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G6 m4-d-lesson 13-t
- 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
Date: 3/24/15 137
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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