7.6 Customary Units of Weight and Capacity

Transcription

1 Chapter 7. Multiplication and Division of Fractions 7.6 Customary Units of Weight and Capacity Introduction Weighing in on Animals Julie has decided that her favorite rainforest topic has to do with the animals. She reads that the red-eyed tree frog weighs about 15 ounces while an male adult gorilla usually weighs 450 pounds. Julie begins writing down facts about each animal in her journal. She isn t sure which facts she ll use in her final report, but she is fascinated with all of the different types of animal species that are found in the rainforest. While she is working, her teacher Mr. Gibbons asks her how it is going. Julie begins to tell him about the gorilla and the tree frog. Wow, Mr. Gibbons says. I wonder how many tree frogs it would take to equal the weight of one gorilla, or how many 90 pound girls it would take? I don t know, says Julie beginning to think about all of the numbers in her mind. Sounds like a problem worth investigating to me, Mr. Gibbons smiles as he walks away. Julie begins by drawing a picture of a balance scale. On one side she draws a gorilla and on the other side she draws a tree frog. Then Julie begins her calculations. You will need information about weight and about the customary units of measurement to figure out this problem. This lesson will teach you all that you need to know. 503

2 7.6. Customary Units of Weight and Capacity What You Will Learn In this lesson you will learn to do the following things: Identify equivalence of customary units of weight. Identify equivalence of customary units of capacity. Choose appropriate customary units of weight or capacity for given measurement situations. Solve real-world problems involving customary measures of weight or capacity. Teaching Time I. Identify Equivalence of Customary Units of Weight You have already learned about measuring length using the customary system of measurement. Remember that the customary system of measurement is what we use here in the United States and it contains units like inches, feet, yards and miles. The metric system is the other system of measurement that is used in science and in countries outside of the United States. This lesson will focus on customary units of weight and volume. Let s begin by looking at the customary units of weight. What are the customary units of weight? First, what do we mean when we talk about weight? We mean the heaviness or the way a mass of something or someone feels due to gravity. The customary units for measuring weight are ounces, pounds and tons. An ounce is the smallest common unit of weight, a pound is what we commonly use for measuring medium sized objects and a ton is what we use to measure very large objects. What about equivalence? Remember, when we see the word equivalent we are referring to something being equal to something else. When working with measures of weight, we can compare the equivalence of a small unit to a larger one. Here are the customary units of equivalence. Here are the units from smallest to largest. 1. Ounce 2. Pound 3. Ton We can find equivalent measures for each unit by using the information in each arrow. We can convert from a larger unit to a smaller unit by multiplying. We can convert from a smaller unit to a larger unit by dividing. 504

3 Chapter 7. Multiplication and Division of Fractions Here is an example. Example How many ounces are 3 pounds of stones? To solve this problem, we need to convert pounds to ounces. A pound is larger than an ounce, so we are going to multiply. There are 16 ounces in one pound. We can multiply the number of pounds times 16 and this will give us the total number of ounces = 48 Our answer is 48 ounces. We can also convert a smaller unit to a larger unit. To do this, we would divide. Example How many tons is 6200 pounds? To solve this problem, we are going to divide. There are 2000 pounds in one ton, so we are going to divide 6200 pounds by 2000 to get our answer in tons = 3.1 tons You can also write your answer in different forms. You could write it as a fraction, a decimal or with a remainder. Here is an example. Example Problem: 100 ounces = lb? We solve this by dividing 100 by 16, since there are 16 ounces in one pound. Fractional answer: = = lb Decimal answer: = = 6.25 lb Remainder answer: = 6 R 4 = 6 lb 4 oz Now it s time for you to try a few of these on your own. Convert the following units of weight. You may write your answer as a fraction or a decimal when necessary tons = pounds ounces = pounds pounds = tons 505

4 7.6. Customary Units of Weight and Capacity Take a few minutes to check your work with a friend. Did you write your answers in fraction form or decimal form? Be sure that both answers match regardless of the form they are written in. II. Identify Equivalence of Customary Units of Capacity We just finished learning about equivalence regarding customary units of weight. We can also find equivalent measures for customary units of capacity. By capacity, we mean volume or the amount of liquid an item can hold. Sometimes, we hear the word capacity with containers or with a milk jug that is one gallon. There are several customary units of capacity. What are the customary units of capacity? Here are the common units from the smallest to the largest. 1. Fluid ounces (fl. oz) 2. Cups 3. Pints 4. Quarts 5. Gallons Sometimes, you will have to figure out how many cups are in a pint or how many quarts are in a gallon. Often, these types of conversions are necessary when you are doing an activity involving liquids, like cooking. To convert different units of capacity, you need to know how much of one unit is equal to another unit. Here is a chart to show you equivalent customary units of capacity. To use the table, make sure you match up one of the red numbers with the units you are changing to. For example, the basic relationship between cups and fluid ounces is 1 cup = 8 fl oz. Between quarts and pints, the basic relationship is 1 qt = 2 pt. Between gallons and pints: 1 gal = 8 pt. Example How many cups are in 36 fluid ounces? 506

