7 MNLEAN876238 7EE1 - kennedyskids.com · in the jar on Friday and adds a ... inches and he wants to have at least 24 1 inches on each side of the television for external speakers

Name ________________________________________ Date ___________________ Class __________________

Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

Grade 7 27 Common Core Assessment Readiness

7.EE.1

SELECTED RESPONSE Select the correct answer.

1. What property allows the expression 4.7x + 10.4 + 15.3x − 8.4x + 15.6 to be simplified to the equivalent expression 20x + 10.4 − 8.4x + 15.6?

Additive inverse property

Associative property of addition

Commutative property of addition

Commutative property of multiplication

2. Which of the following correctly uses the additive inverse property?

− 2

3x − 2

3x − 4

5y = 0 − 4

5y

5(x − 3) = 5x − 15

72

x − 12

y + 12

y = 72

x + 0

13

x + 54

y⎛⎝⎜

⎞⎠⎟+ 3

4y = 1

3x + 5

4y + 3

4y

⎛⎝⎜

⎞⎠⎟

Select all correct answers.

3. Which of the following uses the associative property of addition to simplify?

53

x + 85

x⎛⎝⎜

⎞⎠⎟− 3

5x = 5

3x + x

14

(x −11) = 14

x − 114

0.4y + (3.6y − 0.6) = 4y − 0.6

45

i54

x + 125

= x + 125

7.8x − 1.3 − 1.8x = 6x − 1.3

4. Which properties are used to simplify

45

y + 3 25

x + 75

y⎛⎝⎜

⎞⎠⎟

to 5y + 6

5x?

Associative property of addition

Associative property of multiplication

Commutative property of addition

Commutative property of multiplication

Distributive property

CONSTRUCTED RESPONSE

5. Explain how the properties of operations

are used to show that − 1

2x + 3

5y

⎛⎝⎜

⎞⎠⎟+ 7

5x

and − 1

2x + 1

5(3y + 7x) are equivalent.

________________________________________

________________________________________

________________________________________

6. Nadine and Walt are delivering the local newspaper throughout the town. Nadine is paid $15 per week plus $9.50 per hour, and Walt is paid $12 per week plus $10.25 per hour. a. Write expressions that represent

how much Nadine and Walt are paid each week using h as the number of hours worked.

________________________________________

________________________________________

b. Add both expressions to represent how much the local newspaper is paying Nadine and Walt each week to deliver the newspapers. Explain how the properties of operations are used to simplify the expression.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7. Jamie is selling tickets for a whale watch

at a local beach. The tickets cost $24.40 for an adult and $14.50 for a child. Jamie

earns a 30% commission on all ticket sales. Write an expression that uses parentheses to represent how much Jamie earns from selling tickets, where

a is the number of adult tickets sold and c is the number of children’s tickets sold. Use the distributive property to simplify the expression.

________________________________________

________________________________________

________________________________________

8. Is

− 1

2x + 6

7⎛⎝⎜

⎞⎠⎟− 7

2x − 4

7⎛⎝⎜

⎞⎠⎟

equivalent to

−4x + 2

7? Use the properties of

operations to justify your answer.

________________________________________

________________________________________

________________________________________

________________________________________

9. Write a linear expression with all rational

coefficients such that simplifying the expression requires using the associative property of addition, the

commutative property of addition, the distributive property, the additive inverse property, and the additive identity property. Show your work and explain

how your expression simplifies.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

10. Explain how the properties of operations

are used to simplify 25

(a + b)+ 35

(a + c).

________________________________________

________________________________________

________________________________________

________________________________________

11. Marlyce’s garden is surrounded by a

fence. A diagram of the fence is shown.

a. Write an expression that represents

the perimeter of the fence as the sum of the side lengths.

________________________________________

b. Show how the properties of

operations are used to simplify the expression from part a.

________________________________________

________________________________________

________________________________________

________________________________________

c. Suppose you know the perimeter of

the fence is 120 feet. Find the lengths of the sides. Show your work.

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7.EE.2


1. Which of the following equations

represents that “y decreased by 35%” is

the same as “0.65 times y”?

y0.35y

= 0.65y

y − 0.35y = 0.65y

y + 0.65y = 0.35y

y + 0.35y = 0.65y

2. Which of the situations described below

can be modeled by the equation n + 0.5n − 0.3n = 1.2n, where n is the number of nickels originally in the jar?

Amanda takes out 50% of the nickels

in the jar on Friday and adds a number of nickels that is equal to

30% of the remaining number of nickels in the jar on Monday. There are 20% fewer nickels in the jar after Monday than before Friday.

Amanda takes out 50% of the nickels

in the jar on Friday and adds a number of nickels that is equal to 30% of the original number of nickels in the jar on Monday. There are 20%

fewer nickels in the jar after Monday than before Friday.

