Convert Measurement Units

Lesson LESSON 25 Overview Convert Measurement Units

CCSS Focus Lesson Objectives Prerequisite Skills Domain Content Objectives • Distinguish between the customary and Measurement and Data metric measurement systems. • Convert from a larger unit of • Be familiar with measurement units used measurement to a smaller unit Cluster in each system, as well as units of time. A. C onvert like measurement units within of measurement within the same a given measurement system. measurement system. • Compute using whole numbers, decimals, and fractions, including mixed • Convert from a smaller unit of Standard numbers. 5.MD.A.1 Convert among different-sized measurement to a larger unit standard measurement units within a of measurement within the same given measurement system (e.g., convert measurement system. Lesson Vocabulary 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. Language Objectives There is no new vocabulary. Review the Additional Standards • List mathematical relationships of following key terms. 5.NBT.A.2, 5.NF.B.3 (See Standards measurement units within the same • convert to write an equivalent Correlations at the end of the book for system; for example, between ounces measurement using a different unit. full text.) and pounds, or among centimeters, • customary system the measurement meters, and kilometers. system commonly used in the United Standards for Mathematical • Record conversions between different- States that measures length in inches, Practice (SMP) sized measurement units. feet, yards, and miles; liquid volume in SMPs 1, 2, 3, 4, 5, and 6 are cups, pints, quarts, and gallons; and integrated in every lesson through the weight in ounces and pounds. Try-Discuss-Connect routine.* • metric system the measurement In addition, this lesson particularly system that measures length based on emphasizes the following SMPs: meters, liquid volume based on liters, 2 Reason abstractly and and mass based on grams. quantitatively. 5 Use appropriate tools strategically. 7 Look for and make use of structure. Learning Progression *See page 305m to see how every lesson includes these SMPs. In Grade 4 students became familiar with system and reason about converting from the relative sizes of different units within one unit of measurement to another. both the metric system and the customary Students convert measurement units of system. Students used models, such as bar length, capacity, weight, and mass in both models and number lines, to show the the metric and customary systems of relationship between two units of measurement, as well as units of time. measurement and used multiplication to Students multiply and divide with whole convert from the larger unit to the smaller numbers, decimals, and fractions in order unit. Earlier in Grade 5, students multiply to convert measurements. and divide with whole numbers, decimals, In the next lesson, students will solve and fractions, including mixed numbers. word problems involving conversions of In this lesson students gain a conceptual measurement units. In Grade 6 students understanding of the relative sizes of will work with measurement units when measurement units within a measurement they learn about ratios and unit rates.

507a Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. Lesson Pacing Guide Teacher Toolbox Whole Class Instruction Small Group Differentiation SESSION 1 Interactive Tutorial* (Optional) Additional Practice PREPARE Explore Prerequisite Review: Lesson pages 511–512 Multiply and Divide Decimals by Powers Ready Prerequisite Lessons 45–60 min of Ten Grade 4 • Lesson 13 Use Multiplication to Convert Converting Measurement Units Measurements • Start 5 min • Lesson 15 Divide Four-Digit Numbers • Try It 10 min • Discuss It 10 min RETEACH • Connect It 15 min • Close: Exit Ticket 5 min Tools for Instruction Grade 4 SESSION 2 Converting Larger Units to Smaller Additional Practice • Lesson 13 Find Equivalent Measurements Units Lesson pages 517–518 Develop • Lesson 15 Divide Four-Digit by One-Digit • Start 5 min Numbers 45–60 min • Try It 10 min Fluency Grade 5 • Discuss It 10 min Converting Larger Units • Lesson 25 Convert Measurement Units • Model It & Solve It 5 min to Smaller Units • Connect It 10 min • Close: Exit Ticket 5 min REINFORCE Math Center Activity SESSION 3 Converting Smaller Units to Larger Additional Practice Grade 5 Units Lesson pages 523–524 Develop • Lesson 25 Converting Units Vocabulary • Start 5 min Fluency Match 45–60 min • Try It 10 min Converting Smaller Units • Discuss It 10 min to Larger Units • Model It & Solve It 5 min EXTEND • Connect It 10 min Enrichment Activity • Close: Exit Ticket 5 min Grade 5 • Lesson 25 Animal Races SESSION 4 Converting Measurement Units Lesson Quiz Refine • Start 5 min or Digital • Example & Problems 1–3 15 min Comprehension Check 45–60 min • Practice & Small Group Differentiation 20 min Independent Learning • Close: Exit Ticket 5 min PERSONALIZE

Lesson Materials i-Ready Lesson* Lesson Per pair: 2 sets of fraction tiles or circles Grade 5 (Required) Activity Sheet: Math Reference Sheet • Express Measurements in Larger Units Activities Per pair: meterstick Per group: 1-cup measuring cup, 1 pint container, 1 quart container, 6 cups of rice or dried beans Activity Sheet: 1-Centimeter Grid Paper Math Toolkit base-ten blocks, fraction tiles, fraction circles, ruler, fraction bars, number lines, grid paper, thousandths decimal place-value charts, math reference sheet

* We continually update the Interactive Tutorials. Check the Teacher Toolbox for the most up-to-date offerings for this lesson.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 507b LESSON 25 Connect to Family, Community, and Language Development

The following activities and instructional supports provide opportunities to foster school, family, and community involvement and partnerships.

Connect to Family Use the Family Letter—which provides background information, math vocabulary, and an activity— to keep families apprised of what their child is learning and to encourage family involvement. Available in Spanish Teacher Toolbox Convert Measurement Units

ACTIVITY CONVERTING Me Me Un Dear Family, 25 Do this activity with your child to convert measurement units. Materials ruler or measuring tape, sheet of paper

This week your child is learning to convert from Play a game with your child to convert measurements in real-life situations. one measurement unit to another. • Choose a place to mark a starting line. It can be inside your home or outside. Your child is learning to make measurement conversions, such as: Make sure there is enough open space if you choose to play inside.

• from one unit of length to another, using kilometers, meters, and centimeters. • Make a paper ball by crumpling a sheet of paper.

• from one unit of weight to another, using pounds and ounces. • Have your child stand at the starting line and toss the paper ball.

• from one unit of capacity to another, using gallons, quarts, and cups. • Together, measure the length of the toss to the nearest foot. Then convert the length of the toss from feet to inches. [1 foot 5 12 inches] So, multiply the You can describe the same measurement using diff erent units. For example, number of feet by 12 to fi nd the number of inches. 1 kilometer describes the same distance as 1,000 meters. The length is the same. The units used to measure the length are diff erent, so the number of units in the • Take turns tossing the ball, measuring, and converting measurements. measurement is diff erent, too. Look out for other real-life opportunities to practice converting measurements Kilometers are a larger unit of with your child. You might convert measurements when you use a recipe, do a measurement than meters. Since 4.5 kilometers 5 ? meters craft project together, make a home repair, or plan a trip. 4.5 3 1,000 5 4,500 there are 1,000 meters in each 4.5 kilometers 5 4,500 meters kilometer, you can multiply the length, or distance, in kilometers by 1,000 to convert the measurement to meters.

Meters are a smaller unit of measurement than kilometers. 6,700 meters 5 ? kilometers 6,700 4 1,000 5 6.7 Since 1 kilometer is equivalent 6,700 meters 5 6.7 kilometers to 1,000 meters, you can divide the length, or distance, in meters by 1,000 to convert the measurement to kilometers.

Your child is becoming familiar with the relative sizes of units by identifying which units are larger and which units are smaller. Also, as your child practices converting units, he or she is applying multiplication and division skills.

Invite your child to share what he or she knows about converting measurement units by doing the following activity together. 507 508 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 507 508 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted.

Goal Math Talk at Home The goal of the Family Letter is to provide opportunities for Encourage students to look for objects at home that can be students and their families to practice converting from one measured and then decide what unit of measurement is best to use. measurement unit to another. Conversation Starters Below are additional conversation starters students can write in their Family Letter or math journal to engage Activity family members: Applying what students know about units of measurement and • When measuring a long distance, what unit of measurement do benchmark measurements will help them identify relationships you use? between one measurement unit and another. Students will make paper balls and measure the distance that the paper balls are • Have you ever had to convert from one unit of measurement to thrown in feet and then convert to inches. another? When?

507–508 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. Connect to Community and Cultural Responsiveness Use these activities to connect with and leverage the diverse backgrounds and experiences of all students.

Session 1 Use with Try It. Sessions 1–4 Use anytime during the sessions. • Students will explore converting feet to inches. Help students • In this lesson, students will be working to convert from one unit of connect different real-world uses of units of length by measurement to another. Ask students to share what they know brainstorming things measured in feet such as measurements of about the metric system of units and the customary system of units. buildings, distance between classrooms, or lengths of sport fields, If time permits, have students research how and where each system and things measured in inches, such as office supplies, or electronic is typically used (e.g., the metric system is almost universally used in devices. Discuss what things might be measured in either feet or science; the customary system is typically used in homes in the inches, such as human height. Replace the items in the problem as United States). needed, for example: change dresser to file cabinet.

