Name _______________________________________
Date __________________
Class _________________
7.NS.1a, 7.NS.1b
SELECTED RESPONSE
3. Which sum does the number line
represent?
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.
−11 + (−9)
−11 + 9
−11 + (−2)
Devon opens a new checking
account with $30. His first purchase,
made with his new debit card, totals
$28.
−11 + (2)
Select all correct answers.
4. On a number line, which of the following
sums is to the left of the first number in
the sum?
1
Joe makes 1 liters of lemonade
2
and drinks it all during the afternoon.
−9 + 1
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.
−
1 4
+
6 3
7 æ 3ö
+ ç- ÷
2 çè 4 ÷ø
15 + (−8)
2. What is the location of the sum 11 + (−5)
with respect to 11 on a number line?
−2 + 6
5 units in the negative direction
5 units in the positive direction
11 units in the negative direction
11 units in the positive direction
Match each expression with the verbal description for the location of the sum.
____ 5. 17 + (−10)
____ 6. −5 + (−7)
____ 7. −
11
+6
4
____ 8. 9 + 20
11
4
11
6 units to the right of −
4
7 units to the left of −5
7 units to the right of −5
10 units to the left of 17
10 units to the right of 17
20 units to the left of −9
20 units to the right of 9
A 6 units to the left of −
B
C
D
E
F
G
H
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
Name _______________________________________
Date __________________
CONSTRUCTED RESPONSE
Class _________________
13. Jayce goes out for a walk. He walks
5
miles from home. He walks back
4
1
mile before meeting up with his friend
2
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?
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?
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
3
gallon of gasoline into her
4
snow thrower’s empty fuel tank. She uses
1
gallon for the snowstorm on Friday,
4
1
gallon for the
and then uses another
4
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.
14. Becky adds
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.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
14
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
7.NS.1c
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
4. Which of the following expressions give
the distance between the endpoints of the
segment shown on the number line
below?
1. What is an equivalent expression for
2 4
− ?
3 5
2 4
+
3 5
2 ⎛ 4⎞
+ −
3 ⎝⎜ 5 ⎠⎟
−
−
2 4
+
3 5
2 ⎛ 4⎞
+ −
3 ⎝⎜ 5 ⎠⎟
2. How does the expression |9 − (−5)| relate
to the numbers −5 and 9 on the number
line?
−
3 ⎛ 4⎞
− −
5 ⎜⎝ 5 ⎟⎠
−
3 4
−
5 5
−
3 4
−
5 5
3 4
−
5 5
4 ⎛ 3⎞
− −
5 ⎜⎝ 5 ⎟⎠
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.
Match each subtraction expression with
an equivalent expression that uses the
additive inverse.
4 8
4 ⎛ 8⎞
A
+
____ 5. − − ⎜ − ⎟
3 5
3 ⎝ 5⎠
4 ⎛ 8⎞
+ ⎜− ⎟
B
4 ⎛ 8⎞
3
− −
____ 6.
⎝ 5⎠
3 ⎝⎜ 5 ⎠⎟
4 ⎛ 8⎞
C − + ⎜− ⎟
4 8
3 ⎝ 5⎠
____ 7. − −
3 5
4 8
D − +
4 8
3 5
____ 8.
−
3 5
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)|
CONSTRUCTED RESPONSE
|−5| − |6|
|5 − 6|
9. Is −10 − 5 equal to −10 + (−5)? Explain in
terms of additive inverses.
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
15
Common Core Assessment Readiness
Name _______________________________________
Date __________________
10. Asher has two bottles of floor cleaner,
each of which contains 2 cups when full.
3
cup and the other
One bottle contains
8
1
bottle is full. He needs 1 cups of floor
4
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
3
1
between
and 1 on the number line.
8
4
Class _________________
13. Emily thinks that −
11 ⎛ 2 ⎞
5
− ⎜ − ⎟ is − .
6 ⎝ 3⎠
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.
________________________________________
________________________________________
11. Cindy has a board that is 7 inches wide
1
and 23 inches long. She needs to use
4
the board to replace a shelf that is
7
15 inches long. Cindy hopes that the
8
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.
________________________________________
________________________________________
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.
________________________________________
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?
________________________________________
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.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
16
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
7.NS.1d
SELECTED RESPONSE
Select all correct responses.
Select the correct answer.
3. Which properties are used to simplify
2 ⎛2 2⎞ 7 7
2
− + ⎜ + ⎟ − + as
without first
9 ⎝9 3⎠ 4 4
3
⎛ 5 1⎞ 5
1. What property allows ⎜ − + ⎟ + to be
⎝ 6 3⎠ 3
5
simplified to − + 2 ?
6
finding a common denominator?
Additive inverse property
Commutative property of
multiplication
Additive identity property
Commutative property of addition
Associative property of addition
Associative property of addition
Commutative property of addition
Multiplicative inverse property
Additive inverse property
2. Which of the following uses the additive
inverse property correctly to simplify the
expression?
Additive identity property
4. Which of the following demonstrates
using the associative property of addition
to simplify?
