Transcript of "Lessons 18 29 quiz review with answers"
1.
Name ____________________________________ Date ________________________
Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review
Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and Subtraction
Read the story problem. Identify the unknown quantity and write an addition or subtraction
expression that is described. Then evaluate your expression given the further information.
Story Problem
Description
with Units
Expression
Evaluate the
Expression if:
Show your Work
and Evaluate
Robby has two
more basketballs
than his brother
Michael.
Let 𝒆 = the
number of balls
Michael has
𝒆 + 𝟐
Michael has 𝟕
basketballs.
𝒆 + 𝟐
𝟕 + 𝟐
𝟗
Robby has 𝟗
basketballs.
Ella baked 𝟖 more
cupcakes than
Anna in the sixth
grade.
Anna baked 𝟏𝟎
cupcakes in the
sixth grade.
Lisa has been
surfing for 𝟑 more
years than Danika.
Danika has
been surfing
for 𝟗 years.
Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an
expression to represent the number of miles Bob ran. Let m = the number of miles Mrs.
Labuski ran.
Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of
miles Bob ran.
If Mrs. Labuski ran 8 miles, how many miles did Bob run?
2.
Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction Expressions
Sara and Tiffany are in 6th
grade and both take drum lessons at School of Rock Music Store.
This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking
lessons throughout high school.
a. Complete the table showing the number of years the girls will have been drumming at the
music store.
Grade
Sara’s Years of Experience
With Drums
Tiffany’s Years of Experience
With Drums
Sixth
Seventh
Eighth
Ninth
Tenth
Eleventh
Twelfth
b. If Sara has been taking drum lessons for 𝑦 years, what expression could represent how many
years has Tiffany been taking lessons?
c. If Tiffany has been taking drum lessons for x years, what expression could represent the
number of years Sara has been taking lessons?
3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor
insists that there are to be 5 more essay writers than poets at all times.
a. How many essay writers are in the Writer’s Club this year?
b. Write two expressions that describes the relationship of the number of poets (𝑝) and the
number of essay writers (𝑒).
c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many
poets will the Writing Club instructor want in the club?
3.
Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division
Joe earns $75.00 per day. Create a table of values that shows the relationship between the
number of days that Joe worked , d, and the amount of money that he earned, e.
a. If we let d represent the number of days that Joe worked, what is the expression that shows
how much money Joe earned.
b. Use your expression to determine how much Joe earned if he worked 12 days.
c. If let e represent how much money Joe earned, what is the expression that shows how many
days he worked.
d. Use your expression to determine how many days Joe worked if he earned $600.00.
4.
Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition
The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is
$350.00 for the weekend. In addition, each student will have to pay $5 for the price of the trip.
Complete the table below to calculate the amount of money the PTA will pay if ten seniors go
on the trip.
a. Write an expression that shows the amount of money the PTA collects if s number of
students attend the trip.
b. Use your expression to determine the amount of money the PTA would collect if 60 students
attend the trip.
Module 4 Lesson 22 Writing and Evaluating Expressions – Exponents
Judah had two children. When those children grew up, each one also had two children, who
later each had two children as well. If this pattern continues, how many children are there in the
5th
generation?
Generation Number of Children
Number of Children written
as a power of 2
a. Write an expression for how many children would be born after g generations.
b. Use your expression to determine how many children would be born after 10 generations.
5.
Module 4 Lesson 23 True or False Number Sentences
Substitute the value for the variable and state in a complete sentence whether the resulting
number sentence is true or false. If true, find a value that would result in a false number
sentence. If false, find a value that would result in a true number sentence.
18b ≥ 54. Substitute 3 for b.
28 + c = 35. Substitute 8 for c.
18 ≥ 33 – t. Substitute 15 for t.
Module 4 Lesson 24 True of False Number Sentences.
State whether the sentence is true or false.
56 – 14 < 48
33 ≥ 13 + 23
State when the following equations and inequalities will be true and when they will be false.
6r > 36
15 = 6 + d
32 – t < 18
6.
Module 4 Lesson 26 One Step Equations – Addition & Subtraction
Find the solution of the equations using a tape diagram. Check your answer.
p + 5 = 11 f – 8 = 10
Find the solution of the equations below algebraically. Check your answer.
k – 29 = 54 46 + m = 100
46 = t – 4 n + 5 = 17
Module 4 Lesson 27 One Step Equations – Multiplication & Division
Find the solution of the equations using a tape diagram. Check your answer.