Connect to Language Development For ELLs, use the Differentiated Instruction chart to plan and prepare for specific activities in every session.

English Language Learners: Prepare for Session 1 ELL Differentiated Instruction Use with Try It.

Levels 1–3 Levels 2–4 Levels 3–5 Speaking/Writing Read the Try It Speaking/Writing Read the Try It Speaking/Writing Have students read problem aloud. Clarify the term problem with students. Ask them to the Try It problem and identify important . Mimic fitting something into a space. underline the known quantity and the information they will use to solve the Have students identify and underline the conversion equation. Have them form pairs problem. Allow time for students to work known quantity (4 feet) and the conversion and restate the problem in their own words. independently to solve the problem in their equation (1 foot 5 12 inches). Organize Encourage partners to decide which tools own way. Organize students into pairs to students into small groups to use gestures, from the Math Toolkit they will use, decide on compare answers and share solution numbers and words to think aloud about a solution strategy, and work together to strategies. Provide the following bank of how to solve the problem. Allow time for solve the problem. terms for students to use as they talk about productive struggle, then display a partially Display the conversion table showing the their methods for solving the problem: completed conversion table showing the relationship between yards and feet from the convert, equivalent measurement, known, relationship between feet and inches. Model Start slide. Ask: How can you use a conversion unknown, and customary system. filling in the table to show that 2 feet equals table to solve the problem? Observe pairs as 24 inches. Have students copy the table and they work to create and complete a work with their group to use it to solve the conversion table, offering support as needed. problem.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 508a LESSON 25 SESSION 1 Explore LESSON 25 SESSION 1

Purpose In this session students draw on Explore Converting Measurement Units their prior knowledge of measurement and the relationship between units within the same Learning Target You have worked with measurement units in earlier grades. Now you • Convert among diff erent-sized measurement system. They use models, tables, will convert between diff erent units in the same measurement standard measurement units within a given measurement system (e.g., and patterns to convert between feet and system. Use what you know to try to solve the problem below. convert 5 cm to 0.05 m), and use these conversions in solving inches and ounces and pounds. They will multi-step, real world problems. examine the effect of converting from a larger Lira fi nds an antique dresser that is 4 feet wide. She wants SMP 1, 2, 3, 4, 5, 6, 7 unit to a smaller unit and a smaller unit to a to know if it will fi t in her room. She measures the space larger unit. in inches. How many inches wide is the dresser? (1 foot 5 12 inches) Start TRY IT Math Toolkit Connect to Prior Knowledge Possible student work: • ruler • yardstick Why Support students’ facility with conversion Sample A • number lines tables. • grid paper Feet Inches • math reference sheet How Have students complete a conversion table for 1 12 the relationship between yards and feet. 2 24 Start 3 36

Complete the conversion table. 4 48 Solution yards (yd) 1 2 3 4 5 There are 48 inches in 4 feet. feet (ft) 3 yards 1 2 3 4 5 The dresser is 48 inches wide. (yd) feet Sample B 3 6 9 12 15 (ft) Each foot has 12 inches. There are 4 feet. Count by 12s. 1 2 3 4 DISCUSS IT Grade 5 Lesson 25 Session 1 | Explore Converting Measurement Units ©Curriculum Associates, LLC Copying is permitted. 12, 24, 36, 48 Ask your partner: Why did you choose that strategy? TRY IT Four feet is 48 inches. Tell your partner: Make Sense of the Problem The dresser is 48 inches wide. I knew . . . So I . . . To support students in making sense of the 509 problem, have them identify the measurement units ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 509 involved, feet and inches. Select and Sequence Student Solutions One possible order for whole class discussion: DISCUSS IT • visual models to represent the problem Support Partner Discussion • lists showing skip counting by 12s Encourage students to use the Discuss It question • equations that include units throughout the calculations and sentence starter on the Student Worktext page. Look for, and prompt as necessary for, Support Whole Class Discussion understanding of: Prompt students to note the relationship between the numbers in each model and • 4 feet as the known quantity the numbers in the problem. • the conversion equation 1 foot 5 12 inches Ask How do [student name]’s and [student name]’s models show how to convert • the number of inches in 4 feet as the unknown 4 feet days to a number of inches? Common Misconception Look for students who Listen for There are 12 inches in one foot, so you can count by 12s to find that say the number of feet is greater than the number of there are 48 inches in 4 feet. A conversion table shows the number of inches by inches because a foot is greater than an inch. Have finding the column or row for the known number of feet. students examine a ruler to see that 12 inches make up 1 foot.

509 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 EXPLORE SESSION 1

CONNECT IT CONNECT IT 1 LOOK BACK 1 LOOK BACK Look for understanding that the number of inches will Look at the problem on the previous page. Is the number of inches be more than the number of feet when converting in 4 feet greater than or less than the number of feet? Explain. Greater than; Possible explanation: An inch is a smaller feet to inches, because you need more of the smaller unit of measure than a foot, so you need more inches measurement unit to measure the same length. than feet to measure the same length. 2 LOOK AHEAD You solved a problem using the relationship between units to Visual Model fi nd the equivalent measure. You can use what you know about Use a model to compare units. unit sizes and operations to convert other measurement units. If . . . students are unsure about the concept of The table shows equivalent measurements of weight. how units relate to each other, a. Is an ounce a smaller unit or larger unit than a pound? Units of Weight smaller unit 1 pound 5 16 ounces Then . . . use this activity to have them model A melon weighs about 2 pounds. the same measurement using different units. How many ounces is 2 pounds? 32 ounces 1 ton 5 2,000 pounds Materials For each student: Activity Sheet b. Suppose a basket of melons weighs 64 ounces. Is the weight in pounds greater than or less than 64 pounds? How do you know? 1-Centimeter Grid Paper Less than; Possible explanation: Pounds is a larger unit than ounces, so the 5 • Have students write “1 week 7 days” at the number of pounds will be less than the number of ounces. top of their paper. • Have students outline a 1 3 7 row of squares Complete the table to convert from ounces to pounds. near the top of their paper and label the Ounces 16 32 48 64 64 ounces 5 4 pounds model 1 week. Have students outline each Pounds 1 2 3 4 square in another 1 3 7 row, number the squares 1 to 7, and label the model 7 days. 3 REFLECT Describe a real-world object that can be measured using two diff erent units and • Ask: How are your models for 1 week and 7 days tell which two units you could use. Which unit would you need more of to measure alike? How are they different? [They are the the object? same length; 1 week is 1 large rectangle and Answers will vary but should give two reasonable units. Students should 7 days is 7 smaller squares.] Which unit, weeks indicate that they will need more of the smaller unit to measure the object. or days, is the larger unit of time? [weeks] 510 • Have students outline a model for 2 weeks and 510 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. a model for the equivalent amount of time in Remind students that when a number of equal-sized sets are added, multiplication days. [two 1 3 7 rectangles; 14 squares]. can be used. Show students using foot-rulers that each ruler represents one set of the 5 • Ask students to write “7 _____ weeks days” same number of inches. In the same way, each pound represents one set of the same on their paper. Ask: What operation symbol number of ounces. Some students may begin to make the connection between goes in the blank to show how to convert from the larger unit, weeks, to the smaller unit, days? multiplication to go from a larger unit to a smaller unit and division to go from a How do your models show this? [3; The model smaller unit to a larger unit. for 7 days has 7 times as many units as the model for 1 week; the model for 14 days has 7 Close: Exit Ticket times as many units as the model for 2 weeks]. 3 REFLECT 2 LOOK AHEAD Look for understanding of how units relate so students can explain if a conversion will result in a greater or lesser number of units. Point out that equations that show equivalent measurements in different units are called Common Misconception If students say you need more of the larger unit, then use conversions. Students will learning more about the objects to represent an ounce and a pound (such as a pencil and a book) to show that concept of equivalent measurements in the you need fewer of the larger unit to weigh another object. Additional Practice. Show students the Math Reference Sheet, which lists many common Real-World Connection conversions. For several conversions, have them Encourage students to think about everyday places or situations in which they say which unit is the larger unit. need to convert measurement units. Have volunteers share their ideas.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 510 LESSON 25 SESSION 1 Additional Practice Name: LESSON 25 SESSION 1

Solutions Prepare for Converting Measurement Units

Support Vocabulary Development 1 Think about what you know about equivalent measurements. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can. 1 Have students say equivalent measurements. In Possible answers: Examples partners, have students discuss what the term equivalent means. You can ask volunteers to share measurements that have what they know about equivalent fractions and how Examples the same value but are in Examples equivalent fractions can help them solve problems. different units

If students need support to provide examples, you 1 gallon 5 4 quarts 1 yard 5 3 feet can list units on the board and invite students to 1 quart 5 4 cups 1 ft 1 ft 1 ft write or say the equivalent measurements. Then 1 yd have students write the examples in the organizer. equivalent measurements 2 Read the problem. For each conversion, have Examples Examples students point to the measurement in the picture. 1 foot 5 12 inches Have them move their finger to the right until they Examples 1 pound 5 16 ounces find the equivalent unit they are looking for. 1 ft 1 ton 5 2,000 pounds

12 in. Supplemental Math Vocabulary 1 day 5 24 hours 1 hour 5 60 minutes • equal • units

2 The picture shows a container with 1 gallon of liquid. The measurements written on the container tell how much 1 gallon liquid there is in cups and in quarts. Use the picture to write the equivalent measurement units.

