2010
Illinois Standards Achievement Test
Mathematics Samples
Form LM
Grade 6
Illinois State Board of Education
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
2
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Structure of the Grade 6 Mathematics ISAT
ISAT Mathematics testing in spring 2010 will consist of 30 norm-referenced items, as well as 45 criterionreferenced items, some of which will be used for developmental purposes. The 30 norm-referenced items are
an abbreviated form of the Stanford 10 Mathematics Problem Solving assessment, developed by Pearson, Inc.
The 45 criterion-referenced items are all written by Illinois educators and pilot tested with Illinois students.
Item Formats
All 75 items are aligned to the Illinois Mathematics Assessment Framework, which deﬁnes the elements of the
Illinois Learning Standards that are suitable for state testing.
Multiple-choice items require students to read, reﬂect, or compute and then to select the alternative that
best expresses what they believe the answer to be. This format is appropriate for quickly determining whether
students have achieved certain knowledge and skills. Well-designed multiple-choice items can measure
student knowledge and understanding, as well as students’ selection and application of problem-solving
strategies. A carefully constructed multiple-choice item can assess any of the levels of mathematical
complexity from simple procedures to sophisticated concepts. They can be designed to reach beyond the
ability of students to “plug-in” alternatives or eliminate choices to determine a correct answer. Such items are
limited in the extent to which they can provide evidence of the depth of students’ thinking.
Short-response items pose similar questions as multiple-choice items and provide a reliable and valid basis
for extrapolating about students’ approaches to problems. These items reduce the concern about guessing
that accompanies multiple-choice items. The short-response items are scored with a rubric and count as
5% of the scale score of the test.
Extended-response items require students to consider a situation that demands more than a numerical
response. These items require students to model, as much as possible, real problem solving in a large-scale
assessment context. When an extended-response item poses a problem to solve, the student must determine
what is required to “solve” the problem, choose a plan, carry out the plan, and interpret the solution in terms
of the original situation. Students are expected to clearly communicate their decision-making processes
in the context of the task proposed by the item (e.g., through writing, pictures, diagrams, or well-ordered
steps). The extended-response items are scored with a rubric and count as 10% of the scale score of the test.
Scoring Extended- and Short-Response Items
Extended- and short-response items are evaluated according to an established scoring scale, called a rubric,
developed from a combination of expectations and a sample of actual student responses. Such rubrics must
be particularized by expected work and further developed by examples of student work in developing a guide
for scorers. Illinois educators play a substantial role in developing these guides used for the scoring of the
short- and extended-response items. Committees of mathematics educators from throughout the state attend
a validation meeting, during which they use the mathematics scoring rubrics to establish task-speciﬁc criteria
that are used to score all short- and extended-response items consistently and systematically.
Answer Document for Grade 6 Mathematics ISAT
Students in grade 6 respond to all test items in a separate answer document. Test administrators should
monitor students carefully during testing to make sure students are using the appropriate pages of the answer
document, especially for the short- and extended-response items.
3
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Mathematics Sessions
All standard time administration test sessions are a minimum of 45 minutes in length. Any student who
is still actively engaged in testing when the 45 minutes have elapsed will be allowed up to an additional 10
minutes to complete that test session. More details about how to administer this extra time will appear in the
ISAT Test Administration Manual. This policy does not aﬀect students who already receive extended time as
determined by their IEP.
ISAT Mathematics Form LM Grades 3-8
Session 1
45 minutes
Session 2
45 minutes
Session 3
45 minutes
40 linguistically modified multiple-choice items
(30 of these are an abbreviated form of the Stanford 10.)
30 linguistically modified multiple-choice items
3 short-response items with 2 options:
1. Short-response items in plain English
2. Side-by-side English/Spanish format from original ISAT text
2 extended-response items with 2 options:
1. Extended-response items in plain English
2. Side-by-side English/Spanish format from original ISAT text
(Some sessions include pilot items.)
Calculator Use for Grade 6 Mathematics ISAT
All students in grade 6 are allowed to use a calculator during all sessions of the mathematics assessment.