4x = 20
3
m
= 9
7.
Find the solution of the equation below algebraically. Check your answer.
7x = 35 12y = 60
5
h
= 6
7
k
= 2
Module 4 Lesson 28 Two-Step Problems – All Operations
Find the solution of the equation below algebraically. Check your answer.
x + 15 − 6 = 18 y + 9 +12 = 40
x + x =12 n + 2n = 9
Barry had 𝟓𝟎 doubles last season which is 𝟏𝟎 more than his best season. Willy had 8 more
doubles than Derek last season. Willy had the same number of as Barry’s best season. Let 𝑏
represent the number of doubles Barry had during his best season, 𝑑 represent the number of
Derek’s doubles last season, and 𝑤 represent the number of Willy’s doubles last season. How
many doubles did Derek have last season?
8.
Lesson 29 Multi-Step Problems – All Operations
Solve the problem using tables and equations, and then check your answer with the word
problem. Try to find the answer only using two rows of numbers on your table.
1. The PE teachers are organizing supplies for this year’s field day. In order to have enough
materials for all of the students, they need twice as many hula hoops as Frisbees. The number
of flags required is ten times more than the number of hula hoops. The number of cones that is
needed is half as many flags. If they have a total of 396 supplies, how many cones do they
have?
ANSWER:
Flags Cones Frisbees Hula hoops total
9.
Name ____________________________________ Date ________________________
Mrs. Labuski / Mrs. Portsmore Period ________ Module 4 Lessons 18-29 Qz Review
Module 4 Lesson 18 Writing and Evaluating Expressions – Addition and Subtraction
Read the story problem. Identify the unknown quantity and write an addition or subtraction
expression that is described. Then evaluate your expression given the further information.
Story Problem
Description
with Units
Expression
Evaluate the
Expression if:
Show your Work
and Evaluate
Robby has two more
basketballs than his
brother Michael.
Let 𝒆 = the
number of balls
Michael has
𝒆 + 𝟐
Michael has 𝟕
basketballs.
𝒆 + 𝟐
𝟕 + 𝟐
𝟗
Robby has 𝟗
basketballs.
Ella baked 𝟖 more
cupcakes than Anna
in the sixth grade.
Let c = the
number of
cupcakes Anna
has
c + 8
Anna baked
𝟏𝟎 cupcakes
in the sixth
grade.
c + 8
10 + 8
18
Ella bakes 18
cupcakes
Lisa has been surfing
for 𝟑 more years than
Danika.
Let d = number
of years Danika
has been
surfing
d + 3
Danika has
been surfing
for 𝟗 years.
d + 3
9 + 3
12
Lisa has been
surfing for 12
years.
Mrs. Labuski went running yesterday. Now she has run 5 more miles than Bob. Write an
expression to represent the number of miles Bob ran. Let m = the number of miles Mrs.
Labuski ran.
m - 5
Write an expression to represent the number of miles Mrs. Labuski ran. Let b = the number of
miles Bob ran.
b + 5
If Mrs. Labuski ran 8 miles, how many miles did Bob run?
m – 5
8-5
3
Bob ran 3 miles
10.
Module 4 Lesson 19 Substituting to Evaluate Addition and Subtraction Expressions
Sara and Tiffany are in 6th
grade and both take drum lessons at School of Rock Music Store.
This is Sara’s first year, while this is Tiffany’s fifth year. Both girls plan to continue taking
lessons throughout high school.
a. Complete the table showing the number of years the girls will have been drumming at the
music store.
Grade
Sara’s Years of Experience
With Drums
Tiffany’s Years of Experience
With Drums
Sixth 1 5
Seventh 2 6
Eighth 3 7
Ninth 4 8
Tenth 5 9
Eleventh 6 10
Twelfth 7 11
b. If Sara has been taking drum lessons for 𝑦 years, what expression could represent how many
years has Tiffany been taking lessons?
y + 4
c. If Tiffany has been taking drum lessons for x years, what expression could represent the
number of years Sara has been taking lessons?
x - 4
3. The elementary school Writer’s Club has 15 poets this year. The Writing Club instructor
insists that there are to be 5 more essay writers than poets at all times.
a. How many essay writers are in the Writer’s Club this year?
