Develop Skills and Strategies
Lesson 21
Part 1: Introduction
CCSS
3.MD.A.1
Solve Problems About Time
In Lesson 20, you learned how to tell time to the minute. Take a look at this
problem.
Beth left her house at 4:30. She arrived at dance class at 5:05. How long did it
take Beth to get to dance class from her house?
AM
PM
AM
PM
Explore It
Use the math you already know to solve this problem.
Draw the hands on the two clocks below to show the correct times.
11
10
12
1
9
3
8
11
10
2
6
5
1
2
9
4
7
12
3
8
Left house
4
7
6
5
Arrived at dance class
Look at the first clock. How many minutes before 5:00 is 4:30? Look at the second clock. How many minutes after 5:00 is 5:05? Explain how you can find the total amount of time it took Beth to get from her
house to dance class. 188
L21: Solve Problems About Time
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Part 1: Introduction
Lesson 21
Find Out More
Elapsed time is the time that has passed between a starting time and an ending
time. To find elapsed time, you can count the number of minutes between the
starting time and the ending time. You can use a clock to help you.
At 4:30, the long hand is on the 6. At 5:05, the long hand is on the 1.
20
35
30
25
12
11
10
1
2
9
15
3
8
4
7
10
6
5
5
In this problem, the starting time and ending time are in different hours on the clock.
Beth left her house at 4:30. She arrived at dance class at 5:05. You can figure out how
many minutes before 5:00 she left (30 minutes) and how many minutes after 5:00 she
arrived (5 minutes). Then you can add these amounts: 30 1 5 5 35.
You can also use a number line to help you understand elapsed time. Each long mark
shows 5 minutes. Count minutes on the number line just like you would on a clock.
5
4:30
10
15
20
25
4:45
30
35
5:00
5:15
Reflect
1 Elsa started eating lunch at 11:25 and finished at 11:45. Explain how to find out
how long it took Elsa to eat lunch. L21: Solve Problems About Time
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189
Part 2: Modeled Instruction
Lesson 21
Read the problem below. Then explore different ways to find the end time
when you know the start time and the amount of elapsed time.
Jenna got home from school at 3:30. She did math homework for 10 minutes.
Then she did science homework for 15 minutes. Then she practiced the piano
for 22 minutes. What time did Jenna finish?
Picture It
You can use a clock to help you find the end time.
The first clock shows 3:30, since that is when Jenna started her homework. 10 minutes
are counted for her math homework, 15 minutes for her science homework, and
22 minutes for her piano practice.
The second clock shows the time Jenna finished.
10
5
15
10
11
10
12
1
15
9
5
3
8
6
22
1
2
3
8
5
5
12
9
4
7
10
11
10
20
2
4
7
6
5
Model It
You can also use a number line to help you find the end time.
This number line shows times instead of ordinary numbers. Each long mark shows
5 minutes.
Start at 3:30. Jump along the number line three times to show how long it took Jenna
to do each thing.
10
3:30
15
3:45
22
4:00
4:15
4:30
The last jump on the number line shows what time Jenna was finished with all
three things.
190
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Part 2: Guided Instruction
Lesson 21
Connect It
Now you will find the end time for the problem from the previous page.
2 Explain how to figure out how many total minutes Jenna spent doing homework
and practicing piano. 3 Explain how you could use the total elapsed time to find what time Jenna finished
doing her homework and practicing the piano. 4 What time did Jenna finish? Why is the hour not 3 anymore?
5 Explain how to find the ending time when you know the start time and the total
elapsed time. Try It
Use what you have learned about finding the end time to help you solve these
problems.
11
10
6 Nate finished supper at 7:10. He did dishes for 15 minutes and then
took a shower for 10 minutes. Then he read for 15 minutes before
he went to bed. What time did Nate go to bed? 12
1
2
9
3
8
4
7
6
5
7 Kari started talking on the phone at 5:45. She talked to her
grandma for 10 minutes, her grandpa for 5 minutes, and
her cousin for 8 minutes. What time did Kari get off the phone? 5:45
6:00
L21: Solve Problems About Time
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6:15
191
Part 3: Modeled Instruction
Lesson 21
Read the problem below. Then explore different ways to find the start time
when you know the end time and the amount of elapsed time.
Marc’s guitar lesson starts at 4:20. It takes 15 minutes to get there from his
house, and before he leaves, he has to do some chores for 25 minutes. What
time should Marc start doing his chores to make it to his lesson on time?
Picture It
You can use a clock to help you find the start time.
The clock shows 4:20, since that is when Marc’s guitar lesson starts. 15 minutes are
counted backward for the time it takes to get to his lesson, and 25 minutes are
counted backward for the time it will take to do his chores.
