# Capacity. Assessment Management

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1 Capacity Objective To review units of capacity. epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family Letters Assessment Management Common Core State Standards Curriculum Focal Points Interactive Teacher s Lesson Guide Teaching the Lesson Ongoing Learning & Practice Differentiation Options Key Concepts and Skills Use division to solve conversion problems. [Operations and Computation Goal 4] Describe relationships among units of capacity. [Measurement and Reference Frames Goal 3] Key Activities Students review equivalencies between units of capacity. They start a classroom Liter and Milliliter Museum. Students compare capacities by measuring. Key Vocabulary cup pint quart gallon capacity liter milliliter Materials Math Journal 2, pp. 305, 305A, and 305B Student Reference Book, p. 137 Study Link 11 6 measuring cup empty milk cartons (pint, quart, 1_ 2 gallon, gallon) chart paper (optional) per group: 1 eyedropper, 1 liter pitcher, 1 graduated beaker, 2 liters of water slate index cards containers of various capacities Creating a Bar Graph Math Journal 2, p. 306 Student Reference Book, p. 302 Students create a bar graph to display population data. Ongoing Assessment: Informing Instruction See page 887. Math Boxes Math Journal 2, p. 307 Students practice and maintain skills through Math Box problems. Ongoing Assessment: Recognizing Student Achievement Use Math Boxes, Problem 4. [Measurement and Reference Frames Goal 3] Study Link Math Masters, p. 334 Students practice and maintain skills through Study Link activities. READINESS Estimating Capacity Math Masters, p. 389 empty containers of various sizes pourable substance, such as sand Students sort containers according to capacity. EXTRA PRACTICE 5-Minute Math 5-Minute Math, p. 132 Students convert among customary units of capacity. ELL SUPPORT Building a Math Word Bank Differentiation Handbook, p. 140 Students add the term capacity to their Math Word Banks. Advance Preparation In preparation for the Liter and Milliliter Museum in Part 1, gather containers of various capacities. See page 886 for more information. For Part 1, you will also need a 1-liter pitcher filled with water, a milliliter of water held in an eyedropper (20 drops), and 5 additional containers of varying capacities (under 2 liters). For the optional Readiness activity in Part 3, identify several containers by letter (A, B, C, ), designating a middle-size container as the target capacity. Teacher s Reference Manual, Grades 4 6 pp. 13, 44 46, , , Unit 11 3-D Shapes, Weight, Volume, and Capacity

2 Getting Started Mental Math and Reflexes Pose problems involving the multiplication of a fraction by a whole number. Have students find each product in simplest form. Suggestions: 10 1_ 2 = _ 10 = 7 7 1_ 2 = 3 1_ _ 6 = _ 9 = _ 4 = _ 8 = _ 5 = 2 2_ 5 6 3_ 8 = 2 1_ 4 Math Message Fill in the missing numbers in the Math Message problems at the top of journal page 305. Study Link 11 6 Follow-Up Have partners compare answers and strategies. Ask volunteers to share the number sentences they wrote for Problems 9 and Teaching the Lesson Math Message Follow-Up (Math Journal 2, p. 305) ELL WHOLE-CLASS DISCUSSION 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 Ps. Each P represents the word pint. Inside each P, there are two Cs. Each C represents the word cup. Explain that cup, pint, quart, and gallon are units of capacity in the U.S. customary system. Capacity is a measure of the amount of liquid or other substance a container can hold. Capacity is a type of volume measure. Tell students that the liter is a unit of capacity in the metric system. A liter and a quart container will hold approximately the same amount of liquid. Math Message Measuring Capacity 1 pint = 2 cups 1 quart = 2 pints 1 half-gallon = 2 quarts 1 gallon = 4 quarts 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? Units of Capacity 1. Circle the unit you would use to measure each amount. A large jug of milk Water in a thimble A glass of juice 137 Adjusting the Activity Have students create a poster of the gallon frame shown on journal page 305 and display it as a reminder of equivalent capacities in the U.S. customary system. ELL Water in a water cooler Water in a fish tank Liquid in a paper cup A tank of gas A spoonful of oil A large bottle of water A can of soup A U D I T O R Y K I N E S T H E T I C T A C T I L E V I S U A L 2. Explain how you decided which unit to use for a can of soup. Sample answer: I chose milliliters because most cans hold less than a liter. Math Journal 2, p _EMCS_S_MJ2_G4_U11_ indd 305 3/16/11 11:14 AM Lesson 885