Amanda adds 50% of the original

number of nickels to the jar on Friday. The number of nickels

Amanda takes out on Monday is equal to 30% of the new number of nickels. There are 20% more nickels in the jar after Monday than

before Friday.

Amanda adds 50% of the original

number of nickels to the jar on Friday. The number of nickels Amanda takes out on Monday is equal to 30% of the original number

of nickels. There are 20% more nickels in the jar after Monday than before Friday.

3. Which of the equations shown correctly

rewrites an expression that represents

the cost for a pair of shoes that is marked down 20% of the regular price r when the sales tax is 5% of the markdown price?

1.05(0.2r) = 0.21r

1.05(r − 0.20r) = 0.84r

1.05r − 0.20r = 0.85r

1.05(r + 0.20r) = 1.26r


4. Which of the following expressions

represent the sum of the areas of the triangles shown?

6 i

12

(x + 4)+ (x − 2)⎡⎣ ⎤⎦

6 1

2(x + 4)+ (x − 2)⎡⎣ ⎤⎦

3[(x + 4) + (x − 2)]

3(2x + 2)

12x + 12


5. Does the expression 1.016x represent a

percent increase greater than 12% if the original amount is x? Rewrite the

expression as a sum of two terms to explain why or why not.

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



6. A rectangle has a base b and a height h.

Another rectangle has a base that is 13

of

the length of the base of the first

rectangle and a height that is 12

of the

height of the first rectangle. Devin writes the area of the smaller rectangle as the

product 13

b • 12

h. Tracy rewrites this as

16

bh. Which student’s expression makes

it easier to see how the areas of the rectangles are related? Explain.

________________________________________

________________________________________

________________________________________

7. A square pool with side length s is

surrounded by tiles that form a border 5 feet wide all around the pool.

a. Draw a sketch of the pool and the

border. Label the side lengths.

b. Write an expression for the perimeter

of the pool and another expression for the perimeter of the outside of the

tile border. Simplify the expressions.

________________________________________

________________________________________

c. Compare the outside perimeter of

the tile border and the perimeter of the pool.

________________________________________

________________________________________

8. Andre’s house, the middle school, and

the library are along the same street. The middle school is between Andre’s house

and the library. The distance between Andre’s house and the middle school is x + 3, and the distance between the middle school and the library is 4x + 12.

a. Write and simplify an expression for

the distance between Andre’s house and the library.

________________________________________

b. Rewrite your expression from part a

so that it describes how many times farther the library is from Andre’s house than the middle school is from

Andre’s house. Explain.

________________________________________

9. The formula for the area of a rectangle is

A = w, where A is the area, is the

length, and w is the width. Rewrite the

equation so it is solved for w. If the length of the rectangle increases, but the area stays the same, how does the width change?

________________________________________

________________________________________

10. Christopher, Jack, and Tamara collect s seashells. Christopher takes 30% of the seashells, and then Tamara takes 40% of the remaining shells.

a. Write a subtraction expression that

represents the number of shells that

are left for Jack. Justify your answer.

________________________________________

b. Simplify the result from part a so it is

a single term with a single coefficient. Show your work. Use the simplified expression to interpret what percent of the collection of shells Jack gets.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7.EE.3


1. A rectangle has a length of 8 feet and a

width of 6 feet. If its length and width

increase by 50% each, what is the area of the new rectangle?

24 square feet

48 square feet

72 square feet

108 square feet

2. A hot air balloon is at an elevation of

3,800 feet. If the balloon falls 40 feet per minute, how long would it take for the balloon to reach 2,000 feet?

45 minutes

50 minutes

95 minutes

145 minutes

3. An airplane takes off 12.5 miles south of

a city and flies due north at a constant speed of 170 miles per hour. What is the

plane’s position relative to the city after 45 minutes?

115 miles south

115 miles north

140 miles south

140 miles north

4. A bridge currently has 975 vehicles

traveling on it per hour during peak time. A traffic engineer estimates that there will be 3.4% more vehicles traveling on the bridge each year for 2 years. How many

more cars will travel on the bridge per hour during peak time in 2 years than are traveling on it now? Round your final answer to the nearest whole vehicle.

33 vehicles

66 vehicles

67 vehicles

1,042 vehicles


5. Don is planning to mount a television on

a wall and wants to center it. The wall is

88 3

4 inches and he wants to have at

least 24 1

2 inches on each side of the

television for external speakers. Don has

researched the lengths for five different televisions. Which of the following lengths would fit?

Television A: length of 36 1

2 inches

Television B: length of 38 1

4 inches

Television C: length of 39 3

4 inches

Television D: length of 40 5

8 inches

Television E: length of 42 1

8 inches

Select the correct answer for each lettered part.

6. Each employee is getting a raise after a

review. Determine if each employee will

now earn at least $600 per week.

a. Amanda made $14.50 per

hour, gets a 10% raise, and works 38 hours per week.

