Download Grade 6 Math Assessments

N.MR.06.01 Understand division of fractions as the inverse of multiplication, e.g.,
1.
If  
6 3
 is true, then which of these number sentences is also true?
12 4
3 6


4 12
6 3
B.
 
12 4
3 6
C.


4 12
6 3
 
D.
12 4
A.




Answer: B
2.
If
1
2
x 
is true, then which of these number sentences is also true?
4
12
1 2


4 12
2 1
B.
 
12 4
2 1
 
C.
12 4
1 2


D.
4 12
A.




Answer: B
3.
If
1
3
x   is true, then which of these number sentences is also true?
2
8
3 1
 
8 2
1 3
 
B.
2 8
3 1
  
C.
8 2
1 3
 
D.
2 8
A.
Answer: A
Sixth Grade Math Assessment – Revised November 2008
1
4.
4 3
Which of the following has the same value as  ?
5 2
4 3
A. 
5 2
5 3
B. 
4 2
4 2
C. 
5 3
5 2
D. 
4 3
Answer: C
5.
Which of the following has the same value as
4 1
 ?
9 4
4 4

9 1
4 1

B.
9 4
9 4

C.
4 1
9 1
D. 
4 4
A.
Answer: A
N.FL.06.02 Given an applied situation involving dividing fractions, write a mathematical
statement to represent the situation.
1.
Daniel had 2/3 yard of string. He needs pieces that are 1/6 yard long. Which of the
following can be used to find the number of pieces of this length that Daniel can cut from
his string?
2 1

3 6
2 1

B.
3 6
1 2

C.
6 3
2 1

D.
3 6
A.
Answer: A
Sixth Grade Math Assessment – Revised November 2008
2
2.
Mary’s Diner has 9/12 of an apple pie. Which of the following can be used to find the
number of slices Mary can serve if each slice is 1/12 of the whole pie?
9
1

12 12
9
1
B.

12 12
1
9
C.

12 12
9
1
D.

12 12
A.
Answer: D
3.
Jose is filling bottles with perfume. Each bottle holds ½ ounce. He has 12 ounces of
perfume. Which of the following can be used to find how many bottles Jose can fill
exactly?
12 1

1 2
1 1

B.
12 2
1 1
C.

12 2
12 1

D.
1 2
A.
Answer: D
4.
1
of a whole cake remaining. She cut the remaining cake into 3 pieces that
2
were all the same size. Which of the following represents this situation?
Melissa had
1 1

2 3
1
B.  3
2
1 1
C. 
2 3
1
D.  3
2
A.
Answer: D
Sixth Grade Math Assessment – Revised November 2008
3
5.
What is 15% of 87?
A.
B.
C.
D.
5.8
13.05
72
1,305
Answer: B
N.MR.06.03 Solve for the unknown in equations such as
1.
What value of m makes the equation true?
3
1 m
4
A. 4
4
B.
3
3
C.
4
1
D.
4
Answer: C
N.FL.06.04 Multiply and divide any two fractions, including mixed numbers, fluently.
1.
Bill buys 5 ¾ pounds of meat for hamburgers. Each hamburger takes ¼ pound of meat. If
Bill uses all of the meat, how many hamburgers can he make?
A.
B.
C.
D.
6
23
60
92
Answer: B
Sixth Grade Math Assessment – Revised November 2008
4
2.
What number goes in the box to make the equation true?
3
3

=
4
2
1
2
9
B.
8
9
C.
4
D. 2
A.
Answer: A
3.
One-half of the students in Jack’s class are girls. One-third of the girls have blue eyes.
What fraction of the students in Jack’s class are blue-eyed girls?
1
6
1
B.
5
1
C.
3
2
D.
3
A.
Answer: A
4.
Divide 7
2
1
3
9
3
1
6
1
B. 4
6
A. 2
2
27
3
D. 21
12
C. 21
Answer: A
Sixth Grade Math Assessment – Revised November 2008
5
5.
Divide
3 7

5 8
21
40
24
B.
35
11
C. 1
24
19
D. 1
21
A.
Answer: B
N.ME.06.05 Order rational numbers and place them on the number line.
1.
What number on the number line is represented by the point P?
A.
5
2
3
4
5
C. 3
10
5
D. 3
12
B. 3
Answer: D
Sixth Grade Math Assessment – Revised November 2008
6
2.
Put each number below in its appropriate place on the number line. Use a dot to represent
its place, and write the number below its dot.
7
3
5
44
3
3
3.5
2.25
2
4
12
12
Answer: The tick marks on the number line divide each unit into twelfths.
7
= 3 + 6 tick marks
2
44
= 3 + 8 tick marks
12
3
3
= 3 + 9 tick marks
4
3
3.5 = 3 + 6 tick marks
5
= 3 + 5 tick marks
12
2.25 = 2 + 3 tick marks
3. Match the numbers below to the correct letter position on the number line.
1.25 _____
1
7
_____
8
1.5 _____
1
1
_____
8
11
_____
8
Answer: C, H, E, B, D
4. Place these numbers in the correct order from smallest to largest.
7
1
1.25
1
8
8
________, ________, ________, ________, ________
1
11
7
Answer: 1 , 1.25,
, 1.5, 1 ,
8
8
8
1.5
1
Sixth Grade Math Assessment – Revised November 2008
7
11
8
5.
Which is a correct graph of the number -5?
Answer: B
N.ME.06.06 Represent rational numbers as fractions or terminating decimals when
possible, and translate between these representations.
1.
Find an equivalent decimal for this fraction. Show your work.
A.
B.
C.
D.
13
4
3.1
3.25
13.4
13.25
Answer: B
2.
Find an equivalent decimal for this fraction. Show your work.
A.
B.
C.
D.
.35
0.6
1.6
3.5
Answer: B
Sixth Grade Math Assessment – Revised November 2008
8
3
5
3.
Find an equivalent decimal for this fraction. Show your work.
A.
B.
C.
D.
11
4
2.75
11.4
2.4
4.11
Answer: A
4.
Which of the following is an equivalent fraction for 3.5?
3
5
35
B.
100
7
C.
2
5
D.
3
A.
Answer: C
5.
Find an equivalent decimal for this fraction. Show your work.
A.
B.
C.
D.
0.78
0.875
1.14
7.8
Answer: B
6.
3
Which of the following is equivalent to ?
8
A.
B.
C.
D.
0.375
0.380
2.667
3.800
Answer: A
Sixth Grade Math Assessment – Revised November 2008
9
7
8
7.
Which decimal number is equivalent to
A.
B.
C.
D.
32
?
1,000
0.003
0.032
0.302
0.320
Answer: B
N.ME.06.07 Understand that a fraction or negative fraction is a quotient of two integers,
e.g., -8/3 is -8 divided by 3.
1.
5 divided by -6 can also be expressed as:
5
6