2 quarts 5 8 cups 12 cups 5 3 quarts

1 gallon 5 16 cups 8 quarts 5 2 gallons 511 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 511

511 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 SESSION 1

3 Assign problem 3 to provide another look at 3 Solve the problem. Show your work. converting measurement units. Marc is fi lling 1-cup containers with juice. This problem is very similar to the problem about He has 5 gallons of juice. How many 1-cup the width of Lira’s dresser. In both problems, containers can he fi ll? (1 gallon 5 16 cups) students must convert from a larger unit to a smaller Possible student work using a picture: unit. The question asks how many 1-cup containers Marc can fill with juice. 16 16 16 16 16 Students may want to use a bar model, a table, number lines, or grid paper. 1 gallon 5 16 cups 2 gallons = 32 cups Suggest that students read the problem three times, 3 gallons 5 48 cups asking themselves one of the following questions 4 gallons 5 64 cups each time: 5 gallons = 80 cups • What is this problem about? • What is the question I am trying to answer? • What information is important? Solution Marc can fill 80 one-cup containers. Solution: 4 Check your answer. Show your work. 1 gallon 5 16 cups. 5 3 16 5 80. Marc can fill Possible student work: 80 one-cup containers. Medium 5 3 16 5 80 Marc can fill 80 one-cup containers. 4 Have students solve the problem a different way to check their answer.

512 512 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. English Language Learners: Prepare for Session 2 ELL Differentiated Instruction Use with Apply It.

Levels 1–3 Levels 2–4 Levels 3–5 Speaking/Writing Read Apply It problem Speaking/Writing Have students form Speaking/Writing Have students read 8 aloud. Have students form pairs and pairs to read and solve Apply It problem 8. and solve Apply It problem 8 individually. Ask identify the amount to be converted, the Provide a list of terms for students to think them to think about the tools and strategies units in the problem, and the conversion about and use as they discuss the problem, they use to solve the problem and create equation. Engage students in a think aloud such as conversion table, pattern, multiply, their own word bank of three to five about using a conversion table to find the relationship, and halfway between. Ask important terms to use in a conversation with 1 number of ounces in 4 pounds. Restate students to copy the list and put a check a partner. Have students form pairs and ··2 student responses, incorporating precise mark next each term they say or hear as they exchange word banks. Encourage students to mathematical terms such as halfway between, solve the problem with their partner. use as many of the words as possible from mixed number, fraction, divide by, and multiply Ask students to count the number of check their partner’s word bank as they talk about by. For example, if a student uses gestures to marks next to each word to determine which the problem. After students compare 1 indicate that 4 is between 4 and 5 on the word they used the most. Find the top three solution strategies, ask: How many of the ··2 1 conversion table, say: Yes, 4 is halfway terms used by students and call on words from your word bank did your partner ··2 between 4 and 5. Have partners draw a volunteers to use each term in a sentence use? Did you and your partner have any words conversion table and complete the problem explaining how they solved the problem. in common? Did you use them the same way? together.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 512 LESSON 25 SESSION 2 Develop LESSON 25 SESSION 2

Purpose In this session students solve a Develop Converting Larger Units to Smaller Units problem that requires converting 3.5 kilometers into meters. Students model the numbers in the Read and try to solve the problem below. word problem either on paper or with manipulatives to develop strategies for In some parts of the world, travel converting measurements from larger units to distances on road signs and maps are given in kilometers. How many smaller units. meters are there in 3.5 kilometers? (1 kilometer 5 1,000 meters) Start TRY IT Math Toolkit Connect to Prior Knowledge Possible student work: • base-ten blocks Why Review multiplying decimals by powers of 10 Sample A • number lines • grid paper to prepare for conversions from larger to smaller I need to multiply 3.5 by 1,000. • thousandths decimal metric units. place-value charts When I multiply a number by 1,000, the placement • math reference sheet How Have students write the five expressions on a of the decimal point changes. The digit 3 from the ones place has a value of 3,000 in the product piece of paper and circle the expressions equivalent because it is in the thousands place. to 1,500. Ask students to use what they know about 3.5 3 1,000 5 3,500 multiplying by powers of 10 to explain their thinking to a partner. 3.5 kilometers 5 3,500 meters Start Solution Sample B Which expressions are 1.5 3 103; 1.5 3 1,000; Kilometers 0 0.5 1 1.5 2 2.5 3 3.5 4 equivalent to 1,500? Explain. 1.5 3 10 3 10 x 10; Meters 0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 1.5 3 100 1.5 3 103 Listen for For each 1 kilometer 5 1,000 meters, so 0.5 kilometer 5 500 meters. 1.5 3 1,000 1.5 3 102 factor of 10 you multiply by, the digits 3.5 kilometers 5 3,500 meters 1.5 3 10 3 10 3 10 shift one place value DISCUSS IT to the left. Ask your partner: Can you explain that again? Tell your partner: I started Grade 5 Lesson 25 Session 2 | Develop Converting Larger Units to Smaller Units ©Curriculum Associates, LLC Copying is permitted. by . . . Develop Language Why Review the prefixes kilo-, centi-, and milli-. 513 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 513 How Create an anchor chart that shows each prefix and it’s meaning. Guide students to make DISCUSS IT connections between the prefix and the meaning of Support Partner Discussion everyday words they are familiar with such as: cent, Encourage students to use the terms kilometers and meters as they discuss. century, millipede, million, and kilowatt. Support as needed with questions such as: • How did you use the relationship between kilometers and meters? TRY IT • Did you think about which unit, kilometers or meters, is larger than the other? Make Sense of the Problem Common Misconception Look for students who seem confused that converting To support students in making sense of the from a larger unit to a smaller unit requires multiplication instead of division. problem, have them identify the units involved, Reinforce that it takes more of the smaller units to make up the larger unit. kilometers and meters. Ask What unit is used to express the distance to Paris? Select and Sequence Student Solutions One possible order for whole class discussion: • concrete models to support conversion work • visual models such as number lines or tables showing corresponding equivalent measurements • place-value charts to support multiplying by 1,000 • equations to show multiplying by 1,000

513 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 DEVELOP

Support Whole Class Discussion Explore one way to understand converting larger measurement Compare and connect the different representations units to smaller measurement units. and have students identify how they are related. In some parts of the world, travel distances on road signs and maps are given in kilometers. Ask How does your model show the number of How many meters are there in 3.5 kilometers? meters equal to each kilometer? How did you handle (1 kilometer 5 1,000 meters) the whole number 3 kilometers in your model? The decimal 0.5 kilometers? Mo It Listen for Students should recognize that accurate You can use a table to help understand the problem. responses account for 1,000 meters being equal to The table below shows the relationship between meters and kilometers. each whole kilometer, giving 3,000 meters for the kilometers 1 2 3 4 5 6 whole number part, and 500 meters for the decimal meters 1,000 2,000 3,000 4,000 5,000 6,000 part of 3.5 kilometers, for a total of 3,500 meters.

So It & Use the information from the table to understand how to solve the problem. MODEL IT SOLVE IT The pattern in the table shows that the number of meters is always 1,000 times the If no student presented a table model, connect it number of kilometers. to the student models by pointing out the ways the tables represent: • the relationship between kilometers and meters kilometers 1 2 3 3.5 4 5 6 • the number of meters in different numbers of meters 1,000 2,000 3,000 3,500 4,000 5,000 6,000 kilometers To fi nd the number of meters in 3.5 kilometers, multiply 3.5 by 1,000. Ask How do the tables show the relationship Write the answer in the table. between kilometers and meters? Listen for In the tables, each kilometer is 1,000 meters. The tables show a pattern of the number of meters going up by 1,000 each time the number of kilometers goes up by 1.

