NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17
6•4
Lesson 17: Write Expressions in Which Letters Stand for
Numbers
Student Outcomes

Students write algebraic expressions that record all operations with numbers and/or letters standing for the
numbers.
Lesson Notes
Large paper is needed to complete this lesson.
Classwork
Fluency Exercise (5 minutes): Addition of Decimals
Sprint: Refer to the Sprints and Sprint Delivery Script sections in the Module Overview for directions on how to
administer a Sprint.
Opening (5 minutes)
Discuss the Exit Ticket from Lesson 16. Students continue to work on writing expressions, so discuss any common
mistakes from the previous lesson.
Exercises (25 minutes)
Students work in groups of two or three to complete the stations. At each station, students write down the problem and
the expression with variables and/or numbers. Encourage students to underline key words in each problem.
Exercises
Scaffolding:
Station One:
1.
The sum of 𝒂 and 𝒃
𝒂+𝒃
2.
Five more than twice a number 𝒄
If students struggled during
Lesson 16, complete some
examples with students before
moving into the exercises.
𝟓 + 𝟐𝒄 or 𝟐𝒄 + 𝟓
3.
Martha bought 𝒅 number of apples and then ate 𝟔 of them.
𝒅−𝟔
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17
6•4
Station Two:
1.
𝟏𝟒 decreased by 𝒑
𝟏𝟒 − 𝒑
2.
The total of 𝒅 and 𝒇, divided by 𝟖
𝒅+𝒇
𝟖
3.
or (𝒅 + 𝒇) ÷ 𝟖
Rashod scored 𝟔 less than 𝟑 times as many baskets as Mike. Mike scored 𝒃 baskets.
𝟑𝒃 − 𝟔
Station Three:
1.
The quotient of 𝒄 and 𝟔
𝒄
𝟔
2.
Triple the sum of 𝒙 and 𝟏𝟕
𝟑(𝒙 + 𝟏𝟕)
3.
Gabrielle had 𝒃 buttons but then lost 𝟔. Gabrielle took the remaining buttons and split them equally among her
𝟓 friends.
𝒃−𝟔
𝟓
or (𝒃 − 𝟔) ÷ 𝟓
Station Four:
1.
𝒅 doubled
𝟐𝒅
2.
Three more than 𝟒 times a number 𝒙
𝟒𝒙 + 𝟑 or 𝟑 + 𝟒𝒙
3.
Mali has 𝒄 pieces of candy. She doubles the amount of candy she has and then gives away 𝟏𝟓 pieces.
𝟐𝒄 − 𝟏𝟓
Station Five:
1.
𝒇 cubed
𝒇𝟑
2.
The quantity of 𝟒 increased by 𝒂, and then the sum is divided by 𝟗.
𝟒+𝒂
𝟗
3.
or (𝟒 + 𝒂) ÷ 𝟗
Tai earned 𝟒 points fewer than double Oden’s points. Oden earned 𝒑 points.
𝟐𝒑 − 𝟒
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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NYS COMMON CORE MATHEMATICS CURRICULUM
Lesson 17
6•4
Station Six:
The difference between 𝒅 and 𝟖
1.
𝒅−𝟖
𝟔 less than the sum of 𝒅 and 𝟗
2.
(𝒅 + 𝟗) − 𝟔
Adalyn has 𝒙 pants and 𝒔 shirts. She combined them and sold half of them. How many items did Adalyn sell?
3.
𝒙+𝒔
𝟐
or
𝟏
𝟐
(𝒙 + 𝒔)
When students reach the final station, they complete the station on larger paper. Students should put all of their work
on the top half of the paper.
After all students have completed every station, they travel through the stations again to look at the answers provided
on the larger paper. Students compare their answers with the answers at the stations and leave feedback on the bottom
MP.3
half of the paper. This may be positive feedback (“I agree with all of your answers” or “Great job”) or critiques (“I think
your subtraction is in the incorrect order” or “Why did you write your answer in that order?”).
Closing (5 minutes)
Discuss feedback that was left on the larger sheets of paper. This answers any questions and provides an opportunity to
discuss common mistakes.

Is it possible to have more than one correct answer? Why or why not?

When writing some of the expressions, it is possible to have more than one correct answer. For
example, when writing an expression with addition, the order can be different. Also, we learned how to
write division expressions in more than one way.