6
B.
5
6
C.
5
5
D.
6
A.

Answer: A

2.
What does this fraction mean?
A.
B.
C.
D.
7
5
-7 minus 5
-7 plus 5
-7 times 5
-7 divided by 5
Answer: D
Sixth Grade Math Assessment – Revised November 2008
10
3.
What does this fraction mean?
A.
B.
C.
D.
8
3
8 divided into thirds
8 divided by 3
3 divided into eighths
3 divided by 8
Answer: B
4.
Which statement is equivalent to the fraction
A.
B.
C.
D.
7
?
2
-2 divided by 7
-2 divided by -7
-7 divided by 2
-7 divided by -2
Answer: C
N.MR.06.08 Understand integer subtraction as the inverse of integer addition. Understand
integer division as the inverse of integer multiplication.
1.
Which is equivalent to  8 
A.
B.
C.
D.
 4

-12
-4
4
12
Answer: B
2.
Which of the following is equivalent to 9 - 10?
A.
B.
C.
D.
-9 – 10
9 + -10
10 – 1
9 + 10
Answer: B
Sixth Grade Math Assessment – Revised November 2008
11
N.FL.06.09 Add and multiply integers between -10 and 1-; subtract and divide integers
using the related facts. Use the number line and chip models for addition and subtraction.
1.
Four friends each owe Cathy $8. What is the total debt owed to Cathy?
A.
B.
C.
D.
$4
$ 12
$ 32
$ 48
Answer: C
2.
Which is equivalent to -8(-4)?
A.
B.
C.
D.
32
2
-12
-32
Answer: A
N.FL.06.10 Add, subtract, multiply and divide positive rational numbers fluently.
1.
Mr. and Mrs. Plott and their 4 children share cell phone minutes. Mr. and Mrs. Plott
together use ½ of the minutes, and the rest are used equally among the 4 children. What
fraction of the minutes does each child use?
1
A.
12
1
B.
8
1
C.
4
3
D.
2
Answer: B
Sixth Grade Math Assessment – Revised November 2008
12
2.
Rick spends ¾ of his money buying 2 gifts. If Rick spends an equal amount on each gift,
what fraction of his money does he spend on each gift?
1
8
1
B.
4
3
C.
8
1
D.
2
A.
Answer: C
3.
Ray walked ¼ of the way around a track. The then ran 3/8 of the way around the track.
Over what fraction of the track did Ray travel?
1
8
3
B.
32
4
C.
12
5
D.
8
A.
Answer: D
4.
Divide 6÷
1
4
2
3
1
B. 1
2
1
C. 6
4
D. 24
A.
Answer: D
Sixth Grade Math Assessment – Revised November 2008
13
N.ME.06.11 Find equivalent ratios by scaling up or scaling down.
1.
Your class photo is 2 inches by 3 inches. Your mother wants to make each side 3 times
larger. What are the new dimensions?
A.
B.
C.
D.
3 inches by 3 inches
4 inches by 6 inches
5 inches by 6 inches
6 inches by 9 inches
Answer: D
2.
You have a photograph with dimensions of 8 inches by 12 inches. You would like to
reduce the length of each side to 1/4 of its original size. Which of the following are the
correct new dimensions?
A.
B.
C.
D.
2 inches by 3 inches
2 inches by 4 inches
3 inches by 5 inches
4 inches by 6 inches
Answer: A
3.
Which of the following is equivalent to
4
?
12
1
4
8
B.
24
8
C.
16
2
D.
3
A.
Answer: B
4.
Which of the following is equivalent to the ratio?
A.
B.
C.
D.
10:15
10:5
3:2
2:3
Answer: C
Sixth Grade Math Assessment – Revised November 2008
14
15:10
5.
Lisa saves $2 of every $5 she earns. Lisa earned $55 last week. How much should Lisa
have saved from her earnings last week?
A.
B.
C.
D.
$11
$20
$22
$33
Answer: C
6.
Esther’s car used 2 gallons of gasoline during a 54-mile trip. Which of the following is an
equivalent ratio of gallons to miles?
A.
B.
C.
D.
4 gallons during a 27-mile trip
8 gallons during a 216-mile trip
16 gallons during a 68-mile trip
32 gallons during a 136-mile trip
Answer: B
7.
The ratio of red flowers to blue flowers in Julie’s garden is 3:2. Which ratio is equivalent
to 3:2?
A.
B.
C.
D.
24:8
24:12
24:16
24:20
Answer: C
N.FL.06.12 Calculate part of a number given the percentage and the number.
1.
What is 20% of 225?
A.
B.
C.
D.
11.25
22.5
41.1
45.0
Answer: D
Sixth Grade Math Assessment – Revised November 2008
15
2.
What is 12% of 90?
A.
B.
C.
D.
9.8
10.8
27.0
108
Answer: B
3.
What is 150% of 16?
A.
B.
C.
D.
24,000
2400
24
8
Answer: C
4.
What is 45% of 800?
A.
B.
C.
D.
36
177
360
450
Answer: C
N.MR.06.13 Solve word problems involving percentages in such contexts as sales taxes and
tips, and involving positive rational numbers.
1.
Kate saved 2% of the 8900 dollars she earned. How much did she save?
A.
B.
C.
D.
$178.00
$203.00
$300.00
$187.00
Answer: A
Sixth Grade Math Assessment – Revised November 2008
16
2.
Mary went to the store with $5.00. She bought birthday cards for $2.50 and an orange soda
for $.50. She was required to pay an 8% sales tax on the total purchase. How much money
does she have left?
A.
B.
C.
D.
$1.56
$1.76
$2.54
$3.24
Answer: B
3.
Mike went to the store and bought a shirt for $19.99, a pair of jeans for $24.99, and a pair
of shoes for $49.99. If he paid a 6% sales tax on the total purchase, how much did he
spend at the store?
A.
B.
C.
D.
$102.42
$104.44
$100.67
$137.88
Answer: C
4.
The total cost, including tax, for David’s lunch was $6.35. He left a tip, which was 20% of
the total cost of his lunch. What was the amount of the tip David left?
A.
B.
C.
D.
$1.17
$1.20
$1.23
$1.27
Answer: D
5.
Amy’s allowance is being increased by 15% next year. If she currently gets $12 per week,