For the table in Model It, prompt students to 514 consider how the table uses the kilometers to 514 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. meters relationship. • Where do you see the conversion equation Deepen Understanding 1 kilometer 5 1,000 meters in the table? Table Model • How can you use the conversion equation to build SMP 7 Use structure. the rest of the table? After they complete the table in Solve It, prompt students to consider For the table in Solve It, prompt students to see relationships among numbers in the table. how the table relates to the table in Model It. • What is the same and different about this table from Ask What relationship does the number 3.5 have to the numbers 3 and 4? the table in Model It? Does 3,500 have this same relationship to 3,000 and 4,000? • Why is the column for 3.5 kilometers inserted where it Listen for 3.5 is halfway between 3 and 4. Yes, 3,500 is halfway between is in the second table? 3,000 and 4,000. Generalize Could you use the patterns in the table to find the number of meters in other numbers of kilometers? Where would you put a column for 5.5 kilometers? for 0.5 kilometers? Have students explain their reasoning. Listen for understanding that you could have a column for any number of kilometers. You would put a column for 5.5 kilometers between the columns for 5 kilometers and 6 kilometers, and a column for 0.5 kilometer to the left of the column for 1 kilometer. The number of meters in 5.5 kilometers is 1,000 3 5.5, or 5,500, and the number of meters in 0.5 kilometer is 1,000 3 0.5, or 500.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 514 LESSON 25 SESSION 2 Develop SESSION 2

Co It CONNECT IT Now you will use the problem from the previous page to help you understand how • Remind students that one thing that is alike about to convert larger measurement units to smaller measurement units. all of the representations is that they use the 1 Which is the smaller unit, meters or kilometers? meters conversion 1 kilometer 5 1,000 meters. How do you know? • Explain that on this page students will generalize Possible answer: because it takes 1,000 meters to make 1 kilometer strategies for using unit conversions to convert larger measurement units to smaller measurement 2 What operation do you use to convert from a larger measurement unit to a smaller units. measurement unit? multiplication 3 3.5 kilometers 5 3,500 meters Monitor and Confirm 4 Use what you learned about the relationship between meters and kilometers to 3 – 5 Check for understanding that: complete the table below.

• 3.5 kilometers 5 3,500 meters kilometers 0.8 1 1.85 2 2.03 3 • to convert any number of kilometers to meters, meters 800 1,000 1,850 2,000 2,030 3,000 you multiply the number of kilometers by 1,000 5 How many meters are in k kilometers? Support Whole Class Discussion Possible answer: 1,000 times k meters 1 2 6 There are 3 feet in 1 yard. Explain how you decide whether to multiply or divide – Tell students that problem 2 refers to how by 3 if you need to convert yards to feet. to use a conversion equation in the form Possible answer: Feet are a smaller measurement unit. To convert from yards “1 larger unit 5 a whole number of smaller units.” to feet, you multiply by 3. Ask How would you explain to a friend why you multiply to convert a quantity from a larger 7 REFLECT measurement unit to a smaller measurement unit? Look back at your Try It, strategies by classmates, and Model It and Solve It. Which models or strategies do you like best for converting larger units to Listen for You know how many smaller units make smaller units? Explain. up 1 larger unit. The number of smaller units needed Some students with strong number sense, who understand that changing to to measure a quantity is greater than the number of smaller units results in larger numbers, may be comfortable using larger units needed to measure that same quantity. You multiply the number of larger units by the multiplication. Others may prefer using a table to follow the pattern. number of smaller units that make up 1 larger unit. 515 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 515 4 When discussing the completed table in problem 4, prompt students to explain the importance of the units associated with the Visual Model numbers, reminding them to attend to precision. Illustrate multiplying by powers of ten to convert metric units. Ask Each column represents a pair of equivalent If . . . students are unsure about multiplying by 1,000 when converting, measurements. Does this mean the numbers in each Then . . . use this activity to review place value and powers of 10. column are equal? Can you write 0.8 5 800? • Draw a place-value chart from thousands to tenths on the board. Include Listen for No, the numbers are not equal. You several rows for numbers. Write 3.5 kilometers to the right of the first row and need to write the numbers with their units to 3.5 3 1,000 meters to the right of the second row. Ask: Are these two expressions show they represent equivalent ways of writing equivalent? Why? [Yes, because 1 kilometer 5 1,000 meters.] the same measure: 0.8 kilometers 5 800 meters. • Remind students that 1,000 is a power of 10 and prompt them to write the expression 3.5 3 1,000 in other forms: 3.5 3 10 3 10 3 10 and 3.5 3 103. 6 Look for the idea that a foot is a smaller • Write 3.5 in the first row. Ask: How does the place value of each digit change measurement unit than a yard, and that you when you convert 3.5 kilometers to meters? Why? [Each digit moves 3 places to multiply by the number of feet in 1 yard to convert the left because you are multiplying by 3 factors of 10. Each time you multiply from the larger unit, yards, to the smaller unit, feet. by 10, the value of the digit is 10 times what is was.] Have a student move each 7 REFLECT digit of 3.5 three places left and insert zeros to write 3,500 in the second row. Have all students focus on the strategies used to • Repeat with numbers from problem 4, or convert 2.37 meters to centimeters. solve this problem. If time allows, have students [1 meter 5 100 centimeters, so 2.37 meters 5 237 centimeters.] share their preferences with a partner.

515 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 DEVELOP SESSION 2

Ap It APPLY IT Use what you just learned to solve these problems. For all problems, encourage students to include 1 8 How many ounces are there in 4 pounds? Show your work. some kind of model to support their thinking. ··2 Remind students to attend to precision in how they (16 ounces 5 1 pound) use units in their work and in stating their solutions. Possible student work: 1 pound 5 16 ounces 4 2 ··2 8 72 ounces; Students may use a table to show 5 8 ounces

the number of ounces in each pound and use 1 Pounds 1 2 3 4 4 5 patterns to find the number of ounces in ··2 1 1 4 pounds. Students may also multiply 4 by Ounces 16 32 48 64 64 1 8 5 72 80 ··2 ··2 16 to get 72 ounces.

9 92.5 millimeters; Students may use Solution 72 ounces multiplication to find the number of millimeters 9 How many millimeters are in 9.25 centimeters? Show your work. in 9.25 centimeters. They may also break apart (1 centimeter 5 10 millimeters) the problem to show that 10 3 9 cm 5 90 mm Possible student work: and 10 3 0.25 cm 5 2.5 mm for a total of 92.5 millimeters. 9.25 3 10 5 92.5

Close: Exit Ticket

10 D; Students may use their understanding of Solution 92.5 millimeters multiplying by a power of 10 to multiply 65 by 10 Ravi’s fi sh tank can hold 65 liters of water. How many milliliters 1,000 to find that the fish tank could hold of water can the fi sh tank hold? (1 liter 5 1,000 milliliters) 65,000 milliliters. Ꭽ 0.065 milliliters Error Alert If students choose A, then they may Ꭾ 6.5 milliliters have divided by 1,000 instead of multiplying by Ꭿ 6,500 milliliters 1,000. Have them write 65 liters as 65 3 1 liter and ൳ 65,000 milliliters then replace 1 liter with its equivalent measure from 516 the conversion 1 liter 5 1,000 milliliters: 516 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. 65 liters 5 65 3 1 liter 5 65 3 1,000 milliliters 5 65,000 milliliters

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 516 LESSON 25 SESSION 2 Additional Practice Name: LESSON 25 SESSION 2

Solutions Practice Converting Larger Units to Smaller Units 1 Study the Example showing how to convert between meters and meters millimeters. Then solve problems 1–10. Basic

2 Multiply 4.06 meters by 1,000; Students may Ex also indicate that you multiply by 1,000 to How many millimeters are in 2.52 meters? convert from the larger unit, meters, to the The table below shows the relationship between meters and millimeters.

smaller unit, millimeters. meters (m) 1 2 3 4 5 Basic millimeters (mm) 1,000 2,000 3,000 4,000 5,000

3 4,060 millimeters; Students may multiply 4.06 To fi nd the number of millimeters in 2.52 meters, multiply 2.52 by 1,000. by 1,000 to find the number of millimeters. 2.52 3 1,000 5 2,520

Students may use what they know about There are 2,520 millimeters in 2.52 meters. multiplying by a power of 10 to complete the multiplication. 1 Which is the larger unit, meters or millimeters? meters Basic 2 How can you fi nd how many millimeters are in 4.06 meters? 4 See the completed table on the student page; Possible answer: You multiply 4.06 meters by 1,000 to find the number of Multiply each number of meters in the table by millimeters. 1,000 to find the number of millimeters. 3 How many millimeters are in 4.06 meters? 4,060 Medium 4 Fill in the missing information in the table. 5 Multiplication; See possible explanation on the student page. meters (m) 0.34 1 1.5 2 2.09 3 3.77 4 Medium millimeters (mm) 340 1,000 1,500 2,000 2,090 3,000 3,770 4,000

5 What operation do you use to convert from a larger measurement unit to a smaller measurement unit? Explain why. Multiplication; Possible explanation: You multiply because it takes more of the smaller unit to equal the same amount of the larger unit. 517 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 517

Fluency & Skills Practice Teacher Toolbox

Assign Converting Larger Units to Fluency and Skills Practice Smaller Units Converting Larger Units to Smaller Units Name: Convert each measurement from the larger unit to the smaller unit.

