Objective To provide practice with a “low-stress” division
algorithm for 2-digit divisors.
1
materials
Teaching the Lesson
Key Activities
Students review and practice a paper-and-pencil algorithm for division that
permits them to build up the quotient by working with “easy” numbers. Students
focus on problems with 2-digit divisors.
Key Concepts and Skills
•
•
•
•
Identify and use multiples of 10. [Number and Numeration Goal 3]
Add multiples of 10. [Operations and Computation Goal 1]
Subtract multidigit numbers. [Operations and Computation Goal 2]
Apply extended multiplication facts to long-division situations.
Math Journal 1, pp. 166 and 167
Study Link 6 9
Teaching Aid Masters (Math Masters, p. 436,
optional; p. 438)
base-10 blocks
slate
[Operations and Computation Goal 3]
• Solve equal-grouping division number stories and problems.
[Operations and Computation Goal 4]
Ongoing Assessment: Recognizing Student Achievement Use journal
page 166. [Operations and Computation Goal 4]
2
Ongoing Learning & Practice
Students take a 50-facts test. They use a line graph to record individual
and class scores. Then students find the median and calculate the mean
of all class scores.
Students practice and maintain skills through Math Boxes and
Study Link activities.
3
Differentiation Options
READINESS
Students play Division Dash to
practice dividing 2- or 3-digit
dividends by 1-digit divisors.
ENRICHMENT
Students perform and explain a
division “magic trick.”
materials
Math Journal 1, p. 168
Study Link Master (Math Masters, p. 197)
Teaching Aid Masters (Math Masters, pp. 413,
414, and 416)
pen or colored pencil
materials
Student Reference Book, p. 241
Teaching Master (Math Masters, p. 198)
Game Master (Math Masters, p. 471)
per partnership: 4 each of number cards 1–9
Technology
Assessment Management System
Journal page 166, Problems 1 and 2
See the iTLG.
Lesson 6 10
455
Getting Started
Mental Math and Reflexes
Math Message
Pose multiplication facts and extended facts. Suggestions:
Egg cartons hold 12 eggs. How many cartons do
you need to pack 246 eggs?
339
428
5 5 25
10 9 90
4 9 36
7 7 49
8 3 24
6 4 24
90 8 720
8 80 640
60 70 4,200
30 90 2,700
Study Link 6 9 Follow-Up
Have students check their partner’s globe labels
and markings.
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
ACTIVITY
Remind students that by packing 246 eggs into cartons, they are
dividing 246 eggs into groups of 12. The problem is a division
problem: How many [12s] are in 246?
Write the problem on the board in four of the ways that division
problems can be written:
246 12
246 / 12
苶4
苶苶
6
12冄2
246
12
Ask several students to give their solutions and describe their
strategies:
Use a Multiplication/Division Diagram (Math Masters,
page 436). Some students may think “What number times 12
equals 246?” while others may reason “246 divided by 12
equals what number?”
cartons
eggs per carton
eggs in all
?
12
246
Take 2 flats, 4 longs, and 6 cubes. Trade the flats for longs.
Divide the longs and cubes into as many groups of 12 cubes as
possible. Continue to exchange longs for cubes as necessary.
20 groups, 6 left over
Draw a picture.
456
Unit 6 Division; Map Reference Frames; Measures of Angles
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
12
Teaching Aid Master
Break 246 into smaller “friendly numbers” such as the following:
●
●
120 120 6 246. There are 10 [12s] in 120 and
10 [12s] in 120. 10 10 20, so there are 20 [12s]
in 246 with 6 left over.
240 6 246. There are 20 [12s] in 246 with 6 left over.
You need 20 full cartons, plus one other carton to hold the 6 eggs
that are left over. So, 21 cartons are needed.
Some students may have used the partial-quotients division
algorithm to solve the Math Message problem. Ask a volunteer
to explain how the algorithm was used.
