Objective To review customary units of capacity.

1 Teaching the Lesson materials Key Activities Math Journal 2, p. 305 Students review equivalencies between units of capacity. They find the weight of one of Study Link 116 uncooked rice and use this information to estimate the weights of an average Thai and measuring cup Bangladeshi family’s annual rice consumption. empty milk cartons (, quart, 1 Key Concepts and Skills 2 , gallon) • Use division to solve conversion problems. [Operations and Computation Goal 4] 1 12 cups rice • Round to the nearest whole number. [Operations and Computation Goal 6] 1 gallon pourable substance (water, • Estimate weight with and without tools. [Measurement and Reference Frames Goal 1] sand, unpopped popcorn, or light • Describe relationships among customary units of capacity. packing pellets) [Measurement and Reference Frames Goal 3] scale (accurate to nearest ) Key Vocabulary cup • pint • quart • gallon • capacity slate; chart paper 2 Ongoing Learning & Practice materials Students create a bar graph to display population data. Math Journal 2, pp. 306 and 307 Students practice and maintain skills through Math Boxes and Study Link activities. Student Reference Book, p. 302 Study Link Master (Math Masters, Ongoing Assessment: Informing Instruction See page 887. p. 334) Ongoing Assessment: Recognizing Student Achievement Use journal page 307. [Measurement and Reference Frames Goal 3] 3 Differentiation Options materials READINESS ENRICHMENT EXTRA PRACTICE ELL SUPPORT Math Journal 2, p. 305 Students sort Students estimate Students convert Students add Teaching Aid Master (Math Masters, containers according the number of among customary capacity to their p. 389) to capacity. containers needed units of capacity. Math Word Banks. Differentiation Handbook to hold a quantity 5-Minute Math, p. 132 of rice. empty containers of various sizes; empty copy-paper carton; measuring cup; pourable substance, such as sand; and calculator

See Advance Preparation

Additional Information Advance Preparation For the optional Readiness activity in Part 3, identify several containers Technology by letter (A, B, C, …), designating a middle-size container as the target capacity. Assessment Management System Math Boxes, Problem 4 See the iTLG.

884 Unit 11 3-D Shapes, Weight, , and Capacity Getting Started

Mental Math and Reflexes Have students write the greater of two integers on their slates. Suggestions: 15 or –20 15 –24 or –240 –24 11.5 or –11.2 11.5 –3 or 1 1 –103 or –130 –103 –48.5 or 5.3 5.3 45 or –62 45 –65 or –605 –65 –2.98 or –2.89 –2.89

Math Message Study Link 11 6 Follow-Up Fill in the missing numbers in the Math Message Have partners compare answers and strategies. problems at the top of journal page 305. Ask volunteers to share the number sentences they wrote for Problems 9 and 10.

1 Teaching the Lesson

WHOLE-CLASS Math Message Follow-Up DISCUSSION (Math Journal 2, p. 305)

Display the cup, pint, quart, half-gallon, and gallon containers. Ask students to identify each. Review the answers to the Math Message. To support English language learners, have students model the equivalencies by pouring water or another substance from one container into the other. Ask: Did anyone figure out the meaning of the picture next to the Math Message problems? The “frame” is in the shape of the letter G. It represents the word gallon. Inside the G, there are four Qs. Each Q represents the word quart. Inside each Q, there are two Student Page Ps. Each P represents the word pint. Inside each P, there are two Date Time

Cs. Each C represents the word cup. LESSON 11 7 Converting Measurements 137 Explain that cup, pint, quart, and gallon are units of capacity in Math Message Capacity 1 pint 2 cups the U.S. customary system. is a measure of the amount 1 quart 2 of liquid or other substance a container can hold. Capacity is a 1 half-gallon 2 quarts 4 type of volume measure. Tell students that the liter is a unit of 1 gallon quarts Think: How can the picture above help you remember how many cups are in a pint, capacity in the metric system. A liter and a quart container will how many pints are in a quart, and how many quarts are in a gallon? hold approximately the same amount of liquid. Rice Consumption Answers vary 1. Round your answer to the nearest ounce. for Problem 1. One cup of dry (uncooked) rice weighs about 8 . Answers for ELL Problems 2–5 2. Use the answer in Problem 1 to complete the following: Adjusting the Activity assume that the a. 1 pint of rice weighs about 16 ounces. answer for b. 1 quart of rice weighs about 32 ounces. Problem 1 is Have students create a poster of the gallon frame shown on journal c. 1 gallon of rice weighs about 128 ounces. 8 ounces. page 305 and display it as a reminder of equivalent capacities in the U.S. d. 1 gallon of rice weighs about 8 pounds. (1 pound 16 ounces)

customary system. 3. On average, a family of 4 in Bangladesh eats about 170 pounds of rice per month.

