585A Chapter 10

About the MathProfessional Development

LESSON AT A GLANCE

Interactive Student Edition

Personal Math Trainer

Math on the Spot Video

iTools: Measurement

iTools: Number Lines

HMH Mega Math

Professional Development Videos

If Students AskCan you add the different amounts of times together and then find the time rather than acting out each step? Tell them that they can do that. However, explain that it might be a good strategy to act out each step to avoid errors when adding times.

As students solve the problems in this lesson, make sure they know whether they are counting forward from a time or counting back from a time.

Problem Solving • Time Intervals

LESSON 10.5

Learning ObjectiveSolve problems involving addition and subtraction of time intervals by using the strategy draw a diagram.

Language ObjectiveStudents give an example to a partner of how you can use the strategy draw a diagram to solve problems about time.

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.

Also 3.OA.D.8, 3.NBT.A.2

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. MP6 Attend to precision.

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 10.5 585B

Daily RoutinesCommon Core

1 23 4 Pages 44–45 in Strategies and Practice for Skills and Facts Fluency provide additional fluency support for this lesson.

How can you use the strategy draw a diagram to solve

problems about time?

with the Interactive Student Edition

Essential QuestionHow can you use the strategy draw a diagram to solve problems about time?

Making ConnectionsInvite students to tell you what they know about time.

How many minutes are in an hour? 60 minutes In two hours?120 minutes Which part of the time tells you the hour? the first part The minute? the second part

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

• What does Lucia want to know? how many minutes the family played golf

• What time did the family start golfing? 10:15

• What time did they finish? 12:06

• How many breaks did they take? 2 breaks

• How long were the breaks? 3 minutes each

Literacy and MathematicsChoose one or more of the following activities.

• Ask a student to repeat the question in their own words, clarifying the goal for the problem.

• Have the students infer what the family did during their breaks.

• Then have students write about what their families did during their breaks.

1 23 4 Fluency BuilderMultiply Using Skip Counting Practice with students skip counting and the related multiplication. Ask students to solve problems similar to these, using mental math and paper and pencil.

Skip count by fives, 7 times. What is the result? What is the multiplication? 35; 7 3 5 5 35

Skip count by threes, 9 times. What is the result? What is the multiplication? 27; 9 3 3 5 27

Skip count by 10s, 6 times. What is the result? What is the multiplication? 60; 6 3 10 5 60

Skip count by 15s, 3 times. What is the result? What is the multiplication?45; 3 3 15 5 45

Problem of the Day 10.5Fran watched one of the movies shown in the table. She rounded the number of minutes twice: to the nearest ten, and to the nearest hundred. She got the same rounded number both times. Which movie did Fran watch?

Movie Lengths

Movie Minutes

A 185

B 198

C 206

D 210

VocabularyInteractive Student EditionMultimedia Glossary e

B

Common Core Fluency Standard 3.OA.C.7

EXPLORE2

7:30 8:00 8:15 9:15 A.M.

230 min 215 min 260 min

Unlock the ProblemUnlock the Problem

MATHEMATICAL PRACTICES 1MathTalk

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Problem Solving • Time IntervalsEssential Question How can you use the strategy draw a diagram to solve problems about time?

Zach and his family are going to New York City. Their airplane

leaves at 9:15 a.m. They need to arrive at the airport 60 minutes

before their flight. It takes 15 minutes to get to the airport. The

family needs 30 minutes to get ready to leave. At what time

should Zach’s family start getting ready?

I need to find

what __

Zach’s family

should start

___.

the time the __ leaves;

the time the family needs to arrive

at the __ ; the time it takes

to get to the __ ; and the time

the family needs to ___

I will use a

number line to find

the answer.

Read the ProblemWhat do I need to find?

What information do I need to use?

How will I use the information?

Solve the Problem

PROBLEM SOLVINGLesson 10.5

Measurement and Data—3.MD.A.1 Also 3.OA.D.8, 3.NBT.A.2

MATHEMATICAL PRACTICESMP1, MP3, MP6

Analyze How can you check your answer by starting with the time the family starts getting ready?

• Find 9:15 a.m. on the number line.

Draw the jumps to show the time.

• Count back _ minutes to find

the time they need to arrive at the

airport.

• Count back _ minutes to find the time they need to leave for the airport.

• Count back _ minutes to find the time they

need to start getting ready.

So, Zach’s family

should start getting ready at _ _.m.

time

getting ready

airplane

airport

airport

get ready

Possible drawing and labels are given.

Possible answer: start with 7:30 and count forward 30 min,

15 min, and 60 min, to get the time the airplane leaves, 9:15.

