basic knowledge and understanding of different measurement systems will allow mathematical communication with people anywhere in the world. As the competition for jobs continues to rise, workers who possess good measuring skills will increase their chances of finding employment in many different fields. The following pages contain exercises that will help build your measuring skills. However, there is no substitute for actual hands-on experience. The more you use these skills the easier it will be to tell others just how far a "hop, skip, and a jump" really is!

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TABLES OF LINEAR MEASUREMENTS Customary 12 inches = 1 foot 36 inches = 3 feet = 1 yard 5,280 feet = 1,760 yards = 1 mile

Metric 10 millimeters = 1 centimeter 10 centimeters = 1 decimeter = 100 millimeters 10 decimeters = 1 meter = 1,000 millimeters 10 meters = 1 dekameter 10 dekameters = 1 hectometer = 100 meters 10 hectometers = 1 kilometer = 1,000 meters

TABLE OF EQUIVALENTS

1 millimeter = 0.03937 inch 1 inch == 2.54 centimeters 1 centimeter = 0.3937 inch 1 foot == 0.3048 meter 1 decimeter = 3.937 inches 1 yard = 0.9144 meter 1 meter = 39.37 inches = 1.094 yards 1 mile == 1.609 kilometers 1 kilometer = 0.621 mile

CONVERSION TABLE

To Convert ... Into ... Multiply by ... Centimeters Inches 0.3937 Meters Feet 3.281 Kilometers Miles 0.6214 Inches Centimeters 2.54 Feet Centimeters 30.48 Feet Meters 0.3048 Yards Meters 0.9144 Miles Kilometers 1.609

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Worksheets Part 1

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Fill in the Blanks Use the words listed below to complete the following sentences.

Customary System Metric System Numerator Denominator Millimeter Yard Ruler Centimeter

1. In the metric system of measurement, 1/1000 of a meter is called a ______.

2. The part of a fraction that is listed below the line is called the ______.

3. The ______, which is also referred to as the English or standard system, is the measurement system used in the United States today.

4. One of the instruments used in measuring is called a ______.

5. In the metric system of measurement, 1/100 of a meter is called a ______.

6. In the customary system of measurement, a ______is equal to 36 inches, or 3 feet.

7. Based on increments of ten, the ______is the most common system of measurement, and is used almost everywhere except the United States.

8. The ______is the part of a fraction listed above the line.

Word Scramble Unscramble the following words and list the correct spelling in the space provided.

1. LURRE ______2. NOTCLAUACIL ______3. ETEF ______4. RIMCNETTEE ______5. CACYRUAC ______6. RINLAE SMEERUA ______7. NOCFRITAS ______8. SHECIN ______9. SICNOVRENO ______10. ADEMLIC ______

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Identifying Customary Measurements For the following exercises write the measurement that corresponds with each indicator.

EXAMPLE 11 5 1 3 7 9 /16" 1 /8" 2 /2" 3 /4" 4 /8" 5 /16"

1 2 3 4 5

1. 1 2 3 4 5

2. 1 2 3 4 5

3. 1 2 3 4 5

4. 1 2 3 4 5

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5. 1 2 3 4 5

6. 1 2 3 4 5

7. 1 2 3 4 5

8. 1 2 3 4 5

9. 1 2 3 4 5

10. 1 2 3 4 5

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Customary Measurements Use the customary side of your ruler to measure the following lines. Write each measurement in the space provided. Use the “ sign to indicate inches.

EXAMPLE

1 ______3 /4”

1. ______

2. ______

3. ______

4. ______

5. ______

6. ______

7. ______

8. ______

9. ______

10. ______

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Identifying Metric Measurements—Centimeters For the following exercises write the measurement that corresponds with the indicator. Express each measurement in centimeters (cm).

EXAMPLE

.8 cm 3.1 cm 5.5 cm .8 cm 11.1 cm 13.8 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

2. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

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5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 6. cm

7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 8. cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 9. cm

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Identifying Metric Measurements—Millimeters For the following exercises write the measurement that corresponds with the indicator. Express each measurement in millimeters (mm).