a. That is about how many pounds per year?2,040 pounds AUDITORY KINESTHETIC TACTILE VISUAL b. How many ?255 gallons

4. On average, a family of 4 in the United States eats about 120 pounds of rice per year. That is about how many gallons per year?15 gallons

1 5. On average, a family of 4 in Thailand eats about 3 2 gallons of rice per week. a. That is about how many gallons per year?182 gallons

b. How many pounds?1,456 pounds

305 Math Journal 2, p. 305

Lesson 117 885 Student Page

Date Time WHOLE-CLASS LESSON 76 302 Finding the Weight 11 7 Largest Cities by Population ACTIVITY

1. Use the data in the Largest Cities by Population table at the top of Student Reference Book, page 302 to complete the bar graph. Round each figure to the nearest million. of a Cup of Rice

Largest Cities by Population (Math Journal 2, p. 305) 36 34 32

ons) 30 i ll i 28 Tell students that in this lesson they will apply their knowledge

n m 26 i 24 of capacity and weight to compare the consumption of rice in 22 20 18 Bangladesh, the United States, and Thailand. Ask: 16 14 ● Number of People ( 12 How would you measure rice if you needed a certain amount 10 Tokyo Mexico New York São Mumbai Calcutta Shanghai for a recipe? Probably with a measuring cup City City Paulo (Bombay)

Cities ● How would you find the weight of one cup of uncooked rice? 2. Make three statements comparing the cities in the bar graph. Sample answer: Weigh an empty measuring cup. Fill it with Example: About 21 million more people live in Tokyo than in Shanghai. Sample answers: About the same number of rice to the 1-cup level. Weigh the filled cup. Subtract the weight people live in Mexico City and New York City; about 1 million more people live in São Paulo of the empty cup from the weight of the cup containing rice. than Mumbai; about twice as many people live in Tokyo as São Paulo. ● About how many ounces do you think a cup of uncooked rice weighs? (Record a few estimates on the board.) Ask two students to weigh 1 cup of rice as accurately as they can. 1 1 306 Expect a range of 7 to 8 ounces for 1 cup. Have the class round Math Journal 2, p. 306 2 2 the result to the nearest ounce and record it in Problem 1 on journal page 305.

PARTNER Solving Problems Involving ACTIVITY Units of Weight and Capacity (Math Journal 2, p. 305)

Students use the weight of 1 cup of rice to solve Problems 2–5 on journal page 305. These problems involve conversions between gallons and pounds. After a few minutes, bring the class together to go over the answers. Problem 2: Assuming that 1 cup of uncooked rice weighs about Student Page 8 ounces, then 1 pint weighs about 16 ounces; 1 quart about World Tour 32 ounces; and 1 gallon about 128 ounces. Because there are Fascinating Facts 16 ounces in 1 pound, 128 ounces is equivalent to 8 pounds Smallest Countries by Population Largest Cities by Population Country Area (sq ) Population City, Country Population (128 16 8). You can use the same procedure if 1 cup of rice Vatican City 0.17 900 Tokyo, Japan 34,450,000 Tuvalu 10 11,000 Mexico City, Mexico 18,066,000 Nauru 8 13,000 New York City, U.S. 17,846,000 is found to weigh about 7 ounces. Then 1 gallon would weigh Palau 177 20,000 Sao Paulo, Brazil 17,099,000 San Marino 24 28,000 Mumbai (Bombay), India 16,086,000 about 7 pounds. Monaco 0.75 32,000 Calcutta, India 13,058,000 Liechtenstein 62 33,000 Shanghai, China 12,887,000 Problem 3: A family of 4 in Bangladesh eats about 170 pounds Languages with the Most Speakers Speakers Language (in millions) Countries of rice per month. That is equivalent to 2,040 pounds per year. Chinese 873 16 Spanish 322 43 To find the number of gallons, divide the total weight by 8. English 309 107 Hindi 180 17 Portuguese 177 33 2,040 8 255 gallons Bengali 171 9 Russian 145 31 Japanese 122 25 Problem 4: 120 8 15 gallons Cellular Telephone Use 1 Number of Cellular Problem 5: A family of 4 in Thailand eats about 3 gallons of Telephone Subscriptions Subscriptions 2 Country (in millions) per 100 People