1 1 1 hour 2 2 hours 3 2__ hours In this activity students convert 2 larger units of measure to smaller minutes minutes minutes

1 4 1 pound 5 8 pounds 6 8__ pounds units within the same measurement 2 ounces ounces ounces system. This activity cultivates 7 1 kilometer 8 5 kilometers 9 5.25 kilometers

fluency in converting measures of meters meters meters

time, weight, mass, length, and __1 __1 10 11 12 4 2 quarts 7 2 days 4.5 meters capacity. Students may use these cups hours centimeters

1 13 7.5 kilograms 14 2.1 meters 15 5__ gallons skills in science classes (for example, 2 when converting kilograms to grams centimeters cups 1 16 6.87 centimeters 17 3__ tons 18 2.15 liters grams) and wood- and metal-shop 2 millimeters pounds milliliters classes (for example, when 1 19 How many feet are in 6__ yards? Describe how you would fi nd the answer. converting meters to centimeters 2 and centimeters to millimeters).

©Curriculum Associates, LLC Copying is permitted for classroom use.

517 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 SESSION 2

6 See the completed table on the student page. 6 The pattern in the table shows that the number of centimeters is always Medium 100 times the number of meters. Fill in the missing number of centimeters. meters (m) 1 1.5 2 2.07 3 3.26 4 1 1 7 40 feet; Students may break apart 13 yards ··2 ··2 centimeters (cm) 100 150 200 207 300 326 400 and multiply the whole number and fraction 1 7 A football player runs for 13 yards. How many feet does he run? Show your work. separately by 3, combining products to find the ··2 (1 yard 5 3 feet) number of feet. Possible student work: Medium 1 3 1 13 3 3 5 39; 3 3 5 or 1 ··2 ··2 ··2 1 1 8 Multiply; See possible explanation on student 39 1 1 5 40 ··2 ··2 1 page. 40 feet Solution ··2 Medium 8 There are 24 hours in a day. If you want to convert days to hours, should you 1 multiply or divide by 24? Explain. 9 60 hours; Students may break apart 2 days and ··2 Multiply; Possible explanation: Hours are a smaller measurement unit than multiply the whole number and fraction days. To convert from days to hours, you multiply the number of days by 24. separately by 24, combining products to find 1 9 Look at problem 8. How many hours are in 2 days? Show your work. the number of hours. ··2 Medium Possible student work: 1 24 2 3 24 5 48; 3 24 5 or 12 ··2 ···2 10 40 ounces; Students may use a multiplication 48 1 12 5 60 equation. They may also draw a model with 60 hours 2 parts that are 16 ounces and one part that is Solution 8 ounces and add 16 1 16 1 8 to get 40 ounces. 10 16 ounces is equivalent to 1 pound. A lion cub born 1 at the zoo weighs 2 pounds. How many ounces Medium ··2 does the lion cub weigh? Show your work. Possible student work: 1 2 3 16 5 40 ··2

Solution 40 ounces 518 518 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. English Language Learners: Prepare for Session 3 ELL Differentiated Instruction Use with Connect It.

Levels 1–3 Levels 2–4 Levels 3–5 Speaking/Listening Have students Speaking/Writing Have students read Speaking/Writing Have students read chorally read Connect It problem 6. Ask Connect It problem 6 with a partner. Ask Connect It problem 6 with a partner. Have students to first look at Try It and name the them to discuss the strategies being used students make a table to take notes on each strategies they used to their partner. Provide before they write their explanation. of the strategies in Connect It. the following names for them to choose Provide the sentence frame below: Then, have students write their explanation from: • I prefer because . of the strategy they like best for converting • Making a table units. Provide a sentence starter: Have students provide a visual support for • Drawing a picture the strategy they identified. • I prefer . • Using a number line Have students work with another set of • Writing an equation partners to discuss the different explanations they gave for why they prefer a particular Ask students to then look at both Model It strategy. and Solve It and point to or name the strategies used. Once complete, have them name what they think is the best strategy for them.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 518 LESSON 25 SESSION 3 Develop LESSON 25 SESSION 3

Purpose In this session students solve a Develop Converting Smaller Units to Larger Units problem that requires converting 6 cups to a number of quarts. Students model the Read and try to solve the problem below. conversion either on paper or with manipulatives to develop strategies for How many quarts are equivalent converting measurements from smaller units to to 6 cups? (1 quart 5 4 cups) larger units.

Start TRY IT 1 quart 1 cup Possible student work:

Connect to Prior Knowledge Sample A Math Toolkit • fraction tiles Materials For each pair: 2 sets of fraction tiles or cups 5 4 3 quarts • fraction circles • number lines circles 6 5 4 3 q • grid paper Why Review using fractions to write quotients of q 5 6 4 4 • math reference sheet division problems with divisors 2 and 4, to prepare 6 6 2 q 5 ; 5 1 ··4 ··4 ··4 for converting among cups, pints, and quarts. 2 1 6 cups 5 1 , or 1 , quarts How Have students use fraction tiles or circles to ··4 ··2 model each equation and find each quotient. Sample B Start Solutions 1 quart 1 quart 1 Use fraction tiles or fraction 1 4 2 5 ; cup cup cup circles to model the equations. ··2 3 1 Then write the quotients. 3 4 2 5 , or 1 ; ··2 ··2 cup cup cup 1 1 4 2 5 ? 3 4 2 5 ? 1 4 4 5 ; quart 1 ؍ quart 2 cups 1 ؍ cups 4 4·· 1 4 4 5 ? 5 4 4 5 ? 2 4 5 5 1 5 4 , or 1 1 DISCUSS IT ··4 ··4 6 cups 5 1 quarts Ask your partner: How did ··2 you get started? Tell your partner: A model

Grade 5 Lesson 25 Session 3 | Develop Converting Smaller Units to Larger Units ©Curriculum Associates, LLC Copying is permitted. I used was . . . It helped Develop Language me . . . Why Clarify the meaning of the word quart. 519 How Encourage students to share what they know ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 519 about quarts. Emphasize that a quart is a unit of measurement for volume or capacity. Point out DISCUSS IT that the word quart is related to the word quarter, Support Partner Discussion which is used to mean one fourth. For example a 1 Encourage students to use the terms cups and quarts as they discuss their solutions. quarter of an hour is of an hour. There are 4 quarts ··4 1 in 1 gallon, so a quart is of a gallon. Support as needed with questions such as: ··4 • How did you use the relationship between cups and quarts? • Did you think about which unit, cups or quarts, is larger than the other? TRY IT Make Sense of the Problem Common Misconception Look for students who multiply 6 by 4 and say that 6 cups is equivalent to 24 quarts. They may think you always multiply when you convert To support students in making sense of the between units. As students present solutions, have them specify which operation problem, have them identify the units involved, they used and why. cups and quarts, as units of liquid volume, or capacity. Select and Sequence Student Solutions Ask What do quarts and cups measure? One possible order for whole class discussion: • concrete models to represent the quantities • drawings to represent the quantities • visual models such as number lines or tables showing corresponding equivalent measurements • equations that show 6 4 4

519 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 DEVELOP

Support Whole Class Discussion Explore one way to understand converting smaller measurement units to larger Compare and connect the different representations measurement units. and have students identify how they are related. How many quarts are equivalent to 6 cups? Ask How did you represent the 6 cups? How does (1 quart 5 4 cups) your model show that 1 quart equals 4 cups? How did you handle the extra 2 cups with your model and Mo It You can use a table to help understand the problem. with your solution? The table below shows the relationship between cups and quarts. Listen for Students should recognize that accurate responses account for 1 quart equaling quarts 1 2 3 4 5 6 1 2 cups 4 8 12 16 20 24 4 cups and the additional 2 cups being or of a ··2 ··4 quart. Correct responses may include the 6 equivalent numerical representations quarts, So It ··4 Use the information from the table to understand how to solve the problem. 2 3 1 1 quarts, quarts, and 1 quarts. ··4 ··2 ··2 The pattern in the table shows that there are 4 cups in every quart. & MODEL IT SOLVE IT 1 quarts 1 1 2 3 4 5 6 If no student presented a table model, connect it ··2 to the student models by pointing out the ways the cups 4 6 8 12 16 20 24

tables represent: To fi nd the number of quarts equivalent to 6 cups, divide by 4. • the relationship between cups and quarts • the number of cups in different numbers of quarts Ask How do the tables show the relationship between cups and quarts? Listen for The tables show that there are 4 cups in 1 quart and 4 additional cups in each additional quart.