EXAMPLE 8 mm 31 mm 55 mm 80 mm 111 mm 138 mm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

2. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

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5. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 6. cm

7. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 8. cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 9. cm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 10. cm 20 35899 Measurement WORKBOOK 5/6/08 12:45 PM Page 26

Metric Measurements—Centimeters Use the metric side of your ruler to measure the following lines. Write each measurement in centimeters in the space provided. Use (cm) to indicate centimeters.

EXAMPLE

______8.5 cm

1. ______

2. ______

3. ______

4. ______

5. ______

6. ______

7. ______

8. ______

9. ______

10. ______21 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 27

Metric Measurements—Millimeters Use the metric side of your ruler to measure the following lines. Write each measurement in millimeters in the space provided. Use (mm) to indicate millimeters.

EXAMPLE

76 mm

1. ______

2. ______

3. ______

4. ______

5. ______

6. ______

7. ______

8. ______

9. ______

10. ______

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Taking Measurements in the Classroom Using both a customary and a metric ruler, take the following measurements and answer the corresponding questions:

1. Measure your desk from top to bottom a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______

2. Measure the board from top to bottom a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______

3. Measure your pen or pencil a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many half-inches is your pen or pencil? ______

4. Measure your shoe a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many millimeters is your shoe? ______

5. Measure the classroom floor from front to back a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many kilometers is your classroom from front to back? ______

6. Measure one of your textbook covers a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many miles is your textbook cover? ______

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Taking Measurements at Home Using both a customary and a metric ruler, take the following measurements and answer the corresponding questions:

1. Measure a kitchen cabinet from top to bottom a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______

2. Measure your bed from headboard to footboard a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______

3. Measure the case of your favorite CD or DVD a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many half-inches is your CD or DVD? ______

4. Measure a window in your house from one side to the other a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many millimeters is the window? ______

5. Measure your kitchen from one wall to the other a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many kilometers is your kitchen from one side to the other? ______

6. Measure a closet in your house from top to bottom a) Length in inches: ______b) Length in feet: ______c) Length in meters: ______d) Length in centimeters: ______e) How many miles is the closet from top to bottom? ______

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Answer Key Fill in the Blanks (page 13) Word Scramble (page 13) 1. millimeter 1. ruler 2. denominator 2. calculation 3. Customary System 3. feet 4. ruler 4. centimeter 5. centimeter 5. accuracy 6. yard 6. linear measure 7. Metric System 7. fractions 8. numerator 8. inches 9. conversion 10. decimal

Identifying Customary Measurements (pages 14-15)

1 3 1 5 5 3 01. /4”1/16”2/8”3/16”4/8”5/4”

5 1 5 11 13 1 02. /8”1/2”2/8”3/16”4/16”5/2”

7 3 1 1 7 3 03. /16”1/8”2/4”3/2”4/16”5/8”

13 3 5 15 11 04. /16”1/4”2/8”3/16”5”5/16”

15 5 9 1 11 5 05. /16” 1 /8” 2 /16” 3 /2” 4 /16” 5 /8”

1 1 7 5 3 15 06. /8” 1 /4” 2 /16” 3 /16” 4 /4” 5 /16”

1 3 1 5 7 3 07. /2” 1 /8” 2 /4” 3 /8” 4 /16” 5 /8”

5 3 3 3 13 7 08. /16”1/16”2/8”3/4”4/16”5/8”

9 5 1 7 1 1 09. /16”1/16”2/2”3/16”4/8”5/4”

3 1 5 13 5 10. /8” 1 /2” 2 /8” 4” 4 /16” 5 /8”

Customary Measurements (page 16 ) 1 7 7 3 5 01. 3 /4” 3. 3 /8” 5. 3 /16” 7. /4” 09. 4 /16” 1 1 3 5 1 02. 1 /8” 4. 4 /2” 6. 2 /8” 8. 3 /8” 10. 2 /2”

