Mathematics
2011 ISAT Grade 6 Sample Book
1
4
One notebook sells for $0.89. Mary
can buy a package of 12 notebooks
for $9.60.
Brian’s calculator display is
587234. In order to change the
8 to a 9, which of the following
could he do?
A
Add 1
B
Add 100
C
Add 10,000
D
Add 100,000
How much money can Mary
save on each notebook if she
buys the package of 12?
XIH110
2
$0.08
$0.09
$0.10
$0.12
A
B
C
D
3349067
5
Tom’s schedule is shown below.
How much total time did he
spend doing these activities?
In the 1988 Olympic Games,
Florence Griffith Joyner of the
United States set an Olympic
record for the women’s
100-meter dash. Her time was
ten and sixty-two hundredths
seconds. How is this time
written as a number?
Tom’s Schedule
Activity
Time
Homework
3
hour
4
1.62 seconds
A
≥B
1
1 hours
4
Television
10.62 seconds
C
100.62 seconds
D
1062.00 seconds
1
hour
2
Dinner
Track Meet
3
Which expression is equivalent
to 7 ! 7 ! 7 ! 7?
7!4
47
74
28
A
B
C
D
37
6
hours
14
A
3
B
3
3 hours
4
1
2 hours
4
C
1
4 hours
2
≥D
3
4 hours
4
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3484192
6
8
What is the value of the
expression shown?
What is the ratio of even
numbers to square numbers in
the set of whole numbers from
1 to 20?
10 ! 16 " 2 • 4
12
42
52
72
A
10:4
C
10:10
A
≥B
C
D
B
4:10
D
3:10
7
3484196
9
Julie has 50 jellybeans in a bag, and
20% of those jellybeans are red.
Which is equivalent to the
expression shown below?
How many of the jellybeans in
Julie’s bag are red?
8 ! (15 " 9)
A
(8 ! 15) " (8 ! 9)
B
(8 " 15) ! (8 " 9)
5
10
20
30
C
(8 ! 15) ! (8 ! 9)
A
≥B
C
D
D
(8 " 15) " (8 " 9)
38
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3528353 3528353.AR1
10
3484200
11
Use your centimeter ruler to help
you answer this question.
3484200_AR1 to AR4
Which rectangle has an area of
24 square units and a perimeter
of 20 units?
Genna drew the rectangle below.
12
A
2
8
B
Which is closest to the length
and width in centimeters of
Genna’s rectangle?
A
5.0 cm by 3.0 cm
B
5.5 cm by 3.5 cm
≥C
5.5 cm by 3.0 cm
D
6.0 cm by 3.5 cm
3
5
C
4
6
≥D
39
4
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3484203
12
3484203_AR1
13
The bar graph below shows the
number of minutes Bruce practiced
piano during each day of the week.
Which is closest to the measure
of ∠XYZ?
Number of
Minutes Practiced
Bruce's Piano Practice
X
Y
Z
20°
90°
130°
A
B
C
45
40
35
30
25
20
15
10
5
0
Sun Mon Tue Wed Thu
160°
≥
Fri
Sat
Day
D
Exactly how many hours did
Bruce practice piano during
these 7 days?
40
A
2 hours
B
2
C
3 hours
D
3
1
hours
2
1
hours
2
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3349080
14
3349080_AR1
3484221
15
Mike has x baseball cards. Tyrone has
3 times as many baseball cards as
Mike. Frank has 20 baseball cards.
Use your centimeter ruler to help
you answer this question.
Liza made the scale drawing
shown below.
Which expression represents
the total number of baseball
cards Mike, Tyrone, and Frank
have all together?
Swing
Tree
≥A
x ! 3x ! 20
B
20 ! 3x " x
C
x ! 3 ! 20
D
20 " 3x ! x
Key: 1 cm represents 5 feet
3484224
16
What is the shortest distance, in
feet, from the tree to the swing?
A
4 feet
B
5 feet
≥
C
20 feet
D
25 feet
What is the value of the
expression below when
x # 6 and y # 2?