Exit Ticket (5 minutes)
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
Name
6•4
Date
Lesson 17: Write Expressions in Which Letters Stand for Numbers
Exit Ticket
Write an expression using letters and/or numbers for each problem below.
1.
𝑑 squared
2.
A number 𝑥 increased by 6, and then the sum is doubled.
3.
The total of ℎ and 𝑏 is split into 5 equal groups.
4.
Jazmin has increased her $45 by 𝑚 dollars and then spends a third of the entire amount.
5.
Bill has 𝑑 more than 3 times the number of baseball cards as Frank. Frank has 𝑓 baseball cards.
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Exit Ticket Sample Solutions
Write an expression using letters and/or numbers for each problem below.
1.
𝒅 squared
𝒅𝟐
2.
A number 𝒙 increased by 𝟔, and then the sum is doubled.
𝟐(𝒙 + 𝟔)
3.
The total of 𝒉 and 𝒃 is split into 𝟓 equal groups.
𝒉+𝒃
𝟓
4.
or (𝒉 + 𝒃) ÷ 𝟓
Jazmin has increased her $𝟒𝟓 by 𝒎 dollars and then spends a third of the entire amount.
𝟒𝟓 + 𝒎
𝟏
or (𝟒𝟓 + 𝒎)
𝟑
𝟑
5.
Bill has 𝒅 more than 𝟑 times the number of baseball cards as Frank. Frank has 𝒇 baseball cards.
𝟑𝒇 + 𝒅 or 𝒅 + 𝟑𝒇
Problem Set Sample Solutions
Write an expression using letters and/or numbers for each problem below.
1.
𝟒 less than the quantity of 𝟖 times 𝒏
𝟖𝒏 − 𝟒
2.
𝟔 times the sum of 𝒚 and 𝟏𝟏
𝟔(𝒚 + 𝟏𝟏)
3.
The square of 𝒎 reduced by 𝟒𝟗
𝒎𝟐 − 𝟒𝟗
4.
The quotient when the quantity of 𝟏𝟕 plus 𝒑 is divided by 𝟖
𝟏𝟕+𝒑
𝟖
5.
or (𝟏𝟕 + 𝒑) ÷ 𝟖
Jim earned 𝒋 in tips, and Steve earned 𝒔 in tips. They combine their tips and then split them equally.
𝒋+𝒔
𝟐
or (𝒋 + 𝒔) ÷ 𝟐
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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This file derived from G6-M4-TE-1.3.0-09.2015
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6.
6•4
Owen has 𝒄 collector cards. He quadruples the number of cards he has and then combines them with Ian, who has 𝒊
collector cards.
𝟒𝒄 + 𝒊
7.
Rae runs 𝟒 times as many miles as Madison and Aaliyah combined. Madison runs 𝒎 miles, and Aaliyah runs 𝒂
miles.
𝟒(𝒎 + 𝒂)
8.
By using coupons, Mary Jo is able to decrease the retail price of her groceries, 𝒈, by $𝟏𝟐𝟓.
𝒈 − 𝟏𝟐𝟓
9.
To calculate the area of a triangle, you find the product of the base and height and then divide by 𝟐.
𝒃𝒉
𝟐
or 𝒃𝒉 ÷ 𝟐
10. The temperature today was 𝟏𝟎 degrees colder than twice yesterday’s temperature, 𝒕.
𝟐𝒕 − 𝟏𝟎
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Number Correct: ______
Addition of Decimals I—Round 1
Directions: Evaluate each expression.
1.
5.1 + 6
23.
3.6 + 2.1
2.
5.1 + 0.6
24.
3.6 + 0.21
3.
5.1 + 0.06
25.
3.6 + 0.021
4.
5.1 + 0.006
26.
0.36 + 0.021
5.
5.1 + 0.0006
27.
0.036 + 0.021
6.
3 + 2.4
28.
1.4 + 42
7.
0.3 + 2.4
29.
1.4 + 4.2
8.
0.03 + 2.4
30.
1.4 + 0.42
9.
0.003 + 2.4
31.
1.4 + 0.042
10.
0.0003 + 2.4
32.
0.14 + 0.042
11.
24 + 0.3
33.
0.014 + 0.042
12.
2 + 0.3
34.