15 + 5 = 20
b. Write two expressions that describes the relationship of the number of poets (𝑝) and the
number of essay writers (𝑒).
p + 5 = e e – 5 = p
c. If there are only 12 essay writers interested in joining the Writer’s Club next year, how many
poets will the Writing Club instructor want in the club?
e - 5 = p
12 - 5 = p
7 = p
The instructor will want 7 poets.
11.
Module 4 Lesson 20 Writing and Evaluating Expressions – Multiplication and Division
Joe earns $75.00 per day. Create a table of values that shows the relationship between the
number of days that Joe worked , d, and the amount of money that he earned, e.
Number of Days Joe Worked, d Amount Earned, e, in Dollars
1 75
2 150
3 225
4 300
a. If we let d represent the number of days that Joe worked, what is the expression that shows
how much money Joe earned.
75d
b. Use your expression to determine how much Joe earned if he worked 12 days.
75d
75 12
900
Joe will earn $900 if he works 12 days.
c. If let e represent how much money Joe earned, what is the expression that shows how many
days he worked.
e ÷ 75
d. Use your expression to determine how many days Joe worked if he earned $600.00.
e ÷ 75
600 ÷ 75
8
Joe worked 8 days.
12.
Module 4 Lesson 21 Writing and Evaluating Expressions – Multiplication and Addition
The PTA is planning a weekend field trip for its graduating seniors. The cost of the bus is
$350.00 for the weekend. In addition, each student will have to pay $5 for the price of the trip.
Complete the table below to calculate the amount of money the PTA will pay if ten seniors go
on the trip.
Number of Students on
the Trip (s)
Total Cost in Dollars
(d)
1 355
2 360
3 365
4 370
5 375
6 380
7 385
8 390
9 395
10 400
a. Write an expression that shows the amount of money the PTA collects if s number of
students attend the trip.
350 + 5s
b. Use your expression to determine the amount of money the PTA would collect if 60 students
attend the trip.
350 + 5s
13.
Module 4 Lesson 22 Writing and Evaluating Expressions – Exponents
Judah had two children. When those children grew up, each one also had two children, who
later each had two children as well. If this pattern continues, how many children are there in the
5th
generation?
Generation Number of Children
Number of Children
written as a power of 2
1 2 21
2 4 22
3 8 23
4 16 24
5 32 25
a. Write an expression for how many children would be born after g generations.
2g
b. Use your expression to determine how many children would be born after 10 generations.
2g
210
1024
Module 4 Lesson 23 True or False Number Sentences
Substitute the value for the variable and state in a complete sentence whether the resulting
number sentence is true or false. If true, find a value that would result in a false number
sentence. If false, find a value that would result in a true number sentence.
18b ≥ 54. Substitute 3 for b.
True. Any value less than 3 will result in a false statement
28 + c = 35. Substitute 8 for c.
False. The number 7 is the only value that will result in a true number sentence.
18 ≥ 33 – t. Substitute 15 for t.
True. Any value 18 or greater will result in a true sentence.
Module 4 Lesson 24 True of False Number Sentences.
State whether the sentence is true or false.
56 – 14 < 48
True
33 ≥ 13 + 23
False
14.
State when the following equations and inequalities will be true and when they will be false.
6r > 36
This inequality is true for any value that is greater than 6 and false then the value is less than
or equal to 6.
15 = 6 + d
This equation is true when the value of d is 9 and false when the value is any other number.
32 – t < 18
This inequality is true for any value that is less than 14 and false then the value is greather
than or equal to 14.
Module 4 Lesson 26 One Step Equations – Addition & Subtraction
Find the solution of the equations using a tape diagram. Check your answer.
p + 5 = 11 f – 8 = 10
p = 6
p + 5 = 11 f – 8 = 10
6 + 5 = 11 18 – 8 = 10
11 + 11 10 = 10
𝒑 𝟓
𝟏𝟏
𝟔 𝟓
𝟏𝟏
𝟔 𝟓
𝒑 𝟓
𝒑
𝟔
𝒇
𝟖 𝟏𝟎
𝒇
𝟏𝟖
𝟖 𝟏𝟎
f = 18
15.