The second clock shows the time Marc should start his chores.
10
15
20
25
11
10
5
12
1
15
2
9
3
8
4
7
6
5
11
10
10
12
1
2
9
5
3
8
4
7
6
5
Model It
You can also use a number line to help you find the start time.
This number line is like the one used for the last problem. It shows times, and each
long mark shows 5 minutes. Each short mark shows 1 minute.
Start where 4:20 would be.
25
3:30
3:45
15
4:00
4:15
4:30
Count backward the time it will take to get to his lesson and do his chores.
192
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Part 3: Guided Instruction
Lesson 21
Connect It
Now you will find the start time for the problem from the previous page.
8 Explain why the times are counted backward on the clock and the number line.
9 What time should Marc start doing his chores? Why is the hour not 4 anymore? 10 Explain how to find the starting time when you know the end time and the
elapsed time. Try It
Use what you’ve learned about finding the start time to help you solve these
problems.
11 Enrique walked 5 minutes from his grandma’s house to the store, stopped at the
store for 20 minutes, and then walked 10 minutes from the store to his house.
He got home at 6:00. What time did he leave his grandma’s house? 11
10
12
1
2
9
3
8
4
7
6
5
12 Mira finished helping make lunch at 12:30. She cut up fruit for 10 minutes and
made sandwiches for 7 minutes. What time did she start helping? 12:00
12:15
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12:30
12:45
1:00
193
Part 4: Guided Practice
Lesson 21
Study the model below. Then solve problems 13–15.
Student Model
The student used what
she knew about telling
time before and after
the hour to find the
answer.
Pair/Share
How else could you
have solved this
problem?
Do you need to count
minutes forward or
backward from 2:15 to
find the time he started
watching his sister?
Malea’s soccer game started at 9:40 and ended at 10:32. How
long was Malea’s game?
Look at how you could show your work.
9:40 is 20 minutes before 10:00.
10:32 is 32 minutes after 10:00.
20 1 32 5 52
Solution: 52 minutes
13 Lamar watched his little sister while his mom was busy. He played
blocks with her for 15 minutes, peek-a-boo for 5 minutes, and
trains for 13 minutes. His mom came back to put her down for a
nap at 2:15. What time did Lamar start watching his sister?
Show your work.
Pair/Share
How did you decide
how you would solve
the problem?
194
Solution: L21: Solve Problems About Time
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Part 4: Guided Practice
14 Mr. Chen started doing yard work at 10:00. He watered flowers
for 6 minutes, weeded his garden for 12 minutes, and trimmed
bushes for 27 minutes. What time was Mr. Chen done with his
yard work?
Lesson 21
I think adding all of the
times together would
make this problem easier
to solve.
Show your work.
Pair/Share
Solution: 15 Carter finished cleaning his room at 11:35. It took him 10 minutes
to put all his toys away and 4 minutes to make his bed. What time
did Carter start cleaning his room? Circle the letter of the correct
answer.
Did you need to draw a
clock or number line to
help you? Why or why
not?
Will the time Carter
started be before or after
11:35?
A11:49
B11:25
C11:21
D10:21
Ann chose A as the correct answer. How did she get that answer?
L21: Solve Problems About Time
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Pair/Share
Does Ann’s answer
make sense?
195
Part 5: Common Core Practice
Lesson 21
Solve the problems.
1 What is the elapsed time between 1:08 and 1:37?
A
25 minutes
C
30 minutes
B
29 minutes
D
31 minutes
2 It took Juan 5 minutes to ride his bike to the park, where he played basketball for
25 minutes. Then it took him 5 minutes to ride home again. He got home at 10:10.
Which clock shows the time Juan left for the park?
11
10
12
1
11
10
2
9
6
4
7
5
A
11
10
12
1
11
10
6
12
1
2
3
8
4
7
5
9
3
8
6
C
2
9
2
3
8
4
7
1
9
3
8
12
4
7
5
B
6
5
D
3 Patty, Joyce, and Stef are getting ready to leave for school. Choose Yes or No to tell
whether each girl will be ready before 7:45.
a. Patty gets up at 7:10. It takes her 10 minutes
to get ready, 7 minutes to pack her lunch, and
15 minutes to eat breakfast.
Yes
No
30 minutes. Then it takes her 20 minutes to
get ready and 12 minutes to eat breakfast.
Yes
No
Stef gets up at 7:15. It takes her 15 minutes
to get ready, 5 minutes to pack her lunch,
and 9 minutes to eat breakfast.
Yes
No
b. Joyce gets up at 6:50 and exercises for
c.
