1. Lesson 13: Writing Division Expressions
Date: 3/24/15 133
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Lesson 13: Writing Division Expressions
Student Outcomes
 Students write numerical expressions in two forms, 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 ÷ 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 and
𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑑𝑖𝑣𝑖𝑠𝑜𝑟
, and note the
relationship between the two.
Classwork
Discussion(8 minutes)
The discussion will serveas a chancefor students to show what they know about division and whatdivision looks like.
The discussion should concludewith the overall idea that writing 𝑎 ÷ 𝑏 as
𝑎
𝑏
is a strategic format when working
algebraically.
 How can we write or show 8 divided by 2? (You can allowstudents to explain or even draw examples for class
to see.
 Answers will vary. Students can draw models, arrays, use the division symbol and some may even use a
fraction.
 When workingwith algebraic expressions,areany of these expressions or models more efficient than others?
 Writing a fraction to show division is more efficient.
 Is
8
2
the same as
2
8
?
 No, they are not the same.
8
2
= 4, while
2
8
=
1
4
.
 How would we show 𝑎 divided by 𝑏 usinga fraction?

𝑎
𝑏
Example 1 (5 minutes)
Example 1
Write an expression showing 𝟏 ÷ 𝟐withouttheuse ofthe division symbol.
 Let’s startby lookingata model of 1 ÷ 2.
 We can make a bar diagram.
MP.6

2. Lesson 13: Writing Division Expressions
Date: 3/24/15 134
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
𝟏
From the model what can we determine?
𝟏÷ 𝟐is thesameas
𝟏
𝟐
.
Example 2 (5 minutes)
Example 2
Write an expression showing 𝒂 ÷ 𝟐withouttheuse ofthe division symbol.
 Here we have a variablebeingdivided by 2. Let’s startby lookingata model of 𝑎 ÷ 2.
 We can make a bar diagram.
From the model what can we determine?
𝒂 ÷ 𝟐 is thesameas
𝒂
𝟐
.
When we write division expressionsusing thedivision symbol werepresent 𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅÷ 𝒅𝒊𝒗𝒊𝒔𝒐𝒓.
How would thislook when we write divisionexpressionsusing a fraction?
𝒅𝒊𝒗𝒊𝒅𝒆𝒏𝒅
𝒅𝒊𝒗𝒊𝒔𝒐𝒓
Example 3 (8 minutes)
Example 3
a. Write an expression showing 𝒂 ÷ 𝒃 withouttheuse ofthe division symbol.
 How can we use what we justlearned in Examples 1 and 2 to help us with this example?
 The dividend is the numerator and the divisor is the denominator.
𝒂
MP.6

3. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
𝒂
𝒃
b. Write an expression for 𝒈divided by thequantity 𝒉 plus 𝟑.
 How would this look with the division symbol?
 𝑔 ÷ (ℎ + 3)
 Now let’s rewrite this usinga fraction.
𝒈
𝒉 + 𝟑
c. Write an expression for thequotient ofthe quantity 𝒎 reduced by 𝟑 and 𝟓.
 Let’s startagain by writingthis usinga division symbol first.
 (𝑚 − 3) ÷ 5
 Next, we will rewriteit usingthe fraction bar.
𝒎 − 𝟑
𝟓
Exercises1–8 (10 minutes)
Have students use a white board or small board to practicethe followingquestions.
Exercises
Write each expression twoways: using the divisionsymbol and asafraction.
1. 𝟏𝟐divided by 𝟒.
𝟏𝟐÷ 𝟒 and
𝟏𝟐
𝟒
2. 𝟑divided by 𝟓.
𝟑 ÷ 𝟓 and
𝟑
𝟓
3. 𝒂 divided by 𝟒.
𝒂 ÷ 𝟒 and
𝒂
𝟒
4. The quotient of 𝟔and 𝒎.
𝟔 ÷ 𝒎 and
𝟔
𝒎
MP.6

4. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
5. Seven divided by thequantity 𝒙 plus 𝒚.
𝟕÷ (𝒙 + 𝒚)and
𝟕
𝒙 + 𝒚
6. 𝒚divided by the quantity 𝒙 minus 𝟏𝟏.
𝒚÷ ( 𝒙 − 𝟏𝟏)and
𝒚
𝒙−𝟏𝟏
7. The sum ofthe quantity 𝒉 and 𝟑divided by 𝟒.
(𝒉+ 𝟑) ÷ 𝟒 and
𝒉+𝟑
𝟒
8. The quotient ofthe quantity 𝒌 minus 𝟏𝟎and 𝒎.
(𝒌− 𝟏𝟎)÷ 𝒎 and
𝒌−𝟏𝟎
𝒎
Closing(4 minutes)
 Explain to your neighbor how you would rewrite any division problemusinga fraction.
 The dividend would become the numerator and the divisor would become the denominator.
Exit Ticket (5 minutes)

5. Lesson 13: Writing Division Expressions
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Name Date
Lesson 13: Writing Division Expressions
Exit Ticket
Rewrite the expressions usingthe division symbol and as a fraction.
1. The quotient of 𝑚 and 7.
2. Five divided by the sum of 𝑎 and 𝑏.
3. The quotient of 𝑘 decreased by 4 and 9.

6. Lesson 13: Writing Division Expressions
Date: 3/24/15 138
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NYS COMMON CORE MATHEMATICS CURRICULUM 6•4Lesson 13
Exit Ticket Sample Solutions
Rewrite the expressionsusing thedivisionsymbol and asafraction.
1. The quotient of 𝒎 and 𝟕.
𝒎 ÷ 𝟕 and
𝒎
𝟕
2. Five divided by the sum of 𝒂 and 𝒃.
𝟓÷ (𝒂+ 𝒃) and
𝟓
(𝒂+𝒃)
3. The quotient of the quantity 𝒌 decreased by 𝟒and 𝟗.
(𝒌− 𝟒)÷ 𝟗 and
(𝒌−𝟒)
𝟗
Problem Set Sample Solutions
1. Rewrite the expressionsusing thedivisionsymbol and asafraction.
a. Three divided by 𝟒.
𝟑 ÷ 𝟒and
𝟑
𝟒
b. The quotient of 𝒎 and 𝟏𝟏.
𝒎 ÷ 𝟏𝟏and
𝒎
𝟏𝟏
c. 𝟒divided by the sum of 𝒉 and 𝟕.
𝟒 ÷ (𝒉 + 𝟕)and
𝟒
𝒉+𝟕
d. The quantity 𝒙 minus 𝟑divided by 𝒚.
(𝒙 − 𝟑)÷ 𝒚and
𝒙−𝟑
𝒚
2. Draw a model to show that 𝒙 ÷ 𝟑isthe same as
𝒙
𝟑
.
𝟏
𝟑
𝒙 𝒐𝒓
𝒙
𝟑
𝒙