3 Comparing Capacities 1. Shade in the appropriate amount to show the capacity of each of your containers. Answers vary. a. b. c. Measuring Capacity in Metric Units (Math Journal 2, p. 305; Student Reference Book, p. 137) WHOLE-CLASS d. U.S. Customary e. Units of Capacity 2. Use the conversion table above to solve the problems. Metric 1 gallon (gal) = 4 quarts (qt) 1,000 milliliter (ml) = 1 liter (L) 1 quart (qt) = 2 pints (pt) 1 milliliter (ml) = 1_ 1,000 liter (L) 1 pint (pt) = 2 cups (c) 1 pint (pt) = 16 fluid ounces (fl oz) a. 6 qt = 12 pt b ml = 8 L c. 3 pt = 48 fl oz d. 6,450 ml = L e. 10 qt = 2 1_ 2 gal f. 500 ml = L g. 4 gal = 64 c h. 32 ml = 0.03 Math Journal 2, p. 305A 305A-305B_EMCS_S_MJ2_G4_U11_ indd 305A f. Circle the container with the largest capacity. Was your prediction accurate? 3/16/11 11:14 AM Tell students that a liter is a metric unit of capacity. Liquids such as water, soft drinks, and fuel are often measured in liters. Smaller amounts of liquid are often measured in milliliters. Have students read Student Reference Book, page 137 and discuss the essay with a partner. Review the relationship between liters and milliliters (1 liter = 1,000 milliliters). Show students the eyedropper and explain that it holds 20 drops of water, which is equivalent to 1 milliliter. Then show them the 1-liter pitcher and explain that this is 1 liter, or 1,000 milliliters. Explain that 1,000 eyedroppers full of water are needed to fill the 1-liter pitcher. Record the following number sentence on the board to illustrate the relationship between these two metric units: 1 liter (L) = 1,000 milliliters (ml) Now have students complete journal page 305 to practice determining the appropriate unit for measuring capacity. Setting up a Liter and Milliliter Museum WHOLE-CLASS 11 7 Solving Capacity Problems 175 Solve. You may draw pictures to help you. 1. Adaline filled her watering can with 1,250 ml of water. After watering her plants she had 485 ml left. How much water did she use? 2. Betty and Don spent the morning squeezing oranges for juice. Betty squeezed 1 2_ 4 L and Don squeezed 1 3_ 4 L. What is the total amount of juice? 3. There are 450 ml of syrup in 1 can. What is the total amount of syrup in 6 cans? 4. Dimitra poured 2_ 5 liter of water into a fish tank. William poured 4_ 5 liter of water into the fish tank. a. How much more water did William pour? 765 ml 3 1_ 4 or L 2,700 ml 2_ 5 L Introduce a project to explore a museum of objects that have different capacities measured in milliliters and liters. Use index cards to label objects in the museum with their capacities. The measuring tools available will determine the range of capacities. Keep a variety of measuring tools near the Liter and Milliliter Museum (for example, an eyedropper, liter pitcher, a measuring cup with a scale in ml, and graduated cylinders of various sizes) so students can measure a wide range of capacities. Discuss the goals for the collection, the kinds of objects to be collected, and the procedures for adding objects to the museum. The procedure for adding items should probably be managed by students. Ask students to bring in objects for the museum over the next week or two. This project will continue into the next unit. To ensure accuracy and to assess students skill in finding the capacity of different objects, require that every item added to the museum be measured by two or three students working independently. This project will be revisited in Lesson b. How many milliliters is that? 400 ml 5. Raina brought a 1,500 ml jug of water to the school picnic. Her water jug has enough water to fill 5 glasses. How much does each glass hold? 6. The teacher set out 24 bowls of glue for the students to use for an art project. Each bowl holds 75 ml of glue. How much glue did the teacher need to fill all the bowls? Math Journal 2, p. 305B 300 ml 1,800 ml Comparing Capacity Using Metric Measures (Math Journal 2, p. 305A) Have students compare the capacity of 5 different size containers. Ask students to predict which containers have the largest and 305A-305B_EMCS_S_MJ2_G4_U11_ indd 305B 3/16/11 11:14 AM 886 Unit 11 3-D Shapes, Weight, Volume, and Capacity