7:30 A

60

15

30

215min

4:45 5:00 5:15 P.M.

215min

4:00

245min

215min

4:45 5:00 5:15 P.M.

215min

Name

4:00 P.M.

home

time

4:00 P.M.

4:45 P.M.

5:15 P.M.

30 minutes

45 minutes

Problem Solving • Time Intervals

As soon as Carter got home, he worked on his book report for 45 minutes. Then he did chores for 30 minutes. He finished at 5:15 P.M. At what time did Carter get home?

Read the Problem Solve the Problem

What do I need to find?

I need to find what Carter

got .

• Find Carter’s 5:15 P.M. finishing time on the number line.

• Count back 30 minutes using two 15-minute jumps to find the time Carter

started his chores.

• Count back 45 minutes for the time Carter worked on his report. The jumps end at

So, Carter got home at

What information do I need to use?

Carter worked for on

his report. He did chores

for . He finished

at .

How will I use the information?

I will use a number line and count back to find the time Carter got home.

Lesson 10.5

Reteach

1. Kiera must be at school at 7:45 A.M.The ride to school takes 15 minutes. She needs 45 minutes to eat breakfast and get ready. At what time should Kiera get up?

2. Jack and his family go to the movies. First, they eat lunch at 1:30 P.M. It takes them 40 minutes to eat. Then they drive 25 minutes to get to the movie theater. At what time do Jack and his family get to the theater?

2:35 P.M.6:45 A.M.

10-13 ReteachChapter Resources© Houghton Mifflin Harcourt Publishing Company

8:30 A.M. 10:00 A.M. 10:30 A.M.

breakfast

9:15 A.M.

craftsday

endsday

starts nature walk fishing

11:30 A.M.

sports lunch

8:00 A.M. 12:15 P.M.

Name

8. How long is a day at camp? Write the elapsed time.

9. Stretch Your Thinking Use the schedule and your number line. Can fishing happen at a different time? Explain.

Spending Time at Camp

Tomas has to make a schedule for a day at camp. Use the

information below to make a possible schedule that includes each

activity. Use the number line to show when each activity will happen.

Hint: Some activities might be possible at more than one time.

1. Breakfast starts at 8:00 A.M. and lasts for 30 minutes.

2. Lunch lasts 45 minutes and ends at 12:15 P.M.

3. The day at camp ends after lunch at 12:15 P.M.

4. Sports last 60 minutes.

5. Craft class starts right after breakfast and lasts 45 minutes.

6. Fishing lessons last 30 minutes.

7. Nature walk lasts 45 minutes and ends before sports.

Lesson 10.5

Enrich

Yes. Possible explanation: The schedule tells me that the nature

walk comes before sports. The schedule does not tell me when

fishing starts or ends. Based on the other activities, it could come

before or after the nature walk or could come before or after sports.

255 minutes, or 4 hours 15 minutes

Possible answers are given.

10-14 EnrichChapter Resources© Houghton Mifflin Harcourt Publishing Company

1

2

3 DifferentiatedInstruction

585 Chapter 10

Enrich 10.5Reteach 10.5

Unlock the ProblemMATHEMATICAL PRACTICES

After students read the problem, discuss the different times that need to be considered when figuring out what time Zach and his family should start getting ready.MP5 Use appropriate tools strategically.• How does the graphic organizer help you

solve the problem? Possible answer: when I fill in the blanks in the graphic organizer, I know what to consider in order to solve the problem.

Be sure students understand the need to include the time the plane leaves on their number line and to jump back to include the times needed to get to the airport and to get ready before leaving for the airport.Remind students that when using a number line to find elapsed time, they can add or subtract time to get to an hour to make calculations with elapsed time easier. Point out that on this number line they are subtracting the times from right to left. It also may help to point out that 60 minutes is 1 hour when students jump back from 9:15 to 8:15.• Is there another way to count back on the

number line? Explain. Possible answer: count back 15 minutes to 9:00, then 60 minutes to 8:00, and 30 minutes to 7:30.

• How could you use a clock face to help you solve the problem? Possible answer: start with 9:15 and move the hands back 60 minutes, then 15 minutes, and then 30 minutes to find the time they need to start getting ready.

MathTalk Use Math Talk to focus on

students’ understanding of when to jump forward and when to jump back on a number line. • Explain how you use the number line to

find an ending time when you know the starting time, and how you find a starting time when you know the ending time. Possible answer: To find an ending time, jump forward from the starting time. To find a starting time, jump back from the ending time.