8x " y
41
84
46
12
4
A
≥B
C
D
GO ON
Mathematics
3484225
17
2011 ISAT Grade 6 Sample Book
3484225_AR1
3349423
18
Which correctly describes the
rule between x and y as shown
in the table?
Which table of values satisfies
the equation shown below?
y=x+4
x
y
x
y
4
9
0
0
5
11
1
1
6
13
2
2
7
15
3
3
x
y
0
4
1
4
2
4
3
4
x
y
0
4
1
5
2
6
3
7
x
y
0
0
1
4
2
8
3
12
A
y!x"6#1
B
y!x•x#1
C
y!x"x#1
≥D
y!x•2"1
A
B
≥C
D
42
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3349091
19
3349091_AR1
21
The graph below represents a
linear equation.
Which graph best represents the
solution to the inequality
shown?
y
m
#3
2
20
18
16
14
A
12
-1 0 1 2 3 4 5 6 7 8
10
8
B
6
-1 0 1 2 3 4 5 6 7 8
4
2
0
2
4
6
8
C
x
10 12 14 16 18 20
D
Using this graph, which value
best represents the y-coordinate
if the x-coordinate is 8?
4
14
A
B
≥
16
18
C
D
3349097
Philip has 18 video games. Emily has
v video games. Together, Philip and
Emily have a combined total of less
than 30 video games.
Which inequality is best
represented by the graph on the
number line below?
-8 -6
-4 -2
A
x!6
B
x#6
0
2
4
6
≥
C
x"6
D
x$6
-1 0 1 2 3 4 5 6 7 8
22
3529997 3529997_AR1
20
-1 0 1 2 3 4 5 6 7 8
Which inequality could be used
to represent this situation?
8
43
A
v ! 18 " 30
≥B
v # 18 $ 30
C
v ! 18 $ 30
D
v # 18 " 30
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3349428
23
25
y
What value of n makes the
equation below true?
4n ! 220
50
55
A
≥B
5
216
220
C
D
4
3
2
3484229
24
3484229_AR1
What should be the value for x
in the triangle shown?
0
50°
60°
40°
A
B
≥
1
3
2
4
x
5
Point A is moved 1 unit to
the right and 2 units up.
What are the coordinates of its
new location?
x
10°
A
1
70°
90°
C
D
44
(2, 1)
(2, 3)
(1, 3)
(3, 2)
A
B
C
D
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
26
Which diagram shows a reflection over the vertical line in the drawing above?
A
B
C
45
D
GO ON
Mathematics
3484232_AR1
XIJ321
28
Lines w and x intersect lines y and z
to form a rectangle as shown.
Ta
ll
XIJ321.AR1
Fra
nk
lin
3484232
27
2011 ISAT Grade 6 Sample Book
ey
Holloway
Pierce
w
Starlight
x
y
z
Which streets on this map
appear to never intersect?
Which statement is true?
≥
A
Line x is parallel to line y.
B
Line x is parallel to line z.
C
Line w is perpendicular
to line y.
D
Line w is perpendicular
to line x.
46
A
Talley and Franklin
B
Starlight and Pierce
C
Franklin and Holloway
≥D
Holloway and Starlight
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3484235
29
3484235_AR1
What three-dimensional
figure would this pattern make
if it were folded along the
dashed line segments?
A
Rectangular pyramid
B
Square pyramid
C
Triangular prism
≥D
Cube
3349451
30
3349451_AR1 to AR4
Which figure does not appear to contain two or more congruent shapes?
≥A
B
C
47
D
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3349454
31
3349454_AR1
3530008 3530008_AR1
32
Triangle RST is similar to
triangle XYZ.
Parallelogram RSTU is similar to
parallelogram HIJK.
S
Y
R
X
R
U
Z
S
T
I
J
T
SR
YZ
XZ
A
B
C
K
H
RS corresponds to which side of
triangle XYZ?
If the measure of !RST is
130°, then what is the measure
of !HIJ?