14 7 7 14
− + =
19 3 3 19
−
10
10 11 ⎛ 11⎞
− + ⎜− ⎟ = −
9
9
4 ⎝ 4⎠
(−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
2 5 3
5
+ + = 1+
5 4 5
4
[12.3 + (−24.6)] − 15.4 = 12.3 + (−40)
15.81+ (4.19 + 10.67) = 20 + 10.67
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
4 ⎛ 5⎞ ⎛ 4⎞ ⎛5 7⎞
in the process of simplifying + ⎜ − ⎟ + ⎜ − ⎟ + ⎜ + ⎟ .
5 ⎝ 3⎠ ⎝ 5⎠ ⎝3 4⎠
a.
4 ⎛ 4⎞ ⎛ 5⎞ ⎛5 7⎞
+ −
+ −
+
+
5 ⎝⎜ 5 ⎠⎟ ⎝⎜ 3 ⎠⎟ ⎝⎜ 3 4 ⎠⎟
Commutative
Associative
Additive inverse
Additive identity
b.
⎛ 5⎞ ⎛5 7⎞
0 + ⎜− ⎟ + ⎜ + ⎟
⎝ 3⎠ ⎝3 4⎠
Commutative
Associative
Additive inverse
Additive identity
c.
−
5 ⎛5 7⎞
+
+
3 ⎝⎜ 3 4 ⎠⎟
Commutative
Associative
Additive inverse
Additive identity
d.
⎛ 5 5⎞ 7
⎜− 3 + 3 ⎟ + 4
⎝
⎠
Commutative
Associative
Additive inverse
Additive identity
e.
0+
Commutative
Associative
Additive inverse
Additive identity
f.
7
4
Commutative
Associative
Additive inverse
Additive identity
7
4
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
17
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
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 2
− + ⎜ + ⎟ + − to one term without
4 ⎝4 5⎠ 6 5
CONSTRUCTED RESPONSE
6. Explain how the properties of addition are
3 4 ⎛ 5⎞ ⎛ 4⎞
used to simplify − + + ⎜ − ⎟ + ⎜ − ⎟ .
2 3 ⎝ 2⎠ ⎝ 3⎠
Find the value of the expression.
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.
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 5
+
+
+ − without
3 ⎜⎝ 3 2 ⎟⎠ 3 2
1
cups of beans in a jar.
4
3
She takes out 4 cups of beans for a
4
recipe. When making the dish, she
decides to cut down on the beans used
1
and returns 1 cups of beans to the jar.
4
3
Then Margie adds another 4 cups of
4
beans from a bag to the jar.
12. Margie has 5
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
1 5 6 ⎛2 6⎞ 4 5
simplify − + + ⎜ − ⎟ + + ?
2 4 5 ⎝3 7⎠ 7 4
a. Write an expression that models this
situation.
________________________________________
Explain your answer using the properties
of operations.
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.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
18
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
7.NS.2a, 7.NS.2b
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
5. Which of the following equations use the
distributive property correctly to multiply
rational numbers?
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?
⎛ 1⎞
⎛ 1⎞
3 ⎜ −4 ⎟ = 3(−4) + 3 ⎜ ⎟
⎝ 2⎠
⎝ 2⎠
The stock lost $0.45 per day.
The stock lost $7.25 over 5 days.
1⎛ 3⎞
1⎛ 3⎞
2 ⎜ 1 ⎟ = 2(1) + ⎜ ⎟
4 ⎝ 4⎠
4 ⎝ 4⎠
The stock lost $11.25 over 5 days.
The stock lost $11.25 per day.
⎛ 1⎞
⎛ 1⎞
−4 ⎜ −5 ⎟ = −4(−5) + (−4) ⎜ − ⎟
⎝ 3⎠
⎝ 3⎠
2. Which of the following products is
negative?
6
1
1
•4
2
4
⎛ 4⎞
−3 ⎜ −2 ⎟
⎝ 5⎠
⎛ 4⎞
4
−2 ⎜ 2 ⎟ = −2(2) +
5
⎝ 5⎠
⎛ 1⎞ ⎛ 1⎞
⎜⎝ −5 2 ⎟⎠ ⎜⎝ − 4 ⎟⎠
−3
⎛ 4 ⎞ ⎛ 1⎞
4 ⎛ 1⎞
4
−4 ⎜ 1 ⎟ = −4 (1) + ⎜ −4 ⎟ ⎜ ⎟
5 ⎝ 3⎠
5
⎝ 5⎠ ⎝ 3⎠
3 5
×
4 6
6. Which of the following fractions are
15
equivalent to − ?
4
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
−$17.50
quotient
= −$2.50?
7
−15
4
15
4
−15
−4
−4
15
15
−4
4
−15
CONSTRUCTED RESPONSE
7. Victoria needs sugar for a certain recipe.
2
The original recipe calls for
cup sugar.
3
However, Victoria wants to make a recipe
1
that is 3 times larger. Use the
2
distributive property to find the product.
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.
________________________________________
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Grade 7
19
Common Core Assessment Readiness
Name _______________________________________
Date __________________
1
cups of water are needed
2
for every cup of rice and you need to
1
cook 2 cups of rice. What is the value
2
and the interpretation of the product
1
1
1 ×2 ?
2
2
Class _________________
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.
8. Suppose 1
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.
________________________________________
1
cups of
2
3
cat food remaining. Her cat eats
cup of
4
cat food per day. What is the value and
1 3
the interpretation of the quotient 2 ÷ ?