Yes

No

b. Bertram made $16.20 per


Yes

No

c. Chuck made $13.90 per


Yes

No

d. Emma made $17.00 per

hour, gets an 8% raise, and works 35 hours per week.

Yes

No

e. Judy made $18.30 per hour, gets a 6% raise, and works

28 hours per week.

Yes

No

Name ________________________________________ Date ___________________ Class __________________




7. Liz wants to hang a painting on her wall

so that it is centered. The wall is

110 5

8 inches long and the painting is

28 3

4 inches wide. Determine how far the

edges of the painting have to be from the ends of the wall. Show your work. Convert fractions to decimals for

intermediate calculations and give your answer as a mixed number.

________________________________________

________________________________________

________________________________________

8. Two trains are both traveling at a

constant speed toward each other on neighboring tracks. The trains are

252 miles apart when they start traveling.

They pass each other 4 1

2 hours later.

One of the trains is traveling at

25 3

4 miles per hour.

a. Use estimation to find the speed of

the other train.

________________________________________

________________________________________

b. Find the speed of the other train.

Show your work and convert all fractions to decimals. Write the speed of the other train as a mixed

number.

________________________________________

________________________________________

c. Is your answer from part b

reasonable? Explain.

________________________________________

________________________________________

9. A new car typically loses 20% of its initial

value during the first year. During the second year, the car loses 15% of its

value after the first year.

a. Estimate the value of a $18,600 car

after the first and after the second year by rounding its initial value to the nearest ten thousand. Show

your work.

________________________________________

b. Find the value of the car after the first

year and after the second year. Show your work.

________________________________________

c. Did the car lose 35% of its initial

value during the 2 years? Explain without calculating.

________________________________________

10. A company’s website advertises that it

serves 9 customers per minute non-stop and that it serves 130,000 customers per week.

a. Verify that the company’s claim is

inaccurate by using mental math and estimation. Show your work.

________________________________________

________________________________________

b. How many customers should the

company advertise that it serves per week based on the rate per minute that is currently on its website? Explain.

________________________________________

________________________________________

c. In order for the company to reach its

advertised weekly rate currently on its website, how many customers should it serve per minute? Explain.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7.EE.4a


1. A fence forms a rectangle and uses 64 meters of fencing. If the width of the enclosed area is 13 meters, what is the length?

19 meters

38 meters

51 meters 154 meters

2. What is a correct method of solving the

equation x3− 6 = 9 for x?

First subtract 6 from both sides of the equation, and then divide both sides of the equation by 3.

First add 6 to both sides of the equation, and then divide both sides of the equation by 3.

First subtract 6 from both sides of the equation, and then multiply both sides of the equation by 3.

First add 6 to both sides of the equation, and then multiply both sides of the equation by 3.


3. Which of the following equations have a solution that is negative?

5x − 11

2= − 7

2

− x

3+ 7

3= 13

3

34

x − 92= − 39

8

6x − 5 = 40

32

x − 194

= − 734

Select the correct answer for each

lettered part.

4. Is the solution of the equation an integer?

a. 5 x − 13

3⎛⎝⎜

⎞⎠⎟= −10

3 Yes No

b. − 3

2x + 11

2⎛⎝⎜

⎞⎠⎟= 45

4 Yes No

c.

56

x − 172

⎛⎝⎜

⎞⎠⎟= − 55

12 Yes No

d. − 5

3(x + 2) = − 35

2 Yes No

e. −9(x + 7) = −39 Yes No


5. Solve the equation 12

y − 214

= − 354

for y.

Identify the sequence of operations used to solve the equation.

________________________________________

________________________________________

6. Cathy earns $13.50 per hour for the first 40 hours worked in a week and $20.25 per hour for hours over 40. If she earns $661.50 one week, how many hours does she work? Show your work using a variable that represents the time, in hours, that Cathy works over 40 hours.

________________________________________

________________________________________

7. Kevin is selling 7 identical alternators and a car wheel for scrap. He knows the wheel weighs 19.5 pounds. He puts all the items on a scale at the scrap yard and the total weight is 112.25 pounds. Find the weight of each alternator a, in pounds, algebraically. Show your work.

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



8. The formula for the area of a trapezoid is

A =

h(b1 + b2)2

, where A is the area of the

trapezoid, h is the height, and b1 and b2 are the lengths of the bases. Use the

formula to find b1 if h is 7 meters, b2 is 10.5 meters, and A is 96.25 square meters. Show your work.

________________________________________

________________________________________

9. Tabitha uses a recipe that calls for sugar.

She decides to make four times as much

as the recipe produces, but she cuts

14

cup of sugar overall. Tabitha uses

5 3

4 cups of sugar. Find how much sugar

the original recipe calls for using

arithmetic.

