573A Chapter 10

About the MathProfessional Development

LESSON AT A GLANCE

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

Animated Math Models

iTools: Measurement

iTools: Number Lines

HMH Mega Math

Professional Development Videos

MP4 Model with mathematics.Using models to explore mathematical concepts provides students with a foundation for understanding. Models, such as number lines, allow students to learn new concepts using a familiar tool.

Students have already used number lines to model addition, subtraction, multiplication, and division. In this lesson, students use this familiar tool and addition to find elapsed times of everyday events. In future lessons, students will use the number line to add and subtract to find starting times and ending times.

Measure Time Intervals

LESSON 10.3

Learning ObjectiveUse a number line or an analog clock to measure time intervals in minutes.

Language ObjectiveStudents explain to a partner and give examples of how you can measure elapsed time in minutes.

MaterialsMathBoard

F C R Focus:Common Core State Standards

3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtration of time intervals in minutes, e.g., by representing the problem on a number line diagram.

MATHEMATICAL PRACTICES (See Mathematical Practices in GO Math! in the Planning Guide for full text.)MP1 Make sense of problems and persevere in solving them. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. MP8 Look for and express regularity in repeated reasoning.

F C R Coherence:Standards Across the GradesBefore2.MD.C.7

Grade 33.MD.A.1

After4.MD.A.2

F C R Rigor:Level 1: Understand Concepts....................Share and Show ( Checked Items)Level 2: Procedural Skills and Fluency.......On Your Own, Practice and HomeworkLevel 3: Applications..................................Think Smarter and Go Deeper

F C R For more about how GO Math! fosters Coherence within the Content Standards and Mathematical Progressions for this chapter, see page 559J.

FOCUS COHERENCE RIGOR

ENGAGE1

Lesson 10.3 573B

Daily RoutinesCommon Core

How can you measure elapsed time

in minutes?

Vocabulary BuilderMaterials Semantic Map (see eTeacher Resources)

Elapsed Time Have students use semantic mapping to understand the meaning and uses of the term elapsed time. Have students list words or phrases that are related to the term.

Problem of the Day 10.3A total of 962 students attend Elm Street Elementary School. There are 849 students attending Maple Street Elementary School. How many more students attend Elm Street Elementary than Maple Street Elementary? ?

Vocabulary elapsed time

Interactive Student EditionMultimedia Glossary e

with the Interactive Student Edition

Essential QuestionHow can you measure elapsed time in minutes?

Making ConnectionsInvite students to tell you what they know about analog clocks.

Which hand shows the minutes? the long hand The hours? the short hand How many minutes are there in 1 hour? 60

Learning ActivityWhat is the problem the students are trying to solve? Connect the story to the problem.

• What does Lucia want to know? how long the travelers were stopped for the picnic

• What time did the travelers arrive? 12:15

• What time is it now? 12:47

• Has more or less than an hour passed? less

Literacy and MathematicsChoose one or more of the following activities.

• Write the word elapsed on the board. Ask students to define the word and use it in their own original sentence.

• Ask students to draw a basket and draw what foods they would bring for a picnic.

• Have students write a list of activities and have them come up with start times and end times of the activities. Then have the students trade papers and find the elapsed times of the activities.

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4:10 4:20 4:51

10 min 1 1 min1 10 min  1 10 min1 10 min 1 min 1 min

4:30 4:40 4:50 4:534:52

Unlock the ProblemUnlock the Problem

MATHEMATICAL PRACTICES 4MathTalk

Chapter 10 573

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Alicia and her family visited the

Kennedy Space Center. They watched

a movie that began at 4:10 p.m. and

ended at 4:53 p.m. How long did the

movie last?

To find elapsed time, find the

amount of time that passes from

the start of an activity to the end of

the activity.

Name

Measure Time IntervalsEssential Question How can you measure elapsed time in minutes?

10 + 10 + 10 + 10 + 1 + 1 + 1 = _

The elapsed time from 4:10 P.M. to

4:53 P.M. is _ minutes.

So, the movie lasted _ minutes.

• Circle the times the movie began and ended.

• Underline the question.

One Way Use a number line.

STEP 1 Find the time on the number line that the movie began.