Introducing the Partial-Quotients
WHOLE-CLASS
ACTIVITY
Algorithm with 2-Digit Divisors
Name
Date
Time
Easy Multiples
17
100 100 50 50 20 20 10 10 5
5
2
2
1
1
100 100 50 50 20 20 10 10 5
5
2
2
1
1
(Math Masters, p. 438)
Explain that most of the division problems in Unit 6 have
involved a 1-digit divisor. In this lesson students will use the
partial-quotients division algorithm to solve problems and number
stories, like the Math Message, that involve 2-digit divisors.
Math Masters, p. 438
The algorithm works the same whether you divide by a 2-digit or a
1-digit divisor. As it often helps to write down some easy facts for
the divisor first, have copies of Math Masters, page 438 readily
available. Remind students to use the relationship between
multiplication and division to check their answers.
Example 1:
Teddy received a carton of 400 baseball cards from his
grandmother. He decided to share them with his classmates.
How many cards did Teddy and each of his 21 classmates get?
One way:
Another way:
Still another way:
苶0
苶苶
0
22冄4
–220
180
–110
70
–22
48
–22
26
–22
4
苶0
苶苶
0
22冄4
–220
180
–110
70
–66
4
22冄4
苶0
苶苶
0
–220
180
–176
4
10
5
1
10
5
10
8
18
3
18
1
1
18
The answer, 18 R4, is the same for each method. Teddy and his
classmates each received 18 baseball cards. There were 4 left over.
Lesson 6 10
457
Student Page
Date
Time
LESSON
Example 2:
Partial-Quotients Division
6 10
1. Raul baked 96 cupcakes. He wants to divide
22 23
Sofia was playing with a set of 743 blocks. She decided to arrange
them in stacks of 12. How many stacks did Sofia make?
them evenly among 3 bake sale tables. How
many cupcakes should he put on each table?
96 3 32
Number model:
32
Answer:
cupcakes
How many cupcakes will be left over?
0
cupcakes
2. The library has boxes to store 132 videotapes.
Each box holds 8 tapes. How many boxes will
be completely filled?
132 8 ∑ 16 R4
Number model:
16
Answer:
boxes
How many videotapes will be left over?
4
videotapes
3. The teacher divided 196 note cards evenly
among 14 students. How many note cards did
each student get?
196 14 14
Number model:
14
Answer:
note cards
How many note cards were left over?
0
note cards
4. There are 652 students at a school. The
auditorium has rows with 22 seats each. How
many rows would be completely filled if all the
students attend an assembly?
Another way:
Still another way:
苶4
苶苶
3
12冄7
–600
143
–60
83
–60
23
–12
11
苶4
苶苶
3
12冄7
–600
143
–120
23
–12
11
苶4
苶苶
3
12冄7
–600
143
–132
11
50
5
5
50
10
50
11
61
1
61
1
61
The answer, 61 R11, is the same for each method. Sofia made
61 stacks of 12 blocks. There were 11 blocks left over.
652 22 ∑ 29 R14
29 rows
Number model:
Answer:
One way:
How many students would be left over?
14
students
166
Using the Partial-Quotients
Math Journal 1, p. 166
PARTNER
ACTIVITY
Algorithm with 2-Digit Divisors
(Math Journal 1, pp. 166 and 167; Math Masters, p. 438)
Students use the partial-quotients algorithm to solve division
problems and number stories on journal pages 166 and 167.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 166, Problems 1 and 2 to assess students’ ability to
solve problems involving the division of multidigit whole numbers by 1-digit
divisors. Students are making adequate progress if they are able to calculate the
quotients in Problems 1 and 2 and express the remainder in Problem 2 correctly.
Some students may be able to solve Problems 3–9, which involve 2-digit divisors.
Student Page
Date
Time
LESSON
6 10
5. 18冄8
苶6
苶4
苶
Partial-Quotients Division
Answer:
6. 509 37 Journal
page 166
Problems 1 and 2
[Operations and Computation Goal 4]
continued
48
13 R28
Try This
203
7. 4,872 / 24 2 Ongoing Learning & Practice
92 R3
8. 3,315 36 Sample answers:
9. There are
462
players in the league.
(Write a number greater than 300.)
16
Taking a 50-Facts Test
There are
players on each team.
(Write a number between 11 and 99.)
How many teams can be made?
Number model:
Answer:
462 16
28
∑ 28 R14
(Math Masters, pp. 413, 414, and 416)
teams
How many players are left over?
