7 mnlean876238 7ns1ab · 10. asher has two bottles of floor cleaner, each of which contains 2 cups...

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 13 Common Core Assessment Readiness

7.NS.1a, 7.NS.1b

SELECTED RESPONSE Select the correct answer.

1. Which of the following situations involve

opposite quantities combining to make 0?

Stella has a new piggy bank. She

adds 3 quarters on Tuesday, and then adds another 3 quarters on Thursday.

Devon opens a new checking

account with $30. His first purchase, made with his new debit card, totals

$28.

Joe makes 11

2 liters of lemonade

and drinks it all during the afternoon.

Brittany is writing a novel. She wrote

4 new pages to finish Chapter 1. When she reviews Chapter 1, she discards these 4 pages and an additional 4 pages.

2. What is the location of the sum 11 + (−5)

with respect to 11 on a number line?

5 units in the negative direction

5 units in the positive direction

11 units in the negative direction

11 units in the positive direction

3. Which sum does the number line

represent?

−11 + (−9)

−11 + 9

−11 + (−2)

−11 + (2)

Select all correct answers.

Match each expression with the verbal description for the location of the sum.

____ 5. 17 + (−10)

____ 6. −5 + (−7)

____ 7. −11

4+ 6

____ 8. 9 + 20

A 6 units to the left of −11

4

B 6 units to the right of −11

4

C 7 units to the left of −5

D 7 units to the right of −5

E 10 units to the left of 17

F 10 units to the right of 17

G 20 units to the left of −9

H 20 units to the right of 9

4. On a number line, which of the following sums is to the left of the first number in the sum?

−9 + 1

1 46 3− +

7 32 4

æ öç ÷+ -ç ÷è ø

15 + (−8) −2 + 6

Name _______________________________________ Date __________________ Class _________________



CONSTRUCTED RESPONSE

9. Jean walks forward 80 feet to his

mailbox. He then walks the 80 feet back. Does Jean end up back where he started? Explain your reasoning.

________________________________________

________________________________________

10. An earned run average (ERA) in baseball

is the number of earned runs a pitcher

gives up per 9 innings. One year, a professional baseball pitcher had a 3.91 ERA. His ERA was 0.74 points lower the next year. What is the sum and its

interpretation?

________________________________________

________________________________________

________________________________________

11. Use the number line below. Think of a

number and its opposite. Find and show the sum using the number line.

________________________________________

12. Think of a situation in which two opposite

quantities combine to make 0.

a. What is the first action?

________________________________________

________________________________________

b. What is the second action?

________________________________________

________________________________________

c. Explain why the actions from parts a

and b combine to make 0.

________________________________________

________________________________________

________________________________________

13. Jayce goes out for a walk. He walks

54

miles from home. He walks back

12

mile before meeting up with his friend

Macy. Write an expression (a sum) that describes this situation and use the number line to find the sum. What is the

meaning of this sum?

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

14. Becky adds 34

gallon of gasoline into her

snow thrower’s empty fuel tank. She uses

14

gallon for the snowstorm on Friday,

and then uses another 14

gallon for the

snowstorm on Sunday. Is the fuel tank empty after Becky uses the snow thrower on Sunday? Explain. If her fuel tank is not

empty again, what single action could have been changed so that it is empty again? Explain.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



7.NS.1c


1. What is an equivalent expression for

2 4 ?3 5−

2 43 5+

2 43 5

⎛ ⎞+ −⎜ ⎟⎝ ⎠

2 43 5

− +

2 43 5

⎛ ⎞− + −⎜ ⎟⎝ ⎠

2. How does the expression |9 − (−5)| relate

to the numbers −5 and 9 on the number line?

The expression shows that 9 is

greater than −5.

The expression shows that −5 is to

the left of 0 and 9 is to the right of 0 on the number line.

The expression represents the sum

of −5 and 9.

The expression represents the

distance between −5 and 9 on the

number line.

3. Which of the following expressions

results in the distance between −5 and 6 on a number line?

|6 − 5|

|6 − (−5)|

|−5| − |6|

|5 − 6|


4. Which of the following expressions give

the distance between the endpoints of the segment shown on the number line below?

− 3

5− − 4

5⎛⎝⎜

⎞⎠⎟

3 45 5

− −

3 45 5

− −

3 45 5−

45− − 3

5⎛⎝⎜

⎞⎠⎟

Match each subtraction expression with an equivalent expression that uses the

additive inverse.

____ 5. 4 83 5

⎛ ⎞− − −⎜ ⎟⎝ ⎠

____ 6. 4 83 5

⎛ ⎞− −⎜ ⎟⎝ ⎠

____ 7. 4 83 5

− −

____ 8. 4 83 5−

A 4 83 5+

B 4 83 5

⎛ ⎞+ −⎜ ⎟⎝ ⎠

C 4 83 5

⎛ ⎞− + −⎜ ⎟⎝ ⎠

D 4 83 5

− +


9. Is −10 − 5 equal to −10 + (−5)? Explain in

terms of additive inverses.

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



10. Asher has two bottles of floor cleaner,

each of which contains 2 cups when full.

One bottle contains 38

cup and the other

bottle is full. He needs 114

cups of floor

cleaner. How many cups from the new bottle does Asher need? Show that the number of cups Asher needs from the second bottle is equal to the distance

between 38

and 114

on the number line.

________________________________________

________________________________________

11. Cindy has a board that is 7 inches wide

and 1234

inches long. She needs to use

the board to replace a shelf that is 7158

inches long. Cindy hopes that the

remaining piece of board is long enough to make a 7-inch by 7-inch square she can use to put under a house plant so it will receive more sunlight. How long is

the remaining piece of board? Is it long enough? Show your work.

________________________________________

________________________________________

12. Tony currently has a balance of −$10.48

in his checking account. His bank requires him to maintain a minimum balance of $20. How much does Tony

need to deposit into his checking account to reach the minimum balance? If his bank charges a $14.99 fee if his account is below the minimum balance, how much

does he need to deposit to reach the minimum balance?