2 4
9. Kendall realizes that she has 2
________________________________________
c. How does the product from part b
differ from the product from part a?
Explain.
________________________________________
________________________________________
________________________________________
13.
________________________________________
10. Can 19 be divided by 6? Explain.
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.
________________________________________
5
5
is equal to
24
24
5
−5
5
because −
=
=
.
24 −24 24
11. Gary thinks that −
________________________________________
________________________________________
a. Identify Gary’s error. Explain.
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.
________________________________________
________________________________________
________________________________________
b. Find two expressions that are
5
equivalent to − . Explain.
24
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
20
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
7.NS.2c
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
3. Which of the following properties can be
used together to simplify the product
5 11 ⎛ 4 ⎞ 6
•
• −
− •
without having to
4 3 ⎜⎝ 5 ⎟⎠ 11
2 7 15
1. Which property allows
to be
•
•
5 3
2
7
simplified to 3 • ?
3
multiply uncommon denominators?
Multiplicative identity property
Associative property of addition
Multiplicative inverse property
Associative property of multiplication
Associative property of multiplication
Commutative property of addition
Commutative property of
multiplication
Commutative property of
multiplication
Multiplicative inverse property
2. Which of the following uses the
multiplicative inverse property correctly to
simplify the expression?
Multiplicative identity property
4. Which of the following uses the
commutative property of multiplication?
4 4 7 7
•
• =
5 5 6 6
0.5 i 10.83 i 60 = 0.5 i 60 i 10.83
7 4 ⎛ 10 ⎞
4
•
• ⎜ − ⎟ = −2 •
5 3 ⎝ 7⎠
3
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
8 2 5 8
•
• = •1
3 5 2 3
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
4
3 4 3
• 1• = •
9
8 9 8
Select the correct answer for each lettered part.
5. Determine the property of multiplication that is used in each step to simplify
⎛ 10 11⎞ 4 7 3 5
• ⎟ •
• • • .
the expression ⎜
4 ⎠ 11 5 5 7
⎝ 3
a.
10 ⎛ 11 4 ⎞ 7 3 5
•
•
• • •
3 ⎜⎝ 4 11⎟⎠ 5 5 7
Associative
Commutative
Inverse
Identity
b.
10
7 3 5
• 1• • •
3
5 5 7
Associative
Commutative
Inverse
Identity
c.
10 7 3 5
•
•
•
5 5 7
3
Associative
Commutative
Inverse
Identity
d.
10 7 5 3
•
•
•
3
5 7 5
Associative
Commutative
Inverse
Identity
e.
10
3
• 1•
3
5
Associative
Commutative
Inverse
Identity
f.
10 3
•
3
5
Associative
Commutative
Inverse
Identity
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
21
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
10. Use the properties of multiplication
to simplify the expression
⎛ 4 15 ⎞ 11 13 4
⎜⎝ 5 • 11 ⎟⎠ • 15 • 3 ÷ 5 . Show
CONSTRUCTED RESPONSE
6. Explain how the properties of
multiplication are used to simplify
8 4 3 4
•
• ÷ . Find the value of the
3 5 8 9
expression.
your work.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
7. What properties of multiplication can help
7 12 12 10
you to simplify
•
÷
•
?
5
5
7
8
Explain.
________________________________________
________________________________________
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.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
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
9
5
5
identity is used to simplify
•
÷ .
4 14 14
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
22
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
7.NS.2d
5. Which of the following is greater
34
than
?
8
SELECTED RESPONSE
Select the correct answer.
1. Convert
8
to a decimal.
14
0.571428
1.75
0.571428
1.75
14
3
17
6
25
9
17
is a
27
repeating decimal. How many digits are
in the repeating part of the decimal?
2. The decimal equivalent of
1
3
2
6
47
11
49
12
3. Suppose the repeating pattern in
0.020020200202002... continues forever.
Is the number rational?
Select the correct answer for each
lettered part.
6. Determine whether the decimal
equivalents of the following rational
numbers are terminating or repeating.
Yes, because the number is
equivalent to the repeating decimal
0.02002.
a.
Yes, because the number is a
terminating decimal.
7
20
Terminating
Repeating
No, because the number is not a
terminating decimal.
b.
No, because the number is not a
repeating decimal.
13
24
Terminating
Repeating
c.
Select all correct answers.
3
11
Terminating
Repeating
4. Which of the following rational numbers
have three digits that repeat in its decimal
equivalent?
d.
27
150
Terminating
Repeating
3
8
e.
10
21
11
12
Terminating
Repeating
11
27
8
35
7
37
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
23
Common Core Assessment Readiness
Name _______________________________________
Date __________________
Class _________________
10. Use long division to find the decimal
19
7 14
equivalents of
,
, and
. Show
54
22 45
your work. Put the rational numbers in
ascending order. Explain.
CONSTRUCTED RESPONSE
7. Use long division to find the decimal
13
equivalent of
. Show your work. Is the
16
decimal equivalent a terminating decimal
or a repeating decimal?
________________________________________
________________________________________
8. Celia has a new cell phone that weighs
5
4 ounces. What is the weight of Celia’s
8
cell phone as a decimal? Use long
division and show your work.
