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Objective
To introduce and provide practice with a “low-stress”
division algorithm for 1-digit divisors.
1
materials
Teaching the Lesson
Key Activities
Students learn and practice a paper-and-pencil algorithm for division that permits
them to build up the quotient by working with “easy” numbers.
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. 144 and 145
Study Link 6 2
Teaching Aid Masters (Math Masters,
pp. 403, 436, and 438) (optional)
slate
See Advance Preparation
[Operations and Computation Goal 3]
• Solve equal-grouping division number stories. [Operations and Computation Goal 4]
Key Vocabulary dividend • divisor • partial quotient
Ongoing Assessment: Informing Instruction See pages 413 and 416.
Ongoing Assessment: Recognizing Student Achievement
Use journal pages 144 and 145. [Operations and Computation Goal 4]
2
materials
Ongoing Learning & Practice
Students solve problems involving various basic skills with decimals.
Students practice and maintain skills through Math Boxes and Study Link activities.
3
materials
Differentiation Options
READINESS
Students play Beat
the Calculator
with extended
multiplication facts.
ENRICHMENT
Students use clues
to solve a division
number story.
Math Journal 1, pp. 146 and 147
Study Link Master (Math Masters, p. 180)
EXTRA PRACTICE
Students play
Division Dash to
practice dividing
2- or 3-digit
dividends by
1-digit divisors.
ELL SUPPORT
Students display
and label parts of
division number
models.
Student Reference Book, pp. 233 and 241
Teaching Master (Math Masters, p. 181)
Game Masters (Math Masters, pp. 461
and 471)
per partnership: 4 each of number cards
1–9
per group: 4 each of number cards 1–10
chart paper; colored markers
10 nickels (optional)
Additional Information
Advance Preparation Make 1 or 2 copies of Math Masters, page 403 for each student.
Have extra copies available throughout this unit.
412
Unit 6 Division; Map Reference Frames; Measures of Angles
Technology
Assessment Management System
Journal pages 144 and 145,
Problems 1, 2, and 5
See the iTLG.
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Getting Started
Mental Math and Reflexes
Pose true or false problems involving equal groups. Suggestions:
There are at least 2 [5s] in 11. true
There are at least 3 [2s] in 5. false
There are at least 4 [3s] in 14. true
There are at least 7 [6s] in 45. true
There are at least 9 [8s] in 67. false
There are at least 8 [9s] in 75. true
There are at least 10 [8s] in 92. true
There are at least 30 [6s] in 157. false
There are at least 40 [9s] in 391. true
Math Message
Study Link 6 2 Follow-Up
How many days are there in 30 weeks?
Partners compare answers. Have volunteers explain
different strategies that could be used to solve Problem 3.
How many weeks are there in 98 days?
1 Teaching the Lesson
Math Message Follow-Up
Ongoing Assessment:
Informing Instruction
WHOLE-CLASS
ACTIVITY
In the first problem, the number of weeks is known; students find
the number of days by multiplying by 7. In the second problem,
the total number of days is given; students divide by 7 to find the
number of weeks.
weeks days per week
30
? 14
days in all
7
weeks days per week
Watch for students who do not understand
where the numeral 7 came from because
they did not see a 7 in the problem and did
not equate a week with 7 days. Remind
students that using another name for an
equal quantity is often necessary to solve
problems.
? 210
days in all
7
Teaching Aid Master
98
Name
Date
Time
Easy Multiples
Introducing the
WHOLE-CLASS
ACTIVITY
Partial-Quotients Algorithm
(Math Masters, pp. 403 and 438)
This lesson formally introduces the partial-quotients algorithm.
100 ⴱ
17
⫽
100 ⴱ
⫽
50 ⴱ
⫽
50 ⴱ
⫽
20 ⴱ
⫽
20 ⴱ
⫽
10 ⴱ
⫽
10 ⴱ
⫽
5ⴱ
⫽
5ⴱ
⫽
2ⴱ
⫽
2ⴱ
⫽
1ⴱ
⫽
1ⴱ
⫽
100 ⴱ
⫽
100 ⴱ
⫽
50 ⴱ
⫽
50 ⴱ
⫽
Begin with an equal-grouping division problem like the following:
●
Amy is 127 days older than Bob. How many weeks older
is Amy?
Briefly work through the steps mentioned in the previous lessons:
Step 1: Decide what you need to find out. How many weeks older
is Amy?