4 smallest capacities. Then have the students use various measuring tools and water to find and compare the capacities of the five containers and to determine if their predictions were correct. Students shade in the pitchers on journal page 305A to record the capacities. Encourage students to develop personal references for units of capacity as they make and check their predictions. Solving Capacity Number Stories (Math Journal 2, p. 305B) PARTNER Have students solve the capacity number stories on journal page 305B. 2 Ongoing Learning & Practice Number of People (in millions) Largest Cities by Population Tokyo 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. Mexico City Largest Cities by Population New York City São Paulo Cities Mumbai (Bombay) 2. Make three statements comparing the cities in the bar graph. Calcutta Shanghai Example: About 21 million more people live in Tokyo than in Shanghai. Sample answers: About the same number of people live in Mexico City and New York City; about 1 million more people live in São Paulo than Mumbai; about twice as many people live in Tokyo as São Paulo Creating a Bar Graph (Math Journal 2, p. 306; Student Reference Book, p. 302) INDEPENDENT Math Journal 2, p _EMCS_S_MJ2_G4_U11_ indd 306 2/15/11 6:15 PM Students create a bar graph to display population data. Ongoing Assessment: Informing Instruction Watch for students who make incorrect statements for Problem 2, such as About twice as many people live in New York City as Calcutta. Point out that the vertical scale for the number of people in each city begins at 10 million. The bar for New York City may be twice the height of the bar for Calcutta, but the population of New York City is approximately 18 million, and the population of Calcutta is approximately 13 million. Math Boxes (Math Journal 2, p. 307) Ongoing Assessment: Recognizing Student Achievement INDEPENDENT Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson The skill in Problem 6 previews Unit 12 content. Math Boxes Problem 4 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. [Measurement and Reference Frames Goal 3] 5. Add. Math Boxes 1. What is the total number of cubes needed to completely fill the box? 96 cubes 3. When you roll a 10-sided die, about what fraction of the time would you expect a multiple of 3 to come up? 3_ 10 Use a probability term to describe the likelihood of this event. unlikely a = b (-18) = c. 16 = 33 + (-17) Calculate the volume. 9 cm Number model: Volume = 90 cm 3 4. Complete. 5 cm If you travel at an average speed of 50 miles per hour, how far will you travel in a. 3 hours? 150 miles b. 1_ 2 hour? 25 miles 2 cm (9 5) 2 = 90 a. 321 cm = 3.21 m b. 56 cm = 560 mm c. 14 ft 4 in. = 172 in. d. 2 mi = 10,560 ft e. 5.3 km = 5,300 m f. 4 mi = 7,040 yd \$ \$ d. = \$ (-\$57.81) e. -\$ (-\$76.98) = c. 2 1_ 2 hours? 125 miles d. 5 3_ 5 hours? 280 miles 47 Math Journal 2, p _EMCS_S_MJ2_G4_U11_ indd 307 2/15/11 6:15 PM Lesson 887

5 Study Link (Math Masters, p. 334) INDEPENDENT Home Connection Students find containers that hold less than 1 pint, 1 pint, 1 quart, and more than 1 quart. They solve problems about equivalent capacities. 3 Differentiation Options READINESS Estimating Capacity (Math Masters, p. 389) 5 15 Min 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. Name STUDY LINK Capacity Study Link Master 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. 1. Less than 1 Pint Answers vary. bottle of hot chili sesame oil 5 fl oz, 148 ml Pint bottle of cooking oil 16 fl oz, 473 ml 3. 1 Quart 4. More than 1 Quart Complete quarts = pints 6. 3 gallons = cups pints = 4 cups 8. quarts = 12 cups pints = quarts 10. quarts = 2 1_ 2 gallons Practice = 12. = 3 + (-7) = 40 + (-80) (-60) = Math Masters, p _EMCS_B_MM_G4_U11_ indd 334 2/14/11 5:00 PM 888 Unit 11 3-D Shapes, Weight, Volume, and Capacity

6 EXTRA PRACTICE 5-Minute Math 5 15 Min To offer students more experience with units of capacity, see 5-Minute Math, page 132. ELL SUPPORT Building a Math Word Bank (Differentiation Handbook, p. 140) 5 15 Min To provide language support for capacity, have students use the Word Bank Template found on Differentiation Handbook, page 140. 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 889

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