11. Todd found that the decimal equivalent of
13
is 0.583. However, he noticed that
24
7
is also
the decimal equivalent of
12
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.
________________________________________
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.
0.5833
24 13.0000
−11.0000
2.0000
−1.9200
800
−720
80
−72
8
________________________________________
0.5833
12 7.0000
−6.0000
1.0000
−9600
400
−360
40
−36
4
________________________________________
________________________________________
________________________________________
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Grade 7
24
Common Core Assessment Readiness
Name ________________________________________ Date ___________________ Class __________________
7.NS.3
5. In the morning, a group of hikers hiked
3
3 miles, took a break, and then hiked
4
3
another 2 miles. The group then
4
stopped for lunch. In the afternoon, the
3
group then hiked 4 miles, took another
4
1
break, and then hiked 2 miles. Which
2
of the following statements are true?
SELECTED RESPONSE
Select the correct answer.
1. How many times does
1
1
go into 1 ?
2
4
2
5
3
4
5
8
2
1
2
3
hours. She
4
3
hour long.
has seven classes that are
4
How many hours is Tamela not in class
while she is at school?
2. Tamela’s school day is 6
1
1
2
6
1
4
18
5
3
mile more in the
4
afternoon than in the morning.
The hikers hiked
3
mile more in the
4
morning than in the afternoon.
The hikers hiked
The hikers hiked the same number of
miles in the morning as in the
afternoon.
3
4
3. Hez is making a bookcase. The boards
that are used to make the bookcase are
13
inch thick. Hez found a board that is
16
1
1 inches thick. By how much does Hez
4
have to reduce the thickness of the new
board to match the other boards?
7
inch
16
1
13
inch
16
2
The hikers hiked 12
entire day.
The hikers hiked 13
Match the number with the equivalent
expression.
15
1 3
____ 6. 3
A 3 ÷
16
2 4
3 3
2
B 4 ×
____ 7. 4
4 4
3
3
7
C 5 −1
3
____ 8. 1
8 16
4
1
7
3
D 5 −3 +2
3
2
8
4
____ 9. 4
8
2 3
E 2 −1
8
8
1
1
1
F 10 − 2 × 3
2
2
2
1
inches
16
Select all correct answers.
4. Which of the following expressions have
a result that is greater than 5?
3 4 1
2 + ÷
8 5 3
3 2
1 ÷
4 7
−
3
miles the
4
entire day.
1
inches
64
1
3
2
3 + 2 −1
5
5
5
1
miles the
2
3
1
4
+ 3 ×1
4
4
5
1 1 5
12 × +
2 5 6
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Grade 7
25
Common Core Assessment Readiness
Name ________________________________________ Date ___________________ Class __________________
14. A science experiment has a catapult
launch a ball. The result of the
experiment is shown in the table.
CONSTRUCTED RESPONSE
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.
Attempt
1
2
3
4
5
Distance
50.7 m
49.4 m
52.3 m
48.9 m
51.6 m
a. What is the average distance of the
5 attempts? Show your work.
________________________________________
________________________________________
________________________________________
11. A factory makes sheet metal. If each
3
inch thick, how tall is the
sheet is
16
stack if there are 14 sheets? 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.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
1
1
3
+ 10 ÷ 3 . His
4
2
4
work is shown. Identify Peter’s error and
find the correct value. Show your work.
15. Peter is evaluating 4
1
12. A picture frame provides 14 inches of
2
space for a row of photos and each photo
1
is 3 inches wide. How many photos
4
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.
4
________________________________________
________________________________________
________________________________________
3
ounce.
16
If a collection of these bolts weighs
3
6 pounds, how many bolts are in the
4
collection? Explain.
13. A type of bolt weighs about
1
1
3 17 21 15
+ 10 ÷ 3 =
+
÷
4
2
4 4
2
4
17 42 15
=
+
÷
4
4
4
59 15
=
÷
4
4
59 4
=
×
4 15
59
=
15
14
=3
15
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7
26
Common Core Assessment Readiness
7.NS.1a, 7.NS.1b Answers
c. Possible answer: The amount of sugar
3
Corey adds to the measuring cup,
4
3
cup, and then uses,
cup, leaves the
4
same amount of sugar in the cup as
before both actions, 0.
1. C
2. A
3. B
4. C, D
5. E
6. C
Rubric
a. 1 point
b. 1 point
c. 2 points
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.
æ 1ö
+ çç- ÷÷ represents this
è 2ø
5
and
situation. To find the sum, start at
4
1
unit to the left.
move
2
13. The expression
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
The sum of
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.
5
4
5
4
æ 1ö
3
+ çç- ÷÷ is . It means that
4
è 2ø
3
mile away from home when
4
he meets Macy.
Jayce is
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
3 1 1 1
she still has − − = gallon
4 4 4 4
remaining. Possible answer: Becky could
1
gallon of gasoline into the empty
add
2
3
fuel tank instead of
gallon. The fuel
4
tank would be empty again after adding
1
1 1 1
gallon and using + = gallon.
2
4 4 2
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
3
-cup
4
measuring cup with sugar to bake a
recipe.
b. Possible answer: Corey uses the
3
entire
cup of sugar for the recipe.