MP6 Attend to precision.• Compare and contrast using a number line

and a clock face to find the family’s starting time. Possible answer: With both methods, you are counting back by minutes. With the number line, you subtract time intervals using jumps that total the elapsed time. With the clock face, you count back by fives and ones by moving the hands to see the jumps.

LESSON 10.53.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.

WRITE Math Show Your Work

Try Another Problem

110 min 110 min 18 min 120 min

2:45 P.M. 2:55 3:05 3:13 3:33

MathTalk MATHEMATICAL PRACTICES 1

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Bradley gets out of school at 2:45 p.m. It takes him

10 minutes to walk home. Then he spends 10 minutes

eating a snack. He spends 8 minutes putting on his

soccer uniform. It takes 20 minutes for Bradley’s father to

drive him to soccer practice. At what time does Bradley

arrive at soccer practice?

1. At what time does Bradley arrive at soccer practice? __

2. How do you know your answer is reasonable?

Read the Problem

Solve the Problem

What do I need to find?

What information do I need to use?

How will I use the information?

Draw a diagram to help you explain your answer.

Analyze Do you need to draw jumps on the number line in the same order as the times in the problem?

3:33 P.M.

Possible answer: I checked my answer by starting at 3:33

and counting back on the number line 20 minutes, 8 minutes,

10 minutes, and 10 minutes to get to the starting time of 2:45.

Math Talk: No; possible explanation:

you can add numbers in any order that

makes sense and get the same answer.

I need to fi nd what time

Bradley arrives at soccer

practice.

the time Bradley gets out of

school; the time it takes to

walk home; the time it takes

to eat a snack; the time it

takes to get dressed; and the

time it takes to get to soccer

practice

I can start with the time

Bradley gets out of school

and draw a number line

to fi nd the time Bradley

arrives at soccer practice.

Possible drawing and

labels are given.

See above.

COMMON ERRORS

Advanced Learners

Lesson 10.5 586

Error Students might count back to find the ending time instead of count forward.

Example In Try Another Problem, students may count back 48 minutes from 2:45 to 1:57 instead of forward to 3:33.Springboard to Learning Have students make a diagram using arrows to indicate the direction they should count from a time.

Try Another ProblemHave students answer the questions in the graphic organizer to solve the problem.• How is this problem different from the

problem on page 585? I need to find a time after the given time, not before the given time.

• How was the way you used the number line to solve this problem different from the problem on page 585? Possible answer:I jumped forward on the number line to find the time.

• How did you decide what size jumps to make on the number line? Possible answer: I made jumps for every elapsed time in the problem.

• How did you find the time Bradley arrived at soccer practice? Possible answer: I looked at the jumps I made on the number line. Then I wrote the time each jump ended.

MathTalk Use Math Talk to help students

recognize that the jumps can be made in any order that makes sense for the problem.

You may suggest that students place completed Try Another Problem graphic organizers in their portfolios.

ELL Strategy: Cooperative Grouping

Group students with similar language levels to explain how timelines can help solve problems about time.• Have pairs of students label a timeline for

one of the problems in the lesson and find the starting or ending time.

• Have them each discuss the process to their partner using sentence frames. First they . It took minutes. Then they . It took minutes. Using the timeline, I can see that they had to by .

• Give students starting and ending times for a class party.

• Have students make a table listing party activities, such as movies, games, or singing, and times for each activity.

• Ask students to use their understanding of elapsed time to write an elapsed time problem that can be solved by using information in the table and acting it out.

• Have students exchange tables and problems and solve the problems. Check students’ work.

VisualIndividual / Partners

EXPLAIN3

11:30 A.M. 11:55 12:00 12:35

125 min 15 min 135 min

On Your OwnOn Your Own

Share and ShShare and ShShare and Show MATHBOARDMATHBOARD

Chapter 10 • Lesson 5 587

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√ Circle the question.

√ Underline important facts.

√ Choose a strategy you know.1. Patty went to the shopping mall at 11:30 a.m.

She shopped for 25 minutes. She spent 40 minutes

eating lunch. Then she met a friend at a movie.

At what time did Patty meet her friend?

First, begin with __ on the number line.

Then, count forward ___ and ___.

So, Patty met her friend at _ _m.

2. What if Patty goes to the mall at 11:30 a.m. and meets a

friend at a movie at 1:15 p.m.? Patty wants to shop and have

45 minutes for lunch before meeting her friend. How much

time can Patty spend shopping?

3. Avery got on the bus at 1:10 p.m. The trip took 90 minutes.

Then she walked for 32 minutes to get home. At what time

did Avery arrive at home?

Think: I can break apart the times into shorter amounts of time that make sense.