0.8 + 2
13.
0.2 + 0.03
35.
0.8 + 0.2
14.
0.02 + 0.3
36.
0.08 + 0.02
15.
0.2 + 3
37.
0.008 + 0.002
16.
2 + 0.03
38.
6 + 0.4
17.
5 + 0.4
39.
0.6 + 0.4
18.
0.5 + 0.04
40.
0.06 + 0.04
19.
0.05 + 0.4
41.
0.006 + 0.004
20.
0.5 + 4
42.
0.1 + 9
21.
5 + 0.04
43.
0.1 + 0.9
22.
0.5 + 0.4
44.
0.01 + 0.09
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M4-TE-1.3.0-09.2015
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Addition of Decimals I—Round 1 [KEY]
Directions: Evaluate each expression.
1.
5.1 + 6
𝟏𝟏. 𝟏
23.
3.6 + 2.1
𝟓. 𝟕
2.
5.1 + 0.6
𝟓. 𝟕
24.
3.6 + 0.21
𝟑. 𝟖𝟏
3.
5.1 + 0.06
𝟓. 𝟏𝟔
25.
3.6 + 0.021
𝟑. 𝟔𝟐𝟏
4.
5.1 + 0.006
𝟓. 𝟏𝟎𝟔
26.
0.36 + 0.021
𝟎. 𝟑𝟖𝟏
5.
5.1 + 0.0006
𝟓. 𝟏𝟎𝟎𝟔
27.
0.036 + 0.021
𝟎. 𝟎𝟓𝟕
6.
3 + 2.4
𝟓. 𝟒
28.
1.4 + 42
𝟒𝟑. 𝟒
7.
0.3 + 2.4
𝟐. 𝟕
29.
1.4 + 4.2
𝟓. 𝟔
8.
0.03 + 2.4
𝟐. 𝟒𝟑
30.
1.4 + 0.42
𝟏. 𝟖𝟐
9.
0.003 + 2.4
𝟐. 𝟒𝟎𝟑
31.
1.4 + 0.042
𝟏. 𝟒𝟒𝟐
10.
0.0003 + 2.4
𝟐. 𝟒𝟎𝟎𝟑
32.
0.14 + 0.042
𝟎. 𝟏𝟖𝟐
11.
24 + 0.3
𝟐𝟒. 𝟑
33.
0.014 + 0.042
𝟎. 𝟎𝟓𝟔
12.
2 + 0.3
𝟐. 𝟑
34.
0.8 + 2
13.
0.2 + 0.03
𝟎. 𝟐𝟑
35.
0.8 + 0.2
14.
0.02 + 0.3
𝟎. 𝟑𝟐
36.
0.08 + 0.02
15.
0.2 + 3
𝟑. 𝟐
37.
0.008 + 0.002
16.
2 + 0.03
𝟐. 𝟎𝟑
38.
6 + 0.4
17.
5 + 0.4
𝟓. 𝟒
39.
0.6 + 0.4
18.
0.5 + 0.04
𝟎. 𝟓𝟒
40.
0.06 + 0.04
19.
0.05 + 0.4
𝟎. 𝟒𝟓
41.
0.006 + 0.004
20.
0.5 + 4
𝟒. 𝟓
42.
0.1 + 9
21.
5 + 0.04
𝟓. 𝟎𝟒
43.
0.1 + 0.9
22.
0.5 + 0.4
𝟎. 𝟗
44.
0.01 + 0.09
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M4-TE-1.3.0-09.2015
𝟐. 𝟖
𝟏
𝟎. 𝟏
𝟎. 𝟎𝟏
𝟔. 𝟒
𝟏
𝟎. 𝟏
𝟎. 𝟎𝟏
𝟗. 𝟏
𝟏
𝟎. 𝟏
177
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Number Correct: ______
Improvement: ______
Addition of Decimals I—Round 2
Directions: Evaluate each expression.
1.
3.2 + 5
23.
4.2 + 5.5
2.
3.2 + 0.5
24.
4.2 + 0.55
3.
3.2 + 0.05
25.
4.2 + 0.055
4.
3.2 + 0.005
26.
0.42 + 0.055
5.
3.2 + 0.0005
27.
0.042 + 0.055
6.
4 + 5.3
28.
2.7 + 12
7.