4
12. a. Possible answer: Corey fills a
Rubric
1 point for answer; 1 point for
explanation; 1 point for correct change
of action; 1 point for explanation
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
11
Common Core Assessment Readiness
7.NS.1c Answers
1. B
11. 23
2. D
3. B
3
1
7
1 ⎛
7⎞
− 15 = 23 + ⎜ −15 ⎟ = 7
8
4
8
4 ⎝
8⎠
3
8
inches long, which is long enough.
The remaining piece of board is 7
4. B, E
5. D
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
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.
12. Tony needs to deposit $30.48 into his
checking account to reach the minimum
balance.
Rubric
1 point for answer; 1 point for explanation
With the fee, Tony needs to deposit
$45.47 into his checking account to
reach the minimum balance.
10. The number of cups Asher needs from
1 3 10 3 7
− = .
the second bottle is 1 − =
4 8
8 8 8
Rubric
1 point for each answer
13. Emily’s error is that she added −
The distance between
2
3
2
instead of adding the opposite of − ,
3
2
which is .
3
1
3
and 1 on the
4
8
7
. So, the number of
8
cups Asher needs from the second bottle
3
is equal to the distance between
8
1
and 1 .
4
number line is also
−
11 ⎛ 2 ⎞
11 ⎡ ⎛ 2 ⎞ ⎤
− ⎜ − ⎟ = − + ⎢− ⎜ − ⎟ ⎥
6 ⎝ 3⎠
6 ⎣ ⎝ 3⎠ ⎦
11 2
+
6 3
11 4
=− +
6 6
7
=−
6
=−
Rubric
1 point for finding the number of cups;
1 point for showing the difference is equal
to the distance on the number line
7
The correct difference is − .
6
Rubric
1 point for identifying error; 1 point for
correcting error; 1 point for difference;
1 point for showing work
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
12
Common Core Assessment Readiness
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
14. a. Possible answer: Guy’s house is
7
mile west of the library and
10
9
mile east of the
Stacie’s house is
10
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
7
represented by −
and Stacie’s
10
9
on the number line.
house by
10
The distance between the points on
8
the number line is . So Guy has to
5
8
miles to get to Stacie’s house.
walk
5
c.
−
7 ⎛ 9⎞
7 ⎛ 9⎞
−⎜ ⎟ = − +⎜− ⎟
10 ⎝ 10 ⎠
10 ⎝ 10 ⎠
= −
16
10
= −
8
5
8
5
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.
=
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Grade 7 Teacher Guide
13
Common Core Assessment Readiness
7.NS.1d Answers
1. C
7. The commutative property of addition is
used.
2. A
3. C, E, F
−7.1 + 5.4 + 7.1 = −7.1 + 7.1 + 5.4
4. A, B, D
The additive inverse property is used.
5. a.
b.
c.
d.
e.
f.
−7.1 + 7.1 + 5.4 = 0 + 5.4
Commutative
Additive inverse
Additive identity
Associative
Additive inverse
Additive identity
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
6. The commutative property of addition is
3 4 ⎛ 5⎞ ⎛ 4⎞
used to rewrite − + + ⎜ − ⎟ + ⎜ − ⎟ as
2 3 ⎝ 2⎠ ⎝ 3 ⎠
−
3 ⎛ 5⎞ 4 ⎛ 4⎞
+ −
+ + − .
2 ⎜⎝ 2 ⎟⎠ 3 ⎜⎝ 3 ⎟⎠
8.
−
4
4
Since
and − are additive inverses,
3
3
the additive inverse property is used to
3 ⎛ 5⎞ 4 ⎛ 4⎞
rewrite − + ⎜ − ⎟ + + ⎜ − ⎟ as
2 ⎝ 2⎠ 3 ⎝ 3 ⎠
−
7
;
3
5 ⎛ 4 5⎞ 8 5
+
+
+ −
3 ⎜⎝ 3 2 ⎟⎠ 3 2
⎛ 5 4⎞ 5 8 5
= ⎜− + ⎟ + + −
⎝ 3 3⎠ 2 3 2
1 5 8 5
=− + + −
3 2 3 2
1 8 5 5
=− + + −
3 3 2 2
1 8
= − + +0
3 3
1 8
=− +
3 3
7
=
3
3 ⎛ 5⎞
+ −
+ 0.
2 ⎜⎝ 2 ⎟⎠
The additive identity property is used to
3 ⎛ 5⎞
3 ⎛ 5⎞
rewrite − + ⎜ − ⎟ + 0 as − + ⎜ − ⎟ ,
2 ⎝ 2⎠
2 ⎝ 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
Rubric
1 point for answer; 1 point for showing
work
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
14
Common Core Assessment Readiness
10. No, because the commutative property of
addition and the additive identity property
are also needed to simplify the
expression.
9. Use the commutative property of addition
and the additive inverse property to
1 5 6 ⎛ 2 6⎞ 4 5
simplify − + + ⎜ − ⎟ + + as
2 4 5 ⎝ 3 7⎠ 7 4
1 6 ⎛ 2 6⎞ 4
+ +
−
+ . Use the associative
2 5 ⎜⎝ 3 7 ⎟⎠ 7
Use the associative property of addition
to move the set of parentheses.
property of addition to simplify the
1 6 2 2
expression as + + − . There is no
2 5 3 7
more simplifying, so the minimum number
of denominators that need to be used to
find a common denominator is 4.