196
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Part 5: Common Core Practice
Lesson 21
4 Joe spent 40 minutes reading a magazine. Choose all the pairs of clocks that show
possible times that he started and finished.
A
B
Start:
Finish:
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
Start:
11 12 1
2
10
9
3
8
4
7 6 5
Start:
Finish:
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
Finish:
Start:
Finish:
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
C
D
5 Mariah played two games of checkers with her brother. The first game took
12 minutes and the second game took 18 minutes. They put the game away at 7:55.
What time did they start?
Show your work.
Answer They started playing at .
6 Seve started writing thank you notes at 5:25. It took him 20 minutes to write them.
He also spent some time writing addresses on the envelopes. He finished at 6:00. How
long did it take Seve to write the addresses?
Show your work.
Answer It took Seve minutes to write the addresses.
Self Check Go back and see what you can check off on the Self Check on page 179.
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197
Develop Skills and Strategies
Lesson 21
(Student Book pages 188–197)
Solve Problems About Time
Lesson Objectives
The Learning Progression
•Measure time intervals in minutes using clock
models and number lines.
At this grade level, students have already learned to tell
time to the nearest minute. They will now apply this
skill to measuring time intervals in minutes, as well as
solving problems involving addition and subtraction of
time intervals.
•Solve word problems involving addition of time
intervals in minutes.
•Solve word problems involving subtraction of time
intervals in minutes.
Prerequisite SkilLs
In order to be proficient with the concepts/skills in this
lesson, students should:
•Tell time to the nearest minute.
•Add and subtract two-digit numbers.
•Count by fives and ones.
Vocabulary
Students learn to reason about the relationship between
start time, elapsed time, and end time. They are asked
to find an unknown start or end time in problems
involving multiple time intervals.
A good understanding of time intervals and elapsed
time will provide a foundation for the next grade level,
where students will measure time using seconds,
minutes, and hours. They will solve problems involving
time intervals using all four operations, as well as
conversions between units.
Teacher Toolbox
elapsed time: the time that has passed between a start
time and an end time
Teacher-Toolbox.com
Prerequisite
Skills
3.MD.A.1
✓
✓
✓
✓
Ready Lessons
Tools for Instruction
Interactive Tutorials
CCSS Focus
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.
STANDARDS FOR MATHEMATICAL PRACTICE: SMP 1, 3, 4, 5, 6 (see page A9 for full text)
L21: Solve Problems About Time
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215
Part 1: Introduction
Lesson 21
At a Glance
Students read a word problem and answer a series of
questions designed to find elapsed time.
Develop skills and strategies
Lesson 21
Part 1: introduction
ccss
3.MD.a.1
solve Problems about time
Step By Step
in Lesson 20, you learned how to tell time to the minute. take a look at this
problem.
•Tell students that this page models how to find the
time that has passed from a start time to an end time.
Beth left her house at 4:30. She arrived at dance class at 5:05. How long did it
take Beth to get to dance class from her house?
•Have students read the problem at the top of the
page.
AM
PM
AM
PM
explore it
•Work through Explore It as a class.
use the math you already know to solve this problem.
Draw the hands on the two clocks below to show the correct times.
•Ask students to explain how they figured out the
number of minutes before and after 5:00 for the two
times given.
11
10
12
1
11
10
2
9
3
8
4
7
6
5
Left house
•Ask student pairs or groups to explain their answer
for the remaining question.
12
1
2
9
3
8
4
7
6
5
arrived at dance class
Look at the first clock. How many minutes before 5:00 is 4:30?
Look at the second clock. How many minutes after 5:00 is 5:05?
30
5
Explain how you can find the total amount of time it took Beth to get from her
house to dance class. Possible answer: you can add the time from 4:30 to
5:00 to the time from 5:00 to 5:05. 30 1 5 5 35 minutes
188
Hands-On Activity
Use a stopwatch and a clock to find elapsed
time.
Materials: paper, pencils, stopwatches (1 per group
of 3 students)
•Make a list of activities that students could time
during the day (math lesson, lunch period, recess,
free reading time, etc.).
•Put students in groups of 3. One student should
record the start time of each activity, one student
should record the end time of each activity, and
one student should use the stopwatch to time each
activity from start to end.
L21: Solve Problems About Time
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Mathematical Discourse
•What is another way you could solve the problem?
Student responses may include counting
by fives starting at the 6 and continuing
around the clock until the 1 (or backwards
from the 1 to the 6).
•The hour on the digital clock changed from 4 to 5.
Why isn’t the answer more than an hour?