STEP 2 Count on to the ending time, 4:53. Count on by tens for each 10 minutes. Count on by ones for each minute. Write the times below the number line.

STEP 3 Draw the jumps on the number line to show the minutes from 4:10 to 4:53. Record the minutes. Then add them.

Lesson 10.3

Measurement and Data—3.MD.A.1

MATHEMATICAL PRACTICESMP2, MP3, MP4

Use Models What is another way you can use jumps on the number line to find the elapsed time from 4:10 P.M. to 4:53 P.M?

43

43

43

Possible description: start at 4:10. Jump

20 minutes to 4:30 to get to the half hour, jump 20 minutes to 4:50, and then

jump 3 minutes to 4:53 for an elapsed time of 20 + 20 + 3 = 43 minutes.

HandsOn

EXPLORE2

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Name

40 minutes

Use the number line to fi nd the elapsed time.

1. Start: 3:15 P.M. End: 3:45 P.M. 2. Start: 11:05 A.M. End: 11:56 A.M.

Find the elapsed time.

3. Start: 4:10 P.M. End: 4:46 P.M. 4. Start: 10:30 A.M. End: 10:59 A.M.

Use a number line to fi nd elapsed time.

Step 1 Begin with the start time, 4:20.

Step 2 Skip count by tens to count the minutes from 4:20 to 5:00.

Step 3 Label the number line. Draw jumps for every 10 minutes until you get to 5:00.

Step 4 Add the minutes that have elapsed. 40 minutes

So, Julia spends doing homework.

Measure Time Intervals

Julia starts her homework at 4:20 P.M. She fi nishes at 5:00

P.M. How much time does Julia spend doing homework?

Elapsed time is the amount of time that passes from the start of an activity to the end of the activity.

Lesson 10.3

Reteach

Possible drawings

and labels are given.

36 minutes 29 minutes

51 minutes30 minutes

10-9 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

Name

How Much Time?

Find the elapsed time.

1. Mia’s soccer practice started at 3:15 P.M. and ended at 4:10 P.M. How long was Mia’s soccer practice?

2. Alex started eating lunch at 1:20 P.M. He finished at 1:55 in the afternoon. How long did it take Alex to eat lunch?

3. Rose started eating breakfast at 7:45 in the morning. She finished at 8:35. How long did it take for Rose to eat breakfast?

4. Jackson went outside to look at the stars at 8:40 in the evening. He went back inside at 9:25 P.M. How long did Jackson look at the stars?

5. Julio started his homework at 4:40 in the afternoon. He finished at 5:05 P.M. How long did it take Julio to finish his homework?

6. Stretch Your Thinking Pilar wakes up at 6:45 A.M. If she eats breakfast 15 minutes later, at what time does Pilar eat breakfast?

Lesson 10.3

Enrich

7:00 A.M.

25 minutes

45 minutes

50 minutes

35 minutes

55 minutes

10-10 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

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573 Chapter 10

Enrich 10.3Reteach 10.3

3.MD.A.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.

Unlock the Problem MATHEMATICAL PRACTICES

Do you know what the term elapsed time means? In this lesson, you will learn to find elapsed time.Check that students understand they are to find the elapsed time between 4:10 P.M. and 4:53 P.M.

ELL Strategy: Cooperative Grouping

Pair students with similar language levels to scaffold language and vocabulary regarding time.• Model the multiple meanings of last. Explain

how it is used to explain how much time has passed. How long did soccer practice last?

• Have partners use sentence frames to communicate about how long their activities last. When I, it lasts

. Possible answer: When I eat dinner, it lasts twenty minutes.

One WayGuide students to follow the steps and find the elapsed time in minutes using the number line. Point out to students that they can make jumps of any size that make sense, and then record the jumps on the number line.MP3 Construct viable arguments and critique the reasoning of others.• Why does it make sense to start counting

by tens in this example? Possible answer: because the start time is 4:10, which is ten minutes after 4:00

• How many minutes is it from 4:10 to 4:50? 40 minutes

• How many minutes is it from 4:50 to 4:53? 3 minutes

• If you combine 40 minutes and 3 minutes, do you get the same answer as counting jumps on the number line from 4:10 to 4:53? Explain. Yes. You get the same total number of minutes.