XY
≥D
48
A
50°
≥B
130°
C
260°
D
520°
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
XJE380
33
XJE380_AR1
3349380
34
Mrs. Robbins’ class voted for their
favorite kinds of books to read.
The Venn diagram below shows
the number of students at
Washington Elementary who play
baseball and football.
Books We Like
8
7
Football
6
5
4
26
3
2
7
1
ts
or
te
ys
Sp
ry
sy
M
Fa
n
ta
im
An
ve
nt
ur
e
al
0
Ad
Number of Votes
3349380_AR1
32
Kind of Book
Baseball
How many more students
voted for books about
adventures than books about
sports?
How many students play
baseball but not football?
0
1
2
3
39
33
A
B
C
≥D
A
B
49
≥
32
26
C
D
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
35
Trista made the chart below using the last names of her friends.
LAST NAMES
WILLIAMS
BANKS
SMITH
ANDRADE
GONZALEZ
CAREY
Which line plot represents the number of letters in each friend’s last name?
X
X
X
X
X X
X X X
X
X X
0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8
A
C
X
X X
X
X
X
X
X
X
0 1 2 3 4 5 6 7 8
X
X X
0 1 2 3 4 5 6 7 8
B
D
50
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3349383
36
3349383_AR1 to AR5
Carl has 16 books in his bookcase. This bar graph shows the number of each type of book.
Number of Books
Carl’s Books
10
8
6
4
2
0
Biography
Art
Fiction
Mystery
Type of Book
Which circle graph best shows the types of books Carl has in his bookcase?
Carl’s Books
Carl’s Books
Biography
Art
Art
Mystery
Fiction
Fiction
Mystery
Biography
A
C
Carl’s Books
Carl’s Books
Art
Art
Fiction
Fiction
Biography
Biography
Mystery
Mystery
≥B
D
51
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3484236
37
Greg took five tests each worth
100 points.
This table represents the first
eight U.S. Presidents and their
years in office.
He earned the following scores:
85, 87, 87, 89, 97
What is Greg’s mean (average)
score for these five tests?
89
88
87
12
≥A
B
C
D
3349387
38
U.S. President
Years in Office
G. Washington
8
J. Adams
4
T. Jefferson
8
J. Madison
8
J. Monroe
8
J.Q. Adams
4
A. Jackson
8
M. Van Buren
4
What are the median and range
for the number of years in office
for these eight U.S. Presidents?
52
A
Median ! 4, Range ! 4
B
Median ! 4, Range ! 8
≥C
Median ! 8, Range ! 4
D
Median ! 8, Range ! 8
GO ON
Mathematics
2011 ISAT Grade 6 Sample Book
3484240
39
3484240_AR1 to AR4
Ms. Simmons has a set of 10 tiles
numbered from 0 to 9 in a bag. The
tiles are the same size and shape.
Which spinner has the greatest
probability of the arrow landing
on a section labeled B?
B
R
G
Y
3530010
40
What is the probability that the
first tile Ms. Simmons randomly
chooses will have an odd
number on it?
A
≥B
B
R
Y
B
B
C
4
9
B
5
9
C
2
5
≥D
1
2
Y
B
R
B
R
Y
D
A
G
B
R
Y
53
STOP
2011 ISAT Grade 6 Sample Book
Mathematics Short-Response Scoring Rubric
The following rubric is used to score the short-response items for all grade levels.
SCORE
LEVEL
DESCRIPTION
2
Completely correct response, including correct work shown and/or correct labels/units if called
for in the item
1
Partially correct response
0
No response, or the response is incorrect
Using Short-Response Samples
Beginning with the spring 2008 ISAT, the sample short-response question and answer (shown below)
that appeared in the 2006 and 2007 ISAT test directions will no longer be included in the directions
immediately prior to session 2. ISBE encourages educators to practice these types of items with students
during the course of the school year so they are familiar with them prior to ISAT testing.
SAMPLE SHORT-RESPONSE QUESTION
Sam can buy his lunch at school. Each day, he wants to buy juice that costs 50¢,
a sandwich that costs 90¢, and fruit that costs 35¢.