Taiwan 25.1 110.8 rice per week. That is equivalent to 182 gallons per year. To find Luxembourg 0.5 106.1 Italy 55.9 101.8 the weight of the rice consumed, multiply 182 by 8. 1,456 pounds Iceland 0.3 96.6 Israel 6.3 95.5 Spain 37.5 91.6 United Kingdom 49.7 84.1 Greece 8.9 78.0 Taiwan has the highest Japan 86.7 68.0 subscription rate for United States 158.7 54.3 cellular telephone use Canada 13.2 41.7 of all countries. Turkey 27.9 40.8 South Africa 16.9 36.4 World 1,340.7 21.9 Student Reference Book, p. 302

886 Unit 11 3-D Shapes, Weight, Volume, and Capacity Student Page

Date Time

LESSON 2 Ongoing Learning & Practice 11 7 Math Boxes 1. What is the total number of cubes needed 2. Calculate the volume. to completely fill the box? 2 cm 96 cubes 5 cm INDEPENDENT 9 cm Creating a Bar Graph ACTIVITY (9 5) 2 90 (Math Journal 2, p. 306; Student Reference Book, p. 302) Number model: Volume 90 cm3

138 138

Students create a bar graph to display population data. 3. When you roll a 10-sided die, about what 4. Complete. fraction of the time would you expect a multiple of 3 to come up? a. 321 cm 3.21 m 3 10 b. 56 cm 560 mm

Use a probability term to describe the c. 14 ft 4 in. 172 in. likelihood of this event. Ongoing Assessment: Informing Instruction d. 2 mi 10,560 ft unlikely e. 5.3 km 5,300 m Watch for students who make incorrect statements for Problem 2, such as 81 f. 4 mi 7,040 yd 129 “About twice as many people live in New York City as Calcutta.” Point out that 5. Add. 6. If you travel at an average speed the vertical scale for the number of people in each city begins at 10 million. The of 50 miles per hour, how far will a. 26 bar for New York City may be twice the height of the bar for Calcutta, but the 46 20 you travel in b. 23 (18) 41 150 population of New York City is approximately 18 million, and the population of a. 3 hours? miles 1 c. 16 33 (17) b. hour? 25 miles Calcutta is approximately 13 million. 2 1 d. $21.27 $36.54 ($57.81) 125 c. 2 2 hours? miles 3 e. $131.09 ($76.98) $208.07 280 d. 5 5 hours? miles

47

307 INDEPENDENT Math Journal 2, p. 307 Math Boxes 11 7 ACTIVITY (Math Journal 2, p. 307)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 11-5. The skill in Problem 6 previews Unit 12 content.

Ongoing Assessment: Math Boxes Problem 4 Recognizing Student Achievement Use Math Boxes, Problem 4 to assess students’ ability to describe the relationships among U.S. customary units of length and among metric units of length. Students are making adequate progress if they are able to complete the equivalencies correctly. Some students may include number models to explain their work. Study Link Master [Measurement and Reference Frames Goal 3] Name Date Time STUDY LINK 11 7 Capacity

Find at least one container that holds each of the amounts listed below. Describe each container and record all the capacity measurements on the label. 137

1. Less than 1 Pint Answers vary. INDEPENDENT Container Capacity Measurements on Label Study Link 11 7 ACTIVITY bottle of hot chili sesame oil 5 fl oz, 148 mL (Math Masters, p. 334)

2. 1 Pint Container Capacity Measurements on Label Home Connection Students find containers that hold bottle of cooking oil 16 fl oz, 473 mL less than 1 pint, 1 pint, 1 quart, and more than 1 quart.

They solve problems about equivalent capacities. 3. 1 Quart Container Capacity Measurements on Label

4. More than 1 Quart Container Capacity Measurements on Label

Complete.