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Identifying Metric Measurements—Centimeters (pages 17-18) 01. 1.3 cm 2.9 cm 4.7 cm 7 cm 9.7 cm 12.9 cm 02. 2.1 cm 4 cm 7.6 cm 10.3 cm 12.5 cm 14.4 cm 03. .5 cm 2.8 cm 4.6 cm 7.2 cm 10.9 cm 13 cm 04. 1.5 cm 4.2 cm 6.9 cm 9.1 cm 11.7 cm 14 cm 05. .2 cm 2.5 cm 5.2 cm 8 cm 10.6 cm 14.2 cm 06. 1.1 cm 3.3 cm 6.5 cm 8.8 cm 12 cm 14.5 cm 07. .5 cm 2.7 cm 5.9 cm 9.1 cm 11.3 cm 14.7 cm 08. .9 cm 3.6 cm 6 cm 8.2 cm 10.7 cm 13.9 cm 09. 1.5 cm 3.9 cm 6.2 cm 9 cm 12.2 cm 14.8 cm 10. 1 cm 3.3 cm 5.9 cm 8.1 cm 11.3 cm 14.1 cm

Identifying Metric Measurements—Millimeters (pages 19-20) 01. 8 mm 27 mm 47 mm 70 mm 99 mm 131 mm 02. 20 mm 42 mm 76 mm 101 mm 125 mm 147 mm 03. 5 mm 27 mm 52 mm 77 mm 109 mm 133 mm 04. 15 mm 43 mm 69 mm 93 mm 117 mm 140 mm 05. 2 mm 27 mm 52 mm 81 mm 106 mm 137 mm 06. 11 mm 37 mm 63 mm 89 mm 120 mm 145 mm 07. 5 mm 30 mm 59 mm 86 mm 115 mm 140 mm 08. 9 mm 33 mm 60 mm 84 mm 107 mm 139 mm 09. 10 mm 39 mm 64 mm 90 mm 124 mm 148 mm 10. 7 mm 28 mm 54 mm 80 mm 113 mm 142 mm

Metric Measurements—Centimeters (page 21) 01. 9.8 cm 6. 6.2 cm 02. 2.8 cm 7. 1.6 cm 03. 9 cm 8. 3.3 cm 04. 10.5 cm 9. 11 cm 05. 7.7 cm 10. 6.4 cm

Metric Measurements—Millimeters (page 22) 01. 99 mm 6. 22 mm 02. 18 mm 7. 6 mm 03. 80 mm 8. 53 mm 04. 106 mm 9. 71 mm 05. 47 mm 10. 65 mm

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Worksheets Part 2

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Adding Fractional Measurements Let's look at adding fractional measurements. All fractions have a numerator (the number above the line) and a denominator (the number below the line). The denominator tells you the total number of parts into which the inch has been divided. The numerator counts the 3 number of parts actually used. In the fraction /8", 3 is the numerator and 8 is the denominator. What this fraction tells us is that the inch has been divided into eight equal parts, and that we have used three of them. When you add fractions that have the same denominator, you simply add the numerators. 1 3 4 Example: /8" + /8" = /8"

But in order for a fraction to be completely correct, you must express it in its simplest form. Any time you can divide the numerator and denominator by the same number greater than 4 1—for instance, in the example above, looking at /8", both the 4 and the 8 can be divided by 4—you must “reduce the fraction” to its simplest form. In this case, after dividing the 4 and 4 1 the 8 by 4, the fraction /8" becomes /2". . 4 . 4 = 1 4 = 1 8 . 4 = 2 8 2

Finding Common Denominators In order to add fractions with different denominators, you must first find the common denominator. Common denominators show us how fractions that look different can be made to look 3 7 the same. Suppose you want to add /8" to /16". Before you can add these two measurements, you must find a number that is common to both 8 and 16 . . . a common denominator. Remember—you can change the look of a fraction without changing its value by multiplying both the numerator and denominator by the same number. Changing denominators to express different units in like terms is called conversion. 2 x 3 = 6 2 x 8 = 16

6 3 6 7 13 /16 has the same value as /8. You can now add the two measurements together: /16" + /16" = /16"

1 5 3 Let's look at another example. Suppose you need to add /2" + /8" + /16". You must first convert all denominators to a common value of 16.

