Download Number Systems Milestones Study Questions

Name _______________________________________ Date __________________ Class __________________
6.NS.1
SELECTED RESPONSE
4. Divide.
Select the correct answer.
7
cup of sour cream to make
8
1
tacos. If each taco requires
cup of
16
sour cream, how many tacos can you
make?
1. You have
3 17

7 19
3
133
51
133
57
119
119
57
5. Nima uses
2
1
cup peanuts,
cup
3
2
3
cup pecans, and some
4
1
raisins in a recipe that makes 2 cups of
4
trail mix. How many cups of peanuts are
there per cup of trail mix?
cashews,
7
taco
128
14 tacos
1
taco
14
2
9
8
27
15 tacos
3
9
27
8
2. How many
1
-cup servings are there in
2
6. Jerry is tiling the wall behind his sink. The
tiles he’s using are square with sides that
3
measure 1 inches. If the area of wall
4
3
he’s tiling is 42 inches long and 29
4
inches high, how many tiles will he need?
7
cup of peanut butter?
8
1
16
4
7
7
16
1
3
4
17
24
3. Carl wants to plant a garden that is
1
1 yards long and has an area of
2
1
3 square yards. How wide should the
2
garden be?
3
yard
7
2
1
yards
3
2 yards
5
1
yards
4
408
1249
1
2
CONSTRUCTED RESPONSE
7. The following division is being performed
using multiplication by the reciprocal.
Find the missing numbers.
5 ? 5
 
12 3 12
? 1

10 ?
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
13
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
8. Ida is cutting a
11
-foot wooden board
12
10. Juan was presented with the following
3
5
problem on a math test: “Divide
by .
7
4
Show your work.” His work is shown
below. What was Juan’s error? Correct
his work and state the correct quotient.
3
-foot sections to do some detail
16
work on a model she is building. How
3
many whole
-foot sections are there in
16
11
the
-foot wooden board? Explain your
12
answer and show your work.
into
5 3 5
 
7 4 7
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
9. Baruka has
4 20

3 21
________________________________________
1
gallon of milk left in the
2
11. Consider the division statement
fridge.
1 7
.

4 16
a. Describe a real world situation that
might involve this expression.
5
-gallon (10-ounce)
64
servings of milk does she have left?
Show your work.
a. How many
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. If she drinks 10 ounces of milk a day,
how many days of milk does she
have left? Explain.
b. Find the quotient.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. Interpret the quotient in terms of the
situation you described in part a.
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.2
SELECTED RESPONSE
CONSTRUCTED RESPONSE
Select the correct answer.
6. A skyscraper with 102 floors is 1,326 feet
tall. Each floor is the same height. How
tall is each floor? Show your work.
1. Divide. 196  28
6
6 R27
________________________________________
7 R1
________________________________________
7
________________________________________
2. Divide. 98 308
________________________________________
3
________________________________________
3 R14
4
7. An apple orchard harvested 3,584 apples
and separated them evenly into
112 bags.
14 R3
3. An art teacher has 192 containers of
paint for 17 students. If the teacher wants
to provide each student with an equal
number of containers, how many
containers will be left over?
a. How many apples are in each bag?
________________________________________
________________________________________
0
________________________________________
5
b. If 56 apples were placed in each bag
instead, how many bags would be
left over?
7
18
4. A local theater can seat 2,254 people.
The seats are arranged into 98 rows.
Each row has the same number of seats.
How many seats are there in each row?
15
23
20
32
________________________________________
________________________________________
________________________________________
8. A movie streaming service charges its
customers $15 a month. Martina has $98
saved up. Will she have any money left
over if she pays for the maximum amount
of months she can afford? Explain.
Select all correct answers.
5. The event staff for a local concert hall has
73 tickets to sell. If they sell all of the
tickets at the same price, they will have
$438. Which of the following people have
enough money to buy a ticket?
________________________________________
________________________________________
Celia has $4.50.
________________________________________
Louis has $7.00.
Jan has $6.50.
________________________________________
Nicola has $6.00.
________________________________________
Chuck has $5.00.
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
9. Maurice says that 1079  62 is 16 with a
remainder of 87.
b. How many groups should there be?
Will all the groups have the same
number of students? Explain.
a. Without seeing his work, how can
you tell Maurice divided incorrectly?
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
11.
b. Maurice is correct about this fact:
16  62  87  1079. Explain how
you can use that fact to find the
correct quotient and remainder for
1079  62 without actually dividing.
Then find the quotient.
a. Find 117  13, 118  13, and
119  13.
________________________________________
________________________________________
________________________________________
b. Without dividing, what is the quotient
of 120  13? Use the pattern you
found in the first three problems to
explain you answer.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
10. The administrator of the school is dividing
342 students into 38 groups to do a teambuilding exercise. One of the guidance
counselors says that the exercise will be
most effective if there are 7 or fewer
students in a group.
________________________________________
________________________________________
c. According to the pattern, 130  13
should be 9 with a remainder of 13.
Explain why that is incorrect and find
the correct quotient.
a. Explain why the administrator’s plan
is not as effective as it can be.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.3
3. Multiply. 1.8762  4.2
SELECTED RESPONSE
Select the correct answer.
7.88004
1. Add. 13.389  1.24
78.8004
13.513
788.004
14.529
7,880.04
14.62
4. Divide. 0.09975  0.007
14.629
1.425
2. Subtract. 102.596  10.478
14.25
92.118
142.5
92.128
1,425
112.122
192.118
Match each multiplication expression with its product.
A 376,236
____ 5. 2.986  1.26
____ 6. 0.2986  0.126
B 37,623.6
____ 7. 29.86  12.6
C 3,762.36
____ 8. 298.6  126
D 376.236
____ 9. 2.986  12.6
E 37.6236
____ 10. 2,986  126
F 3.76236
____ 11. 298.6  12.6
G 0.376236
____ 12. 2.986  0.126
H 0.0376236
CONSTRUCTED RESPONSE
13. Elsa has $45.78 in her savings account and $21.38 in her wallet.
a. How much money does Elsa have?
________________________________________________________________________________________
________________________________________________________________________________________
b. If Elsa puts half of the money in her wallet in the bank, how much money will she have
in her savings account?
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
14. Mariposa needs a number of 0.3125-inch
strips of wood for a model she is building.
How many of these strips can she get
from a 5.625-inch wooden board? Show
your work.