Student responses should indicate an
understanding that just because the hour digit
changes, it does not mean that a full hour has
gone by. Think of the elapsed time from 4:59 to
5:00. The hour digit changes, but only 1 minute
has elapsed.
•Once all activities are complete, groups should get
together to figure the elapsed time based on the
start and end times recorded. Then compare their
answers with the elapsed times recorded on the
stopwatch.
216
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Part 1: Introduction
Lesson 21
At a Glance
Students use clocks and number lines to help
understand elapsed time.
Step By Step
•Read Find Out More as a class.
•Have students use their fingers to trace the jumps
around the outside of the clock to practice counting
to find elapsed time.
•Discuss how to use time before and after the hour to
write an addition problem to find the answer. Point
out that the answer is the same as when they counted
the minutes around the clock.
•Emphasize that this addition method can only be
used when the times are in consecutive hours
(hours that are right next to each other). Give
examples of situation where it would not work.
(4:30 to 4:45 is not 30 1 45 5 75 minutes or
4:30 to 6:05 is not 30 1 5 5 35 minutes.) Discuss
alternate ways to find elapsed time in those
situations.
•Point out that counting elapsed time on a number
line is much like counting it on a clock.
Part 1: introduction
Lesson 21
Find out More
elapsed time is the time that has passed between a starting time and an ending
time. To find elapsed time, you can count the number of minutes between the
starting time and the ending time. You can use a clock to help you.
At 4:30, the long hand is on the 6. At 5:05, the long hand is on the 1.
20
35
30
25
12
11
10
1
2
9
15
3
8
4
7
10
5
6
5
In this problem, the starting time and ending time are in different hours on the clock.
Beth left her house at 4:30. She arrived at dance class at 5:05. You can figure out how
many minutes before 5:00 she left (30 minutes) and how many minutes after 5:00 she
arrived (5 minutes). Then you can add these amounts: 30 1 5 5 35.
You can also use a number line to help you understand elapsed time. Each long mark
shows 5 minutes. Count minutes on the number line just like you would on a clock.
5
10
4:30
15
20
4:45
25
30
35
5:00
5:15
reflect
1 Elsa started eating lunch at 11:25 and finished at 11:45. Explain how to find out
how long it took Elsa to eat lunch. Possible answer: at 11:25, the long hand is
on the 5. at 11:45, the long hand is on the 9. start at the 5 on the clock and
count by fives to the 9 on the clock: 5, 10, 15, 20. it took elsa 20 minutes to
eat lunch.
L21: Solve Problems About Time
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189
•Discuss students’ answers to the Reflect question.
Concept Extension
Real-World Connection
See the connection between a clock and the
number line.
Encourage students to think about everyday places
or situations where people need to determine
elapsed time. Have volunteers share their ideas.
•Draw the number line shown on the board.
Write the corresponding digit from the clock
underneath the times given and each large mark
that shows 5 minutes. For example, under 4:30
write a 6. Under the next large mark, write a 7.
Examples: determining the length of a movie,
recording how many minutes they read at home or
practice an instrument, figuring out how long they
have to wait until recess
•Explain to students that the digits written below
the given times and large marks tell where the
minute hand points at each given time.
•Guide students to see that moving from the
6 to the 7 on the clock is the same as moving
5 minutes on the number line.
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217
Part 2: Modeled Instruction
Lesson 21
At a Glance
Part 2: Modeled instruction
Students use models and number lines to solve
problems involving the addition of time intervals.
read the problem below. then explore different ways to find the end time
when you know the start time and the amount of elapsed time.
Step By Step
Jenna got home from school at 3:30. She did math homework for 10 minutes.
Then she did science homework for 15 minutes. Then she practiced the piano
for 22 minutes. What time did Jenna finish?
•Read the problem at the top of the page as a class.
Picture it
•Read Picture It. Have students trace the jumps
around the clock with their fingers as they count
aloud the time for each activity. Have a volunteer
explain why the hour hand moved from the 3 to the
4, even though the elapsed time was less than an
hour. [Because the minute hand went past the 12.]
you can use a clock to help you find the end time.
The first clock shows 3:30, since that is when Jenna started her homework. 10 minutes
are counted for her math homework, 15 minutes for her science homework, and
22 minutes for her piano practice.
The second clock shows the time Jenna finished.
10
5
15
10
12
11
10
1
15
5
3
8
10
22
4
7
6
11
10
20
2
9
•Read Model It together as a class. Discuss that the
number line shows the same information as the clock
model above, just in a different way.
12
1
3
8
5
2
9
4
7
6
5
5
Model it
you can also use a number line to help you find the end time.
This number line shows times instead of ordinary numbers. Each long mark shows
5 minutes.