5 Chapter 7. Multiplication and Division of Fractions First, figure out if you need to multiply or divide. Check units. fluid ounces (small) to cups (large) = DIVIDE Next, multiply by what? Go to the table. 8 fl oz = 1 cup = DIVIDE BY 8 Finally, Calculate. 36 8=4 1 2 cups Our answer is 4 1 2cups or 4.5 cups. Example How many ounces are there in 4 quarts? First, figure out if you need to multiply or divide? Check units. quarts (large) to ounces (small) = multiply Next, Divide by what? Go to the table. 32 fl. oz = 1 qt = Multiply by 32. Finally, Calculate.32 4 = 128 fluid ounces Next, it is time for you to practice. Use the chart to find equivalent units quarts = pts gallons = quarts fl. ounces = cups Take a few minutes to check your work with a partner. III. Choose Appropriate Customary Units of Weight or Capacity for Given Measurement Situations Choosing the correct units can make all the difference for a measurement. You would not measure how tall you are in miles. Neither would you measure length of a football field in inches. The same idea applies for weight and volume. When measuring to cook, it could be pretty complicated if you were trying to measure cups of water in ounces. Think of how challenging that would be as you are measuring. To get an idea of the size of the units of weight and volume, take a look at the table below. 507

6 7.6. Customary Units of Weight and Capacity This chart is useful as a reference for many of the different ways to measure weight and capacity. Which unit would you use to measure each of the following items? 1. A baby bottle of milk? 2. A cord of wood 3. Water for a cake? Take a few minutes to check your answers with a neighbor. 508

7 Chapter 7. Multiplication and Division of Fractions Real Life Example Completed Weighing in on Animals Now it is time to use what you have learned. Begin, by rereading this problem and underline all of the important information. Julie has decided that her favorite rainforest topic has to do with the animals. She reads that the red-eyed tree frog weighs about 15 ounces while an male adult gorilla usually weighs 450 pounds. Julie begins writing down facts about each animal in her journal. She isn t sure which facts she ll use in her final report, but she is fascinated with all of the different types of animal species that are found in the rainforest. While she is working, her teacher Mr. Gibbons asks her how it is going. Julie begins to tell him about the gorilla and the tree frog. Wow, Mr. Gibbons says. I wonder how many tree frogs it would take to equal the weight of one gorilla, or how many 90 pound girls it would take? I don t know, says Julie beginning to think about all of the numbers in her mind. Sounds like a problem worth investigating to me, Mr. Gibbons smiles as he walks away. Julie begins by drawing a picture of a balance scale. On one side she draws a gorilla and on the other side she draws a tree frog. Then Julie begins her calculations. Next, it is time to answer the two questions. The first one is how many tree frogs will it take to equal the weight of one gorilla. Julie begins by converting pounds to ounces. 450 pounds (Gorilla) = ounces To solve this, we multiply 450 by 16 since there are 16 ounces in one pound. 509

8 7.6. Customary Units of Weight and Capacity pounds = 7200 ounces. Next, the tree frog weighs 15 ounces. Julie divides 7200 by 15. She gets an answer of 480. It will take 480 tree frogs to equal the weight of one gorilla. The second question is the one that Mr. Gibbons asked Julie. How many 90 pound girls is equal to one gorilla? Julie divides 450 by = 5 It takes five 90 pound girls to equal one gorilla. Vocabulary Here are the vocabulary words that are found in this lesson. Weight measurement of the heaviness or mass of someone or something Ounces the smallest common unit of weight in the customary system, used to measure very small items. Pounds the most common unit for measuring weight, most things are measured in pounds. Tons the largest common unit for measuring weight-very large items are measured by the ton-for example, a car or truck. Fluid Ounce the smallest common unit for measuring liquid capacity. A baby bottle is measured in fluid ounces. Cup Pint a common small unit for measuring liquid capacity. 2 cups is equal to one pint of liquid capacity. Quart 2 pints is equal to one quart of liquid capacity. Gallon the largest common unit of liquid capacity Resources Here are a few websites to read more about the animals of the rainforest. 510

9 Chapter 7. Multiplication and Division of Fractions Technology Integration MEDIA Click image to the left for more content. KhanAcademyUS Customary and MetricUnits MEDIA Click image to the left for more content. James Sousa Converting Between Unitsof Volume in the Customary System MEDIA Click image to the left for more content. James Sousa Converting Between Unitsof Weight in the Customary System Other Videos: This is a great video on the customary and metric units of weight and capacity. Time to Practice Directions: Convert each customary unit of weight to an equivalent form ounces = pounds 2. 6 pounds = ounces 511

10 7.6. Customary Units of Weight and Capacity pounds = ounces ounces = pounds 5. 9 pounds = ounces pounds = tons 7. 4 tons = pounds tons = pounds pounds = tons tons = pounds Directions: Convert each customary unit of capacity to an equivalent form cups = fl. oz fl. oz = cups cups = pints pints = cups quarts = pints gallons = quarts quarts = gallons quarts = gallons gallon = pints fl. oz = pints Directions: Name the appropriate unit of measure for each item below. 21. A television set 22. A baby bottle 23. A bucket of milk 24. An automobile 25. The water in a pool 26. A pile of pennies 512