5. 2 quarts 4 pints 6. 3 gallons 48 cups

7. 2 pints 4 cups 8. 3 quarts 12 cups

1 9. 6 pints 3 quarts 10. 10 quarts 2 gallons 2

Practice 11. 3 7 4 12. 4 3 (7) 13. 40 40 (80) 14. 60 (60) 120 Math Masters, p. 334

Lesson 117 887 3 Differentiation Options

READINESS SMALL-GROUP ACTIVITY

Estimating Capacity 5–15 Min (Math Masters, p. 389)

To explore capacity, have students sort empty containers (identified by letter) according to whether they will hold more than, less than, or about the same as a target container. Ask students to label three columns on an Exit Slip (Math Masters, page 389) more than, less than, and about the same. Have them sort the containers according to the categories. Provide students with a pourable substance such as sand, rice, pasta, or beans to check their estimates. Have students rearrange the groups as necessary.

ENRICHMENT SMALL-GROUP ACTIVITY

Modeling the Capacity of 30+ Min Annual Rice Consumption (Math Journal 2, p. 305)

To apply students’ understanding of capacity, have them estimate how many empty copy-paper cartons would be needed to hold a year’s supply of rice for an average Thai family of four. A family of four eats about 182 gallons, or 1,456 pounds, of uncooked rice per year, assuming that 1 gallon of rice weighs about 8 pounds. Display an empty copy-paper carton. Ask students to estimate Student Page about how many cartons of this size would be needed to store all Date Time of the rice. LESSON 11 7 Converting Measurements 137 Math Message Write students’ estimates on the board. Then ask students to

1 pint 2 cups propose a method for checking their estimates. 1 quart 2 pints 1 half-gallon 2 quarts The most obvious approach is to find about how many pounds 1 gallon 4 quarts a copy-paper carton of rice weighs and divide the number of Think: How can the picture above help you remember how many cups are in a pint, how many pints are in a quart, and how many quarts are in a gallon? pounds of rice consumed in a year by the weight of a carton of Rice Consumption Answers vary rice. But this is not practical, because you would need a large 1. Round your answer to the nearest ounce. for Problem 1. One cup of dry (uncooked) rice weighs about 8 ounces. Answers for quantity of rice to fill the carton. Problems 2–5 2. Use the answer in Problem 1 to complete the following: assume that the Another way is to find about how many gallons a copy-paper a. 1 pint of rice weighs about 16 ounces. answer for b. 1 quart of rice weighs about 32 ounces. Problem 1 is carton holds. Then divide the number of gallons of rice c. 1 gallon of rice weighs about 128 ounces. 8 ounces. d. 1 gallon of rice weighs about 8 pounds. (1 pound 16 ounces) consumed in a year by the number of gallons a carton holds. Use any pourable substance to fill the carton to about 1 of 3. On average, a family of 4 in Bangladesh eats about 170 pounds of rice per month. 6 2,040 a. That is about how many pounds per year? pounds its height, measure the material with a measuring cup, and b. How many gallons?255 gallons multiply the result by 6. Divide by 16 to convert the answer 4. On average, a family of 4 in the United States eats about 120 pounds of rice per year. That is about how many gallons per year?15 gallons to gallons.

1 5. On average, a family of 4 in Thailand eats about 3 2 gallons of rice per week. a. That is about how many gallons per year?182 gallons

b. How many pounds?1,456 pounds

305 Math Journal 2, p. 305

888 Unit 11 3-D Shapes, Weight, Volume, and Capacity Once the capacity of a carton has been determined, encourage students to estimate the number of cartons needed to hold the total yearly consumption of rice. Students can check their estimates on their calculators. Have students present their strategies and solutions in a brief report. Sample answer: The 1 capacity of a carton of copy paper is about 72 gallons. This means that 4 cartons hold about 30 gallons and that 24 cartons hold about 180 gallons.

EXTRA PRACTICE SMALL-GROUP ACTIVITY

5-Minute Math 5–15 Min

To offer students more experience with units of capacity, see 5-Minute Math, page 132.

ELL SUPPORT SMALL-GROUP ACTIVITY

Building a Math Word Bank 5–15 Min (Differentiation Handbook)

To provide language support for capacity, have students use the Word Bank Template found in the Differentiation Handbook. Ask students to write the term capacity, draw pictures relating to the term, and write other related words. See the Differentiation Handbook for more information.

Lesson 117 889