NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6•4
Lesson 14: Writing Division Expressions Student Outcomes 
Students write numerical expressions in two forms, and , and note the relationship between the two. Scaffolding: Lesson Notes The sets of eight questions used in the Exercises can be tailored to fit the level at which students are working. You can write a set for lower level learners and/or a set for advanced learners as needed.
This is the second day of a two‐day lesson. Fluency Exercise (5 Minutes) Long Division Algorithm White Board Exchange Classwork Example 1 (5 minutes) Example 1 Fill in the three remaining squares so that all the squares contain equivalent expressions. MP.2 The quotient of and Equivalent Expressions Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
Example 2 (3 minutes) Lesson 14
6•4
Example 2 Fill in a blank copy of the four boxes using the words dividend and divisor so that it is set up for any example. MP.2 The quotient of the dividend and the divisor divisor
dividend Equivalent Expressions dividend divisor
Exercises (20 minutes) Students will work in pairs. Each pair will be given 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 equivalent expressions. Set A Answers 1.
divided by , , p 5 2.
The quotient of and 3.
w 23 4.
5.
, , h g divided by , 3 m  11 7.
8.
, x  8 y divided by the sum of and , divided by the quantity minus 6.
, , , a  6 7 The sum of and divided by , The sum of and divided by , , , g
The quotient of minus and plus , f 2 , d  3 c  9 Set B 1.
Answers: The quotient of and 2.
The quotient of and 3.
5 j , 1 1 h , , n m , The quotient of and , , Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
4.
5.
Lesson 14
18 a  5 7.
8.
, g  1 1 f , The sum of and divided by , The quantity minus divided by , x y  3 , , The quantity plus divided by the quantity minus , 6•4
, m  4 h divided by the quantity minus , divided by the quantity minus 6.
h  11 g  5
, Set C Answers: 1.
divided by , k 6 , 2.
The quotient of and 3.
10 a 4.
5.
, , divided by the quantity minus , , h  1 1 3 , divided by the sum of and 3 c  18 7.
j , divided by 6.
8.
, k
The sum of plus ,
f  2 15
divided by , , The quantity minus divided by , m h  2 , The quantity minus divided by the sum of and , , n  11 4  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 are equivalent. 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: Set B: Set C: 3, 5, 10 4, 8, 10
2, 10, 6 Exit Ticket (3 minutes) Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
Name Lesson 14
Date 6•4
Lesson 14: Writing Division Expressions Exit Ticket 1.
Write the division expression in words and as a fraction. 12
2.
Write the following division expression using the division symbol and as a fraction: divided by the quantity minus3. Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6•4
Exit Ticket Sample Solutions 1.
Write the division expression in words and as a fraction. The sum of and divided by , . 2.
Write the following division expression using the division symbol and as a fraction: divided by the quantity minus . and Problem Set Sample Solutions Complete the missing spaces in each rectangle set. Answers: The quotient of and , 16 h , Answers: divided by the quantity minus , b  33
m , divided by Answers: x
7 , , Answers: The sum of and divided by , , Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6•4
Exercise Handout Set A 1.
5
2.
The quotient of and 3.
w 23 4.
5.
7 divided by the quantity minus 6 6.
3 m  11 7.
2 8.
Set B 1.
11 2.
The quotient of and 3.
5 j 4.
5.
divided by the quantity minus 11 6.
18 a  5 7.
3 8.
Set C 1.
6
2.
The quotient of and 3.
10 a 4.
5.
13 divided by the sum of and 1 6.
3 c  18 2
7.
8.
Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 14
6•4
White Board Exchange: Long Division Algorithm Progression of Exercises: Answers: 1.
3,282
6
547
2.
2,712
3
904
3.
15,036
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
7
2148
Fluency work such as this exercise should take 5–12 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 place card stock inside sheet protectors to use as the personal white boards and to cut sheets of felt into small squares to use as erasers. It is best to prepare the problems in a way that allows you to reveal them to the class one at a time. For example, use a flip chart or PowerPoint presentation; write the problems on the board and cover with paper beforehand, allowing you 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 be appropriate to verbally call out the problem to the students. The teacher reveals or says the first problem in the list and announces, “Go.” Students work the problem on their personal white boards, holding their answers up for the teacher to see as soon as they have them ready. The teacher gives immediate feedback to each student, pointing and/or making eye contact with the student and responding with an affirmation for correct work such as, “Good job!”, “Yes!”, or “Correct!” For incorrect work, respond with guidance such 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 is able to go through each problem in quick succession without pausing to go through the solution of each problem individually. If only one or two students have not been able to get a given problem correct when the rest of the students are finished, it is appropriate to move the class forward to the next problem without further delay; in this case, find a time to provide remediation to that student before the next fluency exercise on this skill is given. Lesson 14: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org Writing Division Expressions
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