how much will she get for an allowance next year?
A.
B.
C.
D.
$13.80 per week
$15.00 per week
$18.00 per week
$27.00 per week
Answer: A
Sixth Grade Math Assessment – Revised November 2008
17
6.
Fritz has a total of 1,240 stamps in his stamp collection. Only 20% of his collection is from
foreign countries; the rest is from the United States. Which number sentence can be used to
find the number of United States stamps in Fritz’s collection?
A.
B.
C.
D.
1,240 x 0.2 = 248
1,240 - 1,240 x 0.2 = 992
1,240 + 1,240 x 0.2 = 1,488
1,240 x 20 - 1,240 = 23,560
Answer: B
7.
The following table shows recommended values of some food components in a healthy
diet. This data is based on adults and children over the age of 4 consuming 2,000 calories
per day.
If one gram of fat contains close to 9 calories,
which is closest to the percent of daily calories
that should come from fat?
A.
B.
C.
D.
9%
14%
29%
33%
Answer: C
N.FL.06.14 For applied situations, estimate the answers to calculations involving
operations with rational numbers.
1.
Emily wants to cut a string into 4 pieces of equal length. The string is 13 inches long.
Which of the following is the best estimate of how long each piece will be?
A.
B.
C.
D.
3 inches
4 inches
9 inches
17 inches
Answer: A
Sixth Grade Math Assessment – Revised November 2008
18
2.
A car is traveling at the rate of 60 miles per hour. Which of the following is closest to how
long it will take the car to travel 178 miles?
A.
B.
C.
D.
2 hours
2 ½ hours
3 hours
3 ½ hours
Answer: C
3.
Mr. Ellis’s dinner bill was $26.65. He gave the waiter an additional 15% of the bill for a
tip. Which of the following is closest to the amount he gave the waiter for the tip?
A.
B.
C.
D.
$3.00
$4.00
$5.00
$6.00
Answer: B
4.
2
cup of sugar for each batch.
3
Which is closest to the total number of cups of sugar that Gwen will need?
Gwen is going to make two batches of cookies. She needs
1
2
1
B. 1
2
1
C. 2
2
D. 3
A.
Answer: B
Sixth Grade Math Assessment – Revised November 2008
19
5.
1
gallons of gasoline. At this rate, which of the
4
1
following is closest to the total number of miles the car can travel on 12 gallons of
2
gasoline?
A certain car can travel 25 miles on 2
A.
B.
C.
D.
50
150
250
300
Answer: B
N.FL.06.15 Solve applied problems that use the four operations with appropriate decimal
numbers.
1.
Donna has $2.50. She buys 5 pencils for $0.15 each and one notepad for $1.75, tax
included. How much money does she have left?
A.
B.
C.
D.
$0.00
$0.60
$1.75
$2.50
Answer: A
2.
A group of 5 friends split the cost of 2 pizzas. Each pizza cost $11.00, tax included. How
much did each friend pay?
A.
B.
C.
D.
$2.20
$2.75
$4.40
$5.50
Answer: C
3.
The Good ‘N’ Clean Company sells laundry detergent in four different sized bottles. The
sizes and prices are shown in the table below.
Which size costs the least per fluid ounces?
A.
B.
C.
D.
Small
Medium
Large
Super
Answer: B
Sixth Grade Math Assessment – Revised November 2008
20
4.
In the city of Marquette, it rained 4.28 inches in September and 8.9 inches in October.
What was the total amount of rain for September and October in Marquette?
A.
B.
C.
D.
5.17 inches
12.00 inches
13.18 inches
38.09 inches
Answer: C
N.ME.06.16 Understand and use integer exponents, excluding powers of negative numbers;
express numbers in scientific notation.
1.
What is -56.1 written in scientific notation?
A.
B.
C.
D.
-5.61 × 10 1
-561 × 10 1
-561 × 10 2
-5.61 × 10 3
Answer: A
2.
What is 148 written in scientific notation?
A.
B.
C.
D.
1.48 x 10¹
1.48 x 10²
14.8 x 10³
148 x 10¹
Answer: B
3.
Which of the following represents 3.2 x 10 3 in standard form?
A.
B.
C.
D.
320
3,200
32,000
320,000
Answer: B
Sixth Grade Math Assessment – Revised November 2008
21
4.
Which shows 17,600,000 written in scientific notation?
A. 176 x 10 5
B. 17.6 x 10 6
C. 1.76 x 10 7
D. 0,176 x 10 8
Answer: B
N.ME.06.17 Locate negative rational numbers (including integers) on the number line;
know that numbers and their negatives add to 0, and are on opposite sides and at equal
distance from 0 on a number line.
1.
Which of the below are a pair of integers that are 13 units from zero on the number line?
A.
B.
C.
D.
9 and -9
13 and -13
4 and -4
11 and -11
Answer: B
2.
Which represents the absolute value of -17?
A.
B.
C.
D.
17
6
8.3
-2
Answer: A
3.
Which best represents the location of point Q?
1
3
1
B.
4
C. 3
D. -4
A.
Answer: C
Sixth Grade Math Assessment – Revised November 2008
22
4.
Which point appears to be located at
A.
B.
C.
D.
15
on the number line below?
4
A
B
C
D
Answer: B
5.
What is the value of -3.21 + 3.21?
A.
B.
C.
D.
-6.42
0
3.21
6.24
Answer: B
6.
Which point appears to be at -4.1 on the number line?
A.
B.
C.
D.
Point A
Point B
Point C
Point D
Answer: C
7.
Which two points on the number line appear to have values that have a sum of zero?
A.
B.
C.
D.
Point L and Point P
Point N and Point Q
Point N and Point S
Point P and Point Q
Answer: B
Sixth Grade Math Assessment – Revised November 2008
