1. Lesson 14: Writing Division Expressions
Date: 3/24/15 139
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
The quotient of 𝟏𝟓and 𝟑
𝟏𝟓÷ 𝟑
Equivalent
Expressions
𝟑 𝟏𝟓
𝟏𝟓
𝟑
Lesson 14: Writing Division Expressions
Student Outcomes
 Students write numerical expressions in two forms, 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ÷ 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 and
𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑑𝑖𝑣𝑖𝑠𝑜𝑟
, and note the
relationship between the two.
Lesson Notes
This is the second day of a two-day lesson.
FluencyExercise (5 Minutes)
Long Division AlgorithmWhite Board Exchange
Classwork
Example 1 (5 minutes)
Example 1
Fill in the threeremaining squaresso that all the squarescontain equivalent expressions.
Scaffolding:
The sets of eight questions
used in the Exercises can be
tailored to fitthe level at which
students are working. You can
write a set for lower level
learners and/or a set for
advanced learners as needed.
MP.2

2. Lesson 14: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
Example 2 (3 minutes)
Example 2
Fill in ablank copy ofthe four boxesusing the words dividend and divisor so that it isset up for any example.
Exercises(20 minutes)
Students will work in pairs. Each pair will begiven a set of expressions to work on. There are several different versions
that can be printed and used so that a variety of questions can be used throughout the classroom. The students will fill
in the four rectangles,one with the given information and three with equivalentexpressions.
Set A Answers
1. 𝟓 ÷ 𝒑 𝟓divided by 𝒑,
𝟓
𝒑
, 5p
2. The quotient of 𝒈and 𝒉 𝒈 ÷ 𝒉,
𝒈
𝒉
, h g
3. 23w 𝟐𝟑divided by 𝒘, 𝟐𝟑÷ 𝒘,
𝟐𝟑
𝐰
4.
𝒚
𝒙+𝟖
𝒚divided by thesum of 𝒙 and 𝟖, 𝒚 ÷ (𝒙 + 𝟖), 8x y
5. 𝟕divided by the quantity 𝒂 minus 𝟔 𝟕 ÷ (𝒂 − 𝟔),
𝟕
𝒂−𝟔
, 6 7a 
6. 3 11m  The sum of 𝒎 and 𝟏𝟏divided by 𝟑, (𝒎 + 𝟏𝟏)÷ 𝟑,
𝒎+𝟏𝟏
𝟑
7. (𝒇 + 𝟐) ÷ 𝒈 The sum of 𝒇 and 𝟐divided by 𝒈,
𝒇+𝟐
𝒈
, 2g f 
8.
𝒄−𝟗
𝒅+𝟑
The quotient of 𝒄minus 𝟗and 𝒅 plus 𝟑, (𝒄 − 𝟗)÷ (𝒅 + 𝟑), 3 9d c 
Set B Answers:
1. 𝒉 ÷ 𝟏𝟏 The quotient of 𝒉 and 𝟏𝟏, 11 h ,
𝒉
𝟏𝟏
2. The quotient of 𝒎 and 𝒏 𝒎 ÷ 𝒏, n m ,
𝒎
𝒏
3. 5 j The quotient of 𝒋 and 𝟓, 𝒋 ÷ 𝟓,
𝒋
𝟓
MP.2 The quotient ofthedividend and
thedivisor
𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅÷ 𝒅𝒊𝒗𝒊𝒔𝒐𝒓
Equivalent
Expressions
divisor dividend
dividend
divisor

3. Lesson 14: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
4.
𝒉
𝒎−𝟒
𝒉 divided by thequantity 𝒎 minus 𝟒, 𝒉 ÷ (𝒎 − 𝟒), 4m h
5. 𝒇 divided by the quantity 𝒈minus 𝟏𝟏 𝒇 ÷ (𝒈− 𝟏𝟏), 11g f ,
𝒇
𝒈−𝟏𝟏
6. 18 5a  The sum of 𝒂 and 𝟓divided by 𝟏𝟖, (𝒂+ 𝟓) ÷ 𝟏𝟖,
𝒂+𝟓
𝟏𝟖
7. (𝒚− 𝟑) ÷ 𝒙 The quantity 𝒚minus 𝟑divided by 𝒙, 3x y  ,
𝒚−𝟑
𝒙
8.
( 𝒈+𝟓)
( 𝒉−𝟏𝟏)
The quantity 𝒈plus 𝟓divided by thequantity 𝒉 minus 𝟏𝟏,
( 𝒈+ 𝟓)÷ ( 𝒉 − 𝟏𝟏),
11 5h g 
Set C Answers:
1. 𝟔÷ 𝒌 𝟔divided by 𝒌, 6k ,
𝟔
𝒌
2. The quotient of 𝒋 and 𝒌 𝒋 ÷ 𝒌, k j ,
𝒋
𝒌
3. 10 a 𝒂 divided by 𝟏𝟎, 𝒂 ÷ 𝟏𝟎,
𝒂
𝟏𝟎
4.
𝟏𝟓
𝒇−𝟐
𝟏𝟓divided by thequantity 𝒇 minus 𝟐, 𝟏𝟓÷ (𝒇 − 𝟐), 2 15f 
5. 𝟏𝟑divided by the sum of 𝒉 and 𝟏 𝟏𝟑÷ (𝒉 + 𝟏), 1 13h  ,
𝟏𝟑
𝒉+𝟏
6. 3 18c  The sum of 𝒄plus 𝟏𝟖divided by 𝟑, (𝒄+ 𝟏𝟖)÷ 𝟑,
𝒄 + 𝟏𝟖
𝟑
7. (𝒉− 𝟐) ÷ 𝒎 The quantity 𝒉 minus 𝟐divided by 𝒎, 2m h  ,
𝒉−𝟐
𝒎
8.
𝟒 −𝒎
𝒏+𝟏𝟏
The quantity 𝟒 minus 𝒎 dividedby thesum of 𝒏 and 𝟏𝟏,
(𝟒− 𝒎)÷ (𝒏+ 𝟏𝟏), 11 4n m 
Closing(7 minutes)
 Have two pairs of students trade pages to check each other’s work. If all of the boxes are correct, students will
need to write a sentence that summarizes why the expressions areequivalent. If there are mistakes,the
students will need to write sentences to explain how to correct it.
 Then have students evaluate some of the expressions. Many answers will need to be written as a fraction or
decimal answer.
Set A: 𝑝 = 3, 𝑤 = 5, 𝑎 = 10
Set B: ℎ = 4, 𝑗 = 8, 𝑎 = 10
Set C: 𝑘 = 2, 𝑎 = 10, 𝑐 = 6
Exit Ticket (3 minutes)