−
9 ⎛ 9 2⎞ 5 2
+
+
+ − =
4 ⎜⎝ 4 5 ⎟⎠ 6 5
⎛ 9 9⎞ 2 5 2
⎜⎝ − 4 + 4 ⎟⎠ + 5 + 6 − 5
Use the commutative property of addition
2
2
to move − next to .
5
5
Rubric
1 point for answer; 2 points for
explanation
⎛ 9 9⎞ 2 5 2
⎜⎝ − 4 + 4 ⎟⎠ + 5 + 6 − 5 =
⎛ 9 9⎞ 2 2 5
⎜⎝ − 4 + 4 ⎟⎠ + 5 − 5 + 6
Use the additive inverse property to
9 9
2 2
simplify − + and − .
4 4
5 5
⎛ 9 9⎞ 2 2 5
5
⎜⎝ − 4 + 4 ⎟⎠ + 5 − 5 + 6 = 0 + 0 + 6
Use the additive identity property to
simplify the expression to one term.
0+0+
5 5
=
6 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
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
15
Common Core Assessment Readiness
1
3
1
3
− 4 +1 + 4
4
4
4
4
1
b. 6 cups; Use the commutative
2
property of addition.
11. Possible answer:
5 ⎛ 5 10 ⎞ 7 2
− +⎜ + ⎟ + −
4 ⎝4 3 ⎠ 6 3
12. a. 5
Use the associative property of addition
to move the set of parentheses.
3
1
3
1
− 4 +1 + 4 =
4
4
4
4
1
1
3
3
5 +1 − 4 + 4
4
4
4
4
Use the additive inverse property to
3
3
simplify −4 + 4 .
4
4
1
1
3
3
1
1
5 +1 − 4 + 4 = 5 +1 + 0
4
4
4
4
4
4
5
5 ⎛ 5 10 ⎞ 7 2
− +⎜ + ⎟ + − =
4 ⎝4 3 ⎠ 6 3
⎛ 5 5 ⎞ 10 7 2
⎜⎝ − 4 + 4 ⎟⎠ + 3 + 6 − 3
Use the additive inverse property to
5 5
simplify − + .
4 4
⎛ 5 5 ⎞ 10 7 2
⎜⎝ − 4 + 4 ⎟⎠ + 3 + 6 − 3 =
10 7 2
0+
+ −
3 6 3
Use the additive identity property.
5
Then add the fractions.
Use the additive identity property to
simplify the expression.
0+
1
1
1
1
+1 + 0 = 5 +1
4
4
4
4
5
10 7 2 10 7 2
+ − =
+ −
3 6 3 3 6 3
1
1
1
+1 = 6
4
4
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
Use the commutative property of addition
2
10
to move − to the right of
.
3
3
10 7 2 10 2 7
+ − =
− +
3 6 3 3 3 6
Use common denominators to simplify
10 2 7
− + .
3 3 6
10 2 7 20 4 7
− + =
− +
3 3 6 6 6 6
23
=
6
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
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
16
Common Core Assessment Readiness
7.NS.2a, 7.NS.2b Answers
1. C
1 3 5 4 20
2
1
÷ = × =
=3 =3 ;
2 4 2 3 6
6
3
Kendall can feed her cat for 3 days but
does not have enough food to feed the
cat on the fourth day.
9. 2
2. D
3. C
4. B
5. C, E
Rubric
1 point for quotient;
1 point for interpretation
6. A, C
1
1
as 3 + and substitute the
2
2
1
new expression for 3 .
2
7. Rewrite 3
10. Yes, because integers can be divided as
long as the divisor is not zero. Because
the divisor, 6, is not 0, the quotient
19
1
= 3 is a rational number.
6
6
2 ⎛ 1⎞ 2 ⎛
1⎞
3 ⎟ = ⎜3 + ⎟
⎜
3 ⎝ 2⎠ 3 ⎝
2⎠
Rubric
1 point for answer; 1 point for explanation
2
2 ⎛ 1⎞
= (3) + ⎜ ⎟
3
3 ⎝ 2⎠
11. a. Gary’s error is saying −
6 2
= +
3 6
1
= 2+
3
1
=2
3
5
is equal to
24
−5
−5
is positive
. The quotient
−24
−24
because it is a quotient of two integers
5
with the same sign. The quotient
24
is also positive because it is a quotient
of two integers with the same sign.
However, the opposite of this quotient,
5
− , is negative. So, the expression
24
5
−5
is not equal to
−
.
24
−24
−5
5
and
b.
; the quotient of two
24
−24
integers with opposite signs is
−5
5
5
negative. So,
=
=− .
24 −24
24
Rubric
1 point for product;
1 point for using distributive property
1
1 3 5 15
3
8. 1 × 2 = × =
= 3 ; you need
2
2 2 2 4
4
3
3 cups of water when cooking
4
1
2 cups of rice.
2
Rubric
1 point for product;
1 point for interpretation
Rubric
a. 1 point for identifying error;
1 point for explanation
b. 0.5 point for each answer;
1 point for explanation
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
17
Common Core Assessment Readiness
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.
12. a. Possible answer: Pick −3 as the
1
negative integer and 3 as the
2
positive mixed number.