17. Shen earns $9.60 per hour at his
part-time job. Last month, he worked
7.25 hours the first week, 8.75 hours the
second week, 5.5 hours the third week,
and 6.75 hours the fourth week. Shen
puts half of his paycheck in the bank
every other week starting with the first.
________________________________________
a. How much money did Shen earn
each week?
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
15. Jean-Paul incorrectly states that
4.2874  1.286  4.416. His work is
shown below. Explain Jean-Paul’s
mistake and correct his work.
1
1
________________________________________
b. How much money did he have in the
bank at the end of last month? Show
your work.
1
4. 2 8 7 4

1. 2 8 6
________________________________________
4. 4 1 6 0
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. How much money did Shen have to
spend from his 4 paychecks? Show
your work.
________________________________________
________________________________________
16. At a local gas station, regular gasoline
sells for $3.499 per gallon, while premium
gasoline sells for $3.879 per gallon.
________________________________________
________________________________________
a. Find the difference in price between
the two types of gasoline.
18. Pablo wants to buy a steak at the grocery
store. He has two options. The first is
1.37 pounds and costs $9.59. The
second is 1.75 pounds and costs $10.85.
Which is the better buy? Explain.
________________________________________
________________________________________
b. How much does a person save on
15.25 gallons of gas by buying
regular instead of premium? Show
your work, and round your answer to
the nearest whole cent.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
19
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.4
SELECTED RESPONSE
CONSTRUCTED RESPONSE
Select the correct answer.
6. Is it possible to use the distributive
property to rewrite 85  99 as a product
of a whole number greater than 1 and a
sum of two whole numbers? Explain your
answer.
1. Find the greatest common factor of
12 and 18.
1
2
3
________________________________________
6
________________________________________
2. Find the least common multiple of
8 and 10.
________________________________________
32
________________________________________
40
________________________________________
50
7. Charlie and Dasha are roommates, and
they have a dog. If neither of them is
home, they hire someone to watch the
dog. Charlie must go on business trips
every 6 months, while Dasha must go on
business trips every 9 months. If they
both just got back from business trips,
how many months will it be before they
need to hire someone to look after the
dog again? Explain your answer.
80
3. Find the greatest common factor of
7 and 11.
1
7
11
77
4. Find the least common multiple of 6
and 12.
________________________________________
6
________________________________________
12
________________________________________
24
________________________________________
72
________________________________________
5. Factor out the greatest common factor of
the expression below using the
distributive property.
8. Salvatore is making some party favors for
his birthday party. He has 96 pencils and
80 boxes of raisins. He wants each party
favor to be the same, and he wants to
use all of the pencils and raisins. Find the
GCF of 96 and 80 to figure out how many
party favors he can make. How many
pencils and boxes of raisins will be in
each one?
90  60
30(3  2)
10(9  6)
15(6  4)
6(15  10)
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
19
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
9.
11. Consider the sum 36  45.
a. What is the LCM of two numbers
when one number is a multiple of the
other? Give an example.
a. Use the distributive property to
rewrite the sum as the product of a
whole number other than 1 and a
sum of two whole numbers.
________________________________________
________________________________________
________________________________________
b. Write the sum as the product of a
whole number different from the one
you chose in part a and a sum of two
whole numbers.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. Can this be done in more than two
ways? Explain.
b. What is the LCM of two numbers that
have no common factors greater than
1? Give an example.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
12. A baker has 72 vanilla cupcakes and
80 chocolate cupcakes. She wants to
make platters for a party that have both
kinds of cupcakes and the same total
number of cupcakes on each platter.
________________________________________
________________________________________
10.
a. Find the greatest common factor of
3 and 5.
a. Can the baker make 10 platters of
cupcakes with no cupcakes left over?
Explain why or why not.
________________________________________
________________________________________
________________________________________
b. Find the greatest common factor of
11 and 13.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. Use your results from parts a and b
to make a conjecture about the GCF
of any pair of prime numbers.
________________________________________
b. What is the greatest number of
platters she can make? How many of
each kind of cupcake will be on each
platter?
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
21
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.5
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
4. Choose all the situations that can be
described with a negative number.
1. Carlos deposited $28.50 into his bank
account after making a $20.00 withdrawal
to pay for some school supplies.
Represent these situations as signed
numbers.
The Titanic rests at a depth of about
12,000 feet.
The temperature of the photosphere
of the Sun is approximately 5,505 C.
28.50, 20.00
The height of the Taipei 101
skyscraper in Taiwan is 1,671 feet.
28.50, 20.00
28.50, 20.00
The average high temperature in
Antarctica in January is 15 F below
zero.
28.50, 20.00
2. In Barrow, Alaska, the northernmost town
in the United States, the record high
temperature is 79 F, recorded on
July 13, 1993. The record low is 56 F
below zero, recorded on February 3,
1924. Represent these situations as
signed numbers.
The world record for deepest scuba
dive is 1,083 feet.
The world record for highest base
jump from a building is 2,205 feet
above sea level.
CONSTRUCTED RESPONSE
79, 56
5. An object’s elevation is its height above
some fixed point. The most commonly
used point is sea level. The word
“altitude” is used to describe an object’s
position above sea level, whereas the
word “depth” is used to describe an
object’s position below sea level. Express
each of the following situations as a
signed number or zero.
79, 56
79, 56
79, 56
3. While on vacation in Australia, Brent and
Giselle decide to explore the Great
Barrier Reef. Brent decides to go
snorkeling near the surface at a depth of
5 feet below sea level. Giselle is an
experienced scuba diver and decides to
explore a little deeper at 80 feet below
sea level. Represent these situations as
signed numbers.
a. An airplane at an altitude of 30,000
feet
________________________________________
b. A submarine at a depth of 1,200 feet
5, 80
5, 80
________________________________________
c. A boat on the surface of the ocean
5, 80
5, 80
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
21
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6. In golf, par is the number of strokes an
average player should need to complete
a particular hole. If a golfer scores under
par, the score is reported as a negative
number representing the number of
strokes less than par. If a golfer scores
over par, the score is reported as a
positive number. Scoring par exactly is
represented by 0. Express each of the
following scores as a signed number
or zero.
8. Use a signed number to represent each
of the following situations. Then describe
what 0 represents in the same situation.
a. Salazar dives to a depth of 73 feet.