________________________________________

________________________________________

13. Emily thinks that 11 26 3

⎛ ⎞− − −⎜ ⎟⎝ ⎠ is

5 .2

−

Identify the error that Emily made. Then correct Emily’s error and find the correct difference. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

14. a. Write a word problem involving

fractions about the distance between two friends’ houses that are in opposite directions from the library.

________________________________________

________________________________________

________________________________________

b. Answer your question by assigning

two numbers with opposite signs and

using a number line to show the distance between the houses relative to the library.

________________________________________

c. Find the absolute value of the

difference between the two numbers that represent the locations of the friends’ houses relative to the library.

________________________________________

d. Explain why the distance between

the two points on the number line from part b is equal to the absolute value of the difference from part c.

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



7.NS.1d


1. What property allows 5 1 56 3 3

⎛ ⎞− + +⎜ ⎟⎝ ⎠ to be

simplified to 5 2?6

− +

Additive inverse property Additive identity property Associative property of addition

Commutative property of addition

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

1419

− 73+ 7

3= 14

19

−10

9− 11

4+ −11

4⎛⎝⎜

⎞⎠⎟= −10

9

25+ 5

4+ 3

5= 1+ 5

4

15.81+ (4.19 +10.67) = 20 +10.67

Select all correct responses.

3. Which properties are used to simplify 2 2 2 7 79 9 3 4 4

⎛ ⎞− + + − +⎜ ⎟⎝ ⎠ as 2

3 without first

finding a common denominator?

Commutative property of multiplication


Associative property of addition

Multiplicative inverse property

Additive inverse property

Additive identity property

4. Which of the following demonstrates using the associative property of addition to simplify?

(−13.36 + 2.17) + 7.83 = −13.36 + 10 9 + (1.4 + 14.3) + 15.7 = 9 + 1.4 + 30 21.36 + 15.32 − 1.36 = 20 + 15.32

[12.3 + (−24.6)] − 15.4 = 12.3 + (−40)

10.14 − 10.14 + 28.93 = 28.93

Select the correct answer for each lettered part.

5. Determine the property of addition used to arrive at each expression

in the process of simplifying 4 5 4 5 7 .5 3 5 3 4

⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ − + − + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠

a. 4 4 5 5 75 5 3 3 4

⎛ ⎞ ⎛ ⎞ ⎛ ⎞+ − + − + +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ Commutative

Associative Additive inverse Additive identity

b. 5 5 703 3 4

⎛ ⎞ ⎛ ⎞+ − + +⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ Commutative


c. 5 5 73 3 4

⎛ ⎞− + +⎜ ⎟⎝ ⎠ Commutative


d. 5 5 73 3 4

⎛ ⎞− + +⎜ ⎟⎝ ⎠ Commutative


e. 704

+ Commutative Associative

Additive inverse Additive identity

f. 74

Commutative Associative

Additive inverse Additive identity

Name _______________________________________ Date __________________ Class _________________




6. Explain how the properties of addition are

used to simplify 3 4 5 4 .2 3 2 3

⎛ ⎞ ⎛ ⎞− + + − + −⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

Find the value of the expression.

________________________________________

________________________________________

________________________________________

7. The outdoor temperature was −7.1 °C.

The temperature rose 5.4 °C, and then rose another 7.1 °C. An expression for

this situation is −7.1 + 5.4 + 7.1. Use the properties of addition to find the final temperature.

________________________________________

________________________________________

________________________________________

8. Simplify 5 4 5 8 53 3 2 3 2

⎛ ⎞− + + + −⎜ ⎟⎝ ⎠ without

having to find common denominators. Show your work.

________________________________________

________________________________________

________________________________________

9. What is the minimum number of

denominators that need to be used to find a common denominator to completely

simplify 1 5 6 2 6 4 5 ?2 4 5 3 7 7 4

⎛ ⎞− + + − + +⎜ ⎟⎝ ⎠

Explain your answer using the properties

of operations.

________________________________________

________________________________________

________________________________________

10. Jamal thinks that he needs to use only

the associative property of addition and the additive inverse property to simplify

9 9 2 5 24 4 5 6 5

⎛ ⎞− + + + −⎜ ⎟⎝ ⎠ to one term without

using common denominators. Is he correct? Explain.

________________________________________

________________________________________

11. Write an expression with all fractional

terms that applies four properties of addition to simplify the expression to one

term. Show your work and explain how your expression simplifies.

________________________________________

________________________________________

________________________________________

________________________________________

12. Margie has 154

cups of beans in a jar.

She takes out 344

cups of beans for a

recipe. When making the dish, she decides to cut down on the beans used

and returns 114

cups of beans to the jar.

Then Margie adds another 344

cups of

beans from a bag to the jar.

a. Write an expression that models this

situation.

________________________________________

b. How many beans are in the jar after

Margie refills the jar? Show how you

used the properties of addition to find this value.

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



7.NS.2a, 7.NS.2b


1. A stock lost $2.25 of its value each day

for 5 consecutive days. What is an

interpretation of the product −$2.25 i 5?

The stock lost $0.45 per day.

The stock lost $7.25 over 5 days.

The stock lost $11.25 over 5 days.

The stock lost $11.25 per day.

2. Which of the following products is

negative?

6 1

2 • 4 1

4

−5 1

2⎛⎝⎜

⎞⎠⎟

− 14

⎛⎝⎜

⎞⎠⎟

−3 −2 4

5⎛⎝⎜

⎞⎠⎟

−3 3

4× 5

6

3. Which of the following is always the result

of dividing an integer by an integer when the divisor is nonzero?

Integer

Whole number

Rational number

0

4. Kelsey’s bank charged her $17.50 for

using her debit card at ATMs that are not owned by her bank 7 times in the last month. What is the interpretation of the

quotient −$17.50

7= −$2.50?