For the Model It table, prompt students to describe patterns in the table. 520 • Going from left to right, from one column to the next, 520 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. by how much does the number of quarts increase? By how much does the number of cups increase? Deepen Understanding • How is this pattern related to the conversion Conversion Tables equation 1 quart 5 4 cups? SMP 2 Reason quantitatively. For the Solve It table, prompt students to consider When discussing the tables, prompt students to consider how a conversion how the table relates to the table in Model It. table shows relationships between quantities in more than one way. • Why is the column for 6 cups inserted where it is in Ask What if the problem also asked how many cups are equal to 6 quarts? the second table? Could you use the same table to show the number of cups equivalent to • What about the pattern in the table helps you fill in 6 quarts? What operation would you use for each conversion? Why? the missing value? Listen for Yes, the table shows that 6 quarts is equivalent to 24 cups. You multiply the number of quarts by 4 to find the number of cups. Quarts are a larger unit than cups, so you multiply by 4 to convert from quarts to cups and you divide by 4 to convert from cups to quarts. Generalize When you are deciding to convert between other measurement units, such as feet to inches or inches to feet, how will you decide whether to multiply or divide? Listen for understanding that if you know how many smaller units make up 1 larger unit, then you multiply to convert from the larger unit to the smaller unit and you divide to convert from the smaller unit to the larger unit.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 520 LESSON 25 SESSION 3 Develop SESSION 3

Co It CONNECT IT Now you will use the problem from the previous page to help you understand how • Remind students that one thing that is alike about to convert smaller measurement units to larger measurement units. all of the representations is that they use the 1 Which is a smaller unit, quarts or cups? cups conversion 1 quart = 4 cups. How do you know? • Explain that on this page students will generalize Possible answer: It takes 4 cups to make 1 quart. strategies for using unit conversions to convert smaller measurement units to larger measurement 2 What operation do you use to convert from a smaller measurement unit to a units. larger measurement unit? division 6 3 1 or or 1 Monitor and Confirm 3 6 cups 5 ··4 ··2 ··2 quarts Write your answer in the table on the previous page. Explain your reasoning. 3 – 4 Check for understanding that: Possible explanation: I divided 6 by 4, the number of cups in 1 quart. • you divide 6 cups by 4 to find an equivalent 4 Use what you learned about the relationship between cups and quarts to number of quarts complete the table below. 1 • 6 cups 5 1 quarts (or an equivalent number 2 1 5 1 9 1 15 3 ··2 quarts or 1 or 1 2 or 2 3 or 3 4 of quarts) ··4 ··2 ··4 ··4 ··4 ··4 ···4 ··4 cups 2 4 5 8 9 12 15 16 • to convert any number of cups to quarts, you divide the number of cups by 4 5 One gallon is equivalent to 8 pints. Describe how to convert from pints to gallons. Explain your reasoning. Support Whole Class Discussion Divide by 8; Possible explanation: Since a pint is smaller than a gallon, there would be fewer units in pints for the same amount. So, you would divide by 8. 1 – 2 Tell students that problem 2 refers to how 6 REFLECT to use a conversion equation in the form Look back at your Try It, strategies by classmates, and Model It and Solve It. “1 larger unit 5 a whole number of smaller units.” Which models or strategies do you like best for converting smaller units to larger Ask How would you explain to a friend why you units? Explain. Some students may prefer using a table to help them recognize the divide to convert a quantity from a smaller measurement unit to a larger measurement unit? relationships and patterns between measurements. Others may find it faster 6 1 to write a division equation, such as 6 4 4 5 or 1 . Listen for You know how many smaller units make ··4 ··2 up 1 larger unit. You want to separate those smaller units into groups equal to the larger unit, so you 521 divide the number of smaller units you have by the ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 521 number of smaller units that make up 1 larger unit. The number of larger units needed to measure a quantity is less than the number of smaller units Hands-On Activity Use measuring cups to understand relationships between units. needed to measure that same quantity. If . . . students are unsure about relationships between cups, pints, and quarts, 5 Look for the idea that a pint is a smaller Then . . . use this activity to provide a concrete experience. measurement unit than a gallon and that you divide Materials For each group: 1-cup measuring cup, 1 pint container, 1 quart by the number of pints in 1 gallon to convert from container, 6 cups of rice or dried beans the smaller unit, pints, to the larger unit, gallons. • Have students repeatedly fill the 1-cup measuring cup with rice or dried beans 6 REFLECT and pour it into the pint container, until the pint container is filled. Ask: How many cups are in a pint? [2] Have students write the conversion 1 pint 5 2 cups. Have all students focus on the strategies used to solve this problem. If time allows, have students • Have students repeat the procedure, using the quart container. Ask: How many share their preferences with a partner. cups are in a quart? [4] Have students write the conversion 1 quart 5 4 cups. • Ask: How can you find the number of pints in a quart without using the pint container to fill the quart container? [Since 2 cups 5 1 pint and 4 cups 5 1 quart, there must be 2 pints in 1 quart.] • Have students repeatedly fill the pint container and pour it into the quart container to see that there are 2 pints in 1 quart.

521 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. LESSON 25 DEVELOP SESSION 3

Ap It APPLY IT Use what you just learned to solve these problems. Use the Math Reference Sheet For all problems, encourage students to include as necessary. some kind of model to support their thinking. 7 How many kilometers is equal to 800 meters? Show your work. Remind students to attend to precision in how they Possible student work: use units in their work and in stating their solutions. 1 kilometer 5 1,000 meters Point out that students can use the Math Reference 800 4 1,000 5 0.8 Sheet for equivalent measurements.

7 0.8 kilometer; Students may use a table and kilometers 0.5 0.8 1 1.5 2 number patterns to show the number of meters 500 800 1,000 1,500 2,000 kilometers in each 100 meters up to 1,000 meters. Students may also use what they 0.8 kilometer know about dividing by a power of 10 to shift Solution each digit 3 places to the right to show that 800 8 How many yards are equal to 25 feet? Show your work. kilometers 4 1,000 5 0.8 kilometer. Possible student work:

1 1 yard 5 3 feet 8 8 yards; Students may write an equation to 25 ··3 25 4 3 5 divide the number of feet, 25, by the number of ···3 1 5 8 feet in each yard, 3, to show the conversion. ··3 Students may also use a table to show that the number of yards equal to 25 feet is between 1 8 yards 8 and 9 yards and to recognize that you divide Solution ··3 the number of feet by 3 to find the number 9 Which of the following measures is equivalent to 3,300 grams? of yards. Ꭽ 330 kilograms Ꭾ 33 kilograms Close: Exit Ticket Ꭿ 3.3 kilograms ൳ 0.33 kilograms 9 C; Students may use their understanding of dividing by a power of 10 to divide 3,300 by 522 1,000 to find that 3,300 grams is equivalent to 522 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. 3.3 kilograms. Error Alert If students choose A, B, or D, then have them use the conversion 1 kilogram 5 1,000 grams to list the number of grams in 1, 2, 3 and 4 kilograms. 1 kilogram 5 1,000 grams 2 kilograms 5 2,000 grams 3 kilograms 5 3,000 grams 4 kilograms 5 4,000 grams Then ask them think about where the equation ? kilograms = 3,300 grams would fit into the list.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 522 LESSON 25 SESSION 3 Additional Practice Name: LESSON 25 SESSION 3

Solutions Practice Converting Smaller Units to Larger Units 1 Study the Example showing how to convert between ounces and pounds. ounces Then solve problems 1–8. Basic

2 division Ex Medium How many pounds are equivalent to 56 ounces? The table below shows the relationship between pounds and ounces. 3 See possible explanation on the student page. pounds (lb) 1 2 3 4 Medium ounces (oz) 16 32 48 64

4 See the completed table on the student page; To fi nd the number of pounds equivalent to 56 ounces, divide by 16. 1 Students may divide the number of ounces by 56 4 16 5 3 ··2 16 to find the equivalent number of pounds. 1 3 pounds is equivalent to 56 ounces. Medium ··2

1 Which is the smaller unit, pounds or ounces? ounces

2 What operation do you use to convert from a smaller measurement unit to a larger measurement unit? division

3 Look at the Example. Explain how you can use multiplication to check the answer. 1 Answers will vary. Possible explanation: To check if 3 pounds is equivalent ··2 1 to 56 ounces, I can multiply 3 by 16 to get 56. Because pounds is the larger ··2 measurement unit, I multiply to convert to the smaller measurement unit.

4 Use the relationship between pounds and ounces complete the table.

1 1 1 pounds (lb) 1 1 2 2 ··2 ··4 ··2 ounces (oz) 8 16 20 32 40

523 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 523

Fluency & Skills Practice Teacher Toolbox

Assign Converting Smaller Units to Fluency and Skills Practice Larger Units Converting Smaller Units to Larger Units Name: Convert each measurement from the smaller unit to the larger unit. In this activity students convert 1 100 centimeters 2 1,000 centimeters 3 10 centimeters smaller units of measure to larger meter(s) meter(s) meter(s) units within the same measurement 4 16 ounces 5 8 ounces 6 120 ounces pound(s) pound(s) pound(s) system. This exercise helps cement 7 4 cups 8 3 cups 9 10 cups

understanding of relationships quart(s) quart(s) quart(s)

between measurement units. 10 2 feet 11 36 hours 12 4,500 milliliters Students may use this skill in their yard(s) day(s) liter(s)

everyday lives. For example, 13 250 grams 14 2,000 millimeters 15 4,500 pounds suppose a soup recipe calls for kilogram(s) meter(s) ton(s) 3 cups of vegetable broth, and the 16 200 minutes 17 850 milligrams 18 6,500 meters hour(s) gram(s) kilometer(s) cook has 1 quart of broth. By 3 19 How could you check your answers to the problems? Use one of the problems as an example. converting 3 cups to quart, the ··4 cook knows there is enough broth

2 5 12 yards; Students may divide 38 feet by 3, the 5 How many yards are equivalent to 38 feet? Show your work. ··3 (1 yard 5 3 feet) number of feet in 1 yard. Possible student work: Medium 2 38 4 3 5 12 ··3 6 2.47 meters; Students may divide 2 12 yards 247 centimeters by 100, the number of Solution ··3 centimeters in 1 meter. 6 How many meters are equivalent to 247 centimeters? Show your work. Medium (1 meter 5 100 centimeters) Possible student work: 7 Answers will vary; See possible answer on the student page. 247 4 100 5 2.47 Medium Solution 2.47 meters 1 8 1 gallons; Students may use what they know ··2 7 When converting between two measurement units, how can you tell which to make multiple conversions from cups to operation to use? quarts and quarts to gallons to divide and find Answers will vary. Possible answer: First, I figure out which measurement unit the number of gallons equivalent to 24 cups. is smaller and which is larger. If I am converting from a larger measurement Challenge unit to a smaller measurement unit, I multiply by the number of smaller units in 1 larger unit. If I am converting from a smaller measurement unit to a larger measurement unit, I divide by the number of smaller units in 1 larger unit.