23
N.ME.06.18 Understand that rational numbers are quotients of integers (non zero
denominators), e.g., a rational number is either a fraction or a negative fraction.
1.
Which of the following is NOT a rational number?
A. 3
B. -27
C. 0.64
5
D.
4
Answer: A
N.ME.06.19 Understand that 0 is an integer that is neither negative nor positive.
1.
Which of the following is an integer?
A. 0
1
B.
3
5
6
D. 0.25
C. 2
Answer: A
2.
Which of the following sets contains a negative integer?
1
, 1.5, 2}
2
B. {-1, 0, 2, 3}
1
1
C. {
, 0, , 0.99}
4
3
D. {-1.9, -1.5, -0.99, 0}
A. {0,
Answer: B
Sixth Grade Math Assessment – Revised November 2008
24
N.ME.06.20 Know that the absolute value of a number is the value of the number ignoring
the sign; or is the distance of the number from 0.
1.
In which of the following pairs do both numbers have the same absolute value?
A. 3.2 and 3.2 2
B. 3.2 and -3.2
C. 3.2 and l
1
D. 3.2 and
3 .2
Answer: B
A.PA.06.01 Solve applied problems involving rates, including speed, e.g., if a car is going 50
mph, how far will it go in 3 ½ hours?
1.
If you biked 120 miles in 30 days, how many miles per day did you bike?
A.
B.
C.
D.
4
15
30
90
Answer: A
2.
If you save $20 per month, how much will you save in 3 years?
A.
B.
C.
D.
$60
$120
$240
$720
Answer: D
3.
If you ride a bike 40 miles in 5 hours, how fast were you biking?
A.
B.
C.
D.
1/8 mile per hour
8 miles per hour
45 miles per hour
200 miles per hour
Answer: B
Sixth Grade Math Assessment – Revised November 2008
25
4.
If you eat 300 hot dogs in 60 days, how many hot dogs per day did you eat, on average?
A.
B.
C.
D.
3
5
18
50
Answer: B
5.
If you ride a bike 40 miles in 5 hours, how fast were you biking?
A.
B.
C.
D.
1/8 mile per hour
8 miles per hour
45 miles per hour
200 miles per hour
Answer: B
6.
If Sam rode his bike at an average rate of 15 miles per hour, what is the total distance he
1
would travel in 2 hours?
2
A. 6 miles
B. 17 miles
1
C. 30 miles
2
1
D. 37 miles
2
Answer: D
7.
A train travels 66 miles in 60 minutes. At this constant rate, how long does it take for the
train to travel 22 miles?
A.
B.
C.
D.
3 minutes
20 minutes
22 minutes
88 minutes
Answer: B
Sixth Grade Math Assessment – Revised November 2008
26
8.
Jan washes 24 dishes in 30 minutes. What is this rate in dishes per minute?
A.
B.
C.
D.
0.8 dishes per minute
1.25 dishes per minute
6 dishes per minute
48 dishes per minute
Answer: A
9.
Yolanda and Heidi each take a walk. Yolanda walks at a speed of 4 miles per hour. Heidi
1
walks at a speed of 2 miles per hour. The girls each walk for 1 hours. How many miles
2
further does Yolanda walk than Heidi?
1
A. 1 miles
2
B. 2 miles
C. 3 miles
1
D. 3 miles
2
Answer: C
A.RP.06.02 Plot ordered pairs of integers and use ordered pairs of integers to identify
points in all four quadrants of the coordinate plane.
1.
What are the coordinates of the point shown below?
A.
B.
C.
D.
(2, 3)
(2, -3)
(-2, 3)
(-2,-3)
Answer: C
2.
Which of these ordered pairs can be found in the first quadrant?
A.
B.
C.
D.
(-2, 3)
(2, 3)
(2, -3)
(-2, -3)
Answer: B
Sixth Grade Math Assessment – Revised November 2008
27
3.
Which of the following ordered pairs can be found in the fourth quadrant?
A.
B.
C.
D.
(2, 1)
(-2, -1)
(2, -1)
(-2, 1)
Answer: C
4.
Which point appears to be located at (-2, 3)?
A.
B.
C.
D.
F
G
H
J
Answer: A
5.
Rectangle ABCD is graphed on the coordinate
plane below.
Which ordered pair best represents the
location of point D?
A.
B.
C.
D.
(2, -3)
(-3, 2)
(2, -3)
(3, -2)
Answer: A
Sixth Grade Math Assessment – Revised November 2008
28
6.
Look at the coordinate grid below. What appear to be the coordinates of point W?
A.
B.
C.
D.
(3, 5)
(5, 3)
(4, 6)
(3, 6)
Answer: A
7.
Look at the coordinate grid below. Which point
appears to have coordinates (7, 6)?
A.
B.
C.
D.
A
B
C
D
Answer: C
8.
What appear to be the coordinates of the point plotted below?
A.
B.
C.
D.
(5, 4)
(5, -4)
(4, 5)
(-4, 5)
Answer: B
Sixth Grade Math Assessment – Revised November 2008
29
A.FO.06.03 Use letters, with units, to represent quantities in a variety of contexts, e.g., y
lbs., k minutes, x cookies.
1.
Juan found he weighs x pounds more now than he did last month. If Juan weighed
105 pounds last month, which of the following represents the amount he weighs now?
A.
B.
C.
D.
105x pounds
105 ÷ x pounds
105 - x pounds
105 + x pounds
Answer: D
2.
Mary has 3 times as many baseball cards as Tom. If t represents the number of cards that
Tom has, which of the following best represents the number of cards Mary has?
A. t + 3
B. t - 3
C. 3t
t
D.
3
Answer: C
3.
Henry is h years old. Frank is 15 years older than 2 times Henry’s age. Which of the
following can be used to find Frank’s age?
A.
B.
C.
D.
2h
h + 2(15)
2h + 15
2h - 15
Answer: C
4.
Allen and Tim are counting pennies. Together the boys have a total of 50 pennies. If a
represents the number of pennies Allen has, which of the following represents the number
of pennies that Tim has?
A.
B.
C.
D.
a + 50
a - 50
50a
50 - a
Answer: D