⎛ 1⎞
⎛ 1⎞
−3 ⎜ 3 ⎟ = −1(3) ⎜ 3 ⎟
⎝ 2⎠
⎝ 2⎠
⎛
1⎞
= −1(3) ⎜ 3 + ⎟
2
⎝
⎠
⎡
⎛ 1⎞ ⎤
= −1⎢3(3) + 3 ⎜ ⎟ ⎥
⎝ 2⎠ ⎦
⎣
⎛
1⎞
= −1⎜ 9 + 1 ⎟
2⎠
⎝
⎛ 1⎞
= −1⎜ 10 ⎟
⎝ 2⎠
1
= −10
2
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.
So, the sign of the product of −3 and
1
3 is negative.
2
1
1
b. The opposite of 3 is −3 .
2
2
⎛ 1⎞
⎛ 1⎞
−3 ⎜ −3 ⎟ = (−1)(3)(−1) ⎜ 3 ⎟
⎝ 2⎠
⎝ 2⎠
⎛
1⎞
= (−1)(−1)(3) ⎜ 3 + ⎟
2⎠
⎝
⎛
1⎞
= 1(3) ⎜ 3 + ⎟
2⎠
⎝
⎛ 1⎞
= 1⎜ 10 ⎟
⎝ 2⎠
1
= 10
2
So, the sign of the product of −3 and
1
−3 is positive.
2
1
c. The product in part b, 10 , is
2
the opposite of the product in
1
part a, −10 .
2
Rubric
a. 1 point
b. 1 point
c. 1 point
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
18
Common Core Assessment Readiness
7.NS.2c Answers
1. D
Also, the multiplicative identity property
reduces the number of factors in the
expression.
2. C
3. D, E, F
7
10 7 10
• 1•
= •
8
7 8
7
4. A, C
5. a.
b.
c.
d.
e.
f.
Associative
Inverse
Identity
Commutative
Inverse
Identity
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.
6. The commutative property of
multiplication is used to rewrite
8 4 3 4
8 3 4 4
•
• ÷ as
•
• ÷ . Since
3 5 8 9
3 8 5 9
8
3
and
are multiplicative inverses, the
3
8
multiplicative inverse property is used to
4 4
8 3 4 4
rewrite
•
• ÷ as 1 • ÷ . The
5 9
3 8 5 9
multiplicative identity property is used to
4 4
4 4
rewrite 1 • ÷ as ÷ , which equals
5 9
5 9
4 9 9
• = .
5 4 5
4.8 • (0.5 • 2.95) = (4.8 • 0.5) • 2.95
= (2.4) • 2.95
Rubric
1 point for answer; 1 point for explanation
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
9
5
5
because the
simplify
•
÷
4 14 14
expression can be rewritten as
5 14
9
5
14
and
are
•
•
. Notice that
5
4 14
14
5
multiplicative inverses and their product is
9
5 14 9
1. So,
•
•
= • 1. By the
4 14
5 4
9
9
multiplicative identity property,
• 1= .
4
4
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
7 12 12 10
because
equals
•
÷
•
8
5
5
7
5 10
7 12
12
and
•
•
•
. The fractions
5 12
7
8
5
5
are multiplicative inverses, so their
12
product is 1.
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
7 12
5 10 7
10
•
•
•
= • 1•
8
5 12
7 8
7
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
19
Common Core Assessment Readiness
10. Use the associative property of
multiplication to regroup the factors.
11. Possible answer:
⎛ 4 15 ⎞ 11 13 4
⎜⎝ 5 • 11 ⎟⎠ • 15 • 3 ÷ 5 =
4 ⎛ 15 11 ⎞ 13 4
•
•
÷
•
5 ⎜⎝ 11 15 ⎟⎠
3 5
8⎞ 3 8
4 ⎛ 7
•⎜
• ⎟ •
÷
7 ⎝ 12 5 ⎠ 11 5
Use the associative property of
multiplication to regroup the factors.
4 ⎛ 7
8⎞ 3 8
•
•
÷ =
•
7 ⎜⎝ 12 5 ⎟⎠ 11 5
⎛4
7⎞ 8 3 8
⎜⎝ 7 • 12 ⎟⎠ • 5 • 11 ÷ 5
Use the multiplicative inverse property to
15 11
simplify the expression
•
.
11 15
Use the commutative property of
multiplication.
4 ⎛ 15 11 ⎞ 13 4
•
•
÷ =
•
5 ⎜⎝ 11 15 ⎟⎠
3 5
4
13 4
• 1•
÷
5
3 5
⎛4
7⎞ 8 3 8
⎜⎝ 7 • 12 ⎟⎠ • 5 • 11 ÷ 5 =
⎛4
7⎞ 3 8 8
⎜⎝ 7 • 12 ⎟⎠ • 11 • 5 ÷ 5
Use the multiplicative identity property to
simplify the expression.
Change division to multiplication by an
inverse. Then use the multiplicative
inverse property to simplify.
4
13 4 4 13 4
•1•
÷ = •
÷
5
3 5 5
3 5
Use the commutative property of
multiplication.