MathTalk Use Math Talk to focus on

students’ understanding of finding an elapsed time using jumps of different sizes on a number line.

LESSON 10.3

HandsOn

Other Ways

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So, the elapsed time is _ minutes.

A Use an analog clock.

STEP 1 Find the starting time on the clock.

STEP 2 Count the minutes by counting on by fives and ones to 4:53 P.M. Write the missing counting numbers next to the clock.

4 :

− 4 :

___

→→

→

end time

start time

elapsed time

Start time: 4:10 P.M. End time: 4:53 P.M.

Try This! Find the elapsed time in minutes two ways.

Start time: 10:05 A.M. End time: 10:30 A.M.

A Use a number line.

STEP 1 Find 10:05 on the number line. Count on from 10:05 to 10:30. Draw marks and record the times on the number line. Then draw and label the jumps.

Think: Count on using longer amounts of time that make sense.

STEP 2 Add to find the total minutes from 10:05 to 10:30.

From 10:05 A.M. to __ is _ minutes.

So, the elapsed time is _ minutes.

B Use subtraction.

Think: The hours are the same, so subtract the minutes.

10 : 30 – 10 : 05

__

B Use subtraction.

STEP 1 Write the ending time. Then write the starting time so that the hours and minutes line up.

STEP 2 The hours are the same, so subtract the minutes.

Compare Strategies Which method do you prefer to use to find elapsed time?

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43

Possible drawing and

labels are given.

Possible explanation: a

number line; I can count on

using amounts of time that

make sense to me.10:30 A.M. 25

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3

3

Advanced Learners

Lesson 10.3 574

Other WaysGuide students to follow the steps and find the elapsed time in minutes by using an analog clock and subtraction.

• Why should you to start counting by fives when you use the analog clock to find the elapsed time? because the start time is 4:10 and the numbers on the analog clock are in five-minute intervals

• How is finding the elapsed time using a clock similar to finding the elapsed time using a number line? I find the starting time on either the clock or the number line, and then I count on until I reach the ending time.

When students use subtraction to find the elapsed time, make sure they line up the minutes and hours like they line up place values before subtracting whole numbers.• How is lining up times before subtracting

similar to lining up whole numbers before subtracting? Before I subtract times, I need to line up the minutes and the hours. This is similar to subtracting whole numbers because I need to line up the digits in the same place values before subtracting.

Try This!Guide students to follow the steps and find the elapsed time in minutes. Discuss how they can decide what size jumps to make on the number line so that recording and calculating the elapsed time is easy. Tell students to focus on the amounts of time and not the length of the jumps as they complete the number line.

• Could you count by fives to find the elapsed time? Explain. Yes; you could count by fives from 10:05 to 10:30.

• Why might you choose to count 10 minutes to 10:15 and then 15 minutes to 10:30? It is quicker to choose larger amounts of time.

MathTalk Use Math Talk to focus on

students’ understanding of different methods they can use to find elapsed time.

COMMON ERRORS

Error Students count incorrectly on a number line or an analog clock.

Example Students f ind the elapsed time in Try This! to be 35 minutes.Springboard to Learning Have students find the elapsed time using one method and check their answers using a different method.

VisualIndividual

• Display the flight schedule. Discuss reasons for differences in travel times, such as taking a different route or traveling at a different speed.

Flights from San Francisco, CA to Sacramento, CA

Depart Travel Time Arrive

Flight 1 7:05 A.M. 43 minutes 7:48 A.M.

Flight 2 10:02 A.M. 48 minutes 10:50 A.M.

Flight 3 3:11 P.M. 46 minutes 3:57 P.M.

Flight 4 8:03 P.M. 53 minutes 8:56 P.M.

• Have students find the unknown times. Which flight is the longest? The shortest? Flight 4; Flight 1

Then

EXPLAIN3

1:15

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1:20 1:30 1:40

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5 min

2:302:15 2:45 2:50 2:52

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1 10 min 1 4 min

11:4011:35 11:50 11:54

5 min

On Your OwnOn Your Own

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MATHEMATICAL PRACTICES 4MathTalk

Chapter 10 • Lesson 3 575

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1. Use the number line to find the elapsed time

from 1:15 p.m. to 1:40 p.m. __

2. Start: 11:35 a.m. End: 11:54 a.m.

3. Start: 4:20 p.m. End: 5:00 p.m.

MATHEMATICALPRACTICE 5 Use Appropriate Tools Find the elapsed time.