8 How many gallons are equivalent to 24 cups? Show your work. (1 gallon 5 4 quarts and 1 quart 5 4 cups) Possible student work:

1 quart 5 4 cups

24 cups divided by 4 cups in a quart 5 6 quarts

4 quarts 5 1 gallon 1 6 quarts divided by 4 quarts in a gallon 5 1 gallons ··2

1 1 gallons Solution ··2 524 524 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. English Language Learners: Prepare for Session 4 ELL Differentiated Instruction Use with Apply It.

Levels 1–3 Levels 2–4 Levels 3–5 Reading/Speaking Have students Speaking/Writing Have students read Speaking/Writing Have students read chorally read Apply It problem 9. Have Apply It problem 9 with a partner. Ask them Apply It problem 9 with a partner. Ask them students point to the width of the desk and to describe the relationship between to describe the relationship between underline the unit of measurement. centimeters and meters. Provide the centimeters and meters and then discuss Then, ask students to circle the measurement following sentence frame: whether the number of meters will be less unit that they are converting to. Provide the • There are centimeters in a meter. than or greater than the number of centimeters. following sentence frames to help students Ask students to discuss with their partner tell whether the number of meters will be whether the number of meters will be Have students write their explanation and less than or greater than the number of less than or greater than the number of then compare their explanation with another centimeters. centimeters. Once complete, have partners set of partners. Have them revise their work if • One centimeter is than one meter. work together to write their explanation. needed. • There are centimeters in a meter. • The number of meters will be the number of centimeters.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 524 LESSON 25 SESSION 4 Refine LESSON 25 SESSION 4

Purpose In this session students solve word Refine Converting Measurement Units problems involving converting from larger to smaller and from smaller to larger measurement Complete the Example below. Then solve problems 1–9 using the units. They then discuss and confirm their Math Reference Sheet as necessary. answers with a partner. Before students begin to work, use their Use division, because EXAMPLE milliliters are smaller responses to the Check for Understanding to How many liters are equivalent to 100 milliliters? than liters. determine those who will benefit from Look at how you could explain your work using conversions. additional support. 1 liter 5 1,000 milliliters As students complete the Example and problems 1–3, observe and monitor their Liters are larger than milliliters, so the number of liters will be less than the number of milliliters. Divide the number of reasoning to identify groupings for milliliters by 1,000 or 103. differentiated instruction. Point out that 100 4 1,000 5 0.1 because dividing by 103 changes the students can use the Math Reference Sheet for placement of the decimal point. The digit 1 from the hundreds equivalent measurements. place has a value of 0.1 in the quotient because it has moved three place values to the right.

1 PAIR/SHARE liter, or 0.1 liter Solution ···10 How can you check your Start answer? Check for Understanding Ap i Materials For each student: Activity Sheet Math 1 1 Jillian makes 10 gallons of lemonade to sell in 1-quart bottles. Reference Sheet; For remediation: 1-liter beaker ··2 How many quarts are 1 How many quarts of lemonade can she make? Show your work. in gallon? ·2 Why Confirm understanding of converting between Possible student work: two measurement units in the same system. 10 gallons 3 4 quarts per gallon 5 40 quarts How Have students convert 250 milliliters to liters 1 gallon 3 4 quarts per gallon 5 2 quarts using any strategy they want. ··2 40 quarts 1 2 quarts 5 42 quarts Start 1 Solution 42 quarts 5 10 gallons PAIR/SHARE ··2 How many liters are equivalent 0.25 liter Draw a picture or make a table to support your to 250 milliliters? answer. Solution 42 quarts 525 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 525

Error Alert Grade 5 Lesson 25 Session 4 | R e ﬁ n e Converting Measurement Units ©Curriculum Associates, LLC Copying is permitted. If the error is . . . Students may . . . To support understanding . . .

Show students a 1-liter beaker. Have them point out where have multiplied by the 250-milliliter mark is on the beaker. Point out that this is 250,000 liters 1,000. less than 1 liter, so their answer is not reasonable. Remind students to divide milliliters by 1,000 to convert to liters.

Review how to divide by a power of 10. Remind students that 1,000 is 10 3 10 3 10, or 103. Discuss with students 2.5 liters or have divided incorrectly. how you shift the digits one place to the right, or change 0.025 liter the placement of the decimal point by one place to the left, for each factor of 10 you divide by.

Remind students that including the measurement unit is 0.25 instead of have forgotten to include units an important part of giving a correct response. Without a 0.25 liter in their solution. measurement unit, the number 0.25 does not show the quantity 0.25 liters.

Example 2 How many kilograms are equivalent to 450 grams? Show your work. Will the number of 1 Possible student work: kilograms be greater or liter or 0.1 liter; The equation showing dividing by ··10 less than 450? a power of 10 is one way to solve the problem. 1 kilogram 5 1,000 grams Students could also solve the problem by writing 450 grams 4 1,000 5 0.45 kilogram 100 the division 100 4 1,000 as a fraction and note ·····1,000 1 that this fraction is equivalent to , or 0.1. ··10 Look for You can check your answer by using multiplication, converting 0.1 liter to milliliters with PAIR/SHARE the equation 0.1 liter 3 1,000 5 100 milliliters. The Did you and your partner solve the problem the answer checks, so 0.1 liter is correct. same way? Solution 0.45 kilogram

3 How many millimeters are in 180 meters? Which is a larger unit, APPLY IT Ꭽ 0.18 millimeter millimeters or meters? 1 42 quarts; Students could solve the problem by Ꭾ 1.80 millimeter 1 multiplying 10 by 4, multiplying by 4, and Ꭿ 180,000 millimeters ··2 then adding the results. ൳ 1,800,000 millimeters DOK 2 Emily chose Ꭽ as the correct answer. How did she get 1 Look for 1 gallon has 4 quarts, so gallon has that answer? ··2 half as many quarts, or 2 quarts. Possible answer: Emily divided by 1,000 instead of multiplying by 1,000. 2 0.45 kilogram; Students could solve the problem by dividing 450 by 1,000 using what they know about dividing by a power of 10. DOK 1 Look for Kilograms are a larger unit than grams, so the number of kilograms will be less PAIR/SHARE than 450. Does Emily’s answer make sense? 3 C; Students could solve the problem by 526 multiplying 180 by 1,000. 526 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. Explain why the other two answer choices are not correct: B is not correct because 180 meters was divided by 100 instead of being multiplied by 1,000 to convert to milliliters. D is not correct because 180 was multiplied by 1,000 incorrectly; the number of zeros in the product should be 3 more than in the factor instead of 4 more. DOK 3

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 526 LESSON 25 SESSION 4 Refine SESSION 4

4 A mining company digs 75 kilograms of silver. They plan to use 1 gram of silver in APPLY IT each special coin they make. How many grams are equivalent to 75 kilograms? 4 75,000; Multiply the number of kilograms, 75, by 1,000. 07050 •••••• DOK 1 0 0 0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 2 5 3 3 3 3 3 3 See the completed equations on the Student 4 4 4 4 4 4 Worktext page; Use the conversions 1 kilometer 5 5 5 5 5 5 5 6 6 6 6 6 6 1,000 meters and 1 meter 5 100 centimeters to 7 7 7 7 7 7 8 8 8 8 8 8 find pairs of equivalent measures. 9 9 9 9 9 9 DOK 2 5 Five measurements are shown below. Write one of the measurements on each of the lines to create two true equations. 6 See the completed equations on the Student Worktext page; Write both quantities on the left 300 millimeters 30 meters 3,000 meters 3 kilometers 3,000 centimeters side of the equation in the unit given on the 3 kilometers 5 3,000 meters

right side of the equation and then combine the 30 meters 5 3,000 centimeters quantities. 6 Complete each conversion below. Show your work. Students show their DOK 2 work using conversions. a. 3 feet 1 7 inches 5 43 inches Error Alert Students may choose the wrong b. 2 gallons 2 5 quarts 5 3 quarts operation when making conversions. For each lettered problem, encourage students to identify c. 5 pounds 2 38 ounces 5 42 ounces whether the unit for the sum or difference they will d. 60 centimeters 1 4 meters 5 460 centimeters write in the blank is a smaller or larger unit than the e. 2,000 meters 1 5,000 meters 5 7 kilometers other unit shown in the problem. f. 1 liter 2 150 milliliters 5 850 milliliters