⎛4
7⎞ 3 8 8
⎜⎝ 7 • 12 ⎟⎠ • 11 • 5 ÷ 5 =
⎛4
7⎞ 3 8 5
⎜⎝ 7 • 12 ⎟⎠ • 11 • 5 • 8 =
⎛4
7⎞ 3
⎜⎝ 7 • 12 ⎟⎠ • 11 • 1
4 13 4 13 4 4
•
÷ =
• ÷
5
3 5 3
5 5
Change division to multiplication by
an inverse.
13 4 4 13 4 5
• ÷ =
•
•
3
5 5 3
5 4
Use the multiplicative identity property to
simplify the expression.
Use the multiplicative inverse property to
4 5
simplify the expression
• .
5 4
⎛4
⎛4
7⎞ 3
7⎞ 3
⎜⎝ 7 • 12 ⎟⎠ • 11 • 1= ⎜⎝ 7 • 12 ⎟⎠ • 11
13 4 5 13
•
• =
•1
5 4 3
3
Simplify.
⎛4
7⎞ 3 1 3
⎜⎝ 7 • 12 ⎟⎠ • 11 = 3 • 11
1
=
11
Use the multiplicative identity property to
simplify the expression.
13
13
• 1=
3
3
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
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
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
20
Common Core Assessment Readiness
7.NS.2d Answers
1. B
8. 4.625; 4
2. C
3. A
4.625
8 37.000
−32.000
5.000
−4.800
200
−160
40
−40
0
4. C, E
5. A, D
6. a.
b.
c.
d.
e.
5 37
=
8 8
Terminating
Repeating
Repeating
Terminating
Repeating
0.8125
7. 16 13.0000
−12.8000
2000
−1600
400
−320
80
−80
0
(Accept answers that instead show
5
4 = 4 + 0.625 = 4.625. )
8
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).
13
is a
16
terminating decimal because there is no
remainder after the 5 is evaluated.
3.8
3.833
5 19.0 6 23.000
−15.0
−18.000
4.0
5.000
−4.0
−4.800
0
200
−180
20
−18
2
0.8125; the decimal equivalent of
Rubric
1 point for answer; 1 point for showing
long division
Rubric
1 point for correct answer; 1 point for
showing each long division
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
21
Common Core Assessment Readiness
10.
Since
0.31818
22 7.00000
−6.60000
40000
−22000
18000
−17600
400
−220
180
−176
4
7
14
= 0.318,
= 0.31,
22
45
19
= 0.3518, and 0.31< 0.318 < 0.3518,
54
the rational numbers in ascending order
14 7
19
are
,
, and
.
45 22
54
Rubric
1 point for all decimal equivalents;
1 point for using long division;
1 point for decimals in ascending order;
1 point for explanation
7
is correct.
12
While calculating the decimal equivalent
13
for
, Todd multiplied 5 by 24
24
incorrectly; 5 × 24 = 120, not 110.
11. Todd’s calculation for
0.311
45 14.000
−13.500
500
−450
50
−45
5
0.54166
24 13.00000
−12.00000
1.00000
−96000
4000
−2400
1600
−1440
160
−144
16
0.3518518
54 19.0000000
−16.2000000
2.8000000
−2.7000000
1000000
−540000
460000
−432000
28000
−27000
1000
−540
460
−432
28
The decimal equivalent of
13
is 0.5416.
24
Rubric
7
is the correct
12
calculation; 1 point for identifying error;
2 points for finding correct decimal
equivalent
1 point for determining
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
22
Common Core Assessment Readiness
7.NS.3 Answers
1. D
12. Four photos can fit in the picture frame.
2. A
14
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 number of photos that can fit in the
frame is different than the quotient of
1
1
14 and 3 because only whole photos
2
4
can fit in the picture frame. It would not
6
of a photo to be
make sense for
13
inside the picture frame.
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
1 29 13
1
÷3 =
÷
4 2
4
2
29 4
=
×
2 13
116
=
26
58
=
13
6
=4
13
5
inches tall.
8
Rubric
1 point for answer; 1 point for showing
work; 1 point for explanation
3
42
× 14 =
16
16
21
=
8
5
=2
8
13. There are 576 bolts in the collection.
Convert the weight of the box from
pounds to ounces.
6
Rubric
1 point for answer;
1 point for showing work
3
27
× 16 =
× 16
4
4
432
=
4
= 108
The box has 108 ounces of bolts.
3
Now divide 108 by
.
16
108 ÷
3
16
= 108 ×
16
3
1,728
=
3
= 576
Rubric
1 point for answer;
2 points for explanation
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
23
Common Core Assessment Readiness
14. a.
15. Peter did not follow the order of
50.7 + 49.4 + 52.3 + 48.9 + 51.6
=
5
operations; he should have divided 10
252.9
= 50.58
5
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
by 3
1
2
3
1
first instead of adding 4 and
4
4
1
10 .
2
4
Rubric
a. 1 point for answer;
1 point for showing work
b. 1 point for answer;
1 point for explanation
1
1
3 17 21 15
+ 10 ÷ 3 =
+
÷
4
2
4 4
2
4
17 21 4
=
+ ×
4
2 15
17 84
=
+
4 30
255 168
=
+
60
60
423
=
60
3
=7
60
1
=7
20
Rubric
1 point for identifying Peter’s error;
1 point for finding the correct value of the
expression; 1 point for showing work
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 7 Teacher Guide
24
Common Core Assessment Readiness