4. Start: 8:35 p.m. End: 8:55 p.m. 5. Start: 10:10 a.m. End: 10:41 a.m.

6. Start: 9:25 a.m. End: 9:43 a.m. 7. Start: 2:15 p.m. End: 2:52 p.m.

Find the elapsed time.

Name

Use a Model How would you use a number line to find the elapsed time from 11:10 A.M. until noon?

25 minutes

19 minutes

18 minutes 37 minutes

20 minutes 31 minutes

40 minutes

Possible drawing and labels are given.

Possible drawing and labels are given.

Possible drawings and labels

are given.

Possible explanation: start at 11:10. Draw a jump for

the 20 min from 11:10 to 11:30. Draw a jump for the

30 min from 11:30 to 12:00. Add the min: 20 +

30 = 50. So, the elapsed time is 50 min.

Quick Check

If

Rt I RR1

2

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Then

EXPLAIN33 EXPLAIN3

575 Chapter 10

On Your OwnIf students complete the checked exercises correctly, they may continue with the On Your Own section.MP5 Use appropriate tools strategically. Tell students that for Exercises 4 to 7 they will use two tools to find the elapsed time—the analog clock and the number line. Have volunteers discuss how to use each tool to find an elapsed time.MP2 Reason abstractly and quantitatively. Have students find the elapsed time for an event that begins at 11:53 A.M and ends at 12:15 P.M. Ask students to explain why changing from A.M. to P.M. can still result in an elapsed time that is only minutes long.

a student misses the checked exercises

Differentiate Instruction with • Reteach 10.3

• Personal Math Trainer 3.MD.A.1

• Rtl Tier 1 Activity (online)

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

Use the checked exercises for Quick Check.

MathTalk Use Math Talk to focus on students’

understanding of using a number line to find elapsed time. • If you made jumps for every 5 or 10

minutes, how many jumps would you make? Ten 5-minute jumps, or five 10-minute jumps.

ELABORATE4

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

WRITE Math Show Your Work

MATHEMATICAL PRACTICES ANALYZE

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8. John started reading his book about outer space

at quarter after nine in the morning. He read

until quarter to ten in the morning. How long

did John read his book?

9. MATHEMATICALPRACTICE 2 Use Reasoning Tim and Alicia

arrived at the rocket display at 3:40 p.m. Alicia

left the display at 3:56 p.m. Tim left at 3:49 p.m.

If the answer is Alicia, what is the question?

10. DEEPER At the space center, Karen bought a

model of a shuttle. She started working on the

model the next day at 11:13 a.m. She worked

until leaving for lunch at 11:51 a.m. After lunch,

she worked on the model again from 1:29 p.m.

until 1:48 p.m. How long did Karen work on the

model?

11. SMARTER Aiden arrived at the rocket display

at 3:35 p.m. and left at 3:49 p.m. Ava arrived at the

rocket display at 3:30 p.m. and left at 3:56 p.m.

Ava spent how many more minutes at the rocket

display than Aiden?

12. SMARTER Kira got on the tour bus at 5:15 p.m. She got

off the bus at 5:37 p.m. How long was Kira on the bus?

Select the number to make the sentence true.

Kira was on the bus for _ minutes.

30 minutes

Possible question: Who spent more time at the

rocket display?

57 minutes

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15

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52

EVALUATE5 Formative Assessment

Math on the Spot videos are in the Interactive Student Edition and at www.thinkcentral.com.

MATHEMATICAL PRACTICES

Lesson 10.3 576

Students complete orange Activity Card 8 by showing time to the minute and elapsed time on analog clocks.

Students read about Kim’s late start and her attempts to get to school on time.

Students practice telling time to the minute to match cards.

GamesMatching Time

LiteratureLate for School

ActivitiesTime Marches On!

Essential QuestionUsing the Language ObjectiveReflect Have students explain to a partner and give examples to answer the Essential Question.How can you measure elapsed time in minutes? Possible answer: find the starting time. Then use a number line, analog clock, or subtraction to count the minutes to the ending time.