________________________________________
________________________________________
________________________________________
b. Nu deposits $16.78 into her bank
account.
a. Margaret completed 18 holes with an
overall score of 9 under par.
________________________________________
________________________________________
________________________________________
b. Anika completed the last hole with a
score of 1 over par.
________________________________________
c. Overnight, the temperature drops by
15 F.
________________________________________
c. Johan completed 9 holes on par.
________________________________________
________________________________________
________________________________________
d. Seamus completed the first hole of
the tournament with a score of 2
under par.
________________________________________
9. Write two situations that could be
described by each of the following
numbers.
________________________________________
7. In a standard savings account, the term
“credit” is used to describe a deposit of
money into the account. The term “debit”
is used to describe a withdrawal of
money from the account. Describe what a
positive number, a negative number, and
zero mean in this context.
a. 50
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. 50
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
22
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.6a, 6.NS.6b
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
6. Which pairs of numbers lie on opposite
sides of 0 on a number line?
1. Describe the locations of 3 and 3 with
respect to 0 on a number line.
8, 7
3 is to the right of 0, and 3 is to the
right of 0.
10, 10
4, 9
3 is to the left of 0, and 3 is to the
left of 0.
8, 15
21, 21
3 is to the left of 0, and 3 is to the
right of 0.
2, 200
3 is to the right of 0, and 3 is to the
left of 0.
CONSTRUCTED RESPONSE
7. Graph 5, 0, 2, and 4 on the number line.
Then, graph their opposites on the same
number line.
2. What is the opposite of 12?
12
-
1
12
–5
1
12
12
–4
–3
–2
–1
0
1
2
3
4
5
8. Elevation is measured as a distance
above or below sea level. Sea level has
an elevation of 0 feet. Johanna is
standing on a hillside 35 feet above sea
level, and Marcus is exploring a cave at
an elevation that is the opposite of
Johanna’s elevation. What is Marcus’s
elevation?
æ
4ö
3. In which quadrant is ç 3, - ÷ ?
5ø
è
Quadrant I
Quadrant II
Quadrant III
________________________________________
Quadrant IV
9. The point (1.235, 987) is in Quadrant IV.
What kind of reflection would move this
point from Quadrant IV to Quadrant III?
Which coordinate(s) would change signs?
4. If the point (1.9, 2) is reflected across
the x-axis, which quadrant will it be in?
Quadrant I
Quadrant II
________________________________________
Quadrant III
________________________________________
Quadrant IV
5. Choose the correct sign description of a
point in Quadrant I.
________________________________________
(, )
________________________________________
(, )
________________________________________
(, )
________________________________________
(, )
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
Gym
Teachers' Lounge
Boys' Room
Main Office
Girls' Room
Science Lab
Classroom
10. To celebrate the 100th anniversary of the
opening of their school, the teachers
organize a treasure hunt for the students.
One of the clues states, “Think of the
main office as 0 on a number line. You
will find the next clue in the room that is
the opposite of the teachers’ lounge.” Use
the diagram below to determine where
the students should go to find the next
clue. Explain.
–3
–2
–1
0
1
2
3
13. The following graph shows the point
(4, 3). It also shows the points that result
when (4, 3) is reflected across the x-axis
and the y-axis.
a. The point (4, 3) reflected across the
x-axis is (4, 3). What do you notice
about the signs of the coordinates?
________________________________________
________________________________________
________________________________________
________________________________________
11.
________________________________________
a. Find the opposites of 8, 1, and 7.
________________________________________
________________________________________
b. The point (4, 3) reflected across the
y-axis is (4, 3). What do you notice
about the signs of the coordinates?
b. Find the opposites of the opposites
from part a.
________________________________________
________________________________________
c. What do you notice about a number
and the opposite of its opposite?
________________________________________
________________________________________
________________________________________
c. What do you think would happen to
the signs of the coordinates of
(4, 3) if it were reflected across the
x-axis and then the result was
reflected across the y-axis? Explain
your answer and provide the
resulting point.
________________________________________
æ2 ö
12. Consider the ordered pair ç , y ÷ . Find a
è3 ø
value of y that places the ordered pair in
each quadrant. If it is not possible for the
ordered pair to be in a certain quadrant,
explain why.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.6c
æ 4 1ö
4. Describe the process of graphing ç , ÷
è5 3ø
on a coordinate plane.
SELECTED RESPONSE
Select the correct answer.
1. Where is
2
on a number line?
3
4
unit in
5
the positive x-direction. Then, move
1
unit in the positive y-direction.
3
Starting at the origin, move
Between 3 and 2
Between 1 and 0
Between 0 and 1
Between 2 and 3
4
unit in
5
the negative x-direction. Then, move
1
unit in the negative y-direction.
3
Starting at the origin, move
2. Identify the point on the number line.
4
unit in
5
the positive x-direction. Then, move
1
unit in the negative y-direction.
3
4
Starting at the origin, move
3.5
3.5
4
4
unit in
5
the negative x-direction. Then, move
1
unit in the positive y-direction.
3
Starting at the origin, move
3. Identify the coordinates of the point.
Select all correct answers.
5. What numbers are graphed on the
vertical number line?
(2, 4)
(4, 2)
(4, 2)
(2, 4)
2.5
1
2.25
1.25
1.75
2
0.75
2.5
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
8. Below is a map showing various places in
relation to Carlos’s house at the origin.
Find the coordinates of the library,
the school, the bike shop, and the
baseball field.
CONSTRUCTED RESPONSE
6. Graph and label (0.75, 1.25), (1.5, 2),
(0.25, 1.75), and (1, 0.75).
7. A group of students is participating in a
tug-of-war contest. The rope is laid out in
a straight line with a knot in the middle.
The students are positioned according to
the following diagram. The object of the
game for both teams is to pull the knot
2 units in their direction. The first team to
do so wins the contest. Assume that each
team pulls in a straight line. If Holden’s
side wins, find the final positions of
Holden and Marishka. Explain your
answers using a number line.
________________________________________
________________________________________
________________________________________
________________________________________
9.
a. Graph and label the point (2, 8).
b. Find the point that represents a
reflection of (2, 8) across the x-axis.
Graph and label the result.
c. Find the point that represents a
reflection of the result from part b
across the y-axis. Graph and label
the result.
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.7a
SELECTED RESPONSE
Select all correct answers.
Select the correct answer.
5. Which statements are equivalent to the
8
inequality -2.5 <
?
