Name
2.3
?
Number and
Operations—5.3.C
MATHEMATICAL PROCESSES
5.1.C
Division with 2-Digit Divisors
Essential Question
How can you use base-ten blocks to model and
understand division of whole numbers?
Investigate
Investigate
Hands
On
Materials ■ base-ten blocks
There are 156 students in the Carville Middle School chorus.
The music director wants the students to stand with 12 students
in each row for the next concert. How many rows will there be?
A. Use base-ten blocks to model the dividend, 156.
B. Place 2 tens below the hundred to form a rectangle. How many
groups of 12 does the rectangle show? How much of the dividend
is not shown in this rectangle? _____
C. Combine the remaining tens and ones into as many groups of 12
as possible. How many groups of 12 are there? ___
D. Place these groups of 12 on the right side of the rectangle to make
a larger rectangle.
E. The final rectangle shows _ groups of 12.
So, there will be _ rows of 12 students.
Draw Conclusions
© Houghton Mifflin Harcourt Publishing Company
1. Explain why you still need to make groups of 12 after Step B.
2. Describe how you can use base-ten blocks to find the quotient 176 ÷ 16.
Module 2
67
Make
Make Connections
Connections
Hands
On
The two sets of groups of 12 that you found in the Investigate
are partial quotients. First you found 10 groups of 12 and then
you found 3 more groups of 12. Sometimes you may need to
regroup before you can show a partial quotient.
10
+
3
12
You can use a quick picture to record the partial products.
Divide. 180 ÷ 15
MODEL Use base-ten blocks.
RECORD Use quick pictures.
STEP 1 Model the dividend, 180, as 1 hundred 8 tens.
Model the first partial quotient by making a
rectangle with the hundred and 5 tens. In the
Record, cross out the hundred and tens you use.
The rectangle shows _ groups of 15.
Draw the first partial quotient.
STEP 2 Additional groups of 15 cannot be made
without regrouping.
Regroup 1 ten as 10 ones. In the Record, cross
out the regrouped ten.
There are now _ tens and _ ones.
STEP 3 Decide how many additional groups of 15 can
be made with the remaining tens and ones. The
number of groups is the second partial quotient.
Draw the first and second partial quotients.
Make your rectangle larger by including these
groups of 15. In the Record, cross out the tens
and ones you use.
There are now _ groups of 15.
So, 180 ÷ 15 is _.
Share
Share and
and Show
Show
Math Talk
Use the quick picture to divide.
13
Explain how your model
shows the quotient.
© Houghton Mifflin Harcourt Publishing Company
+
1. 143 ÷ 13
68
Mathematical Processes
Name
Use base-ten blocks or a quick picture to divide.
2. 168 ÷ 12
3. 187 ÷ 11
4. 182 ÷ 13
5. 228 ÷ 12
Problem
Problem Solving
Solving
Write Math
Show Your Work
The Pony Express used men riding horses to deliver mail between
St. Joseph, Missouri, and Sacramento, California, from April 1860
to October 1861. The trail between the cities was approximately
2,000 miles long.
6.
Multi-Step Two Pony Express
riders each rode part of a 176-mile trip. Each rider
rode the same number of miles. They changed
horses every 11 miles. How many horses did each
rider use?
7. Suppose a Pony Express rider was paid $192 for 12 weeks of
work. If he was paid the same amount each week, how much
was he paid for each week of work?
© Houghton Mifflin Harcourt Publishing Company
8.
Multi-Step It took 19 Pony Express riders a
total of 11 days 21 hours to ride from St. Joseph to Sacramento.
If they all rode the same number of hours, how many hours
did each rider ride?
Module 2 • Lesson 3 69
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
9. Use Diagrams A rover brings 144 rock samples back from Mars.
The samples will be divided among 12 teams of scientists for analysis.
Which quick picture shows the correct division of the samples between
the 12 teams?
A
C
B
D
10. Analyze The Mars rover is going to travel across a crater that is 360 cm
(about 12 ft) in diameter. The rover must stop every 15 cm to recharge
its batteries. How many times will the rover recharge while it crosses the
crater?
A
24
C
30
B
15
D
25
11. Multi-Step On Monday, the rover traveled 330 cm. On Tuesday, it
traveled 180 cm. If the rover stopped every 15 cm to recharge, how many
more times did it need to recharge on Monday than on Tuesday?
A
24
C
12
B
22
D
10
12. Analyze Three Pony Express riders each rode part of a 252-mile trip.
If they used a total of 18 horses, and rode each horse the same number
of miles, how many miles did they ride before replacing each horse?
70
A
54 miles
C
84 miles
B
14 miles
D
42 miles
© Houghton Mifflin Harcourt Publishing Company
TEXAS Test Prep
H o mewo rk
and Practice
2.3
Number and Operations—5.3.C
MATHEMATICAL PROCESSES 5.1.C
Name
Division with 2-Digit Divisors
Use base-ten blocks or a quick picture to divide.
1. 180 ÷ 12
2. 216 ÷ 18
3. 224 ÷ 16
4. 176 ÷ 16
Problem
Problem Solving
Solving
5. Ryan read 145 pages of his book. If he read
© Houghton Mifflin Harcourt Publishing Company
29 pages every night, how many nights did it
take him to complete the book?
6. Mrs. McDonald passed out 189 photos that
she had taken during the school year. If each of
her 21 students received the same number of
photos, how many did each receive?
Module 2 • Lesson 3 71
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
fundraiser. She sold pizza combo meals for
$12 each. How many combo meals did
Susanna sell?
of 336 times. If the horse ran 21 laps each
day, how many days did it take the horse to
complete all of the laps?
A
10
A
20
B
11
B
16
C
13
C
18
D
12
D
12
9. Milos rode his bicycle in a marathon for
10. There are 325 books on the library wall. There
154 miles. He took a rest stop every 22 miles.
How many rest stops did Milos take during
the marathon?
are 13 rows of books, each with an equal
number of books. How many books are in
each row?
A
8
A
28
B
7
B
21
C
10
C
25
D
9
D
19
11. Multi-Step Lilly was paid $308 for 14 weeks
of work. If she was paid the same amount each
week, how much did she earn after 2 weeks?
72
8. Carlos’ horse ran around the track a total
A
$38
B
$28
C
$22
D
$44
12. Multi-Step Manny drove 910 miles during a
two-week period. If he drove the same number
of miles each day, how many miles had he
driven after 5 days?
A
182 miles
B
250 miles
C
650 miles
D
325 miles
© Houghton Mifflin Harcourt Publishing Company
7. Susanna made a total of $132 for the school