20 ⴱ
⫽
20 ⴱ
⫽
10 ⴱ
⫽
10 ⴱ
⫽
5ⴱ
⫽
5ⴱ
⫽
2ⴱ
⫽
2ⴱ
⫽
1ⴱ
⫽
1ⴱ
⫽
Math Masters, p. 438
Lesson 6 3
413
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Step 2: Identify the data you need to solve the problem. The
number of days in all and the number of days per week. Write
the data in the appropriate spaces in the diagram.
weeks days per week
?
7
days in all
127
Step 3: Decide what to do to find the answer. 127 days must be
equally grouped (divided) so that there are 7 days in each week.
Step 4: Do the computation. Model the following algorithm while
students follow along with paper and pencil.
1. Write the problem in the traditional form: 71
2
7
. Point out
that the dividend—the number that is being divided—is 127.
The divisor—the number that the dividend is being divided
by—is 7. To support English language learners, label the
dividend and the divisor on the board.
2. Draw a vertical line so that the problem looks like the problem
below. The vertical line will separate subtractions from partial
quotients.
71
2
7
Adjusting the Activity
Suggest that students first make
a list of “easy” multiples of the divisor. For
example, if the divisor is 7, students might
make the following list:
3. Suggest that one way to proceed is to use a series of “at
least/not more than” multiples of the divisor. A good strategy
is to start with easy numbers, such as 100 times the divisor or
10 times the divisor.
●
Are there at least 100 [7s] in 127? No, because 100 7 700, which is more than 127.
●
Are there at least 10 [7s] in 127? Yes, because 10 7 70,
which is less than 127.
●
Are there at least 20 [7s]? No, because 20 7 140, which
is more than 127.
●
So there are at least 10 [7s], but not more than 20 [7s].
Try 10.
100 7 700
50 7 350
20 7 140
10 7 70
5 7 35
2 7 14
17 7
Depending on the students and the divisor,
the list can be extended or reduced.
Students can use their list of easy multiples
to take the guesswork out of successive
multiples and focus on solving the division
problem.
Students will realize that they can work
more quickly if they begin with a more
extensive list of multiples. Math Masters,
page 438 provides an optional form for
writing multiples.
AUDITORY
414
KINESTHETIC
TACTILE
Write 10 7, or 70, under 127. Write 10 at the right. 10 is
the first partial quotient. Partial quotients will be used to
build up the final quotient.
71
2
7
70
10 (The first partial quotient) 10 7 70
4. The next step is to find out how much is left to divide.
Subtract 70 from 127.
VISUAL
Unit 6 Division; Map Reference Frames; Measures of Angles
71
2
7
70
57
10 (The first partial quotient) 10 * 7 = 70
Subtract. 57 is left to divide.
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5. Now find the number of 7s in 57. Following are two ways
to do this:
Use a fact family: 8 7 56, so there are at least 8 [7s]
in 57. Record as follows:
71
2
7
70
57
56
10 (The first partial quotient) 10 * 7 = 70
Subtract. 57 is left to divide.
8 (The second partial quotient) 8 * 7 = 56
Use “at least / not more than” multiples with easy
numbers. For example, ask:
●
Are there at least 10 [7s] in 57? No, because 10 7 70.
●
Are there at least 5 [7s]? Yes, because 5 7 35.
Next, subtract 35 from 57 and continue by asking:
●
How many 7s are in 22? 3
71
2
7
70
57
35
22
21
10
(The first partial quotient) 10 * 7 = 70
Subtract. 57 is left to divide.
5 (The second partial quotient) 5 * 7 = 35
Subtract. 22 is left to divide.
3 (The third partial quotient) 3 * 7 =21
6. For both ways, the division is complete when the subtraction
leaves a number less than the divisor (7 in this example). The
final step is to add the partial quotients—the numbers of 7s
that were subtracted. 18 is the quotient. There is 1 left over.
So, 1 is the remainder.
71
2
7
70 10
57
56 8
1 18
71
2
7
70 10
57
35 5
22
21 3
1 18
7. Have students record the final answer in the traditional
position above the dividend. To support English language
learners, label the quotient and the remainder.
18 R1
2
7
71
8. Conclude by interpreting the answer: Amy is 18 weeks and
1 day older than Bob.
Lesson 6 3
415
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Student Page
Date
LESSON
6 3
䉬
Time
Partial-Quotients Division Algorithm
22 23
These notations for division are equivalent:
6冄1
苶3
苶4
苶
夹
134 ⫼ 6
1. There are 6 pencils in each pack. How
夹
2. Phil has $79 to purchase books. Books cost
many packs can be made from 96 pencils?
Number model:
Answer:
16
96 ⫼ 6 ⫽ 16
packs
$7 each. How many books can Phil buy?