Kelsey’s bank loses $2.50 each time

Kelsey uses her debit card at an ATM that is not owned by her bank.

Kelsey is charged $2.50 each time

she uses her debit card at an ATM that is not owned by her bank.

Kelsey earns $2.50 each time she

uses her debit card at an ATM that is not owned by her bank.

Kelsey is charged $17.50 each time

she uses her debit card at an ATM

that is not owned by her bank.


5. Which of the following equations use the

distributive property correctly to multiply rational numbers?

3 −4 1

2⎛⎝⎜

⎞⎠⎟= 3(−4)+ 3 1

2⎛⎝⎜

⎞⎠⎟

2 1

413

4⎛⎝⎜

⎞⎠⎟= 2(1)+ 1

434

⎛⎝⎜

⎞⎠⎟

−4 −5 1

3⎛⎝⎜

⎞⎠⎟= −4(−5)+ (−4) − 1

3⎛⎝⎜

⎞⎠⎟

−2 2 4

5⎛⎝⎜

⎞⎠⎟= −2(2)+ 4

5

−4 4

511

3⎛⎝⎜

⎞⎠⎟= −4 4

5(1)+ −4 4

5⎛⎝⎜

⎞⎠⎟

13

⎛⎝⎜

⎞⎠⎟

6. Which of the following fractions are

equivalent to −15

4?

−154

154

−15−4

−415

15−4

4−15


7. Victoria needs sugar for a certain recipe.

The original recipe calls for 23

cup sugar.

However, Victoria wants to make a recipe

that is 3 1

2 times larger. Use the

distributive property to find the product.

________________________________________

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



8. Suppose 11

2 cups of water are needed

for every cup of rice and you need to

cook 2 1

2 cups of rice. What is the value

and the interpretation of the product

11

2× 2 1

2?

________________________________________

________________________________________

9. Kendall realizes that she has 2 1

2 cups of

cat food remaining. Her cat eats 34

cup of

cat food per day. What is the value and

the interpretation of the quotient 2 1

2÷ 3

4?

________________________________________

________________________________________

10. Can 19 be divided by 6? Explain.

________________________________________

________________________________________

________________________________________

11. Gary thinks that − 5

24 is equal to

524

because − 5

24= −5−24

= 524

.

a. Identify Gary’s error. Explain.

________________________________________

________________________________________

________________________________________

b. Find two expressions that are

equivalent to − 5

24. Explain.

________________________________________

________________________________________

12. Use the distributive property, the fact that a mixed number can be rewritten as the sum of an integer and a fraction, and the fact that −a = (−1)a for parts a and b. a. Pick a negative integer and a positive

mixed number. Find the sign of their product.

________________________________________

b. Use the negative integer and the opposite of the mixed number from part a to find the sign of their product.

________________________________________

c. How does the product from part b differ from the product from part a? Explain.

________________________________________

________________________________________

13. a. Use what you know about the sum of an integer and its opposite to explain why −3[2 + (−2)] = 0.

________________________________________

________________________________________

b. Use the distributive property to express −3[2 + (−2)] in another way. Explain why it is reasonable to conclude that (−3)(−2) = 6.

________________________________________

________________________________________

c. Suppose j and k are two positive integers. Generalize the work in parts a and b to justify why the product of the two negative integers −j and −k must be equal to the positive product jk.

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



7.NS.2c


1. Which property allows 25

• 73

• 152

to be

simplified to 3 • 7

3?

Multiplicative identity property


Associative property of multiplication


2. Which of the following uses the multiplicative inverse property correctly to simplify the expression?

45

• 45

• 76= 7

6

75

• 43

• −107

⎛⎝⎜

⎞⎠⎟= −2 • 4

3

83

• 25

• 52= 8

3 • 1

49

• 1 • 38= 4

9 • 3

8


3. Which of the following properties can be used together to simplify the product

− 5

4 • 11

3 • − 4

5⎛⎝⎜

⎞⎠⎟

• 611

without having to

multiply uncommon denominators?

Associative property of addition

Associative property of multiplication




Multiplicative identity property

4. Which of the following uses the commutative property of multiplication?

0.5 i 10.83 i 60 = 0.5 i 60 i 10.83

0.25 i (16.4 i 4.7) = (0.25 i 16.4) i 4.7

1.2 i 9.61 i 1.5 = 1.2 i 1.5 i 9.61

2.5 i 0.4 i 13.8 = 13.8

15.5 i (0.2 i 12.9) = (15.5 i 0.2) i 12.9


5. Determine the property of multiplication that is used in each step to simplify

the expression

103

• 114

⎛⎝⎜

⎞⎠⎟

• 411

• 75

• 35

• 57

.

a.

103

• 114

• 411

⎛⎝⎜

⎞⎠⎟

• 75

• 35

• 57

Associative Commutative Inverse Identity

b. 103

• 1 • 75

• 35

• 57


c. 103

• 75

• 35

• 57


d. 103

• 75

• 57

• 35


e. 103

• 1 • 35


f. 103

• 35


Name _______________________________________ Date __________________ Class _________________




6. Explain how the properties of multiplication are used to simplify

83

• 45

• 38÷ 4

9. Find the value of the

expression.

________________________________________

________________________________________

________________________________________

________________________________________

7. What properties of multiplication can help

you to simplify 78

• 125

÷ 125

• 107

?

Explain.

________________________________________

________________________________________

________________________________________

________________________________________

8. James thinks that the commutative property of multiplication simplifies 4.8 i (0.5 i 2.95) to 2.4 i 2.95. Is James correct? Explain your reasoning.

________________________________________

________________________________________

________________________________________

9. Explain why 1 is the multiplicative identity and why 0 is not the multiplicative identity. Explain how the multiplicative

identity is used to simplify 94

• 514

÷ 514

.