1 8 5 10 /2" = /16" and /8" = /16"

8 10 3 21 Your problem now looks like this: /16" + /16" + /16" = /16"

Often when adding fractions the numerator will be greater than the denominator. This is called an improper fraction. Whenever the numerator is greater than the denominator the value of the fraction will be greater than 1. To make the fraction read correctly you must reduce it by dividing the numerator by the denominator.

. 21 5 21 . 16 = 1 with a remainder of 5. The correct answer is /16" = 1 /16"

1 5 3 5 /2" + /8" + /16" = 1 /16" 28 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 34

Adding Customary Measurements Use the Customary side of your ruler to measure the following lines. After you have listed each measurement in the space provided, add the three measurements together to find the sum. Remember, in order to add fractions, you will need to find the common denominators. Fractions must be expressed in the simplest form.

EXAMPLE

1 4 1 /2”= 1/8”

3 6 2 /4”= 2/8”

1 1 1 /8”= 1/8”

11 3 TOTAL 4 /8”= 5/8”

TOTAL =

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TOTAL =

TOTAL = 30 35899 Measurement WORKBOOK 5/6/08 12:46 PM Page 36

TOTAL =

TOTAL = 31 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 37

TOTAL =

10.

TOTAL = 32 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 38

Taking Measurements on the Job 1. Imagine that you have just started working in a fabric store. A woman calls to order a length of blue ribbon. You tell her that you will cut it for her when she comes into the store, but she asks if you can have it ready for her when she arrives, as she is in a rush. She gives you the following measurements and asks you to add them and cut one piece of ribbon that matches the total of these amounts exactly:

1 3 4 11 inches; 15 /2 inches; 2 feet; 43 /8 inches; 3 /16 inches; 5 feet

What is the total length of ribbon you need in inches? In feet?

2. You are working in an ice cream store and the owners have decided to redecorate. You are on the job one day when your boss calls—she has found a great wallpaper border for the room, but she doesn’t have the correct measurements with her for the store. She asks if you can measure the width of each of the four walls, add an extra 18 inches, and give her the total.

5 5 You measure the walls and get the following lengths: 12’ 7”; 14’ /16”; 12’ 7”; 14’ /16”.

With the extra 18 inches, what is the total measurement you should give your boss in feet? In inches?

3. In the shoe department where you work, the staff is reorganizing the storeroom. There is one empty wall left, and the staff is trying to determine how many shoeboxes will fit across the length of the wall, if the boxes are stored horizontally. You measure the length of the 3 wall to be 9 feet /8 inches. Other staff members tell you that they are hoping to fit 8 shoeboxes against this wall lengthwise. Four of the shoeboxes are exactly one foot each, 5 lengthwise. The other four shoeboxes are 1’ /6”.

Will these eight shoeboxes fit against the wall? Why or why not?

4. An architecture firm is testing your knowledge of measurement and fractions, and they ask you the following question: What common denominator will work for the following fractions? 2 6 8 13 /3; /7; /9; /21

After you find the common denominator and add these fractions together, what is the sum?

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Answer Key Adding Customary Measurements (pages 29-32) 7 7 75 55 1. /8” = 1 /86” 2. 1 /8”1 =1 /81” 1 22 33 66 0 3 /4”=3/81”2/41”= 2 /81” 1 44 11 22 0 1 /2”=1/81”2/41”= 2 /81” 13 5 13 5 0 4 /8” = 5 /8”5/81” = 6 /8”

3 73 15 15 03. 1 /16”= 1 /16” 0 4. 1 /16”= 1 /16” 7 14 31 68 0 2 /8”=2/16”2/21”= 2 /16” 1 44 15 10 0 1 /4”=1/16”1/81”= 2 /16” 21 5 33 1 0 4 /16” = 5 /16”3/16” = 5 /16”