How many pencils are left over?
0
pencils
Answer:
23
11
How many dollars are left over?
Number model:
pots
Answer:
0
2
dollars
among 9 classes. How many cookies did
each class receive?
184 ⫼ 8 ⫽ 23
How many plants are left over?
books
4. The principal shared 395 cookies equally
Each pot can hold 8 plants. How many pots
are needed?
Number model:
79 ⫼ 7 ∑ 11 R2
Number model:
Answer:
3. There are 184 plants to be put into pots.
134
ᎏᎏ
6
134 / 6
Lead students through several more problems on the board. Ask:
How many [ns] are there in m? Each n should be a 1-digit number;
each m should be a 2- or 3-digit number. Some students may be
ready for a 2-digit divisor. Suggestions:
plants
395 ⫼ 9 ∑ 43 R8
43
●
How many [4s] are there in 92? 23
●
How many [3s] are there in 87? 29
●
How many [7s] are there in 301? 43
●
How many [8s] are there in 925? 115 R5
●
How many [12s] are there in 588? 49
●
How many [15s] are there in 556? 37 R1
cookies
How many cookies were left over?
8
cookies
Have the class pose a division problem, and ask partnerships to try
to find the answer. Have volunteers share their work with the
class. Look for students who got the same results in different ways.
Ongoing Assessment: Informing Instruction
144
Math Journal 1, p. 144
Watch for students using multiples that are not too large and that are easy to
work with. Using such multiples may require more steps, but it will make the
work go faster. Also, students should not be concerned if they pick a multiple
that is too large. If that happens, they will quickly realize that they have a
subtraction problem involving a larger number below.
Using the Partial-Quotients
INDEPENDENT
ACTIVITY
Algorithm
(Math Journal 1, pp. 144 and 145)
Students use the partial-quotients algorithm to solve number
stories and computation problems. Have copies of Math Masters,
pages 436 and 438 readily available for students who choose to
use them. Encourage students to use the relationship between
multiplication and division to check their answers.
Student Page
Date
LESSON
6 3
䉬
Time
Partial-Quotients Division Algorithm
cont.
Divide.
夹
6. 331 ⫼ 7
5. 3冄8
苶7
苶
Answer:
29
Answer:
Try This
Sample answers:
7. Twelve shirts fit into a box. There are 372
8. There are
shirts to be put into boxes. How many boxes
are needed?
Number model:
Answer:
47 R2
31
372 ⫼ 12 ⫽ 31
players in the league.
(Write a number greater than 100.)
There are 6 players on each team.
(Write a number between 3 and 9.)
How many teams can be made?
boxes
How many shirts are left over?
250
0
shirts
Number model:
Answer:
41
250 ⫼ 6 ∑ 41 R4
teams
How many players are left over?
4
players
Ongoing Assessment:
Recognizing Student Achievement
Journal pages
144 and 145
Problems 1, 2, 5
Use journal pages 144 and 145, Problems 1, 2, and 5 to assess students’
ability to solve division problems and number stories with 1-digit divisors and
2-digit dividends. Students are making adequate progress if they are able to
compute the answers using the partial-quotients division algorithm. Some
students may be able to solve Problems 3, 4, and 6–8, which involve
2-digit divisors or 3-digit dividends.
[Operations and Computation Goal 4]
145
Math Journal 1, p. 145
416
Unit 6 Division; Map Reference Frames; Measures of Angles
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Student Page
Date
2 Ongoing Learning & Practice
Time
LESSON
Place Value in Decimals
6 3
䉬
1. Write these numbers in order from smallest
0.58
1.09
0.35
0.58
1.09
1.091
1.26
INDEPENDENT
ACTIVITY
in Decimals
(Math Journal 1, p. 146)
1.091
6
4
5
9
0.35
smallest
in
in
in
in
the
the
the
the
tenths place,
ones place,
hundredths place, and
tens place.
Write the number.
9 4
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 147)
6 5
4. What is the value of the digit 4 in the
with the following digits:
numerals below?
3
a. 37.48
6
4
7
2
23,467 (whole number)
and .23467 (decimal)
b. 49.08
c. 0.942
d. 1.664
Math Boxes 6 3
.
largest
3. Write the smallest number you can make
Students solve problems involving ordering of decimals, naming
place value in decimals, and reading and writing decimals.
31
to largest.
1.26
Reviewing Place Value
30
2. A number has
5. Write each number using digits.
4 tenths
4 tens
4 hundredths
4 thousandths
6. I am a four-digit number less than 10.
䉬 The digit in the tenths place is the result
a. four and seventy-two hundredths
of dividing 36 by 4.