13
1. If 3  7 and 1  7, where are 3 and
1 relative to 7 on a number line?
3 and 1 are both to the right of 7.
3 and 1 are both to the left of 7.
2.5 is to the left of
3 is to the right of 7 and 1 is to the
left of 7.
number line.
8
on a
13
8
is to the right of 2.5 on a
13
number line.
3 is to the left of 7 and 1 is to the
right of 7.
8
is to the left of 2.5 on a
13
number line.
4 3
1 3
4
1
and
> and < , where are
3 5
2 5
3
2
3
relative to
on a number line?
5
2. If
2.5 is less than
4
1
3
and
are both to the right of .
3
2
5
8
.
13
2.5 is to the right of
4
1
3
and
are both to the left of .
3
2
5
8
on a
13
number line.
8
< -2.5
13
4
3
1
is to the right of , and
is to
3
5
2
3
the left of .
5
8
> -2.5
13
8
is less than 2.5.
13
4
3
1
is to the left of , and
is to the
3
5
2
3
right of .
5
CONSTRUCTED RESPONSE
6. Describe the positions of 10 and 17
relative to each other on a number line in
two different ways, given that 17  10.
3. A number x is to the left of 10.2 on a
number line. Which inequality describes
this situation?
x  10.2
________________________________________
x  10.2
________________________________________
10.2  x
________________________________________
x  10.2
7. 0.001  x and x  10,000. Is x between
0.001 and 10,000, to the left of 0.001, or
to the right of 10,000? Explain your
reasoning.
4. On a number line, a number p is to the
right of 18. Which of the following choices
describes this situation?
18  p
p  18
18  p
p  18
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
10. Matthias says that the inequality 1  2.2
is true because 1 is to the right of 2.2 on
a number line. Helga says that the
inequality is true because 2.2 is to the
left of 1 on a number line. Who is correct?
Explain your answer by graphing 1 and
2.2 on a number line and interpreting
the result.
8. Look at the following inequalities.
7
7
7
, 0 < , 22 > ,
23
23
23
7
18 7 7
-1,000 < , < ,
> 0.2,
23 19 23 23
7 1 7
1
< ,
<4
23 2 23
6
a. Which of the numbers above are to
7
the right of
on a number line?
23
1,000,000 >
________________________________________
________________________________________
________________________________________
________________________________________
b. Which of the numbers above are to
7
the left of
on a number line?
23
________________________________________
________________________________________
11. Consider the inequality 5.5  4.
________________________________________
a. Graph the two numbers on a
number line.
________________________________________
9. Consider the three points on the
number line.
b. Describe the positions of 5.5 and
4 relative to each other on a number
line in two different ways.
a. Pick any two of the points and write
an inequality statement. Explain your
answer using the positions of the two
numbers relative to each other on the
number line.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
c. Write an inequality using 5.5 and a
number to the left of 5.5 on the
number line.
________________________________________
________________________________________
________________________________________
d. Write an inequality using 4 and a
number to the right of 4 on the
number line.
________________________________________
b. Could the relationship between the
two numbers you chose be
represented in a different way? If so,
write the inequality.
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
28
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.7b
4. Anthony has $53.43 in his savings
account, Maxine has $54.78, Rodolfo
has $54.98, and Nicola has $53.29. Who
has saved the most money? Who has
saved the least?
SELECTED RESPONSE
Select the correct answer.
1. The thermometer at Bruce’s house
shows a temperature of 2 F. The
thermometer at Zan’s house reads
5 F. Which inequality represents this
situation? Whose thermometer shows a
warmer temperature?
Maxine has saved the most money,
and Anthony has saved the least.
Maxine has saved the most money,
and Nicola has saved the least.
2 F  5 F; Bruce’s thermometer
shows a warmer temperature.
Rodolfo has saved the most money,
and Nicola has saved the least.
2 F  5 F; Zan’s thermometer
shows a warmer temperature.
Rodolfo has saved the most money,
and Anthony has saved the least.
2 F  5 F; Bruce’s thermometer
shows a warmer temperature.
Select all correct answers.
2 F  5 F; Zan’s thermometer
shows a warmer temperature.
5. Jack needs a piece of wood at least
13
inch long for some detail work on a
16
project he is working on. Which of the
following lengths of wood would meet
his requirements?
2. Marco and Randy decide to have a foot
race on a local field. Marco can maintain
a speed of 8 miles per hour, while Randy
runs at 6 miles per hour. Which inequality
represents this situation? Who is faster?
1
inch
2
8 mph  6 mph; Marco is faster.
8 mph  6 mph; Randy is faster.
7
inch
8
8 mph  6 mph; Marco is faster.
3
inch
4
8 mph  6 mph; Randy is faster.
3. In a cooking class, each student needs
2
cup of sugar for a recipe. Zach has
3
3
cup of sugar at his cooking station,
4
1
while Suzanne has
cup at her cooking
2
station. Who has enough sugar to make
the recipe?
27
inch
32
5
inch
8
CONSTRUCTED RESPONSE
2
cup strawberries,
3
1
1
3
cup sugar,
cup walnuts, and
cup
4
2
4
flour. Order the amounts from least to
greatest. Which ingredient does the
recipe require the least amount of?
6. A recipe calls for
Zach has enough sugar.
Suzanne has enough sugar.
Zach and Suzanne both have
enough sugar.
Neither Zach nor Suzanne has
enough sugar.
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
7. While climbing a mountain, Chuck and
Marissa decided to take separate trails
and meet at the peak. Chuck took the
easier trail and was at an elevation of
about 425 feet after an hour. Marissa
took the more advanced trail and made
it to 550 feet in an hour. Marissa started
to get tired and was only able to climb
150 more feet in the next hour. Since
Chuck took the easier trail, he was able
to climb an additional 350 feet in the
second hour. Write inequalities that
express their locations on the mountain
after 1 hour and after 2 hours. Who was
at a higher elevation after 2 hours?
9. The record low temperatures for three
towns in Alaska are given in the table
below. Write three inequalities using
three different pairs of temperatures.
Which of the three towns has the
highest record low?
Town
Record Low
Anchorage
34 F
Barrow
56 F
Juneau
22 F
________________________________________
________________________________________
________________________________________
________________________________________
10. Sam and Nima have part-time jobs for
the summer. Over the last three weeks,
Sam has made deposits of $40.25,
$58.50, and $28.40 into his savings
account. During the same time, his sister
Nima has deposited $60.85, $20.00, and
$62.13 into her savings account.