Sixth Grade Math Assessment – Revised November 2008
30
A.FO.06.04 Distinguish between an algebraic expression and an equation.
1.
Which of the following is an algebraic equation?
A.
B.
C.
D.
2.
m÷3
m=3
m+3
m•3
Which of the following is an algebraic expression?
A.
B.
C.
D.
y=2
3x + 2y
y = 3x + 2
y+2=x–5
Answer: B
A.FO.06.05 Use standard conventions for writing algebraic expressions, e.g., 2x + 1 means
“two times x, plus 1” and 2(x + 1) means “two times the quantity (x + 1).”
1.
Which of the following represents the phrase below?
ten less than two times x
A.
B.
C.
D.
2x - 10
10 - 2x
2(x - 10)
2(10 - x)
Answer: A
2.
Which algebraic expression represents “three times the quantity of x – 5”?
A.
B.
C.
D.
3x – 5
3x – 5x
3(x – 5)
3(x – 5x)
Answer: C
Sixth Grade Math Assessment – Revised November 2008
31
A.FO.06.06 Represent information given in words using algebraic expressions and
equations
1.
Which of the following represents the statement below?
the quotient of a number, y, and 7
A. y + 7
B. y - 7
C. 7y
y
D.
7
Answer: D
2.
In a classroom of 35 students, 23 are girls. Which of the following can be used to determine
b, the number of students in the classroom that are boys?
23
 35
b
B. 23b = 35
C. 23 – b = 35
D. 23 + b = 35
A.
Answer: D
3.
Kelly has two brothers who weigh a total of 191 pounds. In the number sentence
x + y = 191, what does y represent?
A.
B.
C.
D.
Kelly’s weight
the weight of one of Kelly’s brothers
the total weight of Kelly’s two brothers
the total weight of all three siblings
Answer: B
4.
When Halley gets up in the morning, the house is 8 degrees colder than it was the night
before. Which of the following can be used to find the temperature in the morning when the
temperature the night before is n?
A.
B.
C.
D.
n+8
n-8
8n
8-n
Answer: B
Sixth Grade Math Assessment – Revised November 2008
32
5.
Which statement can be correctly represented by the number sentence below?
9 x (79 - 47) = ?
A.
B.
C.
D.
The number of pages to be copied is 9 times 79 plus 47.
The total cost is 9 times the sum of 79 and 47.
The number of buttons needed. was 9 times 79 minus 47.
The amount of money saved was 9 times the difference of 79 and 47.
Answer: D
A.FO.06.07 Simplify expressions of the first degree by combining like terms, and evaluate
using specific values.
1.
What is the value of 2r + 3s when r = -2 and s = 6?
A.
B.
C.
D.
6
9
14
22
Answer: C
A.RP.06.08 Understand that relationships between quantities can be suggested by graphs
and tables.
1.
Select the equation that correctly expresses the relationship shown in the table between
what a person is paid and the number of hours she works.
A.
B.
C.
D.
5.35 x H
H + 5.35
5.35 ÷ H
5.35
Answer: A
Sixth Grade Math Assessment – Revised November 2008
33
2.
Lynn plays on the basketball team. The graph below shows how
many points Lynn scores in each of the first games of the season.
Which statement best describes the relationship between the number
of points scored by Lynn in each game and in the game before?
A. Lynn scores twice as many points each game as the
game before.
B. Lynn scores two more points each game than she did
the game before.
C. Lynn scores three more points each game than she did
the game before.
D. Lynn scores three fewer points each game than she did
the game before.
Answer: C
A.PA.06.09 Solve problems involving linear functions whose input value are integers; write
the equation; graph the resulting ordered pairs of integers, e.g., given c chairs, the “leg
function” is 4c; if you have 5 chairs, how many legs?; if how many chairs?
1.
It costs $8 to go to a movie, for the ticket and snacks. Your school is going to a movie one
afternoon. Which of the following equations shows how to find the cost of the movie for a
class of students?
Let c = total cost for the class
Let n = number of students in a class
A.
B.
C.
D.
c=n+8
c = 8n (this is the same as c = 8 x n)
c=n÷8
c = 80 – n
Answer: B
Sixth Grade Math Assessment – Revised November 2008
34
2.
The graph below shows how much money a
person will make at $6 per hour. Use the graph to
find how much money you would make if you
worked 35 hours. Circle the point on the graph
that gives the answer, and then select it from the
list below.
A.
B.
C.
D.
$35
$41
$160
$210
Answer: D
3.
Every car has 4 tires. Which graph will let you find how many tires there are on any
number of cars? The scale on each axis is 1 (every square represents 1 car or 1 tire).
A.
B.
C.
D.
A
B
C
D
Answer: C
Sixth Grade Math Assessment – Revised November 2008
35
4.
Which of the following appears to be a graph of y = 2x?
Answer: A
A.RP.06.10 Represent simple relationships between quantities using verbal descriptions,
formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square,
distance-time graphs, and conversions such as feet to inches.
1.
Which table shows the correct relationship between feet and inches?
Answer: C
Sixth Grade Math Assessment – Revised November 2008
36
2.
The following graph shows how far a car can go depending on the amount of gasoline used.