________________________________________

________________________________________

________________________________________

10. Use the properties of multiplication to simplify the expression

45

• 1511

⎛⎝⎜

⎞⎠⎟

• 1115

• 133

÷ 45

. Show

your work.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

11. Write an expression with all fractional terms that applies four properties of multiplication to simplify the expression to one term. Include at least one term being divided. Show your work and explain how your expression simplifies.

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

________________________________________

Name _______________________________________ Date __________________ Class _________________



7.NS.2d


1. Convert 8

14 to a decimal.

0.571428 1.75

0.571428 1.75

2. The decimal equivalent of 1727

is a

repeating decimal. How many digits are in the repeating part of the decimal?

1 3

2 6

3. Suppose the repeating pattern in

0.020020200202002... continues forever. Is the number rational?

Yes, because the number is

equivalent to the repeating decimal

0.02002.

Yes, because the number is a

terminating decimal.

No, because the number is not a

terminating decimal.

No, because the number is not a

repeating decimal.


4. Which of the following rational numbers

have three digits that repeat in its decimal equivalent?

38

1021

1127

835

737

5. Which of the following is greater

than 348

?

143

176

259

4711

4912


6. Determine whether the decimal

equivalents of the following rational numbers are terminating or repeating.

a. 720

Terminating

Repeating

b. 1324

Terminating

Repeating

c. 311

Terminating

Repeating

d. 27

150 Terminating

Repeating

e. 1112

Terminating

Repeating

Name _______________________________________ Date __________________ Class _________________




7. Use long division to find the decimal

equivalent of 1316

. Show your work. Is the

decimal equivalent a terminating decimal or a repeating decimal?

________________________________________

8. Celia has a new cell phone that weighs

4 5

8 ounces. What is the weight of Celia’s

cell phone as a decimal? Use long division and show your work.

________________________________________

9. At a cafe, one table, with 5 people, has a $19 bill. Another table, with 6 people, has

a $23 bill. If each group decides to split the cost of the bill equally among the people at the table, which table has a greater cost per person? Use long

division to justify your answer.

________________________________________

10. Use long division to find the decimal

equivalents of 722

, 1445

, and 1954

. Show

your work. Put the rational numbers in ascending order. Explain.

________________________________________

11. Todd found that the decimal equivalent of

1324

is 0.583. However, he noticed that

the decimal equivalent of 7

12 is also

0.583 from an earlier problem. Todd’s work is shown below. Which calculation is correct? Identify Todd’s error in the

other calculation and determine the correct decimal equivalent of that rational number.

24 13.0000−11.0000

2.0000−1.9200

800−720

80−72

8

0.5833

12 7.0000−6.00001.0000−9600

400−360

40−36

4

0.5833

________________________________________

________________________________________

________________________________________

Name ________________________________________ Date ___________________ Class __________________



7.NS.3


1. How many times does 12

go into 11

4?

25

34

58

2 1

2

2. Tamela’s school day is 6 3

4 hours. She

has seven classes that are 34

hour long.

How many hours is Tamela not in class

while she is at school?

11

2 6

5 1

4

18 3

4

3. Hez is making a bookcase. The boards

that are used to make the bookcase are

1316

inch thick. Hez found a board that is

11

4 inches thick. By how much does Hez

have to reduce the thickness of the new board to match the other boards?

7

16 inch

1 1

64 inches

1316

inch 2 1

16 inches


4. Which of the following expressions have

a result that is greater than 5?

3 1

5+ 2 3

5−12

5

2 3

8+ 4

5÷ 1

3

13

4÷ 2

7

− 3

4+ 3 1

4×14

5

12 1

2× 1

5+ 5

6

5. In the morning, a group of hikers hiked

3 3

4 miles, took a break, and then hiked

another 2 3

4 miles. The group then

stopped for lunch. In the afternoon, the

group then hiked 4 3

4 miles, took another

break, and then hiked 2 1

2 miles. Which

of the following statements are true?

The hikers hiked 34

mile more in the

afternoon than in the morning.

The hikers hiked 34

mile more in the

morning than in the afternoon.

The hikers hiked the same number of

miles in the morning as in the afternoon.

The hikers hiked 12 1

2 miles the

entire day.

The hikers hiked 13 3

4 miles the

entire day.

Match the number with the equivalent expression.

____ 6. 315

16

____ 7. 4 2

3

____ 8. 13

4

____ 9. 4 3

8

A 3 1

2÷ 3

4

B 4 3

4× 3

4

C 5 3

8−1 7

16

D 5 1

2− 3 7

8+ 2 3

4

E 2 2

8−13

8

F 10 1

2− 2 1

2× 3 1

2

Name ________________________________________ Date ___________________ Class __________________




10. Courtney adds 2 dimes, 3 quarters, and

6 nickels into a money jar. Courtney then takes out 2 quarters and 5 dimes the next day. Write an expression that shows how

the overall amount of money in the jar increased or decreased. Then simplify the expression.

________________________________________

________________________________________

11. A factory makes sheet metal. If each

sheet is 3

16 inch thick, how tall is the

stack if there are 14 sheets? Show your work.

________________________________________

________________________________________

________________________________________

12. A picture frame provides 14 1

2 inches of

space for a row of photos and each photo

is 3 1

4 inches wide. How many photos

can fit in the picture frame? Show your

work. Explain why the number of photos that can fit in the frame is different than the exact answer from your calculations.

________________________________________

________________________________________

________________________________________

13. A type of bolt weighs about 3

16 ounce.

If a collection of these bolts weighs

6 3

4 pounds, how many bolts are in the

collection? Explain.

________________________________________

________________________________________

14. A science experiment has a catapult

launch a ball. The result of the experiment is shown in the table.

a. What is the average distance of the

5 attempts? Show your work.

________________________________________

________________________________________

b. How far does the ball have to travel on the sixth attempt so that the

average of all 6 of the attempts is 50.9 meters? Explain.

________________________________________

________________________________________

15. Peter is evaluating 4 1

4+10 1

2÷ 3 3

4. His

work is shown. Identify Peter’s error and find the correct value. Show your work.