________________________________________

________________________________________

________________________________________

10. Becky buys a notebook for $1.59 and

pens for $0.29 each. She spends $5.07. Assume there is no sales tax where Becky lives.

a. Define a variable that can be used for

this situation.

________________________________________

b. Write an equation using the variable

from part a.

________________________________________

c. Solve the equation from part b. Show

your work. What does the solution of the equation mean?

________________________________________

________________________________________

________________________________________

11. The sum of two consecutive even

integers is 114. Find the two integers by writing and solving an equation using

n to represent the smaller of the two integers. Explain your reasoning and show your work.

________________________________________

________________________________________

________________________________________

12. Wally buys two books at a bookstore. He

spends $44.52 after 6% sales tax is

applied, but the clerk does not provide him with a receipt. He knows that book A costs $17.50 before sales tax, but he is not sure how much book B costs.

a. Use an arithmetic solution to find the cost of book B.

________________________________________

b. Determine how the cost of book B

can be represented in an equation. Write an equation using the distributive property that represents this situation.

________________________________________

________________________________________

c. Use the equation from part b to find

the cost of book B. Show your work.

________________________________________

________________________________________

________________________________________

d. Explain how finding the cost of

book B using the arithmetic solution compares to finding the cost of book B using the algebraic solution.

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7.EE.4b


1. Which of the following inequalities has a solution set described by the graph on the number line below?

−5x + 19

2≥ 59

2

53

x − 83> − 28

3

−6x − 17

4≤ 79

4

− 4

5x + 14

5≤ − 2

5

2. Your middle school is having a carnival. Admission into the carnival is $8, and each game inside the carnival costs $0.50. Which of the following inequalities represents the possible number of games g that can be played with $20?

8g + 0.50 ≤ 20

8g + 0.50 ≥ 20

0.50g + 8 ≤ 20

0.50g + 8 ≥ 20

3. Which of the following inequalities represents a solution set that has the variable x being greater than or equal to some number?

− 3

8x +17 ≥ 53

45

x + 75> −5

57

x − 167

≤ 397

− 4

9x + 34

3≤ 8

4. Which of the following graphs describes

the solution set of − 4

5x − 13

5≥ −9?


5. Which of the following inequalities has the set of positive numbers as part of its solution set?

4x + 15 < −21

− 5

3x + 17

3< 9

14

x −16 > −18

− 3

2x − 11

4≥ 31

4

− 8

3x + 5 ≤ 9

Select the correct answer for each lettered part.

6. Determine whether the following inequalities have a solution set of x ≤ −6.

a. 7x − 5

3≤ −131

3 Yes No

b. 54

x + 4 ≤ 232

Yes No

c. − 2

3x + 19

3≤ 31

3 Yes No

d. − 7

4x − 27

4≥ 15

4 Yes No

e. 67

x + 257

≥ −117

Yes No

Name ________________________________________ Date ___________________ Class __________________




7. Reese has enough money to buy 115 cm

of framing. He wants the frame to be 28.5 cm long.

a. Use the perimeter of a rectangle

formula, P = 2 + 2w to write an

inequality that determines how wide the framing can be.

________________________________________

b. Solve the inequality from part a.

________________________________________

c. Graph the solution on the number

line. What is the interpretation of the solution?

________________________________________

________________________________________

8. Erin is training for a marathon and wants

to run at least 14 12

miles. She has

already run 3 7

8 miles and starts to jog at

a steady rate of 8 1

2 miles per hour. Write

an inequality using the time t, in hours, to find the possible amounts of time remaining for her jog. Show your work.

________________________________________

________________________________________

9. Cliff earns a base pay of $275 per week

plus an 8% commission on all of his sales. Write an inequality that represents

the minimum amount of sales s, in dollars, Cliff must make to earn at least $560 per week. What is the interpretation of the solution set?

________________________________________

________________________________________

10. Allison is having a birthday party at a

reception hall. She is willing to spend no more than $400 to rent the hall. The hall

charges a flat fee of $120 plus $24 per invited person.

a. Determine how the number of people

invited can be represented by an inequality. Write an inequality that

represents this situation.

________________________________________

b. Solve the inequality from part a.

Show your work.

________________________________________

c. Would you use a ray or a set of

points for this solution on a number line? Explain.

________________________________________

d. Graph the solution set on the number

line below.

11. Tim is making a fence in the shape of a

triangle for his livestock. He wants one side of the triangle to be two times as

long as another side and the third side to be 21 m long. Tim wants the perimeter of the triangle to be more than 42 m and less than 84 m.

a. How can the lengths of the unknown

sides be represented by variables?

________________________________________

b. Write two inequalities that represent

this situation. One inequality represents the minimum perimeter, and the other inequality represents the maximum perimeter.