Which of the following best describes this graph?
A.
B.
C.
D.
It constantly increases.
It constantly decreases.
It increases and decreases.
It neither increases nor decreases.
Answer: A
3.
Sam has a square game board that has a perimeter of 64 inches. What is the length of one
side of the game board?
A.
B.
C.
D.
8 inches
16 inches
32 inches
256 inches
Answer: B
A.FO.06.11 Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 =
10, to particular contexts and solve.
1.
What value of p makes the following true?
A.
B.
C.
D.
-4p = 16
-20
-12
-4
4
Answer: C
2.
Barry and Shin are playing a board game. Barry has 30 points. The number of points that
Shin has, s, can be represented by the following: S + 5 = 30
How many points does Shin have?
A.
B.
C.
D.
6 points
25 points
35 points
150 points
Answer: B
Sixth Grade Math Assessment – Revised November 2008
37
3.
Hector and Tony both collect baseball cards. Hector has 28 cards. The number of cards
owned by Tony, t can be represented by the following: 2t = 28
How many cards does Tony own?
A.
B.
C.
D.
14 cards
26 cards
30 cards
56 cards
Answer: A
4.
On Saturday, Mark ran 3 times the distance that he ran on Wednesday. On Saturday he ran
12 kilometers. The distance Mark ran on Wednesday, w, can be represented by the
following: 12 = 3w
How many kilometers did Mark run on Wednesday?
A.
B.
C.
D.
4 kilometers
9 kilometers
15 kilometers
36 kilometers
Answer: A
A.FO.06.12 Understand that adding or subtracting the same number to both sides of an
equation creates a new equation that has the same solution.
1.
How should you solve the equation x + 5 = 25?
A.
B.
C.
D.
Add 5 to both sides of the equation to get x + 10 = 25.
Subtract 5 from both sides of the equation to get x - 5 = 20.
Multiply both sides of the equation by 5 to get x + 25 = 125.
Subtract 5 from both sides of the equation to get x = 20.
Answer: D
2.
What can you do mathematically to change the equation x + 5 = 25 into x = 20?
A.
B.
C.
D.
Add 5 to both sides of the equation.
Subtract 5 from both sides of the equation.
Let x = 5.
Graph the equation on the number line.
Answer: B
Sixth Grade Math Assessment – Revised November 2008
38
3.
Which value for x correctly solves this number sentence? x – 5 = -3
A.
B.
C.
D.
x = -8
x = -2
x=2
x=8
Answer: C
4.
Which is equivalent to x + 11 = 4?
A.
B.
C.
D.
x + 11 – 11 = 4 - l1
x -11 = 4 - 11
x + 11 – 4 = 4 + 4
x + l1 = 4 + 11
Answer: A
5.
Which number can be put in the blank below to make the statement true?
b - 7 = 18
b - 7 + ____ = 18 + 7
b = 25
A.
B.
C.
D.
-18
-7
7
18
Answer: C
6.
Which value or x correctly solves this number sentence?
A.
B.
C.
D.
x = -10
x = -1
x=1
x = 19
Answer: B
Sixth Grade Math Assessment – Revised November 2008
39
x + 10 = 9
7.
Which number sentence has the same solution as x + 6 = 3?
A.
B.
C.
D.
x = -3
x=3
x=6
x=9
Answer: A
A.FO.06.13 Understand that multiplying or dividing both sides of an equation by the same
non-zero number creates a new equation that has the same solutions.
1.
Which single step will correctly solve for p in the statement below?
4p = 12
A.
B.
C.
D.
Add 4 to both sides.
Subtract 4 from both sides.
Multiply both sides by 4.
Divide both sides by 4.
Answer: D
2.
Which number sentence has the same solution as
x
= 5?
2
5
2
B. x = 5
C. x = 10
D. x = 20
A. x =
Answer: C
3.
Which value for y correctly solves this number sentence?
A.
B.
C.
D.
y=5
y = 12
y = 18
y = 45
Answer: D
Sixth Grade Math Assessment – Revised November 2008
40
y
 15
3
4.
Which value for y correctly solves this number sentence? 2y = 21
2
21
21
B. y =
2
C. y = 19
D. y = 23
A. y =
Answer: B
A.FO.06.14 Solve equations of the form ax + b = c, e.g., 3x + 8 = 15 by hand for positive
integer coefficients less than 20, use calculators otherwise, and interpret the results.
1.
Solve this equation: 2x + 8 = 14
Then explain below how you got your answer.
A.
B.
C.
D.
x=3
x=6
x = 11
x = 16
Answer: A
2.
Phil added 10 to a number and multiplied the sum by 2. The new number was 30. What
was the original number?
A.
B.
C.
D.
5
10
15
20
Answer: A
3.
What value of x makes the statement below true?
2x + 3 = 33
A.
B.
C.
D.
15
18
28
30
Answer: A
Sixth Grade Math Assessment – Revised November 2008
41
M.UN.06.01 Convert between basic units of measurement within a single measurement
system, e.g., square inch to square feet.
1.
A rod is 2 m long. How long is it in mm?
A.
B.
C.
D.
20 mm
200 mm
2,000 mm
20,000 mm
Answer: C
2.
A rectangle has sides of 2 feet and 3 feet. Its area is 6 square feet. What is the area of this
rectangle in square inches?
A.
B.
C.
D.
60 square inches
120 square inches
144 square inches
864 square inches
Answer: D
3.
Sarah would like to fence in her back yard. She needs 180 feet of fencing to do this. How
many yards of fencing would she need?
A.
B.
C.
D.
3 yards
15 yards
60 yards
540 yards
Answer: C
4.
John has ordered 10 square yards of carpet for his living room. How many square feet of
carpet is this?
A.
B.
C.
D.
90 sq. ft.
100 sq. ft.
144 sq. ft.
900 sq. ft.