Students are allowed to use any calculator they normally use in their mathematics classes. Schools, teachers,
and parents should be advised that when students attempt to use calculators with which they are unfamiliar,
their performance may suﬀer. In a like manner, students who are not taught when and how to use a
calculator as part of their regular mathematics instructional program are also at risk.
Rulers for Grade 6 Mathematics ISAT
All students in grade 6 will be provided with a ruler to use during all sessions of the mathematics assessment.
This ruler will allow students to measure in both inches and centimeters.
5
6
1
2
2
3
4
ISAT GRADES FOUR–EIGHT
Centimeters
3
4
5
6
7
8
9
10
1
11
12
13
Inches
0
0
14
15
Scratch Paper for Grade 6 Mathematics ISAT
Students must be provided with blank scratch paper to use during only session 1. Only session 1 contains
norm-referenced items, which were normed under such conditions. Students may not use scratch paper
during session 2 or session 3, but they may use the test booklet itself as scratch paper. However, students
must show their work, when required, for each short-response item in session 2 on the appropriate page in
the answer document. Students must show their work for each extended-response item in session 3 on the
appropriate pages in the answer document.
4
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
XIH110
1
3484196
3
There are 50 beans in a bag.
Twenty percent (20%) are red.
Anna runs 100 meters in ten
and sixty-two hundredths
seconds.
How many are red?
How is her time written as
a number?
A
≥B
5
10
20
30
A
≥B
C
D
1.62 seconds
C
10.62 seconds
100.62 seconds
D
1062.00 seconds
3528353 3528353.AR1
4
Use your centimeter ruler to answer
the question.
3484192
2
What number goes in the
?
10 16 y 2 4
12
42
52
72
A
≥B
C
D
About how long and wide in
centimeters is the 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
GO ON
5
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484200
5
3484200_AR1 to AR4
3484203
6
Which rectangle has an area of
24 square units and a perimeter
of 20 units?
3484203_AR1
Which is closest to the measure
of ∠XYZ?
12
A
X
2
Y
8
B
3
5
C
4
20°
90°
130°
A
B
C
160°
≥D
3484221
7
Mike has x baseball cards.
Tyrone has 3 times as many baseball
cards as Mike.
Frank has 20 baseball cards.
6
≥D
Z
4
Which expression represents
how many cards they have in
all?
≥A
x ⫹ 3x ⫹ 20
B
20 ⫹ 3x ⫺ x
C
x ⫹ 3 ⫹ 20
D
20 ⫺ 3x ⫹ x
GO ON
6
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484224
8
3349428
10
What value of n makes the
equation below true?
What is the value of the expression below
when x = 6 and y = 2?
4n ⫽ 220
8x ⫺ y
84
A
≥
46
12
4
B
C
D
3484225
9
50
55
A
≥B
220
C
D
3484229
11
3484225_AR1
216
3484229_AR1
What should be the value for x
in the triangle shown?
Which correctly describes the
rule between x and y ?
x
x
y
4
9
5
11
6
13
7
15
A
y⫽x⫹6⫺1
B
y⫽x•x⫺1
C
y⫽x⫹x⫺1
≥D
y⫽x•2⫹1
50°
60°
10°
40°
A
B
≥
70°
90°
C
D
GO ON
7
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484232_AR1
XIJ321.AR1
13
Lines w and x intersect lines y and z
to make a rectangle.
Ta
ll
Fra
nk
lin
3484232
12
ey
Holloway
Pierce
w
Starlight
x
y
z
Which streets do not intersect?
Which is true?
A
Line x is parallel to line y.
A
Talley and Franklin
B
Line x is parallel to line z.
B
Starlight and Pierce
Line w is perpendicular
to line y.
C
Franklin and Holloway
≥D
Holloway and Starlight
≥C
D
Line w is perpendicular
to line x.
GO ON
8
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484235
14
3484235_AR1
3349454
15
3349454_AR1
Triangle RST is similar to
triangle XYZ.
What solid figure will this
pattern make when it is folded
along the dotted lines?
Y
X
R
Z
S
T
RS corresponds to which side of
triangle XYZ?