________________________________________

________________________________________

________________________________________

________________________________________

Attempt Distance 1 50.7 m 2 49.4 m 3 52.3 m 4 48.9 m 5 51.6 m

4 14+10 1

2÷ 3 3

4= 17

4+ 21

2÷ 15

4

= 174

+ 424

÷ 154

= 594

÷ 154

= 594

× 415

= 5915

= 31415


Grade 7 Teacher Guide 11 Common Core Assessment Readiness

7.NS.1a, 7.NS.1b Answers 1. C

2. A

3. B

4. C, D

5. E

6. C

7. B

8. H

9. Yes, because walking forward 80 feet and walking backward 80 feet are opposite actions. The result of adding two opposite actions is 0.

Rubric

1 point for answer;

1 point for explanation

10. The pitcher’s ERA is 3.17 the next year. He gave up 0.74 fewer runs per 9 innings.

Rubric 1 point for sum; 1 point for interpretation

11. Possible answer: One number on the

number line is −4 and its opposite is 4. To find the sum −4 + 4, start at −4. Then move 4 units in the positive direction. The sum −4 + 4 is 0.

The sum of −4 and 4 is 0.

Rubric 0.5 points each for a number and its

opposite; 2 points for correct number line; 1 point for sum

12. a. Possible answer: Corey fills a 34

-cup

measuring cup with sugar to bake a recipe.

b. Possible answer: Corey uses the

entire 34

cup of sugar for the recipe.

c. Possible answer: The amount of sugar

Corey adds to the measuring cup, 34

cup, and then uses, 34 cup, leaves the

same amount of sugar in the cup as before both actions, 0.

Rubric a. 1 point b. 1 point c. 2 points

13. The expression 5 14 2


represents this

situation. To find the sum, start at 54 and

move 12 unit to the left.

The sum of 5 14 2


is 34 . It means that

Jayce is 34 mile away from home when

he meets Macy. Rubric 1 point for expression; 1 point for correct number line; 1 point for sum; 1 point for meaning of sum

14. Becky’s fuel tank is not empty because

she still has 3 1 1 14 4 4 4− − = gallon

remaining. Possible answer: Becky could

add 12 gallon of gasoline into the empty

fuel tank instead of 34 gallon. The fuel

tank would be empty again after adding 12 gallon and using 1 1 1

4 4 2+ = gallon.

Rubric 1 point for answer; 1 point for explanation; 1 point for correct change of action; 1 point for explanation



7.NS.1c Answers 1. B

2. D

3. B

4. B, E

5. D

6. A

7. C

8. B

9. Yes, −5 is the additive inverse of 5 and subtracting a number is the same as adding the additive inverse of the number.

Rubric 1 point for answer; 1 point for explanation

10. The number of cups Asher needs from

the second bottle is

11

4− 3

8= 10

8− 3

8= 7

8.

The distance between 38

and 11

4 on the

number line is also 78

. So, the number of

cups Asher needs from the second bottle

is equal to the distance between 38

and 11

4.

Rubric 1 point for finding the number of cups; 1 point for showing the difference is equal to the distance on the number line

11.

23 1

4−15 7

8= 23 1

4+ −15 7

8⎛⎝⎜

⎞⎠⎟= 7 3

8

The remaining piece of board is 7 3

8

inches long, which is long enough.

Rubric 1 point for determining the length of the remaining piece of board; 1 point for determining that the remaining piece of board is long enough

12. Tony needs to deposit $30.48 into his checking account to reach the minimum balance.

With the fee, Tony needs to deposit $45.47 into his checking account to reach the minimum balance.

Rubric 1 point for each answer

13. Emily’s error is that she added − 2

3

instead of adding the opposite of − 2

3,

which is 23

.

−116− − 2

3⎛⎝⎜

⎞⎠⎟= −11

6+ − − 2

3⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

= −116+ 2

3

= −116+ 4

6

= − 76

The correct difference is − 7

6.

Rubric 1 point for identifying error; 1 point for

correcting error; 1 point for difference; 1 point for showing work



14. a. Possible answer: Guy’s house is

7

10 mile west of the library and

Stacie’s house is 9

10 mile east of the

library. How far does Guy have to walk from his house to Stacie’s house?

b. On the number line, the library is

represented by 0. Guy’s house is

represented by − 7

10 and Stacie’s

house by 9

10 on the number line.

The distance between the points on

the number line is 85

. So Guy has to

walk 85

miles to get to Stacie’s house.

c.

− 710

− 910

⎛⎝⎜

⎞⎠⎟= − 7

10+ − 9

10⎛⎝⎜

⎞⎠⎟

= −1610

= − 85

= 85

d. The distance between two points on

the number line is the difference between the greater value and the lesser value. Finding the absolute

value of the difference ensures that the difference is positive no matter which value is subtracted from the other. The difference must always be

positive because distance cannot be negative.

Rubric a. 1 point for a word problem that

satisfies the criteria

b. 0.5 point for plotting each number on

the number line correctly; 1 point for answering the question from part a correctly

c. 1 point for the correct distance

d. 1 point for any reasonable explanation



7.NS.1d Answers 1. C

2. A

3. C, E, F

4. A, B, D

5. a. Commutative

b. Additive inverse

c. Additive identity

d. Associative

e. Additive inverse

f. Additive identity

6. The commutative property of addition is

used to rewrite

− 3

2+ 4

3+ − 5

2⎛⎝⎜

⎞⎠⎟+ − 4

3⎛⎝⎜

⎞⎠⎟

as

− 3

2+ − 5

2⎛⎝⎜

⎞⎠⎟+ 4

3+ − 4

3⎛⎝⎜

⎞⎠⎟.

Since 43

and − 4

3 are additive inverses,

the additive inverse property is used to

rewrite

− 3

2+ − 5

2⎛⎝⎜

⎞⎠⎟+ 4

3+ − 4

3⎛⎝⎜

⎞⎠⎟

as

− 3

2+ − 5

2⎛⎝⎜

⎞⎠⎟+ 0.