Answer: D
Sixth Grade Math Assessment – Revised November 2008
42
5.
Which of the following is equivalent to 2 meters?
A
B
C
D
2,000 mm
200 mm
20mm
0.2mm
Answer: A
6.
What is the total number of square inches in 5 square feet?
A.
B.
C.
D.
25
60
300
720
Answer: D
7.
John needs 270 square feet of carpet. The carpet is sold by the square yard. How many
square yards of carpet does John need? (I square yard = 9 square feet)
A.
B.
C.
D.
15 square yards
18 square yards
30 square yards
90 square yards
Answer: C
8.
A slice of bread weighs one ounce. A loaf of bread contains 32 slices. Not counting the
wrapper, how much does the loaf of bread weigh, in pounds? (1 pound = 16 ounces)
A.
B.
C.
D.
1.0 pound
2.0 pounds
3.2 pounds
4.0 pounds
Answer: B
Sixth Grade Math Assessment – Revised November 2008
43
9.
A recipe calls for a pint of milk. Harold is making 4 times the amount called for by the
recipe. How much milk, in quarts, does Harold need? (1 quart = 2 pints)
1
quart
2
B. 1 quart
C. 2 quarts
D. 4 quarts
A.
Answer: C
M.PS.06.02 Draw patterns (of faces) for a cube and rectangular prism that, when cut, will
cover the solid exactly (nets).
1.
Which is a net of a cube?
Answer: B
Sixth Grade Math Assessment – Revised November 2008
44
2.
Which net, when folded, will cover all of the faces of the cube?
Answer: B
M.TE.06.03 Compute the volume and surface area of cubes and rectangular prisms given
the lengths of their sides, using formulas.
1.
Find the surface area of this rectangular prism. The surface area is how many square inches
of wrapping paper would be needed to cover all of the sides without overlapping.
A.
B.
C.
D.
12 square inches
16 square inches
24 square inches
52 square inches
Answer: D
2.
Find the volume of this rectangular prism with sides of 2 inches, 4 inches and 3 inches.
A.
B.
C.
D.
9 cubic inches
18 cubic inches
24 cubic inches
27 cubic inches
Answer: C
Sixth Grade Math Assessment – Revised November 2008
45
3.
What is the volume of the rectangular prism below?
A.
B.
C.
D.
21 cm3
63 cm3
240 cm3
256 cm3
Answer: C
G.GS.06.01 Understand and apply basic properties of lines, angles, and triangles.
1.
In the parallelogram shown below, the diagonals intersect each other and make four angles,
a, b, c and d. Name one pair of vertical angles:
A.
B.
C.
D.
angle a and angle b
angle a and angle c
anglea and angle d
there are no vertical angles in this drawing
Answer: B
2.
In the parallelogran shown below, which of the following is true?
A. measure of angle a = measure of angle b
B. measure of angle a = measure of angle c
+ measure of angle d
C. measure of angle a = measure of angle c
D. measure of angle c + measure of angle d
= 90o
Answer: C
3.
In the parallelogran shown below, name two angles that are supplementary.
A.
B.
C.
D.
angle a and angle b
angle a and angle c
angle b and angle d
angle c and angle a
Answer: A
Sixth Grade Math Assessment – Revised November 2008
46
4.
If these two horizontal lines are parallel, what is true about angles p and r?
A.
B.
C.
D.
measure of angle p + measure of angle r = 90o
measure of angle p + measure of angle r = 180o
measure of angle p > measure of angle r
measure of angle p = measure of angle r
Answer: D
5.
If these two horizontal lines are parallel, name two angles that are supplementary.
A.
B.
C.
D.
angle p and angle r
angle p and angle s
angle q and angle s
none of the angles listed here are supplementary
Answer: B
6.
Joan was making a box as a gift. She wanted the box to be a perfect rectangle. To see if the
opposite sides were parallel, she drew one of the diagonals on the top of the box. The
diagonal made several angles, as shown.
Which angles have to be equal in order for the opposite
sides to be parallel?
A.
B.
C.
D.
<a and <b
<a and <c
<a and <d
<a and <e
Answer C
7.
In the rectangle shown below, identify two angles that are complimentary.
A.
B.
C.
D.
<a and <b
<b and <c
<c and <e
<d and <e
Answer: A
Sixth Grade Math Assessment – Revised November 2008
47
8.
Roads L and M are parallel. On a map, Road L passes through (2, 1) and (3, 2). Road M
passes through point P (2, 2).
Through which other point does Road M also pass?
A.
B.
C.
D.
(1, 3)
(2, 3)
(3, 3)
(4, 3)
Answer: C
G.GS.06.02 Understand that for polygons, congruence means corresponding sides and
angles have equal measures.
1.
These two rhombuses are congruent. Therefore the measure of angle x is ________.
A.
B.
C.
D.
30o
60o
115o
120o
Answer: B
2.
These two rhombuses are congruent. Therefore the measure of angle x is ________.
Explain how you got your answer.
A.
B.
C.
D.
30o
60o
115o
120o
Answer: 60o. Since these rhombuses are congruent, all corresponding angles are equal. Angle x
corresponds to the 60o angle in the first figure.
Sixth Grade Math Assessment – Revised November 2008
48
3.
Triangle LNM is congruent to triangle PQR, as shown below.
What side of triangle PQR corresponds to LN in triangle LNM?
A. PQ
B. QR
C. RP
D. NM
Answer: A
4.
In the figure below ΔFGH is similar to ΔJKL. Which angle must be congruent to