________________________________________

________________________________________

c. Solve the inequalities from part b.

________________________________________


Grade 7 Teacher Guide 25 Common Core Assessment Readiness

7.EE.1 Answers

1. C

2. C

3. A, C

4. C, E

5. Use the associative property of addition

to rewrite

− 1

2x + 3

5y

⎛⎝⎜

⎞⎠⎟+ 7

5x as

− 1

2x + 3

5y + 7

5x

⎛⎝⎜

⎞⎠⎟. Then use the

distributive property to rewrite

− 1

2x + 3

5y + 7

5x

⎛⎝⎜

⎞⎠⎟

as − 1

2x + 1

5(3y + 7x).

Rubric 1 point for using associative property; 1 point for using distributive property

6. a. Nadine: 9.50h + 15;

Walt: 10.25h + 12

b. 9.50h + 15 + 10.25h + 12 = 9.50h + 10.25h + 15 + 12 =

19.75h + 27

The commutative property of addition allows 15 and 10.25h to be switched.

This allows 9.50h and 10.25h to be added together and 15 and 12 to be added together.

The distributive property is used to add

the terms with the variable: 9.50h + 10.25h = (9.50 + 10.25)h =

19.75h.

Rubric a. 1 point for each expression

b. 1 point for answer; 1 point for

explanation of properties used

7. 0.3(24.40a + 14.50c); 0.3(24.40a + 14.50c) = 0.3(24.40a) + 0.3(14.50c) =

7.32a + 4.35c

Rubric 1 point for expression with parentheses;

1 point for using distributive property; 1 point for simplified expression

8. No.

− 1

2x + 6

7⎛⎝⎜

⎞⎠⎟− 7

2x − 4

7⎛⎝⎜

⎞⎠⎟

is equal to

− 1

2x + 6

7⎛⎝⎜

⎞⎠⎟+ − 7

2x − 4

7⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ because

subtracting is adding the opposite. Distribute the negative sign to each term in the parentheses.

− 12

x + 67

⎛⎝⎜

⎞⎠⎟+ − 7

2x − 4

7⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥ =

− 12

x + 67

⎛⎝⎜

⎞⎠⎟+ − 7

2x

⎛⎝⎜

⎞⎠⎟+ 4

7

Drop the parentheses and use the commutative property of addition to move

− 7

2x to the left of

67

.

− 12

x + 67+ − 7

2x

⎛⎝⎜

⎞⎠⎟+ 4

7=

− 12

x + − 72

x⎛⎝⎜

⎞⎠⎟+ 6

7+ 4

7

Combine like terms and simplify.

− 12

x + − 72

x⎛⎝⎜

⎞⎠⎟+ 6

7+ 4

7= − 8

2x + 10

7

= −4x + 107

So,

− 1

2x + 6

7⎛⎝⎜

⎞⎠⎟− 7

2x − 4

7⎛⎝⎜

⎞⎠⎟

is equivalent

to −4x + 10

7, not

−4x + 2

7.

Rubric 1 point for answer; 1 point for using

distributive property; 1 point for using commutative property of addition; 1 point for simplified expression



9. Possible answer:

58− 9

4y

⎛⎝⎜

⎞⎠⎟+ 3

4(3y − 5)− 3

8= 5

8− 9

4y

⎛⎝⎜

⎞⎠⎟+ 9

4y − 15

4− 3

8Distributive property

= 58+ − 9

4y + 9

4y

⎛⎝⎜

⎞⎠⎟− 15

4− 3

8Associative property of addition

= 58+ 0 − 15

4− 3

8Additive inverse property

= 58− 15

4− 3

8Additive identity property

= 58− 3

8− 15

4Commutative property of addition

= − 72

Simplify.

= −3 12

Rubric 1 point for writing an expression that requires all five properties; 1 point for each property used in simplifying; 1 point for correctly simplifying result

10. Possible answer:

25

(a + b)+ 35

(a + c) = 25

a + 25

b + 35

a + 35

c Distributive property

= 25

a + 35

a + 25

b + 35

c Commutative property of addition

= a 25+ 3

5⎛⎝⎜

⎞⎠⎟+ 2

5b + 3

5c Distributive property

= a(1)+ 25

b + 35

c Simplify.

= a + 25

b + 35

c Multiplicative identity property

Rubric 1 point for each property used; 1 point for simplified result



11. a. 5a + 3a + 14 + 4(a − 6) + 10

b. Possible answer:

5a + 3a +14 + 4(a − 6)+10 = 5a + 3a +14 + 4a − 24 +10 Distributive property= 5a + 3a + 4a +14 − 24 +10 Commutative prop. of addition= 5a + 3a + 4a +14 +10 − 24 Commutative prop. of addition= 5a + 3a + 4a + 24 − 24 Simplify.= 5a + 3a + 4a + 0 Additive inverse property= 5a + 3a + 4a Additive identity property= (5 + 3 + 4)a Distributive property= 12a Simplify.

c. One side is 10 feet long.