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
Name Date
Lesson 14: Writing Division Expressions
Exit Ticket
1. Write the division expression in words and as a fraction.
(𝑔 + 12) ÷ ℎ
2. Write the followingdivision expression usingthedivision symbol and as a fraction: 𝑓 divided by the quantity
ℎ minus 3.

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
Exit Ticket Sample Solutions
1. Write the division expressionin wordsand asafraction.
(𝒈+ 𝟏𝟐)÷ 𝒉
The sum of 𝒈and 𝟏𝟐divided by 𝒉,
𝒈+𝟏𝟐
𝒉
.
2. Write the following division expression using the division symboland asafraction: 𝒇 divided by the quantity 𝒉
minus 𝟑.
𝒇 ÷ (𝒉 − 𝟑)and
𝒇
𝒉−𝟑
Problem Set Sample Solutions
Complete themissing spacesin eachrectangleset.
Answers: The quotient of 𝒉 and 𝟏𝟔, 16 h ,
𝒉
𝟏𝟔
Answers: 𝒎 divided by thequantity 𝒃minus 𝟑𝟑, 33b m , 𝒎 ÷ (𝒃 − 𝟑𝟑)
Answers: 7x , 𝟕÷ 𝒙,
𝟕
𝒙
Answers: The sum of 𝒚and 𝟏𝟑divided by 𝟐, ( 𝒚+ 𝟏𝟑)÷ 𝟐,
𝒚+𝟏𝟑
𝟐
𝒉 𝟏𝟔
𝒎
𝒃 − 𝟑𝟑
𝟕divided by 𝒙 𝟐 𝒚 + 𝟏𝟑

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
Exercise Handout
Set A
1. 5 ÷ 𝑝
2. The quotient of 𝑔 and ℎ
3. 23w
4.
𝑦
𝑥+8
5. 7 divided by the quantity 𝑎 minus 6
6. 3 11m 
7. (𝑓 + 2) ÷ 𝑔
8.
𝑐−9
𝑑+3
Set B
1. ℎ ÷ 11
2. The quotient of 𝑚 and 𝑛
3. 5 j
4.
ℎ
𝑚−4
5. 𝑓 divided by the quantity 𝑔 minus 11
6. 18 5a 
7. (𝑦 − 3) ÷ 𝑥
8.
( 𝑔+5)
(ℎ−11)
Set C
1. 6 ÷ 𝑘
2. The quotient of 𝑗 and 𝑘
3. 10 a
4.
15
𝑓−2
5. 13 divided by the sum of ℎ and 1
6. 3 18c 
7. (ℎ − 2) ÷ 𝑚
8.
4 −𝑚
𝑛+11

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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 14
White Board Exchange: Long Division Algorithm
Progression of Exercises: Answers:
1. 3,282 ÷ 6 547
2. 2,712 ÷ 3 904
3. 15,036 ÷ 7 2148
4. 1,788 ÷ 8 223.5
5. 5,736 ÷ 12 478
6. 35,472 ÷ 16 2217
7. 13,384 ÷ 28 478
8. 31,317 ÷ 39 803
9. 1,113 ÷ 42 26.5
10. 4082 ÷ 52 78.5
Fluency work such as this exerciseshould take5–12 minutes of class.
How to Conduct a White Board Exchange:
All students will need a personal white board, white board marker, and a means of erasing their work. An economical
recommendation is to placecard stock insidesheet protectors to use as the personal whiteboards and to cut sheets of
felt into small squaresto use as erasers.
It is bestto prepare the problems in a way that allows you to reveal them to the class oneat a time. For example, use a
flip chartor PowerPoint presentation; write the problems on the board and cover with paper beforehand, allowingyou
to reveal one at a time; or, write only one problem on the board at a time. If the number of digits in the problem is very
low (e.g., 12 divided by 3), it may also beappropriateto verbally call outthe problem to the students.
The teacher reveals or says the firstproblem in the listand announces,“Go.” Students work the problem on their
personal white boards,holdingtheir answers up for the teacher to see as soon as they have them ready. The teacher
gives immediate feedback to each student, pointingand/or makingeye contactwith the student and respondingwith an
affirmation for correctwork such as,“Good job!”, “Yes!”, or “Correct!” For incorrectwork, respond with guidancesuch
as “Look again!”,“Try again!”, or “Check your work!”
If many students have struggled to get the answer correct, go through the solution of that problem as a class before
moving on to the next problem in the sequence. Fluency in the skill has been established when the class isableto go
through each problem in quick succession withoutpausingto go through the solution of each problem individually. If
only one or two students have not been ableto get a given problem correct when the rest of the students are finished,it
is appropriateto move the classforward to the next problem without further delay; in this case,find a time to provide
remediation to that student before the next fluency exerciseon this skill is given.