Exactly how much money does Sam need to buy lunch for 5 days?
Show your work and label your answer.
SAMPLE SHORT-RESPONSE ANSWER
$1.75
50¢ + 90¢ + 35¢r =each
day
fo
My answer
$8.75
3 2
1.75
1.75
1.75
1.75
5
1.7_
+_
_
$8.75 for five days
Please refer to the 2008 and 2009 ISAT sample books for additional short-response items and student
samples (online at www.isbe.net/assessment/htmls/sample_books.htm).
58
2011 ISAT Grade 6 Sample Book
Mathematics Short-Response Sample Item 1
Below is a short-response sample item, followed by 3 samples of student responses.
This short-response sample item is classified to assessment objective 6.6.20. “Read, write,
recognize, and model percents from 0% to 100%.”
1
Use the two figures below to answer the questions.
Figure A
Figure B
1. What percent of Figure A is shaded?
2. What percent of Figure B is shaded?
In your answer document, clearly state which answer goes to Figure A and Figure B.
60
2011 ISAT Grade 6 Sample Book
Mathematics Short-Response Sample Item 2
Below is a short-response sample item, followed by 3 samples of student responses.
This short-response sample item is classified to assessment objective 8.6.10, “Solve word
problems involving unknown quantities.”
2
Matthias has 15 coupon books to sell for the school fundraiser. Matthias sells all of his
coupon books plus 3 additional coupon books.
If Matthias collects $198, how much does 1 coupon book cost?
Show your work.
64
2011 ISAT Grade 6 Sample Book
Using Extended-Response Samples
Beginning with the spring 2008 ISAT, the sample extended-response problem and solution (shown
below) that appeared in the 2006 and 2007 ISAT test directions will no longer be included in the
directions immediately prior to session 3. ISBE encourages educators to practice these types of items
with students during the course of the school year so they are familiar with them prior to ISAT testing.
SAMPLE EXTENDED-RESPONSE PROBLEM
Mrs. Martin wants to put tiles on the floor by the front door of her house. She wants
to use 3 different colors of tiles in her design.
She also wants
1
— of the tiles to be blue,
2
1
— of the tiles to be gray, and
4
1
— of the tiles to be red.
4
Use the grid below to design a floor for Mrs. Martin. Label each tile with the first
letter of the color that should be placed there.
Show all your work. Explain in words how you found your answer. Tell why you
took the steps you did to solve the problem.
SAMPLE EXTENDED-RESPONSE SOLUTION
B
B
G
R
B
B
G
R
B
B
G
R
B
B
G
R
B
B
G
R
B
B
G
R
–1
2 blue
–1 gray
4
–1
4 red
First , I know that there are 4 equal rows, so 2 rows is half and
1 row is –41 . So I made 2 rows B for blue because she wants
half the tiles blue. Then I made 1 row G for gray because she
wants –41 of the tiles to be gray. Since she wants gray and red
to be the same amount of tiles, I made the last row R for red.
Please refer to the 2008 and 2009 ISAT sample books for additional extended-response items and
student samples (online at www.isbe.net/assessment/htmls/sample_books.htm).
70
2011 ISAT Grade 6 Sample Book
Mathematics Extended-Response Sample Item 1
Below is an extended-response sample item, followed by 3 student samples.
This extended-response sample item is classified to assessment objective 6.6.13, “Solve problems
and number sentences involving addition, subtraction, and multiplication of decimals.”
1
Amy sells the following items at a farmer’s market:
•
•
•
•
•
5 pounds of apples for $3.50
1 pound of cherries for $5.00
2 pounds of pears for $3.00
5 pounds of carrots for $5.50
2 pounds of beans for $2.50
If Amy sells 10 pounds of apples, 3 pounds of cherries, and 5 pounds of beans to one
customer, how much money did she collect for what was sold?
Show all your work. Explain in words how you found your answer. Write why you
took the steps you did to solve the problem.
73