Unlock the Problem

4. DEEPER Kyle and Josh have a total of 64 CDs. Kyle has

12 more CDs than Josh. How many CDs does each boy

have?

60 minutes, or 1 hour

3:12 P.M.

Kyle: 38 CDS; Josh: 26 CDS

11:30

40 minutes25 minutes

12:35 P.

Possible drawing and labels are given.

Quick Check

If

Rt I RR1

2

3

Then

587 Chapter 10

a student misses the checked exercises

Differentiate Instruction with • Reteach 10.5

• Personal Math Trainer 3.MD.A.1

• Rtl Tier 1 Activity (online)

Share and Show MATHBOARDMATHBOARDMBMMMBBBMATHABOARDMMMAAATHATHTHHAAAAAAAAATTAAAABOARDBOARDBOARD

The first problem connects to the learning model. Have students use the MathBoard to explain their thinking.• Why do you jump forward on the number

line to solve the first problem? Possible answer: to find a time after 11:30

Use the checked exercises for Quick Check. Students should show their answers for the Quick Check on the MathBoard.

MP3 Construct viable arguments and critique the reasoning of others. To extend their thinking, have students explain how they could solve Exercise 2 a different way.

On Your OwnIf students complete the checked exercises correctly, they may continue with the On Your Own section.

DEEPER

Exercise 4 requires students to use logical reasoning to determine the answers. Students must think of two numbers that have a sum of 64 and a difference of 12.

ELABORATE4

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIES

MATHEMATICAL PRACTICES COMMUNICA E CONSTRUCT ARGUMENTS

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5. Jamal spent 60 minutes using the computer. He spent a

half hour of the time playing games and the rest of the

time researching his report. How many minutes did

Jamal spend researching his report?

6. SMARTER When Caleb got home from

school, he worked on his science project for

20 minutes. Then he studied for a test for

30 minutes. He finished at 4:35 p.m. At what

time did Caleb get home from school?

7. MATHEMATICALPRACTICE 6 Miguel played video games each day for a

week. On Monday, he scored 83 points. His score went

up 5 points each day. On what day did Miguel score

103 points? Explain how you found your answer.

8. SMARTER When Laura arrived at the library, she spent

40 minutes reading a book. Then she spent 15 minutes

reading a magazine. She left the library at 4:15 p.m.

Circle the time that makes the sentence true.

Laura arrived at the library at 3:20 p.m.

3:35 p.m.

5:10 p.m.

30 minutes

3:45 P.M.

Friday;

possible explanation: I added 5 until I got a sum of 103. Since

I added 4 fi ves, I counted 4 days after Monday to reach Friday.

EVALUATE5 Formative Assessment

Differentiated Centers Kit

DIFFERENTIATED INSTRUCTION INDEPENDENT ACTIVITIESD

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

MATHEMATICAL PRACTICES

Lesson 10.5 588

MP6 Attend to precision. Exercise 7 can be solved in a number of different ways. Students may choose to add 5 to Miguel’s total number of points until they reach 103 and then determine how many 5s were added. Students may also begin by finding the difference between 103 and 83 and then dividing that difference by 5 to determine the number of days it took Miguel to score 103 points.

SMARTER

This item assesses a student’s ability to solve multi-step problems involving elapsed time. Students will need to count back from the end time for each of two time intervals to find the start time. Students who select an incorrect answer likely used only one of the two intervals or used the end time as the beginning time.

SMARTER

Essential QuestionUsing the Language ObjectiveReflect Have students give an example to a partner to answer the Essential Question.How can you use the strategy draw a diagram to solve problems about time? Possible answer: I can draw a number line to find the solution to an elapsed time problem.

Math Journal WRITE MathWrite a multistep word problem that has at least two amounts of elapsed time. The problem may require finding a starting time or ending time. Include a solution.

Students read the book and measure time intervals.

LiteratureA Walk on the Path

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

ActivitiesTime Marches On!

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

11:45 12:45 1:05 1:20

60 min + 20 min +15 min

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Chapter 10 589

Solve each problem. Show your work.

Problem Solving • Time Intervals

1. Hannah wants to meet her friends

downtown. Before leaving home, she does

chores for 60 minutes and eats lunch for

20 minutes. The walk downtown takes

15 minutes. Hannah starts her chores at

11:45 a.m. At what time does she meet

her friends?

_____

2. Katie practiced the flute for 45 minutes.

Then she ate a snack for 15 minutes. Next,

she watched television for 30 minutes,

until 6:00 p.m. At what time did Katie start

practicing the flute?