Since 12a = 120, a = 10.

Substitute 10 for a for each of the unknown sides.

5a = 5(10) = 50

The side that has length 5a is 50 feet long.

3a + 14 = 3(10) + 14 = 30 + 14 = 44

The side that has length 3a + 14 is 44 feet long.

4(a − 6) = 4(10 − 6) = 4(4) = 16

The side that has length 4(a − 6) is 16 feet long.

Rubric a. 1 point

b. 2 points for showing properties used; 1 point for correct simplified expression

c. 1 point for side lengths; 1 point for showing work



7.EE.2 Answers 1. B

2. D

3. B

4. A, C, D

5. No, because the expression 1.016x can

be rewritten as x + 0.016x, and 0.016x means a 1.6% increase of x, which is less than 12%.

Rubric 1 point for answer; 1 point for rewriting expression; 1 point for explanation

6. Tracy’s expression makes it easier to see how the areas of rectangles are related because the area of the larger rectangle is bh. Since the area of the smaller

rectangle is 16

bh, the area of the

smaller rectangle is 16

the area of the

larger rectangle.

Rubric 1 point for answer; 2 points for explanation

7. a. Possible sketch:

b. Perimeter of pool: 4s Perimeter of the outside of the tile

border: 4(s + 10) or 4s + 40

c. The perimeter of the tile border,

4s + 40, is 40 feet longer than the perimeter of the pool, 4s.

Rubric a. 1 point

b. 1 point for each expression

c. 1 point

8. a. x + 3 + 4x +12 = x + 4x + 3 +12

= 5x +15

b. 5x + 15 = 5(x + 3)

The distance from Andre’s house to

the middle school is x + 3, and the distance from Andre’s house to the

library is 5(x + 3). This shows that the library is 5 times farther from Andre’s house than the middle school is.

Rubric a. 1 point for writing expression;

1 point for simplifying expression

b. 1 point for rewriting expression;

1 point for explanation



9.

A = w

A = w

The width gets shorter when the area stays the same and the length gets

longer because when the numerator stays the same in a fraction, and the denominator gets larger, the value of the fraction gets smaller.

Rubric 1 point for solving for w; 2 points for stating the relationship between the length and the width

10. a. Possible answer:

s − 0.3s − 0.4(s − 0.3s); Since Christopher is taking 30% of the seashells, he takes 0.3s seashells. So, there are s − 0.3s seashells remaining. Tamara is taking 40% of those

remaining seashells, so the expression 0.4(s − 0.3s) represents the number of seashells Tamara takes. So, there are s − 0.3s − 0.4(s − 0.3s) seashells for

Jack.

b. s − 0.3s − 0.4(s − 0.3s)

= s − 0.3s + −0.4(s − 0.3s)⎡⎣ ⎤⎦= s − 0.3s − 0.4s + 0.12s= (1− 0.3 − 0.4 + 0.12)s= 0.42s

Jack gets 42% of the seashells the

group collects.

Rubric a. 1 point for expression;


b. 1 point for simplified expression;

1 point for interpretation



7.EE.3 Answers 1. D

2. A

3. B

4. C

5. A, B, C

6. a. Yes

b. No

c. Yes

d. Yes

e. No

7. Convert the mixed numbers to decimals.

110 5

8= 110.625 ;

28 3

8= 28.375

Subtract 28.375 from 110.625 to

determine the length of the wall that is not

covered by the painting.

110.625 − 28.375 = 82.25

Since the painting is centered on the wall,

the length from the end of the wall to the edge of the painting for each side is the same. Divide 82.25 by 2.

82.25

2= 41.125

Convert 41.125 to a fraction.

41.125 = 41 125

1000= 411

8

The edges of the painting have to be

411

8 inches away from each end of

the wall.

Rubric 1 point for converting fractions to

decimals; 1 point for showing work; 1 point for correct mixed number answer

8. a. Possible answer: Round 252 to 300,

25 3

4 to 25, and

4 1

2 to 5. The first

train travels 25 × 5 = 125 miles. So, the second train travels

300 − 125 = 175 miles and, thus, the

second train travels 175

5= 35 miles

per hour. (Accept answers that use different rounding, such as rounding

252 to 250 and 25 3

4 to 30.)

b. The speed of the other train is

30 1

4 miles per hour.

Convert 25 3

4 and

4 1

2 to decimals.

25 3

4= 25.75 ;

4 1

2= 4.5

The first train travels 25.75 × 4.5 = 115.875 miles. So, the second train

travels 252 − 115.875 = 136.125 miles. Divide 136.125 by 4.5.

136.125

4.5= 30.25

Convert 30.25 to a mixed number.