4.72
䉬 The digit in the hundredths place is the
b. nine hundred thirty-five thousandths
result of dividing 42 by 7.
0.935
䉬 The digit in the ones place is the result
Mixed Practice Math Boxes in this lesson are paired
with Math Boxes in Lesson 6-1. The skill in Problem 5
previews Unit 7 content.
of dividing 72 by 8.
䉬 The digit in the thousandths place is the
result of dividing 35 by 5.
What number am I?
9
146
Writing/Reasoning Have students write a response to the
following: Explain how the exponent in Problem 4a changes
the value of 10. Sample answer: The exponent tells how many
times the base 10 is used as a factor. For example, 104 10 10 10 10, or 10,000.
Study Link 6 3
.
9 6 7
Math Journal 1, p. 146
INDEPENDENT
ACTIVITY
(Math Masters, p. 180)
Home Connection Students practice using the partialquotients division algorithm.
Student Page
Study Link Master
Name
Date
STUDY LINK
63
䉬
1.
Number model:
22
2.
83 ⫼ 6 ∑ 13 R5
13
Date
Time
LESSON
Division
Bernardo divided a bag of 83 marbles
evenly among five friends and himself.
How many marbles did each get?
Answer:
Time
The carnival committee has 360 small prizes
to share equally with 5 carnival booths.
How many prizes will each booth get?
Number model:
marbles
23
Answer:
72
䉬
1. Measure each line segment to the nearest millimeter.
a.
P
360 ⫼ 5 ⫽ 72
prizes
Math Boxes
6 3
About
S
9
cm
3
mm
6
cm
5
mm
b.
A
How many marbles are left over?
5
How many prizes are left over?
0
marbles
B
About
128
prizes
2. Round 5,906,245 to the nearest
3.
4冄苶9
苶1
苶
Answer:
22 R3
4.
427 / 8
Answer:
53 R3
3. Multiply. Use a paper-and-pencil method.
3,016
a. million.
6,000,000
⫽ 58 ⴱ 52
b. ten thousand.
5,910,000
c. thousand.
5,906,000
d. hundred.
5,906,200
182 183
4
5
⫽ 10 ⴱ 10 ⴱ 10 ⴱ 10 ⴱ 10
c. 100 ⫽ 10
Practice
5.
36.54
⫽ 34.96 ⫹ 1.58
6.
7.
43.27 ⫺ 12.67 ⫽
30.60
8.
302.578 ⫽ 300.2 ⫹ 2.378
43.545
19
10,000
a. 10 ⫽
b. 10
18
1
5. Circle ᎏ2ᎏ of the squares.
4. Complete.
2
d. 10 to the seventh power ⫽
10,000,000
74.6 ⫺ 31.055 ⫽
44
5
147
Math Masters, p. 180
Math Journal 1, p. 147
Lesson 6 3
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5:19 AM
Date
LESSON
Page 418
3 Differentiation Options
Time
A Pen Riddle
63
䉬
Mrs. Swenson bought 2 pens for each of her 3 daughters.
◆
She gave the clerk a $10 bill.
◆
Each pen cost the same amount.
◆
Her change was all in nickels.
◆
No sales tax was charged.
◆
Her change was less than 50 cents.
READINESS
Playing Beat the Calculator
$1.60 or $1.65
1.
What was the cost of each pen?
2.
Show or explain how you got your answer.
Sample answer:
SMALL-GROUP
ACTIVITY
5–15 Min
(Student Reference Book, p. 233; Math Masters, p. 461)
I needed an amount between $9.55 and $9.95 that can
be evenly divided by 6. Both $9.60 and $9.90 are evenly
divided by 6. $9.60 ⫼ 6 ⫽ $1.60; $9.90 ⫼ 6 ⫽ $1.65.
To provide experience with multiplying extended facts, students
play a version of Beat the Calculator in which the caller attaches
a 0 to one or both of the factors shown on the cards.
Math Masters, page 181
ENRICHMENT
Determining the Cost of Pens
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, p. 181)
To apply students’ understanding of division, have them use clues
to find the cost of several pens. Encourage students to use money
to model the problem if necessary.
PARTNER
ACTIVITY
EXTRA PRACTICE
Playing Division Dash
5–15 Min
(Student Reference Book, p. 241; Math Masters, p. 471)
To practice dividing 2- or 3-digit dividends by 1-digit divisors,
have students play Division Dash. See Lesson 6-4 for additional
information.