________________________________________
________________________________________
________________________________________
8. Sally plants four flowers in her garden
and measures their heights (Height 1).
One month later, she measures their
heights again (Height 2). Which flower
grew the most? Show your work.
Flower
1
2
3
4
a. Write an inequality that compares
Sam’s total deposits with Nima’s
total deposits. Who deposited more
money?
Height 1 Height 2
1
6 in.
2
3
7 in.
4
7
5 in.
8
5
6
in.
16
________________________________________
5
8
in.
16
1
8 in.
4
3
9
in.
16
1
7 in.
2
________________________________________
b. Sam and Nima both make
withdrawals from their accounts.
Nima withdraws $37.28. After the
withdrawals, Sam has more money
in his account than Nima does.
What is the largest amount Sam
could have withdrawn for this to be
true? Explain your reasoning.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.7c, 6.NS.7d
SELECTED RESPONSE
9
2
or 1 ? Which
13
3
number has the greater absolute value?
9
2
2
is greater than 1 , but 1 has
13
3
3
the greater absolute value.
2
9
9
1 is greater than - , but 3
13
13
has the greater absolute value.
4. Which is greater,
Select the correct answer.
1. Marlene is about to write a check for
$103.48 to pay for groceries. When she
subtracts the amount of the check from
her account balance, she sees that the
new balance would be $28.80. Rather
than overdraw her checking account,
Marlene asks the cashier to remove
some items. For Marlene to be able to
pay by check without overdrawing her
account, what is the minimum value of
the items the cashier must remove?
9
2
9
is greater than 1 , and 13
3
13
has the greater absolute value.
-
$103.48
2
9
2
is greater than , and 1
3
13
3
has the greater absolute value.
1
$28.80
$28.80
$103.48
Select all correct answers.
5. Which numbers have an absolute value
of 2?
2. Which of the following pairs of numbers
have the same absolute value?
1, 0.1
3
1 1
- ,
2 2
1
2
0, 1
0
4, 40
1
2
3. How do the numbers 3 and 2 compare?
How do their absolute values compare?
3
3 is greater than 2, but 2 has the
greater absolute value.
CONSTRUCTED RESPONSE
6. Identify the pairs of numbers on the
number line that have the same
absolute value.
2 is greater than 3, but 3 has the
greater absolute value.
3 is greater than 2, and 3 has the
greater absolute value.
2 is greater than 3, and 2 has the
greater absolute value.
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
7. Both Vince and Betty use their debit
cards to make purchases. After their
purchases, Vince’s checking account
balance shows a transaction of $25.00,
while Betty’s shows $18.25. Who spent
more money? Justify your answer by
writing an inequality.
10. In a town, Talbot Street is the main
commercial center. The number line
shown represents Talbot Street, where
each unit represents 100 feet.
________________________________________
________________________________________
________________________________________
a. Yvette and Naomi are at the
intersection of Second Street and
Talbot Street. If Yvette goes to the
grocery store and Naomi goes to the
fruit stand, who travels farther from
Second Street? Justify your answer.
8. Find two numbers a and b with the
following properties.
a. a  b, a > b
________________________________________
b. a  b, a < b
________________________________________
________________________________________
________________________________________
c. a  b, a = b
________________________________________
b. Anzelm is at the intersection of First
Street and Talbot Street. How many
feet is Anzelm from Second Street?
Justify your answer.
________________________________________
9. Monica is hiking in California’s Death
Valley. Along her route, she sees a sign
that says “282 feet below sea level.”
Elevation is the height above or below
a fixed point. Positive elevations indicate
heights above the point, and negative
elevations indicate heights below
the point.
________________________________________
________________________________________
________________________________________
11. Suppose a and b are two negative
numbers. If a  b, is it possible that
a > b ? Explain your answer, using a
a. What is the elevation of the sign
relative to sea level? Explain.
________________________________________
number line and examples as needed.
________________________________________
________________________________________
b. How far up or down must Monica
hike from the sign to reach sea
level? Explain.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
14
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.8
SELECTED RESPONSE
CONSTRUCTED RESPONSE
Select the correct answer.
4. Jerry and Meena are riding their bicycles
through the city to meet at the park, as
shown on the coordinate plane. On the
coordinate plane, north is in the positive
y-direction, and 1 unit represents 1 city
block. Jerry starts at the point (2, 5)
and rides north toward the park at the
point (2, 1). Meena starts at east of the
park at the point (5, 1) and rides west
toward the park. How far does each
person travel to reach the park?
1. On a coordinate plane, point A is located
at (5, 3). To get to point B, move 8 units
to the right, 6 units down, and 1 unit to
the left. What are the coordinates of
point B?
(12, 9)
(12, 3)
(2, 3)
(2, 9)
2. What is the distance between point A
at (7, 5) and point B at (2, 5)?
________________________________________
9
________________________________________
5
________________________________________
9
5. Point A is located at (3, 1), point B is
located at (3, 4), and point C is located
at (3, 1) on a coordinate plane.
10
3. North is the positive y-direction on a
coordinate plane, and 1 unit on the plane
represents 1 foot. A soccer ball is kicked
directly east from point (3, 4). The ball
travels a horizontal distance of 23 feet
through the air and rolls an extra 14 feet.
Where does the ball stop?
a. What is the distance between points
A and B?
________________________________________
________________________________________
b. What is the distance between points
A and C?
(34, 4)
(40, 4)
________________________________________
(20, 4)
________________________________________
(11, 4)
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
15
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
7. Jamie’s house is in the center of town, at
point (0, 0). He is doing some errands in
town and stops at the other four labeled
points on the coordinate plane. One unit
on the coordinate plane represents
1 block. He travels 4 blocks to his first
stop. His second stop is 7 blocks from
his first stop. He can only travel on the
sidewalks, which are represented by the
grid lines.
6. Ravel wants to build a fence around his
garden. The shape of his garden is
shown on the coordinate plane, where
each unit represents 1 foot. Use absolute
values to find the length of each section
of fence. How many feet of fence does
Ravel need? Show your work.
________________________________________
________________________________________
a. Where did Jamie go first?
List all possible answers. Justify
your answers.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
b. Where did Jamie go second?
List all possible answers. Justify
your answers.