angle  G?
A.
B.
C.
D.
F
L
J
K
Answer: D
5.
If three angles of a triangle are congruent to the three angles of another triangle, which of
the following is true?
A. The triangles cannot be congruent.
B. The two triangles must be congruent.
C. The two triangles may be congruent, but only if the triangles are right
triangles.
D. The two triangles may be congruent, depending on whether corresponding
sides are equal in length.
Answer: D
Sixth Grade Math Assessment – Revised November 2008
49
6.
Which of the following statements about congruent polygons must be true?
A. If the side of a square is equal in length to the side of another square, the
squares are congruent.
B. lithe length of a rectangle is equal to the length of another rectangle, the
rectangles arc congruent.
C. If the hypotenuse of a right triangle is equal in length to the hypotenuse of
another right triangle, the triangles are congruent.
D. If two sides of a triangle are the same length as the corresponding sides of
another triangle, the triangles are congruent.
Answer: A
G.TR.06.03 Understand the basic rigid motions in the plane (reflections, rotations,
translations), relate these to congruence, and apply them to solve problems.
1.
Which transformation moves rectangle A into
rectangle B?
A. two translations: first down, and then to
the right
B. a rotation around point P
C. a reflection through the line
D. an expansion from quadrant 2 to
quadrant 1
Answer: C
Sixth Grade Math Assessment – Revised November 2008
50
2.
Which of the following appears to show the reflection of the figure below over XZ ?
Answer: A
3.
What transformation occurs when ΔABC becomes
ΔM’B’C?
A.
B.
C.
D.
ΔABC is reflected over the x-axis,
ΔABC is reflected over the y-axis.
ΔMBC is rotated 180° around the origin
ΔM8C is rotated 360° around the origin.
Answer: A
Sixth Grade Math Assessment – Revised November 2008
51
4.
Which object below can be rotated 90 degrees about its center and have its final orientation
appear the same as the original orientation?
Answer: B
5.
Look at the figure below.
Triangle ABC is translated left 2 units.
What are the coordinates of the image of
point C?
A.
B.
C.
D.
(2, 5)
(4, 3)
(4, 7)
(6, 5)
Answer: B
Sixth Grade Math Assessment – Revised November 2008
52
G.TR.06.04 Understand and use simple compositions of basic rigid transformations, e.g., a
translation followed by a reflection.
1.
Part 1: In the figure below, first draw the rotation of the rectangle 90o around point Q.
Part 2: Then draw the translation of the rectangle six units downward. You may ask your
teacher for graph paper for this item.
2.
Where is point B relative to point A?
A. Point B is 5 units from point A.
B. Point B is 7 units from point A.
C. Point B is 4 units to the right and 4 units up relative to
point A.
D. Point B is 4 units to the left and 4 units down relative
to point A.
Answer: C
D.PR.06.01 Express probabilities as fractions, decimals, or percentages between 0 and 1;
know that 0 probability means an event will not occur and that probability 1 means an
event will occur.
1.
A jar holds 4 red marbles and 3 green marbles. What is the probability of selecting a red
marble at random?
1
4
4
B.
7
4
C.
4
4
D.
3
A.
Answer: B
Sixth Grade Math Assessment – Revised November 2008
53
2.
Fourteen out of 20 students in Mrs. Taylor’s class wore red today. What is the probability
that a student selected at random is wearing red?
A.
B.
C.
D.
14%
34%
60%
70%
Answer: D
3.
An apartment complex is offering a raffle with a 1 in 50 probability of winning a car.
Which number represents the probability of wining a car?
A.
B.
C.
D.
0.02
0.15
1.50
50
Answer: A
4.
If a letter in the word MICHIGAN is randomly selected, what is the probability that the
letter selected will be an “I” or an “A”?
2
8
3
B.
8
3
C.
5
5
D.
8
A.
Answer: B
Sixth Grade Math Assessment – Revised November 2008
54
5.
Elizabeth is going to roll a fair six-sided number cube on which each face is labeled with a
different numeral. If the numerals are 1 through 6, what is the probability she will roll a 3
on the first roll?
1
2
1
B.
3
1
C.
5
1
D.
6
A.
Answer: D
D.PR.06.02 Compute probabilities of events from simple experimentations with equally
likely outcomes, e.g., tossing dice, flipping coins, spinning spinners, by listing all
possibilities and finding the fraction that meets given conditions.
1.
What is the probability of randomly selecting 1 blue marble from a bag of 4 blue marbles
and 7 red marbles?
1
4
1
B.
11
4
C.
7
4
D.
11
A.
Answer: D
Sixth Grade Math Assessment – Revised November 2008
55
2.
Anna has a bag of gumballs all the same shape and size. In the bag there are the following:
•
•
•
•
2 green gumballs
3 yellow gumballs
4 orange gumballs
4 brown gumballs
If Anna selects only 1 gumball from the bag without looking, what is the probability that it
will be orange?
1
13
1
B.
4
4
C.
13
4
D.
9
A.
Answer: C
Sixth Grade Math Assessment – Revised November 2008
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