The additive identity property is used to

rewrite

− 3

2+ − 5

2⎛⎝⎜

⎞⎠⎟+ 0 as

− 3

2+ − 5

2⎛⎝⎜

⎞⎠⎟,

which equals −4.

Rubric 1 point for using commutative property of

addition; 1 point for using additive inverse property; 1 point for final value

7. The commutative property of addition is used.

−7.1 + 5.4 + 7.1 = −7.1 + 7.1 + 5.4

The additive inverse property is used.

−7.1 + 7.1 + 5.4 = 0 + 5.4

The additive identity property is used.

0 + 5.4 = 5.4

The final temperature is 5.4 °C.

Rubric 1 point for using commutative property of addition; 1 point for using additive inverse property; 1 point for using additive identity property; 1 point for final temperature

8. 73

;

− 53+ 4

3+ 5

2⎛⎝⎜

⎞⎠⎟+ 8

3− 5

2

= − 53+ 4

3⎛⎝⎜

⎞⎠⎟+ 5

2+ 8

3− 5

2

= − 13+ 5

2+ 8

3− 5

2

= − 13+ 8

3+ 5

2− 5

2

= − 13+ 8

3+ 0

= − 13+ 8

3

= 73

Rubric 1 point for answer; 1 point for showing

work



9. Use the commutative property of addition and the additive inverse property to

simplify

12− 5

4+ 6

5+ 2

3− 6

7⎛⎝⎜

⎞⎠⎟+ 4

7+ 5

4 as

12+ 6

5+ 2

3− 6

7⎛⎝⎜

⎞⎠⎟+ 4

7. Use the associative

property of addition to simplify the

expression as 12+ 6

5+ 2

3− 2

7. There is no

more simplifying, so the minimum number of denominators that need to be used to find a common denominator is 4.

Rubric 1 point for answer; 2 points for explanation

10. No, because the commutative property of addition and the additive identity property are also needed to simplify the expression.

Use the associative property of addition to move the set of parentheses.

− 94+ 9

4+ 2

5⎛⎝⎜

⎞⎠⎟+ 5

6− 2

5=

− 94+ 9

4⎛⎝⎜

⎞⎠⎟+ 2

5+ 5

6− 2

5

Use the commutative property of addition

to move − 2

5 next to

25

.

− 94+ 9

4⎛⎝⎜

⎞⎠⎟+ 2

5+ 5

6− 2

5=

− 94+ 9

4⎛⎝⎜

⎞⎠⎟+ 2

5− 2

5+ 5

6

Use the additive inverse property to

simplify − 9

4+ 9

4 and

25− 2

5.

− 9

4+ 9

4⎛⎝⎜

⎞⎠⎟+ 2

5− 2

5+ 5

6= 0 + 0 + 5

6

Use the additive identity property to simplify the expression to one term.

0 + 0 + 5

6= 5

6

Rubric 1 point for answer; 1 point for identifying that commutative property of addition is needed; 1 point for identifying that additive identity property is needed;

1 point for correctly simplifying result



11. Possible answer:

− 5

4+ 5

4+ 10

3⎛⎝⎜

⎞⎠⎟+ 7

6− 2

3

Use the associative property of addition to move the set of parentheses.

− 54+ 5

4+ 10

3⎛⎝⎜

⎞⎠⎟+ 7

6− 2

3=

− 54+ 5

4⎛⎝⎜

⎞⎠⎟+ 10

3+ 7

6− 2

3


simplify − 5

4+ 5

4.

− 54+ 5

4⎛⎝⎜

⎞⎠⎟+ 10

3+ 7

6− 2

3=

0 + 103

+ 76− 2

3

Use the additive identity property to simplify the expression.

0 + 10

3+ 7

6− 2

3= 10

3+ 7

6− 2

3

Use the commutative property of addition

to move − 2

3 to the right of

103

.

103

+ 76− 2

3= 10

3− 2

3+ 7

6

Use common denominators to simplify

103

− 23+ 7

6.

103

− 23+ 7

6= 20

6− 4

6+ 7

6

= 236

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

1 point for correctly simplifying result

12. a. 5 1

4− 4 3

4+11

4+ 4 3

4

b. 6 1

2 cups; Use the commutative

property of addition.

5 14− 4 3

4+11

4+ 4 3

4=

5 14+11

4− 4 3

4+ 4 3

4


simplify −4 3

4+ 4 3

4.

5 1

4+11

4− 4 3

4+ 4 3

4= 5 1

4+11

4+ 0

Use the additive identity property.

5 1

4+11

4+ 0 = 5 1

4+11

4

Then add the fractions.

5 1

4+11

4= 6 1

2

Rubric a. 1 point

b. 1 point for answer; 1 point for using commutative property of addition;

1 point for using additive inverse property; 1 point for using additive identity property



7.NS.2a, 7.NS.2b Answers 1. C

2. D

3. C

4. B

5. C, E

6. A, C

7. Rewrite 3 1

2 as

3 + 1

2 and substitute the

new expression for 3 1

2.

23

3 12

⎛⎝⎜

⎞⎠⎟= 2

33 + 1

2⎛⎝⎜

⎞⎠⎟

= 23

(3)+ 23

12

⎛⎝⎜

⎞⎠⎟

= 63+ 2

6

= 2+ 13

= 2 13

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

8. 11

2× 2 1

2= 3

2× 5

2= 15

4= 3 3

4; you need

3 3

4 cups of water when cooking

2 1

2 cups of rice.

Rubric 1 point for product; 1 point for interpretation

9. 2 1

2÷ 3

4= 5

2× 4

3= 20

6= 3 2

6= 3 1

3;

Kendall can feed her cat for 3 days but does not have enough food to feed the cat on the fourth day.