•You may wish to draw the number line on the board
and draw the jumps to mirror those shown on the
clock. (5, 10; 5, 10, 15; 5, 10, 15, 20, 21, 22)
Start at 3:30. Jump along the number line three times to show how long it took Jenna
to do each thing.
10
SMP Tip: Using both clocks and number lines
helps students see the value of using various models
in mathematics (SMP 4). You can encourage
students to solve problems involving elapsed time
using either of these models and to share their
solutions with others. Students may also want to
use equations to model their thinking.
Lesson 21
3:30
15
3:45
22
4:00
4:15
4:30
The last jump on the number line shows what time Jenna was finished with all
three things.
190
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Mathematical Discourse
•Which model do you prefer to use to help solve the
problem? Explain why.
Students may choose either model, but should
justify their choice with why that method is
more helpful to them.
•What is another way you could solve this problem?
Student responses may include using an
equation to find the total elapsed time before
starting to count from 3:30. They may also
include breaking up the total elapsed time of
47 minutes into chunks of 30 and 17 minutes
to help them find the end time mentally.
218
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Part 2: Guided Instruction
Lesson 21
At a Glance
Students revisit the problem on page 190 to learn how
to find the end time when the start time and the
amount of elapsed time is known.
Part 2: guided instruction
Lesson 21
connect it
now you will find the end time for the problem from the previous page.
2 Explain how to figure out how many total minutes Jenna spent doing homework
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 190.
•Review how to find the total elapsed time.
•Ask: What do you need to do when you count around
the clock and go past the 12? [Make the hour
1 greater.]
•Ask: What would be the end time if Jenna had started
her homework at 3:00? [3:47] Why didn’t the hour
change? [The minute hand did not go past the 12
when counting the elapsed time.]
SMP Tip: Considering a simpler form of the
original problem is one way students can make
sense of problems and persevere in solving them
(SMP 1). By having students use a start time of 3:00,
they can gain insight into when and why they need
to advance the hour in problems involving elapsed
time. Throughout the rest of the lesson, ask
students to consider the same situation using a
different start or end time.
•Have students share their responses to item 5 with a
partner.
and practicing piano. Possible answer: add 10 1 15 1 22 to get 47.
3 Explain how you could use the total elapsed time to find what time Jenna finished
doing her homework and practicing the piano. Possible answer: start at 3:30
on the clock and count 47 minutes around the clock.
4 What time did Jenna finish?
4:17
Why is the hour not 3 anymore?
Possible answer: the minute hand went past the 12 so the hour moved to
the 4.
5 Explain how to find the ending time when you know the start time and the total
elapsed time.
Possible answer: From the start time, you count around the
clock the number of minutes equal to the elapsed time. Where you end up
on the clock is the end time. if you count past the 12, you have to add 1 to
the hour.
try it
use what you have learned about finding the end time to help you solve these
problems.
11
10
6 Nate finished supper at 7:10. He did dishes for 15 minutes and then
took a shower for 10 minutes. Then he read for 15 minutes before
7:50
he went to bed. What time did Nate go to bed?
12
1
2
9
3
8
4
7
6
5
7 Kari started talking on the phone at 5:45. She talked to her
grandma for 10 minutes, her grandpa for 5 minutes, and
her cousin for 8 minutes. What time did Kari get off the phone?
5:45
6:00
6:08
6:15
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191
Try It Solutions
6Solution: 7:50; Students may write an equation to
find the total elapsed time of 40 minutes and then
draw jumps around the clock to find the end time.
Error Alert: Students who wrote 8:50
mistakenly advanced the hour when it was not
needed.
7Solution: 6:08; Students may write an equation to
find the total elapsed time of 23 minutes and then
draw jumps on the number line to find the end time.
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219
Part 3: Modeled Instruction
Lesson 21
At a Glance
Part 3: Modeled instruction
Students use models and number lines to solve
problems involving the subtraction of time intervals.
read the problem below. then explore different ways to find the start time
when you know the end time and the amount of elapsed time.
Step By Step
Marc’s guitar lesson starts at 4:20. It takes 15 minutes to get there from his
house, and before he leaves, he has to do some chores for 25 minutes. What
time should Marc start doing his chores to make it to his lesson on time?
•Read the problem at the top of the page as a class.
•Read Picture It. Have students trace the jumps
backward around the clock with their fingers as they
count aloud the time for each activity. Have a
volunteer explain why they are now going backward
around the clock instead of forward like they did on
the previous page. [Because you know the end time
and you have to count backward to find the start
time.]
Picture it
you can use a clock to help you find the start time.