Find the solution of the equations below algebraically. Check your answer.
k – 29 = 54 46 + m = 100
k – 29 + 29 = 54 + 29 46 + m – 46 = 100 – 46
k = 83 m = 54
check check
k – 29 = 54 46 + m = 100
83 – 29 = 54 46 + 54 = 100
54 = 54 100 = 100
46 = t – 4 n + 5 = 17
46 + 4 = t – 4 + 4 n + 5 – 5 = 17 – 5
50 = t n = 12
check check
46 = t – 4 n + 5 = 17
46 = 50 – 4 12 + 5 = 17
46 = 46 17 = 17
Module 4 Lesson 27 One Step Equations – Multiplication & Division
Find the solution of the equations using a tape diagram. Check your answer.
4x = 20
3
m
= 9
x = 5
check check
4x = 20
3
m
= 9
4(5) = 20 27 ÷ 3 = 9
20 = 20 9 = 9
𝒙
𝟓𝟓 𝟓𝟓
𝟐𝟎
𝒙𝒙 𝒙𝒙
𝟐𝟕
𝒎
𝒎 ÷ 𝟑
𝟗
𝒎 ÷ 𝟑𝒎 ÷ 𝟑 𝒎 ÷ 𝟑
𝟗𝟗 𝟗
𝒎
16.
Find the solution of the equation below algebraically. Check your answer.
7x = 35 12y = 60
7x ÷ 7 = 35÷ 7 12y ÷ 12 = 60 ÷ 12
x = 5 y = 5
check check
7x = 35 12y = 60
7(5) = 35 12(5) = 60
35 = 35 60 = 60
5
h
= 6
7
k
= 2
h ÷55 = 65 k÷ 77 = 27
h = 30 k = 14
check check
h ÷5 = 6 k÷ 7 = 2
30 ÷5 = 6 14÷ 7 = 2
6 = 6 2 = 2
Module 4 Lesson 28 Two-Step Problems – All Operations
Find the solution of the equation below algebraically. Check your answer.
x + 15 − 6 = 18 y + 9 +12 = 40
x + 9 = 18 y + 21 = 40
x + 9 - 9= 18 - 9 y + 21 – 21 = 40 - 21
x = 9 y = 19
check check
x + 15 − 6 = 18 y + 9 +12 = 40
9 + 15 − 6 = 18 19 + 9 +12 = 40
18 = 18 40 = 40
x + x =12 n + 2n = 9
2x = 12 3n = 9
2x ÷ 2 = 12÷ 2 3n ÷ 3 = 9 ÷ 3
x = 6 n = 3
check check
x + x =12 n + 2n = 9
6 + 6 =12 3 + 2(3) = 9
12 = 12 3 + 6 = 9
9 = 9
17.
Barry had 𝟓𝟎 doubles last season which is 𝟏𝟎 more than his best season. Willy had 8 more
doubles than Derek last season. Willy had the same number of as Barry’s best season. Let 𝑏
represent the number of doubles Barry had during his best season, 𝑑 represent the number of
Derek’s doubles last season, and 𝑤 represent the number of Willy’s doubles last season . How
many doubles did Derek have last season?
Solution:
Barry
50
b 10
Willy
b
d 8
Derek
d
Let’s Start with Barry
b + 10 = 50
b + 10 – 10 = 50 – 10
b = 40
Now we can solve Willy’s tape diagram
b = d + 8
40 = d + 8
40 – 8 = d + 8 – 8
32 = d
Derek had 32 doubles
18.
Lesson 29 Multi-Step Problems – All Operations
Solve the problem using tables and equations, and then check your answer with the word
problem. Try to find the answer only using two rows of numbers on your table.
1. The PE teachers are organizing supplies for this year’s field day. In order to have enough
materials for all of the students, they need twice as many hula hoops as Frisbees. The number
of flags required is ten times more than the number of hula hoops. The number of cones that is
needed is half as many flags. If they have a total of 396 supplies, how many cones do they
have?
ANSWER:
Flags Cones Frisbees Hula hoops total
20 10 1 2 33
240 120 12 24 396
They will have a total of 120 cones.
Let f represent the number of Frisbees. Therefore, 2f represents the number of hula hoops, and
20frepresents the number of flags and 10f represents the number of cones.
f + 2f + 10f + 20 f = 396
33f = 396
33f ÷ 33 = 396 ÷ 33
f = 12
Therefore, the PE teachers have 120 cones because 10(12)=120
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