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6
34
Common Core Assessment Readiness
Name _______________________________________ Date __________________ Class __________________
6.NS.1 Answers
1. C
10. Juan set up the problem incorrectly as
5 3
3
is the dividend
 . In the problem,
7 4
4
5
and
is the divisor. The correct work is
7
2. D
3. C
4. B
5. C
3 5 3
 
4 7 4
6. C
7 21
.

5 20
7. 10, 3, 8
The quotient is
Rubric
1 point for each number
Rubric
2 points for error description;
1 point for corrected work;
1 point for quotient
3
8. There are 4 whole
-foot sections.
16
11 3 11


12 16 12
21
.
20
16 176 44


3
36
9
11. a. Possible answer: Sally requires
several rectangular pieces of
construction paper for an art project.
The pieces need to have an area of
1
square inch. She has several strips
4
of paper left from the last art project
7
that are each
inch wide. How long
16
should each piece be cut to meet her
requirements for this project?
1 7 1 16 4



b.
4 16 4
7 7
c. Possible answer: Sally should cut the
4
strips into lengths of
inch.
7
44
is not a whole number. However,
9
44
8
since
 4 , there are 4 whole
9
9
3
-foot sections, with some left over that
16
Ida cannot use.
Rubric
1 point for answer;
1 point for work;
1 point for explanation
1 5 1 64 64 32
2




6
2 64 2
5 10 5
5
servings
32
2
 6 , she has enough milk
b. Since
5
5
for 6 full days.
9. a.
Rubric
a. 2 points for reasonable situation
b. 1 point
c. 1 point for correct interpretation of
answer according to part a
Rubric
a. 1 point for answer;
1 point for work
b. 1 point for 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 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.2 Answers
1. D
9. a. The remainder, 87, is larger than the
divisor, 62, so 16 is not the maximum
number of times 62 can go into 1079.
b. Maurice found a quotient that is too
small, so increase 16 by 1 in the
expression 16  62  87, subtract 62
from 87, and see if that gives a
remainder of less than 62. If you
multiply 62 by 17, you get 1054, which
is 25 less than the dividend of 1079.
The correct quotient is 17 with a
remainder of 25.
Rubric
1 point for the error;
1 point for the correct answer;
3 points for explaining an appropriate
method that doesn’t involve division
2. B
3. B
4. C
5. B, C, D
6.
13
102 1326
1020
306
306
0
The floors are 13 feet tall.
Rubric
1 point for work; 1 point for answer
10. a. The administrator’s plan will not be as
effective because there will be
342  38  9 students on each team.
This is more than 7 students per team.
b. Divide the number of students by 7.
7. a. 32 apples
b. 48 bags
Rubric
a. 1 point
b. 2 points
48
7 342
8. Yes;
280
62
56
6
6
15 98
90
8
There will be 49 teams. The teams will
not all have the same number of
students because there will be
48 teams of 7 students and 1 team
of 6 students.
Martina has enough money to pay for
6 months of the service. She will have $8
left over.
Rubric
1 point for the answer; 1 point for
explaining the remainder in the context of
the problem; 1 point for explaining the
quotient in the context of the problem
Rubric
a. 2 points
b. 1 point for stating there will be
49 teams; 1 point for stating the teams
do not all have the same number of
students; 1 point for stating why
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
11. a.
9
13 117
9
13 118
9
13 119
117
0
117
1
117
2
b. 120  13 will be 9 with a remainder of
3. In each of the three quotients, the
remainder increased by 1 every time
the dividend increased by 1.
c. The remainder cannot be the same as
the divisor. The correct quotient is 10.
Rubric:
a. 1 point for each quotient;
b. 1 point for the quotient of 120  13;
1 point for explaining the pattern
c. 1 point for explaining the error; 1 point
for correct quotient
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.3 Answers
1. D
Rubric
1 point for error;
2 points for corrected work;
1 point for answer
2. A
3. A
4. B
16. a. The difference in price is $0.38 per
gallon.
b. $0.38  15.25  $5.795  $5.80
5. F
6. H
7. D
Rubric
a. 1 point
b. 1 point for answer; 1 point for work
8. B
9. E
10. A
17. a. Shen earned $69.60 the first week,
$84.00 the second week, $52.80
the third week, and $64.80 the
fourth week.
b. Shen had 0.5  69.60  0.5  52.80 
$61.20 in the bank at the end of
last month.
c. Shen had earned $69.60  $84.00 
$52.80  64.80  $271.20 for the
month. He put $61.20 in the bank, so
he has $271.20  $61.20  $210.00 to
spend at the end of last month.
11. C
12. G
13. a. $67.16
b. $56.47
Rubric
a. 1 point
b. 1 point
14. 0.3125 5.625  3,125 56,250.
18
3,125 56,250
Rubric
a. 0.5 point for each amount
b. 1 point for answer; 1 point for work
c. 1 point for answer; 1 point for work
3,125 0
25,000
25, 000
18. The second steak is the better buy.
0
The first steak costs $7.00 per pound and
the second costs $6.20 per pound.
Mariposa can get eighteen 0.3125-inch
strips from the 5.625-inch wooden board.
Rubric
1 point for answer;
2 points for an explanation that includes
the prices per pound
Rubric
1 point for work;
1 point for answer
15. Jean-Paul did not line the numbers up by
place value when adding. The easiest
way to do this is to line up the decimal
points.
1
1
4. 2 8 7 4
 1. 2 8 6 0
5. 5 7 3 4
4.2874  1.286  5.5734
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
15
Common Core Assessment Readiness
6.NS.4 Answers
1. D
10. a. 1
b. 1
c. The only factors of a prime number
are 1 and itself, so the greatest
common factor of two prime
numbers is always 1.
2. B
3. A
4. B
5. A
6. No, the greatest common factor of
85 and 99 is 1. The only way to rewrite
85  99 using the distributive property
is to write 1(85  99).
Rubric
a. 1 point
b. 1 point
c. 2 points
Rubric
1 point for answer;
2 points for explanation
11. Possible answer:
a. 36  45  3(12  15)
b. 36  45  9(4  5)
c. This cannot be done in more than two
ways because 3 and 9 are the only
common factors of 36 and 45 other
than 1.
7. The LCM of 6 and 9 is 18. Therefore,
Charlie and Dasha will both be traveling
on business trips in 18 months, and so
will need to hire someone then.