_____

3. Nick gets out of school at 2:25 p.m. He has

a 15-minute ride home on the bus. Next,

he goes on a 30-minute bike ride. Then he

spends 55 minutes doing homework. At

what time does Nick finish his homework?

_____

1:20 P.M.

Lesson 10.5Practice 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.

4. WRITE Math Write a multistep word problem that has

at least two amounts of elapsed time. The problem may

require finding a starting time or ending time. Include a

solution.

4:30 P.M.

Check students’ work.

4:05 P.M.

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.

589 Chapter 10

Extend the Math Activity

Estimating TimeMaterials clock or watch

Investigate Students have measured elapsed time in minutes. In this activity, students will estimate and then measure elapsed time.

• Share the following problem with students.

Arturo gets in the checkout line at the grocery store. Three people are standing in front of him. It takes the first person 4 minutes to check out. If it takes each person the same amount of time, about how much time will pass before Arturo is finished checking out? about 16 minutes

• Have students work in pairs to solve the problem. Discuss their solutions. Point out that they can use repeated addition ( 4 1 4 1 4 1 4 5 16) or multiplication (4 3 4 5 16) to find the estimated elapsed time.

• Give students the following table to complete.

Place Number of People

in Line

Estimated Time for

Each Person

Total Estimated

Waiting Time

Movie Theater 6 2 minutes 12 min

Snack Counter 3 3 minutes 9 min

Post Office 5 3 minutes 15 min

• Have students measure the waiting time for each place by using a clock or watch to determine how long it takes for the last person in line to finish checking out. Ask students to compare their estimated waiting times to the actual times.

Summarize Discuss why estimating time intervals is a good skill to have. Ask students to discuss situations where estimating time is important. For example, getting to an appointment on time.

Personal Math Trainer

FOR MORE PRACTICE GO TO THE

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Lesson Check (3.MD.A.1)

Spiral Review (3.OA.A.2, 3.OA.A.4, 3.NF.A.2, 3.NF.A.3d)

1. Gloria went to the mall and spent

50 minutes shopping. Then she had

lunch for 30 minutes. If Gloria arrived

at the mall at 11:00 A.M., at what time

did she finish lunch?

2. The ball game begins at 2:00 P.M.

It takes Ying 30 minutes to get to

the ballpark. At what time should

Ying leave home to get to the game

30 minutes before it starts?

3. Write the fractions 2 __ 4

, 2 __ 8

, and 2 __ 6

in order

from least to greatest.

4. Find the unknown factor.

6 × ■ = 36

5. There were 405 books on the library

shelf. Some books were checked

out. Now there are 215 books left

on the shelf. How many books were

checked out?

6. Savannah has 48 photos. She places

8 photos on each page of her photo

album. How many pages in the

album does she use?

12:20 P.M.

2 __ 8 , 2 __

6 , 2 __

4

190 books

1:00 P.M.

6

6 pages

Monitoring Common Core Success

Maintaining Focus on the Major WorkPart of the major work in Grade 3 is solving problems involving measurement of time (3.MD.A). In Lessons 10.1–10.5, students explore concepts of time. In Lessons 10.1–10.2, students focus on telling time to the nearest minute. Students understand that each number on the face of a clock represents 5 minutes and each incremental step between numbers represents 1 minute. In Lessons 10.3–10.5, students measure time intervals and use addition and subtraction to solve problems involving time.

Connecting Content Across Domains and ClustersIn Lessons 10.3–10.5, a connection is made between estimating and measuring time (3.MD.A) and multi-digit arithmetic (3.NBT.A). In order to work with time intervals and add and subtract increments of time, students must be fluent in adding and subtracting whole numbers. Students apply some of the strategies they used in arithmetic to working with time, including skip counting and using jumps on a number line. As students work with time intervals, they may recognize how the relationship between minutes and hours is similar to the place value

relationships they have used with whole numbers. They not only recognize that they can rename 1 ten as 10 ones, but they may also recognize that they can rename 1 hour as 60 minutes.

Building FluencyIn Grade 3, Standard 3.NBT.A.2 requires students to fluently

add and subtract within 1,000. Students continue to build fluency when adding and subtracting units of time. In Lessons 10.3–10.5, the increased attention to detail required when adding and subtracting units of time furthers students’ fluency with addition and subtraction.

Build fluency with associated fact fluency activities and strengthen students’ proficiency with various math strategies. Use Strategies and Practices for Skills and Fact Fluency—Intermediate, G3–6: Level 3, Worksheets 3A–3B to strengthen students’ mastery of adding and subtracting within 1,000.

1 23 4

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 10.5 590