SMALL-GROUP
ACTIVITY
ELL SUPPORT
Building Vocabulary
Student Page
5–15 Min
Games
To provide language support for division, have students write
division number models on chart paper in the following ways:
Division Dash
Materials number cards 1–9 (4 of each)
1 score sheet
Players
1 or 2
Skill
Division of 2-digit by 1-digit numbers
42 / 5 → 8 R2
Object of the game To reach 100 in the fewest
divisions possible.
Directions
2. Shuffle the cards and place the deck number-side down
on the table.
♦ Turn over 3 cards and lay them down in a row, from left
to right. Use the 3 cards to generate a division problem.
The 2 cards on the left form a 2-digit number. This is the
dividend. The number on the card at the right is the divisor.
the result. This result is your quotient. Remainders are
ignored. Calculate mentally or on paper.
♦ Add your quotient to your previous score and record your new
score. (If this is your first turn, your previous score was 0.)
Label and circle the quotient in a third color.
4. Players repeat Step 3 until one player’s score is 100 or more.
The first player to reach at least 100 wins. If there is only
one player, the object of the game is to reach 100 in as few
turns as possible.
6
Label and circle the remainder in a fourth color.
4
5
4
6
64 is the dividend.
5
He divides 82 by 1. Quotient 82.
The score is 82 12 94.
5 is the divisor.
Quotient
Score
12
82
7
12
94
101
Turn 3: Bob then draws 5, 7, and 8.
He divides 57 by 8. Quotient 7.
Remainder is ignored. The score is 7 94 101.
Bob has reached 100 in 3 turns and the game ends.
Point out that both the quotient and the remainder are part of the
answer. Display this chart throughout the division lessons.
Student Reference Book, p. 241
418
8 R2
54
2
Label and underline the divisor (the number the dividend is
being divided by) in blue.
♦ Divide the 2-digit number by the 1-digit number and record
Turn 2: Bob then draws 8, 2, and 1.
42 5 → 8 R2
Label and underline the dividend (number being divided) in
red.
3. Each player follows the instructions below:
Turn 1: Bob draws 6, 4, and 5.
He divides 64 by 5. Quotient 12.
Remainder is ignored. The score is 12 0 12.
→ 8 R2
Have students do the following for each number model:
1. Prepare a score sheet like the one shown at the right.
Example
42
5
Unit 6 Division; Map Reference Frames; Measures of Angles
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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]
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
• Apply extended multiplication facts to long-division situations.
[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
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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
122
4
6
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
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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 ⴱ
⫽
100 ⴱ
⫽
50 ⴱ
⫽
50 ⴱ
⫽
20 ⴱ
⫽
20 ⴱ
⫽
10 ⴱ
⫽
10 ⴱ
⫽
5ⴱ
⫽
5ⴱ
⫽
2ⴱ
⫽
2ⴱ
⫽
1ⴱ
⫽
1ⴱ
⫽
100 ⴱ
⫽
100 ⴱ
⫽
50 ⴱ
⫽
50 ⴱ
⫽
20 ⴱ
⫽
20 ⴱ
⫽
10 ⴱ
⫽
10 ⴱ
⫽
5ⴱ
⫽
5ⴱ
⫽
2ⴱ
⫽
2ⴱ
⫽
1ⴱ
⫽
1ⴱ
⫽
(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:
224
0
0
–220
180
–110
70
–22
48
–22
26
–22
4
0
0
224
–220
180
–110
70
–66
4
224
0
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
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Student Page
Date
Time
LESSON
Example 2:
Partial-Quotients Division
6 10
䉬
1. Raul baked 96 cupcakes. He wants to divide
22 23
夹
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
夹
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:
4
3
127
–600
143
–60
83
–60
23
–12
11
4
3
127
–600
143
–120
23
–12
11
4
3
127
–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
䉬
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
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Student Page
Math Boxes 6 10
INDEPENDENT
ACTIVITY
(Math Journal 1, p. 168)
Date
Time
LESSON
Math Boxes
6 10
䉬
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 ⴱ 3) ⴱ 8
100 ⫺ 62
18 ⫹ 13 ⫹ 17
M
12 ⴱ 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
ᎏ1ᎏ ᎏ2ᎏ
3 3
1 2
1 1ᎏ3ᎏ 1ᎏ3ᎏ
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
䉬
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 ⴱ 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
䉬
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 ⴱ 63
6.
8.
2,233 ⫽ 319 ⴱ 7
16,287
89 ⴱ 183 ⫽
Math Masters, p. 197
Math Masters, page 198
Lesson 6 10
459