Rubric
1 point for answer; 1 point for explanation
Rubric
a. 1 point
b. 1 point
c. 1 point for stating that it cannot be
done in more than two ways; 1 point
for explanation
8. The GCF of 96 and 80 is 16, so Salvatore
can make 16 party favors. Each one will
have 6 pencils and 5 boxes of raisins.
Rubric
1 point for using the GCF to find the
number of party favors;
1 point for number of pencils per party
favor;
1 point for number of boxes of raisins per
party favor
12. a. No, she cannot make 10 platters of
cupcakes; 72 is not divisible by 10.
b. The GCF of 72 and 80 is 8, so she can
make 8 platters. Each platter
will have 9 vanilla cupcakes and
10 chocolate cupcakes.
9. Possible answers:
a. The LCM is the greater of the two
numbers. For example, the LCM of
3 and 9 is 9.
b. The LCM is the product of the two
numbers. For example, the LCM of
5 and 9 is 45.
Rubric
a. 1 point for answer; 1 point for
explanation
b. 1 point for number of platters; 1 point
for number of vanilla and chocolate
cupcakes
Rubric
a. 1 point for answer; 1 point for valid
example
b. 1 point for answer; 1 point for valid
example
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
11
Common Core Assessment Readiness
6.NS.5 Answers
1. C
9. a. Possible answers: climbing to a height
of 50 feet; depositing $50 into a bank
account
b. Possible answers: diving to a depth of
50 feet; withdrawing $50 from a bank
account
2. C
3. B
4. A, D, E
5. a. 30,000
b. 1,200
c. 0
Rubric
a. 1 point for each reasonable answer
b. 1 point for each reasonable answer
Rubric
1 point for each part
6. a.
b.
c.
d.
9
1
0
2
Rubric
1 point for each part
7. A positive number indicates money being
deposited, so it is a credit to the account.
A negative number indicates money
being withdrawn, so it is a debit to the
account. Zero means that money is
neither being deposited nor withdrawn, so
there is no change.
Rubric
1 point for positive number interpretation;
1 point for negative number
interpretation; 2 points for interpretation
of zero
8. a. 73; 0 represents sea level
b. 16.78; 0 represents no deposit or
withdrawal
c. 15; 0 represents no change in
termperature
Rubric
a. 1 point for signed number; 1 point for
interpreting 0
b. 1 point for signed number; 1 point for
interpreting 0
c. 1 point for signed number; 1 point for
interpreting 0
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
12
Common Core Assessment Readiness
6.NS.6a, 6.NS.6b Answers
11. a. 8, 1, and 7
b. 8, 1, and 7
c. The opposite of the opposite of a
number is the same as the original
number.
1. D
2. A
3. D
4. B
5. A
Rubric
a. 0.5 point for each opposite
b. 0.5 point for each opposite
c. 1 point
6. B, C, E
7. The opposite of 5 is 5.
The opposite of 0 is 0.
The opposite of 2 is 2.
The opposite of 4 is 4.
–5
–4
–3
–2
–1
0
1
12. Quadrant I: Possible answer: y  1
Quadrant IV: Possible answer: y  1
2
3
4
æ2 ö
The ordered pair ç , y ÷ cannot be in
è3 ø
Quadrant II or Quadrant III because the
x-coordinate is positive.
5
Rubric
0.5 point for each nonzero point;
1 point for zero and its opposite (they are
the same point)
Rubric
1 point for Quadrant I value;
1 point for Quadrant IV value;
1 point for stating the point cannot be in
Quadrant II or Quadrant III;
1 point for explanation
8. 35 feet
Rubric
1 point for the correct number; 1 point for
including units
9. A reflection across the y-axis would
move the point to Quadrant III. The
x-coordinate would change from positive
to negative.
13. a. The y-coordinate of the point (4, 3)
has the opposite sign of the
y-coordinate of (4, 3).
b. The x-coordinate of the point (4, 3) has
the opposite sign of the x-coordinate of
(4, 3).
c. A reflection across the x- and then the
y-axis would result in a change to the
signs of both coordinates. If
(4, 3) were reflected across the
x-axis and then that point was
reflected across the y-axis, the
resulting point would be (4, 3).
Rubric
1 point for identifying the transformation;
1 point for identifying sign change
10. The students should go to the science
lab. The teachers’ lounge is represented
by 2 on the number line. The opposite of
2 is 2, so the next clue is in the room
represented by 2 on the number line, the
science lab.
Rubric
2 points for answer;
2 points for the explanation
Rubric
a. 1 point for noting the sign change
b. 1 point for noting the sign change
c. 1 point for noting the sign changes;
1 point for the coordinates of the result
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.6c Answers
1. C
8. The coordinates of the library are
(4, 1). The coordinates of the school
are (3, 4). The coordinates of the bike
shop are (4, 3). The coordinates of the
baseball field are (3, 3).
2. B
3. D
4. A
5. B, D, F, G
Rubric
1 point for each ordered pair
6.
9. The points are graphed and labeled
below.
Rubric
1 point for each graphed and labeled
point
Rubric
a. 1 point for graphed and labeled point
b. 1 point for coordinates of point;
1 point for graphed and labeled point
c. 1 point for coordinates of point;
1 point for graphed and labeled point
7. Holden will be at 5 and Marishka will be
at 1. Holden’s side pulls the knot 2 units
in the negative direction, so all the
students move 2 units in the negative
direction, as shown on the number line.
Rubric
1 point for Holden’s position;
1 point for Marishka’s position;
2 points for correct number line and
labels
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.7a Answers
1. A
10. They are both correct. As shown on
the number line, 1 is to the right of 2.2. It
is also correct to say that 2.2 is to the
left of 1.
2. C
3. B
4. D
5. A, B, D, G
6. 10 is to the left of 17 on a number line.
Rubric
1 point for the answer;
1 point for the explanation;
1 point for each graphed number
17 is to the right of 10 on a number line.
Rubric
1 point for each answer
7. x is between 0.001 and 10,000. Since
0.001  x, x is to the right of 0.001 on a
number line. Since x  10,000, x is to the
left of 10,000. Since x is to the right of
0.001 and to the left of 10,000, x is
between the two numbers.
11. a.
b. 5.5 is to the left of 4; 4 is to the
right of 5.5.
c. Possible answer: 6  5.5
d. Possible answer: 4  3
Rubric
1 point for answer; 2 points for
explanation
Rubric
a. 0.5 point for each graphed number
b. 0.5 point for each description
c. 1 point
d. 1 point
1
1
, 4 , 22, and 1,000,000
2
6
18
b. 1,000, - , 0, and 0.2
19
8. a.