Rubric 1 point for quotient;

1 point for interpretation

10. Yes, because integers can be divided as long as the divisor is not zero. Because the divisor, 6, is not 0, the quotient

196

= 3 16

is a rational number.


11. a. Gary’s error is saying − 5

24 is equal to

−5−24

. The quotient −5−24

is positive

because it is a quotient of two integers

with the same sign. The quotient 524

is also positive because it is a quotient

of two integers with the same sign. However, the opposite of this quotient,

− 5

24, is negative. So, the expression

− 5

24 is not equal to

−5−24

.

b. −524

and

5−24

; the quotient of two

integers with opposite signs is

negative. So, −524

= 5−24

= − 524

.

Rubric a. 1 point for identifying error;

1 point for explanation

b. 0.5 point for each answer; 1 point for explanation



12. a. Possible answer: Pick −3 as the

negative integer and 3 1

2 as the

positive mixed number.

−3 3 12

⎛⎝⎜

⎞⎠⎟= −1(3) 3 1

2⎛⎝⎜

⎞⎠⎟

= −1(3) 3 + 12

⎛⎝⎜

⎞⎠⎟

= −1 3(3)+ 3 12

⎛⎝⎜

⎞⎠⎟

⎡

⎣⎢

⎤

⎦⎥

= −1 9 +112

⎛⎝⎜

⎞⎠⎟

= −1 10 12

⎛⎝⎜

⎞⎠⎟

= −10 12

So, the sign of the product of −3 and

3 1

2 is negative.

b. The opposite of 3 1

2 is

−3 1

2.

−3 −3 12

⎛⎝⎜

⎞⎠⎟= (−1)(3)(−1) 3 1

2⎛⎝⎜

⎞⎠⎟

= (−1)(−1)(3) 3 + 12

⎛⎝⎜

⎞⎠⎟

= 1(3) 3 + 12

⎛⎝⎜

⎞⎠⎟

= 1 10 12

⎛⎝⎜

⎞⎠⎟

= 10 12

So, the sign of the product of −3 and

−3 1

2 is positive.

c. The product in part b, 10 1

2, is

the opposite of the product in

part a, −10 1

2.

Rubric a. 1 point

b. 1 point

c. 1 point

13. a. Since 2 and −2 are opposites, their

sum is 0, so 2 + (−2) = 0. The product of any integer and 0 is 0, so

−3(2 + (−2)) = −3(0) = 0.

b. −3[2 + (−2)] = −3(2) + (−3)(−2) = −6 + (−3)(−2); use the result from part

a to conclude that −6 + (−3)(−2) = 0, so the expression (−3)(−2) must equal 6.

c. Because the sum k + (−k) = 0,

−j[k + (−k)] = −j(0) = 0.

By the distributive property,

− j[k + (−k)] = − j(k)+ (− j)(−k)= − jk + (− j)(−k)= 0

Because −jk and (−j)(−k) have a sum

of 0, they are opposites, so (−j)(−k) = −(−jk) = jk.

Rubric a. 1 point

b. 1 point

c. 1 point for using a generalized

expression such as −j[k + (−k)] or −k[j + (−j)]; 1 point for a valid argument establishing (−j)(−k) = jk.



7.NS.2c Answers 1. D

2. C

3. D, E, F

4. A, C

5. a. Associative

b. Inverse

c. Identity

d. Commutative

e. Inverse

f. Identity

6. The commutative property of multiplication is used to rewrite

83

• 45

• 38÷ 4

9 as

83

• 38

• 45÷ 4

9. Since

83

and 38

are multiplicative inverses, the

multiplicative inverse property is used to

rewrite 83

• 38

• 45÷ 4

9 as

1 • 4

5÷ 4

9. The

multiplicative identity property is used to

rewrite 1 • 4

5÷ 4

9 as

45÷ 4

9, which equals

45

• 94= 9

5.

Rubric 1 point for using commutative property of multiplication; 0.5 point for using multiplicative inverse property; 0.5 point

for using multiplicative identity property; 1 point for final value

7. The multiplicative inverse property can help you simplify the expression

because 78

• 125

÷ 125

• 107

equals

78

• 125

• 512

• 107

. The fractions 125

and

5

12 are multiplicative inverses, so their

product is 1.

78

• 125

• 512

• 107

= 78

• 1 • 107

Also, the multiplicative identity property

reduces the number of factors in the

expression.

78

• 1 • 107

= 78

• 107

Rubric 1 point for using multiplicative inverse property; 1 point for using multiplicative

identity property; 1 point for explanation

8. No, because the associative property of multiplication is being used to simplify the expression.

4.8 • (0.5 • 2.95) = (4.8 • 0.5) • 2.95= (2.4) • 2.95


9. When multiplying a number a by 1, the result is a. The multiplicative identity is not 0, because multiplying a by 0 results in 0 and not a.

The multiplicative identity is used to

simplify 94

• 514

÷ 514

because the

expression can be rewritten as

94

• 514

• 145

. Notice that 5

14 and

145

are

multiplicative inverses and their product is

1. So, 94

• 514

• 145

= 94

• 1. By the

multiplicative identity property, 94

• 1= 94

.

Rubric 1 point for explaining why 1 is the multiplicative identity; 1 point for explaining why 0 is not the multiplicative

identity; 1 point for simplifying expression using multiplicative inverse and identity; 1 point for explanation



10. Use the associative property of

multiplication to regroup the factors.

45

• 1511

⎛⎝⎜

⎞⎠⎟

• 1115

• 133

÷ 45=

45

• 1511

• 1115

⎛⎝⎜

⎞⎠⎟

• 133

÷ 45

Use the multiplicative inverse property to

simplify the expression 1511

• 1115

.

45

• 1511

• 1115

⎛⎝⎜

⎞⎠⎟

• 133

÷ 45=

45

• 1 • 133

÷ 45

Use the multiplicative identity property to

simplify the expression.

45

• 1 • 133

÷ 45= 4

5 • 13

3÷ 4

5

Use the commutative property of

multiplication.