30.25 = 30 1

4

c. Yes, because the answer from part b,

30 1

4, is close to the estimate of 35.

Rubric a. 2 points

b. 1 point for answer; 1 point for showing

work; 1 point for converting all fractions to decimals

c. 0.5 point for answer;

0.5 point for explanation



9. a. Round 18,600 to 20,000. Subtract the

product of 20,000 and 0.2 from 20,000.

20,000 − 20,000 × 0.2 = 16,000

The value of the car is about $16,000 after the first year.

Subtract the product of 16,000 and 0.15 from 16,000.

16,000 − 16,000 × 0.15 = 13,600

The value of the car is $13,600 after

the second year.

b. Subtract the product of 18,600 and 0.2

from 18,600.

18,600 − 18,600 × 0.2 = 14,880

The value of the car is $14,880 after

the first year.

Subtract the product of 14,880 and

0.15 from 14,880.

14,880 − 14,880 × 0.15 = 12,648

The value of the car is $12,648 after the second year.

c. No, because the car did not lose 20%

of its initial value in the first year and then lose 15% of its initial value in the

second year. The car’s value lost 15% of a lower amount in the second year, so the car’s value lost less than 35% of its initial value during the 2 years.

Rubric a. 1 point for answer; 0.5 point for

rounding; 0.5 point for showing work

b. 0.5 point for value after first year;

0.5 point for value after second year; 1 point for showing work

c. 1 point for answer;


10. a. Possible answer: The expression

9 × 60 × 24 × 7 represents the number of customers that the company serves

per week. Notice that 9 × 60 × 24 × 7 is less than 10 × 60 × 24 × 7, which is also less than 10 × 60 × 25 × 8. Notice that 25 × 8 equals 50 × 4.

10 × 60 × 25 × 8 = 10 × 60 × 50 × 4= 10 × 60 × 200= 120,000

Since 130,000 is greater than 120,000

and 120,000 is greater than the customers served per week, the

company’s claim is inaccurate.

b. Possible answer: Since 9 × 60 × 24 × 7 = 90,720, the company

should claim that it serves 90,000 customers per week.

c. Possible answer: The company should

serve about 13 customers per minute so it can advertise that it serves 130,000 customers per week.

First, find how many minutes there are

in a week.

60 × 24 × 7 = 1,440 × 7 = 10,080

Then, divide 130,000 by 10,080 to find how many customers should be

served per minute. Round up.

130,00010,080

≈12.90 ≈13

Rubric a. 2 points

b. 1 point for answer;


c. 1 point for answer; 1 point for explanation



7.EE.4a Answers 1. A

2. D

3. B, C, E

4. a. No

b. Yes

c. Yes

d. No

e. No

5. y = −7; Add 214

to both sides of

the equation.

12

y − 214

+ 214

= − 354

+ 214

12

y = −144

Multiply both sides of the equation by 2.

12

y i 2 = −144

i 2

y = − 284

y = −7

Rubric

1 point for solution; 1 point for adding 214

to both sides of the equation; 1 point for multiplying both sides of the equation by 2

6. Let t be the time, in hours, Cathy works over 40 hours. An equation that represents this situation is 13.50 i 40 + 20.25t = 661.50, which

simplifies to 540 + 20.25t = 661.50.

Subtract 540 from both sides of the equation.

540 − 540 + 20.25t = 661.50 − 54020.25t = 121.5020.25t20.25

= 121.5020.25

t = 6

Since 6 is the number of hours Cathy works over 40 hours, she works 40 + 6 = 46 hours that week.

Rubric 1 point for equation; 1 point for solution;

1 point for interpretation

7. Each alternator weighs 13.25 pounds. An equation that represents this situation is 7a + 19.5 = 112.25. Solve the equation for a.

7a +19.5 −19.5 = 112.25 −19.57a = 92.757a7

= 92.757

a = 13.25

Rubric 1 point for answer; 1 point for equation; 1 point for showing work

8.

96.25 =7(b1 +10.5)

227

i 96.25 = 27

i7(b1 +10.5)

227.5 = b1 +10.5

27.5 −10.5 = b1 +10.5 −10.517 = b1

Thus, b1 is 17 meters.

Rubric 1 point for answer; 1 point for showing work

9. Add 14

to 5 3

4 to find the amount of sugar

needed for four recipes.

5 3

4+ 1

4= 6

Divide 6 by 4 to find the amount of sugar in the original recipe.

64= 3

2= 11

2

The original recipe calls for 11

2 cups

of sugar.

Rubric 1 point for answer; 1 point for using arithmetic



10. a. The variable p is used to represent the

number of pens Becky buys.

b. 0.29p + 1.59 = 5.07

c.

0.29p +1.59 = 5.070.29p +1.59 −1.59 = 5.07 −1.59

0.29p = 3.48

p = 3.480.29

p = 12

The solution of the equation is p = 12, and it means that Becky buys 12 pens.