The clock shows 4:20, since that is when Marc’s guitar lesson starts. 15 minutes are
counted backward for the time it takes to get to his lesson, and 25 minutes are
counted backward for the time it will take to do his chores.
The second clock shows the time Marc should start his chores.
25
•The end time is 20 minutes after 4:00. Why can’t you
just subtract the total number of minutes for the
activities combined from 20 minutes?
Students’ responses should indicate an
understanding that the total elapsed time is
greater than 20 minutes, so they would
somehow have to borrow and rename if they
used a subtraction equation.
•Explain how finding an unknown start time is
different than finding an unknown end time.
Responses may mention that you need to count
backward to find an unknown start time, and
you need to count forward to find an unknown
end time.
220
11
10
5
12
1
15
2
9
3
8
4
7
6
5
11
10
10
12
1
2
9
5
3
8
4
7
6
5
Model it
you can also use a number line to help you find the start time.
This number line is like the one used for the last problem. It shows times, and each
long mark shows 5 minutes. Each short mark shows 1 minute.
•Read Model It together as a class. Explain that the
number line shows the same information as the clock
model above, just in a different way.
Mathematical Discourse
10
15
20
•Ask: Why did the hour change from 4 to 3? [Because
the minute hand went back over the 12.]
•You may wish to draw the number line on the board
and draw the jumps to mirror those shown on the
clock. (5, 10, 15; 5, 10, 15, 20, 25)
Lesson 21
Start where 4:20 would be.
25
3:30
3:45
15
4:00
4:15
4:30
Count backward the time it will take to get to his lesson and do his chores.
192
L21: Solve Problems About Time
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ELL Support
•Students may be confused when trying to identify
the end time in this item because the sentence
uses the word “starts” even though the problem
does not ask students to find the start time;
“Marc’s guitar lesson starts at 4:20.”
•Discuss with students that even though the
sentence uses the word “start,” that does not mean
that it is the start time they are looking for as the
answer.
•Emphasize that the start time of the lesson is the
same as the end time of the other activities.
L21: Solve Problems About Time
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Part 3: Guided Instruction
Lesson 21
At a Glance
Students revisit the problem on page 192 to learn how
to find the end time when the start time and the
amount of elapsed time is known.
Part 3: guided instruction
Lesson 21
connect it
now you will find the start time for the problem from the previous page.
8 Explain why the times are counted backward on the clock and the number line.
Step By Step
•Read Connect It as a class. Be sure to point out that
the questions refer to the problem on page 192.
•Ask: What do you need to do when you count backward
around the clock and go past the 12? [Make the hour
1 less.]
•Ask: What would the start time be if Marc’s guitar
lesson started at 4:45? [4:05] Why didn’t the hour
change? [The minute hand did not go past the 12
when counting the elapsed time.]
•Have students share their responses to item 10 with
a partner.
Concept Extension
Understand number lines as a mathematical
tool.
•Draw three different number lines on the board:
one that shows whole numbers from 0 to 10, one
that shows fourths from 0 to 2, and one that
shows times from 12:00 to 12:30.
•Discuss with students how the number lines are
the same [all show numbers in order] and how
they are different [each shows a different type of
number].
•Discuss how number lines can be useful tools
when solving problems.
Possible answer: 4:20 is the time we need to end at. to find the beginning
time, you have to go backward.
9 What time should Marc start doing his chores?
3:40
Why is the hour not 4 anymore? Possible answer: the minute hand went back
over the 12, so the hour moved back to the 3.
10 Explain how to find the starting time when you know the end time and the
elapsed time. Possible answer: First, you find the total elapsed time. then,
use a clock or number line to help you count backward the right number of
minutes to find the starting time.
try it
use what you’ve learned about finding the start time to help you solve these
problems.
11 Enrique walked 5 minutes from his grandma’s house to the store, stopped at the
store for 20 minutes, and then walked 10 minutes from the store to his house.
5:25
He got home at 6:00. What time did he leave his grandma’s house?
11
10
12
1
2
9
3
8
4
7
6
5
12 Mira finished helping make lunch at 12:30. She cut up fruit for 10 minutes and
made sandwiches for 7 minutes. What time did she start helping?
12:00
12:15
12:30
12:45
12:13
1:00
L21: Solve Problems About Time
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193
Try It Solutions
11 Solution: 5:25; Students may write an equation to
find the total elapsed time of 35 minutes and then
draw jumps backward around the clock to find the
start time.
Error Alert: Students who wrote 6:35
mistakenly counted forward instead of backward
around the clock.
12 Solution: 12:13; Students may write an equation to
find the total elapsed time of 17 minutes and then
draw jumps backward on the number line to find
the start time.