Math Journal WRITE MathDescribe two different methods to find the elapsed time from 2:30 P.M. to 2:58 P.M.

SMARTER

This item assesses a student’s ability to measure intervals of elapsed time. Students should recognize that since the hour did not change, they can subtract the numbers of minutes to find the elapsed number of minutes. Students who select an incorrect answer likely used the wrong operation or misread the question. Help students understand the problem by writing it as a missing addend equation, such as 15 minutes past 5 plus ___ minutes = 37 minutes past 5.

Math on the Spot Video TutorUse this video to help students model and solve this type of Think Smarter problem.

MP2 Reason abstractly and quantitatively. For Exercise 9, have students find how much time each person spent at the display to help them determine the question.

DEEPER

Exercise 10 requires students to use higher order thinking to solve this multistep problem and find the total elapsed time.

SMARTER

Problem Solving • Applications

Cross-Curricular

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Problem SolvingProblem Solving

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Measure Time Intervals

Chapter 10 577

Find the elapsed time.

1. Start: 8:10 a.m. End: 8:45 a.m.

_______

2. Start: 6:45 p.m. End: 6:54 p.m.

_______

5. A show at the museum starts at

7:40 p.m. and ends at 7:57 p.m.

How long is the show?

_______

6. The first train leaves the station at

6:15 a.m. The second train leaves

at 6:55 a.m. How much later does the

second train leave the station?

_______

35 minutes

3. Start: 3:00 p.m. End: 3:37 p.m.

_______

4. Start: 5:20 a.m. End: 5:47 a.m.

_______

Lesson 10.3Practice and Homework

COMMON CORE STANDARD—3.MD.A.1 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

7. WRITE Math Describe two different methods to find

the elapsed time from 2:30 p.m. to 2:58 p.m.

Possible drawings and labels are given.

9 minutes

37 minutes 27 minutes

17 minutes 40 minutes later

Check students’ work.

Practice and HomeworkUse the Practice and Homework pages to provide students with more practice of the concepts and skills presented in this lesson. Students master their understanding as they complete practice items and then challenge their critical thinking skills with Problem Solving. Use the Write Math section to determine student’s understanding of content for this lesson. Encourage students to use their Math Journals to record their answers.

577 Chapter 10

SOCIAL STUDIES

Materials clock faces

Present this information to students:• Two groups measured the outside

temperature each day for a week using the same tools. One group measured daily at 10:05 A.M. and the other group measured at 10:59 A.M. The average temperature for the first group was 55°F, and the second group’s was 57°F.

• One way to explain the difference is that the second group measured the temperature later in the morning when it usually gets warmer. How much time elapsed between the times the two groups measured the temperature? 54 minutes

• Water trails are recreational waterways on a lake, river, or ocean.

• The Middle Allegheny River Water Trail in northwestern Pennsylvania is 107 miles long. Three sections of this river trail are part of the National Wild Scenic Rivers System. This list was made to raise awareness about the fragile nature of America’s river resources.

• Max and his family went canoeing on the Allegheny River. They got into their canoe at 9:02 A.M. and got out to take a break at 9:49 A.M. For how long were Max and his family in the canoe? 47 minutes

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (3.MD.A.1)

Spiral Review (3.OA.A.1, 3.OA.B.6, 3.NBT.A.2, 3.NBT.A.3)

1. Marcus began playing basketball

at 3:30 p.m. and stopped playing at

3:55 p.m. For how many minutes did

he play basketball?

2. The school play started at 8:15 p.m.

and ended at 8:56 p.m. How long was

the school play?

3. Each car has 4 wheels. How many

wheels do 7 cars have?

4. What number completes the

equations?

3 × ■ = 27 27 ÷ 3 = ■

5. There are 20 napkins in each

package. Kelli bought 8 packages for

her party. How many napkins did

Kelli buy in all?

6. Mr. Martin drove 290 miles last week.

This week he drove 125 miles more

than last week. How many miles did

Mr. Martin drive this week?

25 minutes

28 wheels

160 napkins

41 minutes

9

415 miles

Continue concepts and skills practice with Lesson Check. Use Spiral Review to engage students in previously taught concepts and to promote content retention. Common Core standards are correlated to each section.

Lesson 10.3 578