14
See Lesson 3-4 for details regarding the administration of the
50-facts test and the recording and graphing of individual and
class results.
players
167
Math Journal 1, p. 167
458
WHOLE-CLASS
ACTIVITY
Unit 6 Division; Map Reference Frames; Measures of Angles
Student Page
Math Boxes 6 10
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 168)
Date
Time
LESSON
Math Boxes
6 10
1. Name the ordered number pair for each
2. Complete the “What’s My Rule?” table
point plotted on the coordinate grid.
A(
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 6-8. The skill in Problem 6 previews
Unit 7 content.
B(
C(
D(
E(
Writing/Reasoning Have students write a response to the
following: True or false? (5,0) and (0,5) are both ordered
number pairs that can be used to describe the location of
point A in Problem 1. Explain your answer. False. The first
number in an ordered number pair tells how far to go to the right,
and the second number tells how far to go up. Only (0, 5) tells the
location of point A.
0
5
2
4
3
5
4
3
3
2
,
,
,
,
,
)
and state the rule.
Rule
5
A
4
)
3
D
C
)
3.38
B
in
out
3.66
7.04
0.42
3.80
8.73
12.11
9.28
12.66
2
E
1
)
0
0
1
2
3
4
5
)
144
obtuse
3. NMO is
162–166
4. Cross out the names that do not belong
(acute or obtuse).
in the name-collection box below.
48
N
(2 3) 8
100 62
18 13 17
M
12 4
O
Measure of NMO 120
°
184 4
93 142
143
5. Round 451,062 to the nearest thousand.
149
6. Fill in the missing fractions on the
Circle the best answer.
number line.
A. 500,000
0
Study Link 6 10
B. 451,000
INDEPENDENT
ACTIVITY
1 2
3 3
1 2
1 13 13
2
C. 451,100
D. 452,000
(Math Masters, p. 197)
182 183
Home Connection Students practice using the partialquotients division algorithm for 2-digit divisors. For some
problems, they may use a division method of their choice.
316
168
Math Journal 1, p. 168
3 Differentiation Options
PARTNER
ACTIVITY
READINESS
Playing Division Dash
15–30 Min
(Student Reference Book, p. 241, Math Masters, p. 471)
To provide experience with 2- or 3-digit dividends and 1-digit
divisors in division problems, have students play Division Dash.
Study Link Master
Name
STUDY LINK
6 10
1.
INDEPENDENT
ACTIVITY
ENRICHMENT
Performing a “Magic Trick”
Date
Division
It takes 14 oranges to make a small pitcher of juice. Annette has 112 oranges.
How many pitchers of juice can she make?
Number model:
Answer:
15–30 Min
(Math Masters, p. 198)
22
23
112 14 8
8
pitchers of juice
0
How many oranges are left over?
2.
Time
oranges
Each bouquet needs 17 flowers. The florist has 382 flowers in his store.
How many bouquets can the florist make?
3.
382 17 ∑ 22 R8
22 bouquets
8 flowers
How many flowers are left over?
69
726 16 45 R6
4. 4冄苶2
苶7
苶6
苶
5.
45 4 Number model:
To further explore the concept of division, have students use
a calculator to perform a division “magic trick.”
Name
LESSON
6 10
Date
Answer:
Time
Division “Magic”
1.
Write a 3-digit number. _______ Enter it into your calculator twice to make a
6-digit number. For example, if you picked 259, then you would enter 259259
in your calculator.
2.
Divide the 6-digit number by 7. Then divide the result by 11.
Finally, divide that result by 13.
3.
What is the final quotient?
4.
Repeat Steps 1 and 2.
5.
Do you think this trick works with any three-digit number? Explain.
the 3-digit number from Problem 1
New number: _______
Final quotient: _______
Yes. Doing Step 1 is the same as multiplying the 3-digit
number by 1001, and Step 2 divides a number by 1001. So
Practice
the two steps reverse each other.
7.
1,827
180
29 63
6.
8.
2,233 319 7
16,287
89 183 Math Masters, p. 197
Math Masters, page 198
Lesson 6 10
459