Rubric
a. 0.5 point per number
b. 0.5 point per number
9. a. Possible answer: 2.25  2; 2.25 is to
the left of 2 on the number line, so
2.25 is less than 2.
b. Yes; Possible answer: 2  2.25
Rubric
a. 1 point for correct inequality;
1 point for explanation
b. 1 point for correct answer;
1 point for inequality
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.7b Answers
9. Possible answer: 34 F  22 F,
34 F  56 F, 22 F  56 F
1. C
2. A
3. A
Juneau has the highest record low.
4. C
Rubric
1 point for each inequality;
1 point for stating Juneau has the highest
record low
5. B, D
6.
1
2
1
3
cup,
cup,
cup,
cup
4
2
3
4
10. a. Sam deposited $127.15 and Nima
deposited $142.98. An inequality
that compares these total deposits
is $127.15  $142.98 (or
$142.98  $127.15). Nima deposited
more money.
b. Nima withdrew $37.28, so she has a
total of $142.98  $37.28  $105.70.
If Sam has more money in his
account, he must have at least
$105.71. That means the largest
withdrawal he could make is
$127.15  $105.71  $21.44.
The recipe requires a smaller amount of
sugar than the other ingredients.
Rubric
2 points for correctly ordered list
of values;
1 point for stating the recipe requires the
least amount of sugar
7. Possible answer: 1 hour: 425 ft  550 ft;
2 hours: 775 ft  700 ft
Chuck was at a higher elevation
after 2 hours.
Rubric
1 point for each inequality;
1 point for who was at a higher elevation
after 2 hours
Rubric
a. 1 point for the total deposits, 1 point
for a correct inequality
b. 1 point for correct answer; 2 points for
appropriate explanation
13
in.
16
1
Flower 2 change in height:
in.
2
5
Flower 3 change in height: 3
in.
16
3
Flower 4 change in height: 1
in.
16
8. Flower 1 change in height: 1
From least growth to most growth, the
order is Flower 2, Flower 4, Flower 1,
and Flower 3. Flower 3 grew the most in
one month.
Rubric
0.5 point for each height difference;
2 points for ordered list;
0.5 point for answer
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.7c, 6.NS.7d Answers
1. C
10. a. Yvette travels farther from Second
Street. The grocery store is |3|  3
units from 0, and the fruit stand is
|1|  1 unit from 0. Thus, Yvette travels
farther from Second Street to the
grocery store than Naomi travels from
Second Street to the fruit stand.
b. On the number line, the location of
First Street is 4. Since Second
Street is represented by 0 on the
number line, the absolute value of the
location is the distance. First Street is
-4 = 4 units from 0. Since each unit
2. B
3. B
4. D
5. B, F
6. 2.25 and 2.25
3
- and 0.75
4
Rubric
1 point for each pair of numbers
7. Vince spent more money;
-$25.00 > -$18.25 .
represents 100 feet, Anzelm is
4  100 feet  400 feet from Second
Street.
Rubric
1 point for correct answer; 1 point for
inequality
Rubric
a. 1 point for answer; 2 points
for justification
b. 1 point for answer; 2 points
for justification
8. a. Possible answer: a  2, b  1
b. Possible answer: a  2, b  3
c. Possible answer: a  2, b  2
Rubric
1 point for each part
11. If a  b and a and b are both negative, it
is not possible for a > b .
9. a. Since the sign is 282 feet below sea
level, the elevation of the sign relative
to sea level is 282 feet.
b. Since the sign is 282 feet below sea
level and the elevation of sea level is
0 feet, Monica must hike up 282 feet to
reach sea level.
Since a  b, a is to the right of b on a
number line. Since a and b are negative
numbers, both a and b are to the left of
0 on a number line. Since the distance
from a to 0 must be less than the
distance from b to 0 on a number line,
a < b .So a > b is not possible.
Rubric
a. 1 point for answer; 1 point for a
reasonable explanation
b. 1 point for answer; 1 point for a
reasonable explanation
Rubric
1 point for answer; 3 points for a
reasonable explanation
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness
6.NS.8 Answers
1. C
7. a. Jamie went to city hall first. The
distance between Jamie’s house and
city hall is 4 blocks. The distance
between Jamie’s house and the
grocery store is 5 blocks. The distance
between Jamie’s house and the mall is
5 blocks. The distance between
Jamie’s house and the doctor’s office
is 5 blocks. City hall is the only
location that is 4 blocks away.
b. Jamie went to either the mall or the
grocery store second. The distance
between city hall and the mall is
7 blocks. The distance between city
hall and the grocery store is 7 blocks.
The distance between city hall and the
doctor’s office is 9 blocks. The mall
and the grocery store are both
7 blocks away. The mall and the
grocery store are the only possible
second stops.
2. C
3. A
4. Meena travels |5  2|  3 blocks, and
Jerry travels |5  1|  6 blocks.
Rubric
1 point for each distance
5. a. |1  (4)|  5 units
b. |3  3|  6 units
Rubric
a. 1 point
b. 1 point
6. Starting at point (1, 4) and moving
clockwise to find each side length:
The distance between (1, 4) and (4, 4)
is |1  4|  |5|  5. The length of this
section is 5 feet.
The distance between (4, 4) and
(4, 5) is |4  (5)|  |9|  9. The length of
this section is 9 feet.
Rubric
a. 1 point for answer; 1 point for
explanation
b. 1 point for each answer; 1 point for
explanation
The distance between (4, 5) and
(4, 5) is 4  (4)  8  8. The length
of this section is 8 feet.
The distance between (4, 5) and
(4, 1) is |5  (1)|  |4|  4. The
length of this section is 4 feet.
The distance between (4, 1) and
(1, 1) is |4  (1)|  |3|  3. The
length of this section is 3 feet.
The distance between (1, 1) and
(1, 4) is |1  4|  |5|  5. The length of
this section is 5 feet.
The perimeter of the garden is the sum of
these distances,
5  9  8  4  3  5  34 feet.
Ravel needs 34 feet of fence.
Rubric
2 points for the lengths of all the sections;
1 point for reasonable work;
1 point for answer
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
Grade 6 Teacher Guide
14
Common Core Assessment Readiness