527 ©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 527 Differentiated Instruction RETEACH EXTEND

Hands-On Activity Challenge Activity Use a ruler to convert between centimeters and millimeters. Complete conversions. Students struggling with concepts that involve converting from smaller to larger and Students who have achieved proficiency larger to smaller units Will benefit from deepening Will benefit from additional work with physical measurements understanding of conversions Materials For each pair: meterstick • Challenge students to complete these • Group students into pairs. Direct one student to measure the length of his or her desk in conversions with missing unit labels. centimeters and direct the other student to measure the length of his or her desk in Possible answers are shown. 1 millimeters. 40 ___ [ounces] 5 2 ___ [pounds] ··2 1 • Remind students that 1 centimeter equals 10 millimeters. Tell the student who measured 3 ___ [quarts] 5 13 ___ [cups] ··4 2 in centimeters to convert the measurement to millimeters, and tell the student who 23 ___ [feet] 5 7 ___ [yards] measured in millimeters to convert the measurement to centimeters. ··3 4.5 ___ [meters] 5 450 ___ [centimeters] • Have partners compare measurements and conversions. • Have partners write and share their own • If time allows, have students measure the width of the desk, switching roles. missing label conversion problems.

7 A; Divide the number of feet, 1,000, by 3. 7 How many yards are equivalent to 1,000 feet? 1 DOK 2 Ꭽ 333 yards ··3 1 Ꭾ 333 yards 8 See the completed table on the Student ··12 4 Worktext page. Use the conversions 1 gallon 5 Ꭿ 83 yards ··12 4 quarts; 1 quart 5 2 pints; and 1 pint 5 2 cups ൳ 3,000 yards to find equivalent measurements. DOK 2 8 Write each measurement below in the table under an equivalent measure, if possible. Some of the measurements may not have an equivalent measure. 1 1 quart 4 pints 16 cups gallon 8 pints ··2 ··4

1 gallon 1 quart 1 pint

1 1 16 cups gallon quart ··4 ··2 8 pints

9 MATH JOURNAL Rafael uses a ruler to measure his desk. It is 85 centimeters wide. If he measures the width of his desk in meters, will the number of meters be less than or greater than 85? What will the measure in meters be? Explain how you know. Less than; 0.85 meters; Possible explanation: There are 100 centimeters in 1 meter, so a meter is the larger measurement unit. The width of the desk measures fewer meters than centimeters. I can determine the width of the desk in meters by finding 85 4 100 5 0.85.

SELF CHECK Go back to the Unit 4 Opener and see what you can check off . 528 528 Lesson 25 Convert Measurement Units ©Curriculum Associates, LLC Copying is not permitted. Close: Exit Ticket REINFORCE PERSONALIZE 9 MATH JOURNAL Problems 4–9 Student responses should indicate understanding Convert measurement units. of the relationship between measurement units, Provide students with how to choose an operation based on that All students will benefit from additional work with opportunities to work relationship to convert between units, and how to converting measurement units by solving problems in on their personalized calculate correctly using a given conversion such as a variety of formats. instruction path 1 meter 5 100 centimeters. • Have students work on their own or with a partner with i-Ready Online Error Alert If students say the equivalent number to solve the problems. Instruction to: of meters is 8,500 meters, then have students • Encourage students to show their work. • fill prerequisite gaps describe the relationship between 1 meter and • build up grade-level 1 centimeter. Ask them if it would take more meters skills or more centimeters to measure their desk.

SELF CHECK Have students consider whether they feel they are ready to check off any new skills on the Unit 4 Opener page.

©Curriculum Associates, LLC Copying is not permitted. Lesson 25 Convert Measurement Units 528 LESSON 25 Name ______Date ______Teacher Toolbox Lesson Quiz Lesson 25 Quiz

Tested Skills Solve the problems. Refer to the Math Reference Sheet as necessary. Assesses 5.MD.A.1 1 How many kilometers are in 3,600 meters? (1 point) Problems on this assessment form require students Ꭽ 3.6 kilometers to be able to use relationships and place value to Ꭾ 36 kilometers convert from a larger unit to a smaller unit and from Ꭿ 360,000 kilometers a smaller unit to a larger unit within the same ൳ 3,600,000 kilometers measurement system. Students will also need to be familiar with the customary and metric measurement systems and their different units, and 2 How many ounces are equivalent to 9 pounds? Show your work. (2 points) with performing operations with whole numbers, Possible student work: fractions, and decimals. 1 pound 5 16 ounces 9 3 16 5 144 Alternately, teachers may assign the Digital Comprehension Check online to assess student 144 ounces understanding of this material. Error Alert Students may: 3 Decide if each measurement is equivalent to 1 yard, 1 foot, 1 inch, or none of these. Choose 1 yard, 1 foot, 1 inch, or None for each measurement. (2 points) • confuse units or conversion factors or make a 1 yard 1 foot 1 inch None conversion mistake. 36 inches Ꭽ Ꭾ Ꭿ ൳ • multiply or divide by the wrong power of 10 when 1 foot ൴ ൵ ൶ ൷ converting within the metric system. ··12 1 yard ൸ ൹ ൺ ൻ • apply the incorrect operation or misapply the ··12 correct operation. 12 feet ർ ൽ ൾ ൿ 1 ඀ ඁ ං ڹ yard ··3 1 Solutions yard ඃ ඄ අ ආ ··36 1 A; Students could solve the problem by dividing 3,600 by 1,000 using what they know about dividing by a power of 10. B is not correct because 3,600 meters was divided by 100 instead of 1,000 to convert to ©Curriculum Associates, LLC kilometers. Grade 5 Lesson 25 Convert Measurement Units 1 Copying permitted for classroom use. C is not correct because 3,600 meters was Short Response Scoring Rubric multiplied by 100 instead of being divided by Points Expectations 1,000 to convert to kilometers. D is not correct because 3,600 meters was Response contains the following: multiplied by 1,000 instead of being divided by • Correct computations, solutions, and/or calculations. (1 point) 1,000 to convert to kilometers. 2 1 point • Well-organized, clear, and concise work that demonstrates thorough understanding of math 5.MD.A.1, DOK 1 concepts and/or procedures. (1 point) 2 144 ounces; See possible work on the student page. Response contains the following: • Mostly correct solution(s). 2 points 1 • Shows partial or good understanding of math 5.MD.A.1, DOK 1 concepts and/or procedures.

Response contains the following: Choice Matrix Scoring Rubric • Incorrect solution(s). 2 points 1 point 0 points 0 • No attempt at find a solution. • No effort to demonstrate an understanding of All answers 1 incorrect answer 2 or more mathematical concepts and/or procedures. are correct incorrect answers

Lesson 25 Quiz continued

4 Landon makes the table below to show the relationship between liters 3 A (1 yard); and milliliters. G (1 inch); L (None); Liters 1 3 5 8 12 P (None); Milliliters 1,000 3,000 5,000 8,000 12,000 R (1 foot); How can Landon find how many milliliters are in 4.2 liters? W (1 inch) Explain your reasoning. (2 points) 2 points Possible answer: He can multiply 4.2 liters by 1,000 to find the number 5.MD.A.1, DOK 2 of milliliters because there are 1,000 milliliters in 1 liter. 4 See possible answer on the student page; Students’ responses may also include multiplying 1,000 by 4, multiplying 1,000 by 0.2, 5 Larissa’s family uses an online map to plan their drive from New York to Alaska. 3 The map calculates drive time with no stops to be 2 days. How many hours will then adding the results. ··4 Larissa’s family drive? Show your work. (2 points) 2 points 5.MD.A.1, DOK 2 Possible student work:

5 2 3 days 3 24 hours 5 (2 3 24) 1 3 3 24 66 hours; See possible student work on the ··4 1 ··4 2 student page. 5 48 1 18 2 points 5 66 5.MD.A.1, DOK 2 Solution 66 hours

Differentiated Instruction Teacher Toolbox RETEACH REINFORCE EXTEND

Tools for Instruction Math Center Activities Enrichment Activities Students who require additional support Students who require additional Students who have achieved proficiency for prerequisite or on-level skills practice to reinforce concepts and skills with concepts and skills and are ready for Will benefit from activities that provide and deepen understanding additional challenges targeted skills instruction Will benefit from small group Will benefit from group collaborative collaborative games and activities games and activities that extend (available in three versions—on-level, understanding below-level, and above-level)