45

• 133

÷ 45= 13

3 • 4

5÷ 4

5

Change division to multiplication by

an inverse.

133

• 45÷ 4

5= 13

3 • 4

5 • 5

4

Use the multiplicative inverse property to

simplify the expression 45

• 54

.

133

• 45

• 54= 13

3 • 1



133

• 1= 133

Rubric 1 point for using associative property of multiplication; 1 point for using commutative property of multiplication;

1 point for using multiplicative inverse property; 1 point using multiplicative identity property

11. Possible answer:

47

• 712

• 85

⎛⎝⎜

⎞⎠⎟

• 311

÷ 85

Use the associative property of multiplication to regroup the factors.

47

• 712

• 85

⎛⎝⎜

⎞⎠⎟

• 311

÷ 85=

47

• 712

⎛⎝⎜

⎞⎠⎟

• 85

• 311

÷ 85

Use the commutative property of

multiplication.

47

• 712

⎛⎝⎜

⎞⎠⎟

• 85

• 311

÷ 85=

47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

• 85÷ 8

5

Change division to multiplication by an

inverse. Then use the multiplicative inverse property to simplify.

47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

• 85÷ 8

5=

47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

• 85

• 58=

47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

• 1



47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

• 1= 47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

Simplify.

47

• 712

⎛⎝⎜

⎞⎠⎟

• 311

= 13

• 311

= 111

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

for correctly simplifying result



7.NS.2d Answers 1. B

2. C

3. A

4. C, E

5. A, D

6. a. Terminating

b. Repeating

c. Repeating

d. Terminating

e. Repeating

7.

16 13.0000−12.8000

2000−1600

400−320

80−80

0

0.8125

0.8125; the decimal equivalent of 1316

is a

terminating decimal because there is no remainder after the 5 is evaluated.

Rubric 1 point for answer; 1 point for showing long division

8. 4.625; 4 5

8= 37

8

8 37.000−32.000

5.000−4.800

200−160

40−40

0

4.625

(Accept answers that instead show

4 5

8= 4 + 0.625 = 4.625. )

Rubric 1 point for answer; 1 point for showing long division

9. The second table has a greater cost per person (about $3.83) than the first table ($3.80).

5 19.0−15.0

4.0−4.0

0

3.86 23.000−18.000

5.000−4.800

200−180

20−18

2

3.833

Rubric 1 point for correct answer; 1 point for showing each long division



10.

22 7.00000−6.60000

40000−2200018000

−17600400

−220180

−1764

0.31818

45 14.000−13.500

500−450

50−45

5

0.311

54 19.0000000−16.2000000

2.8000000−2.7000000

1000000−540000460000

−43200028000

−270001000−540460

−43228

0.3518518

Since 722

= 0.318, 1445

= 0.31,

1954

= 0.3518, and 0.31< 0.318 < 0.3518,

the rational numbers in ascending order

are 1445

, 722

, and 1954

.

Rubric 1 point for all decimal equivalents; 1 point for using long division;

1 point for decimals in ascending order; 1 point for explanation

11. Todd’s calculation for 7

12 is correct.

While calculating the decimal equivalent

for 1324

, Todd multiplied 5 by 24

incorrectly; 5 × 24 = 120, not 110.

24 13.00000−12.00000

1.00000−96000

4000−24001600

−1440160

−14416

0.54166

The decimal equivalent of 1324

is 0.5416.

Rubric

1 point for determining 7

12 is the correct

calculation; 1 point for identifying error; 2 points for finding correct decimal

equivalent



7.NS.3 Answers 1. D

2. A

3. A

4. B, E

5. A, E

6. C

7. A

8. F

9. D

10. 2(0.10) + 3(0.25) + 6(0.05) − 2(0.25) −

5(0.10) = 0.20 + 0.75 + 0.30 − 0.50 − 0.50 = 0.25

The overall amount of money in the jar

increased by $0.25.

Rubric 1 point for expression; 1 point for answer

11. The stack of sheets is 2 5

8 inches tall.

316

×14 = 4216

= 218

= 2 58

Rubric 1 point for answer; 1 point for showing work

12. Four photos can fit in the picture frame.

14 12÷ 3 1

4= 29

2÷ 13

4

= 292

× 413

= 11626

= 5813

= 4 613

The number of photos that can fit in the

frame is different than the quotient of

14 1

2 and

3 1

4 because only whole photos

can fit in the picture frame. It would not

make sense for 6

13 of a photo to be

inside the picture frame.

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

13. There are 576 bolts in the collection.

Convert the weight of the box from pounds to ounces.

6 34×16 = 27

4×16

= 4324

= 108

The box has 108 ounces of bolts.

Now divide 108 by 3

16.

108 ÷ 316

= 108 × 163

= 1,7283

= 576

Rubric 1 point for answer; 2 points for explanation



14. a. 50.7 + 49.4 + 52.3 + 48.9 + 51.6

5=

252.9

5= 50.58

The average of the 5 attempts is

50.58 meters.

b. The sixth attempt would have to travel 52.5 meters because 52.5 is the

difference between the sum of the five attempts and what the sum of the six attempts has to be in order for the average to be 50.9 meters.

50.9 × 6 = 305.4

305.4 − 252.9 = 52.5

Rubric a. 1 point for answer;

1 point for showing work

b. 1 point for answer; 1 point for explanation

15. Peter did not follow the order of

operations; he should have divided 10 1

2

by 3 3

4 first instead of adding

4 1

4 and

10 1

2.

4 14+10 1

2÷ 3 3

4= 17

4+ 21

2÷ 15

4

= 174

+ 212

× 415

= 174

+ 8430

= 25560

+ 16860

= 42360

= 7 360

= 7 120

Rubric 1 point for identifying Peter’s error; 1 point for finding the correct value of the

expression; 1 point for showing work

7 mnlean876238 7ns1ab · 10. asher has two bottles of floor cleaner, each of which contains 2 cups...

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