L21: Solve Problems About Time
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221
Part 4: Guided Practice
Lesson 21
Part 4: guided Practice
Lesson 21
study the model below. then solve problems 13–15.
14 Mr. Chen started doing yard work at 10:00. He watered flowers
Malea’s soccer game started at 9:40 and ended at 10:32. How
for 6 minutes, weeded his garden for 12 minutes, and trimmed
bushes for 27 minutes. What time was Mr. Chen done with his
yard work?
long was Malea’s game?
Show your work.
Look at how you could show your work.
Possible student work:
Student Model
The student used what
she knew about telling
time before and after
the hour to find the
answer.
Part 4: guided Practice
Lesson 21
I think adding all of the
times together would
make this problem easier
to solve.
6 1 12 1 27 5 45
9:40 is 20 minutes before 10:00.
45 minutes after 10 is 10:45
10:32 is 32 minutes after 10:00.
Pair/share
How else could you
have solved this
problem?
Do you need to count
minutes forward or
backward from 2:15 to
find the time he started
watching his sister?
Pair/share
20 1 32 5 52
Solution: 52 minutes
Solution: 10:45
13 Lamar watched his little sister while his mom was busy. He played
to put all his toys away and 4 minutes to make his bed. What time
did Carter start cleaning his room? Circle the letter of the correct
answer.
Show your work.
a 11:49
Possible student work using an analog clock:
b
11:25
c
11:21
20
25
11
10
30
33
Pair/share
194
15 Carter finished cleaning his room at 11:35. It took him 10 minutes
blocks with her for 15 minutes, peek-a-boo for 5 minutes, and
trains for 13 minutes. His mom came back to put her down for a
nap at 2:15. What time did Lamar start watching his sister?
15 1 5 1 13 5 33
How did you decide
how you would solve
the problem?
Did you need to draw a
clock or number line to
help you? Why or why
not?
15
12
1
9
3
8
D 10:21
10
2
Ann chose a as the correct answer. How did she get that answer?
5
Possible answer: ann counted 14 minutes forward
4
7
6
Will the time Carter
started be before or after
11:35?
5
instead of backward.
Pair/share
Does Ann’s answer
make sense?
Solution: 1:42
L21: Solve Problems About Time
L21: Solve Problems About Time
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195
At a Glance
Solutions
Students use models, number lines, or equation to solve
problems about elapsed time.
Ex An equation is shown as one way to solve the
problem. Students could also draw a clock model or
number line and count the elapsed time.
Step By Step
•Ask students to solve the problems individually and
show how they figured out the correct answer using
a model, number line, or equation.
•When students have completed each problem, have
students discuss their solutions with a partner or in a
group. Also, have them discuss the Pair/Share
questions that correspond with each item.
222
13 Solution: 1:42; Students may use an equation to find
the total elapsed time and then draw jumps
backward around the clock to find the start time.
(DOK 2)
14 Solution: 10:45; Students may use an equation to
find the total elapsed time and then reason that
45 minutes after 10:00 is 10:45. (DOK 2)
15 Solution: C; From 35 minutes, subtract the number
of minutes it took Carter to put away his toys and
make his bed. Keep the hours the same.
Explain to students why the other two answer
choices are not correct:
B is not correct because it is only 10 minutes of
elapsed time.
D is not correct because it is 1 hour and 14 minutes
of elapsed time. (DOK 3)
L21: Solve Problems About Time
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Part 5: Common Core Practice
Part 5: common core Practice
Lesson 21
Lesson 21
Solve the problems.
1
2
Part 5: common core Practice
4
Joe spent 40 minutes reading a magazine. Choose all the pairs of clocks that show
possible times that he started and finished.
What is the elapsed time between 1:08 and 1:37?
A
25 minutes
C
30 minutes
B
29 minutes
D
31 minutes
A
It took Juan 5 minutes to ride his bike to the park, where he played basketball for
25 minutes. Then it took him 5 minutes to ride home again. He got home at 10:10.
Which clock shows the time Juan left for the park?
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B
5
2
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A
6
5
Lesson 21
Start:
Finish:
11 12 1
2
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7 6 5
11 12 1
2
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7 6 5
C
Start:
Finish:
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
Start:
Finish:
Start:
Finish:
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
11 12 1
2
10
9
3
8
4
7 6 5
D
Mariah played two games of checkers with her brother. The first game took
12 minutes and the second game took 18 minutes. They put the game away at 7:55.
What time did they start?
Show your work.