0.4 + 5.3
29.
2.7 + 1.2
8.
0.04 + 5.3
30.
2.7 + 0.12
9.
0.004 + 5.3
31.
2.7 + 0.012
10.
0.0004 + 5.3
32.
0.27 + 0.012
11.
4 + 0.53
33.
0.027 + 0.012
12.
6 + 0.2
34.
0.7 + 3
13.
0.6 + 0.02
35.
0.7 + 0.3
14.
0.06 + 0.2
36.
0.07 + 0.03
15.
0.6 + 2
37.
0.007 + 0.003
16.
2 + 0.06
38.
5 + 0.5
17.
1 + 0.7
39.
0.5 + 0.5
18.
0.1 + 0.07
40.
0.05 + 0.05
19.
0.01 + 0.7
41.
0.005 + 0.005
20.
0.1 + 7
42.
0.2 + 8
21.
1 + 0.07
43.
0.2 + 0.8
22.
0.1 + 0.7
44.
0.02 + 0.08
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M4-TE-1.3.0-09.2015
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Lesson 17
NYS COMMON CORE MATHEMATICS CURRICULUM
6•4
Addition of Decimals I—Round 2 [KEY]
Directions: Evaluate each expression.
1.
3.2 + 5
𝟖. 𝟐
23.
4.2 + 5.5
𝟗. 𝟕
2.
3.2 + 0.5
𝟑. 𝟕
24.
4.2 + 0.55
𝟒. 𝟕𝟓
3.
3.2 + 0.05
𝟑. 𝟐𝟓
25.
4.2 + 0.055
𝟒. 𝟐𝟓𝟓
4.
3.2 + 0.005
𝟑. 𝟐𝟎𝟓
26.
0.42 + 0.055
𝟎. 𝟒𝟕𝟓
5.
3.2 + 0.0005
𝟑. 𝟐𝟎𝟎𝟓
27.
0.042 + 0.055
𝟎. 𝟎𝟗𝟕
6.
4 + 5.3
𝟗. 𝟑
28.
2.7 + 12
𝟏𝟒. 𝟕
7.
0.4 + 5.3
𝟓. 𝟕
29.
2.7 + 1.2
𝟑. 𝟗
8.
0.04 + 5.3
𝟓. 𝟑𝟒
30.
2.7 + 0.12
𝟐. 𝟖𝟐
9.
0.004 + 5.3
𝟓. 𝟑𝟎𝟒
31.
2.7 + 0.012
𝟐. 𝟕𝟏𝟐
10.
0.0004 + 5.3
𝟓. 𝟑𝟎𝟎𝟒
32.
0.27 + 0.012
𝟎. 𝟐𝟖𝟐
11.
4 + 0.53
𝟒. 𝟓𝟑
33.
0.027 + 0.012
𝟎. 𝟎𝟑𝟗
12.
6 + 0.2
𝟔. 𝟐
34.
0.7 + 3
13.
0.6 + 0.02
𝟎. 𝟔𝟐
35.
0.7 + 0.3
14.
0.06 + 0.2
𝟎. 𝟐𝟔
36.
0.07 + 0.03
15.
0.6 + 2
𝟐. 𝟔
37.
0.007 + 0.003
16.
2 + 0.06
𝟐. 𝟎𝟔
38.
5 + 0.5
17.
1 + 0.7
𝟏. 𝟕
39.
0.5 + 0.5
18.
0.1 + 0.07
𝟎. 𝟏𝟕
40.
0.05 + 0.05
19.
0.01 + 0.7
𝟎. 𝟕𝟏
41.
0.005 + 0.005
20.
0.1 + 7
𝟕. 𝟏
42.
0.2 + 8
21.
1 + 0.07
𝟏. 𝟎𝟕
43.
0.2 + 0.8
22.
0.1 + 0.7
𝟎. 𝟖
44.
0.02 + 0.08
Lesson 17:
Write Expressions in Which Letters Stand for Numbers
This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org
This file derived from G6-M4-TE-1.3.0-09.2015
𝟑. 𝟕
𝟏
𝟎. 𝟏
𝟎. 𝟎𝟏
𝟓. 𝟓
𝟏
𝟎. 𝟏
𝟎. 𝟎𝟏
𝟖. 𝟐
𝟏
𝟎. 𝟏
179
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