7 77 11 11 5. 1 /16”= 1 /16” 0 6. 2 /4”1 =2/44” 1 14 31 62 0 2 /4”=2/16”1/21”= 1 /4” 4 11 11 0 3” = 3” /16” 3 /41”= 3 /46” 11 11 34 0 6 /16” = 6 /16” 6 /46” = 7”

7 77 11 11 7.1 /8”= /86” 0 8. 2 /16”= 2 /16” 1 14 33 66 0 1 /2” = 1 /86” 2 /81” = 2 /16” 7 17 4 13 13 0 1 /8”=1/86” /16 3 /16”= 3 /16” 18 2 11 10 5 0 2 /8” = 4 /8”= 4 /4”7/16” = 7 /8”

3 76 11 11 9. 2 /4”=2/86” 0 10. 1 /4”6 =1/4” 3 13 31 62 0 2 /8” = 2 /86” 3 /21” = 3 /4” 3 16 4 13 13 0 1 /4”=1/86” /16 1 /46”= 1 /4” 15 7 16 2 1 0 5 /8” = 6 /8”5/4” = 6 /4”= 6 /2”

Taking Measurement on the Job (page 33) 1 9 1 9 1. 157 /8 inches (156 /8); 13 feet, 1 /8 inches (13 feet, /8 inch)

5 5 5 2. 54 feet, 8 /8 inches (52 feet, 14 /8 inches plus 18 inches); 656 /8 inches

1 20 3. Yes. The length of the shoeboxes equals 8 feet, 3 /3 inches (8 feet /6 inches), less than the length of the wall.

2 191 4. Common denominator is 63; Sum is 3 /63 inches ( /63 inches)

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For Discussion

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Measurement at Work Systems of measurement, measurement knowledge, and measurement tools are everyday aspects of many careers, jobs, and tasks. The film featured some professionals who utilize measurement regularly as a key part of their working lives. Why do architects need to understand measurement? Why is measurement crucial to success as a carpenter or contractor? What about measurement on a larger scale, such as in astronomy?

When considering measurement and careers, there are certain jobs that immediately come to mind, for instance, builders, construction workers, interior designers, architects, and city planners. Can you think of examples in each of these careers in which measurement might come into play? For example, interior designers must know the dimensions of the rooms with which they are working before ordering furniture or flooring. A builder also has to take measurement very seriously while constructing new buildings and adding on to exist- ing ones. What might be the result if a wall turned out to be too short to reach the other side of the building, or if the opening for a window was longer on one side than the other?

What are some other careers that use measurement? Consider a cartographer, or mapmak- er—someone who creates maps using many measurement skills and related tools, such as latitude and longitude. Think about maps: they have to accurately represent distances on a much smaller scale than real-life. How do you think a cartographer is able to accomplish this? http://math.rice.edu/~lanius/pres/map/ is an excellent resource for learning more.

Another career in which measurement plays a central role is that of a surveyor. Surveyors might collect information about land and create maps of this data, maps that often become legal documents. For instance, surveyors might determine the exact boundaries of a piece of property, perhaps doing so through technological means. Surveyors working in the construction field might verify buildings against their original plans, and hydrographic surveyors might map out the landscape under water, noting oil deposits or unseen dangers. Without measurement knowledge and tools, these important jobs would not happen successfully.

Even something as seemingly simple as a running race could not take place without measurement. If you are a runner, you might know that you should practice running a certain distance to prepare for a race of that distance. But when it actually comes time for the race, how do you know when to stop, when you have actually covered the distance of the race? Organizers of the event need to measure and map out the course of the race so that runners know when to start and stop! What tools and skills do you think they use to do so?

What are some other ways in which measurement affects our daily lives? Brainstorm with a partner or the class to create a list.

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Notes 35899 Measurement WORKBOOK 11/13/06 3:58 PM Page 44

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