Rubric a. 1 point

b. 1 point

c. 0.5 point for solution; 0.5 point for

showing work; 1 point for meaning of solution

11. The difference between consecutive even integers is 2. Since n is the smaller

consecutive even integer, n + 2 is the larger consecutive even integer. An equation that represents two consecutive even integers whose sum is 114 is n + (n + 2) = 114, or 2n + 2 = 114. Solve the equation for n.

2n + 2− 2 = 114 − 22n = 1122n2

= 1122

n = 56

Since n = 56, 56 is the smaller consecutive even integer and the larger consecutive even integer is 56 + 2, or 58. The two consecutive even integers are 56 and 58.

Rubric 1 point for equation; 0.5 point for each consecutive even integer; 1 point for explanation; 1 point for showing work

12. a. A 6% sales tax increases the price of

the two books by 6% and can be represented as multiplying by 1.06.

So, divide the total cost, $44.52, by 1.06.

$44.521.06

= $42.00

Subtract the cost of book A, $17.50,

from $42.00 to find the cost of book B.

$42.00 − $17.50 = $24.50

The cost of book B is $24.50.

b. The cost of book B can be represented

as the variable b in an equation. An equation that represents this situation is 1.06(b + 17.50) = 44.52.

c.

1.06(b +17.50)1.06

= 44.521.06

b +17.50 = 42.00b +17.50 −17.50 = 42.00 −17.50

b = 24.50

The cost of book B is $24.50.

d. The arithmetic solution divides $44.52 by 1.06 and subtracts $17.50 from the

quotient. The algebraic solution divides both sides of the equation by 1.06 and subtracts 17.50 from both sides of the equation. The two

solutions use the same operations in the same order.

Rubric a. 1 point

b. 1 point for representing the cost of book B in an equation; 1 point for

equation

c. 1 point for answer; 1 point for showing work

d. 1 point



7.EE.4b Answers 1. C

2. C

3. D

4. A

5. B, C, E

6. a. Yes

b. No

c. No

d. Yes

e. No

7. a.

P ≥ 2 + 2w115 ≥ 2(28.5)+ 2w115 ≥ 57 + 2w

b.

115 − 57 ≥ 57 − 57 + 2w58 ≥ 2w582

≥ 2w2

29 ≥w

c.

The solution means that the width of

the frame is greater than 0 cm but at most 29 cm.

Rubric a. 1 point

b. 1 point

c. 1 point for number line; 1 point for interpretation

8. 8 1

2t + 3 7

8≥14 1

2; Rewrite

8 1

2,

3 7

8, and

14 1

2 as improper fractions and solve

for t.

172

t + 318

≥ 292

172

t + 318

− 318

≥ 1168

− 318

172

t ≥ 858

217

i172

t ≥ 217

i858

t ≥ 54

Erin needs to run at least another hour

and fifteen minutes to meet her goal.

Rubric 1 point for inequality; 1 point for solution;

1 point for showing work

9. 0.08s + 275 ≥ 560;

0.08s + 275 − 275 ≥ 560 − 2750.08s ≥ 2850.08s0.08

≥ 2850.08

s ≥ 3,562.5

Cliff must have at least $3,562.50 in sales

per week in order for him to earn at least $560 per week.

Rubric 1 point for inequality; 1 point for solution set; 1 point for interpretation



10. a. The variable p can be used to

represent the number of people invited to Allison’s party.

24p + 120 ≤ 400

b.

24p +120 −120 ≤ 400 −12024p ≤ 28024p24

≤ 28024

p ≤ 353

p ≤1123

c. I would use a set of points because

only whole numbers of people can be invited. The solution set is integers from 0 to 11 because Allison can invite

no more than 112

3 people and a

negative number of people cannot be invited.

d.

Rubric a. 1 point for using a variable to

represent the number of invited people; 1 point for inequality

b. 1 point for solution; 1 point for

showing work

c. 0.5 point for stating a set of points should be used; 0.5 point

for explanation

d. 1 point

11. a. Possible answer: The variable s can

be used to represent the length of the shorter unknown side, and 2s can be

used to represent the length of the longer unknown side.

b. To write an inequality that represents

the minimum perimeter, add s, 2s, and 21 and set it greater than 42.

s + 2s + 21> 42

3s + 21> 42

To write an inequality that represents

the maximum perimeter, add s, 2s, and 21 and set it less than 84.

s + 2s + 21< 84

3s + 21< 84

c.

3s + 21− 21> 42− 213s3

> 213

s > 7

3s + 21− 21< 84 − 213s3

< 633

s < 21

The length of the shorter unknown side is greater than 7 m and less than

21 m.

Rubric a. 1 point

b. 1 point for each inequality

c. 1 point for each solution

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