5
C
10
Possible student work using an analog clock:
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10
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10
2
9
3
8
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B
3
1
Patty gets up at 7:10. It takes her 10 minutes
to get ready, 7 minutes to pack her lunch, and
15 minutes to eat breakfast.
15
2
9
20
3
8
4
7
6
5
Answer
D
Patty, Joyce, and Stef are getting ready to leave for school. Choose Yes or No to tell
whether each girl will be ready before 7:45.
a.
196
12
6
They started playing at
7:25
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25
5
30
.
Seve started writing thank you notes at 5:25. It took him 20 minutes to write them.
He also spent some time writing addresses on the envelopes. He finished at 6:00. How
long did it take Seve to write the addresses?
Show your work. Possible student work using a number line:
3 Yes
No
b.
Joyce gets up at 6:50 and exercises for
30 minutes. Then it takes her 20 minutes to
get ready and 12 minutes to eat breakfast.
Yes
3 No
c.
Stef gets up at 7:15. It takes her 15 minutes
to get ready, 5 minutes to pack her lunch,
and 9 minutes to eat breakfast.
3 Yes
No
20
5:00
Answer
L21: Solve Problems About Time
It took Seve
Copying is not permitted.
At a Glance
Students use models, number lines, and equations to
solve problems involving time intervals that might
appear on a mathematics test.
Solutions
1Solution: B; Use a clock model to count the elapsed
time or subtract 8 from 37. (DOK 1)
2Solution: C; Add 5, 25, and 5 to find the total
elapsed time. Then count backward from 10:10 to
find the start time. (DOK 2)
3Solution: a. Yes; b. No; c. Yes (DOK 2)
L21: Solve Problems About Time
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5:30
5:45
6:00
minutes to write the addresses.
self check Go back and see what you can check off on the Self Check on page 179.
L21: Solve Problems About Time
©Curriculum Associates, LLC
15
5:15
15
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197
4Solution: A; 2:45 is 15 minutes before 3:00 and 3:25
is 25 minutes after 3:00. Add 15 and 25 to find the
elapsed time, which is 40 minutes.
D; 1:10 is 10 minutes after 1:00 and 1:50 is
50 minutes after 1:00. Subtract 10 from 50 to find
the difference between the two times, which is
40 minutes. (DOK 1)
5Solution: 7:25; Add 12 and 18 to find the total
elapsed time. Then count backward from 7:55 to
find the start time. (DOK 1)
6Solution: 15; Start at 5:25 and count forward 20
minutes. Then find the number of minutes between
that time and 6:00. (DOK 2)
223
Differentiated Instruction
Lesson 21
Assessment and Remediation
•Ask students to find the start time if the end time is 8:20 and the elapsed time is 36 minutes. [7:44]
•For students who are still struggling, use the chart below to guide remediation.
•After providing remediation, check students’ understanding. Ask students to find the end time if the start
time is 1:55 and the elapsed time is 42 minutes. [2:37]
If the error is . . .
Students may . . .
To remediate . . .
8:56
not understand they
need to count backward
to find the start time.
Give students a situation including the start time, elapsed time,
and end time. Have them model the end time on a clock and
then physically move the minute hand backward to get to the
start time.
8:44
not realize they need to
go back an hour.
Remind students that because the hour increases when the
minute hand goes past the 12 going forward, it also must
decrease when the minute hand goes backward past the 12.
have counted the
minutes incorrectly.
Review with students how to count minutes using both a clock
model and a number line diagram.
any other time
Hands-On Activity
Challenge Activity
Use manipulatives to represent elapsed time.
Use equations and renaming to solve time
problems.
Materials: toothpicks, rubber bands
•Give each student 150 toothpicks. Tell students
each toothpick represents 1 minute. Have students
bundle the toothpicks into groups of 60. (There
should be 2 groups of 60 with 30 left over.)
•Tell students their toothpicks can represent the
time 2:30 (since they show 2 hours and 30
minutes). Give students 40 more toothpicks to
represent an activity that took 40 minutes to
complete. Ask students to use the toothpick to
find the end time. [Students should make an
additional bundle of 60 toothpicks and have 10
left over. The time represented is 3:10.]
Tell students that they can write addition and
subtraction problems to solve start and end time
problems, but they have to rename in a different way.
Start with the problem Joe started mowing at 5:30 and
it took him 50 minutes to mow his lawn. What time did
he finish? Show them how to set up the addition
problem:
1
5 hours 30 minutes
1 0 hours 50 minutes
6 hours 20 minutes (or 6:20)
Discuss why 30 minutes 1 50 minutes led to
20 minutes with 1 hour renamed.
Repeat with other problems, including those that
would use subtraction to find a start time.
224
L21: Solve Problems About Time
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