A
Rectangular pyramid
B
Square pyramid
SR
YZ
XZ
C
Triangular prism
A
B
C
≥D
XY
≥D
Cube
GO ON
9
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
XJE380
16
XJE380_AR1
Students voted for their favorite books.
7
Football
6
5
4
26
3
2
7
1
ts
or
te
ys
M
Sp
ry
sy
ta
Fa
n
al
im
An
ve
nt
ur
e
0
Ad
Number of Votes
3349380_AR1
The Venn diagram shows how many
students play baseball and football.
Books We Like
8
3349380
17
32
Kinds of Books
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
A
B
C
≥D
39
33
≥ 32
26
A
B
C
D
GO ON
10
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349383
18
3349383_AR1 to AR5
Carl has 16 books. The 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?
Carl’s Books
Carl’s Books
Biography
Art
Art
Mystery
Fiction
Fiction
Biography
A
Mystery
C
Carl’s Books
Carl’s Books
Art
Art
Fiction
Fiction
Biography
Biography
Mystery
Mystery
≥B
D
GO ON
11
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484236
19
3484240
20
Greg took five tests.
Each test is worth 100 points.
3484240_AR1 to AR4
Which spinner is most likely to
have the arrow stop on B?
Here are Greg’s 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
B
R
G
Y
B
R
Y
B
A
≥B
B
C
Y
B
R
B
R
Y
D
G
B
R
Y
GO ON
12
3349451
3349451_AR1 to AR4
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349080
22
21
3349080_AR1
Tom's Work List
Work
Time
Read Book
3
hour
4
Cut Grass
1
1 hours
4
B
C
D
Key: 1cm = 5 feet
!
1
2 hours
4
Fix Car
3
Tree
1 hour
2
Clean Room
A
Swing
6
hours
14
3
3 hours
4
1
4 hours
2
3
4 hours
4
≥
A
4 feet
B
5 feet
C
20 feet
D
25 feet
≥
3349454
GO ON
13
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349423
23
24
!#
"best quation?
y
y=x+4
20
18
16
A
x
y
14
0
0
12
1
1
2
2
6
3
3
4
10
8
2
B
≥C
D
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
0
2
4
6
8
10 12 14 16 18 20
x
If x is 8 on the graph, what is y?
≥
25
A
4
B
14
C
16
D
18
≥
≥
Jan has 18 cards.
Ray gives her v cards.
Jan now has less than 30 cards.
Which best describes Jan's cards?
A
v ⫺ 18 ⬎ 30
≥B
v ⫹ 18 ⬍ 30
C
v ⫺ 18 ⬍ 30
D
v ⫹ 18 ⬎ 30
STOP
14
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Answer Key with Assessment Objectives Identiﬁed
Item
Number
Correct
Answer
1
B
6.6.05 Read, write, recognize, and model equivalent representations of
decimals and their place values through thousandths.
2
B
6.6.15 Identify and apply order of operations to simplify numeric expressions
involving whole numbers.
3
B
6.6.21 Solve number sentences and problems involving percents.
4
C
7.6.01 Select and use appropriate standard units and tools to measure length,
mass/weight, capacity, and angles.
5
D
7.6.02 Solve problems involving the perimeter and area of a triangle,
parallelogram, or irregular shape using diagrams, models, and grids or by
measuring or using given formulas (may include sketching a figure from its
description).
6
D
7.6.03 Compare and estimate length (including perimeter), area, volume,
weight/mass, and angles (0° to 180°) using referents.
7
A
8.6.02 Write an expression using variables to represent unknown quantities.
8
B
8.6.03 Evaluate algebraic expressions with up to two whole number variable
values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2).
9
D
8.6.04 Determine a rule having two operations from an input–output table
(e.g., multiply by 3 and add 2).
10
B
8.6.09 Solve for the unknown in an equation with one operation (e.g., 8x=24,
m÷2=25).
11
C
9.6.03 Solve problems using properties of triangles and quadrilaterals (e.g.,
sum of interior angles of a quadrilateral is 360°).
12
C
9.6.07 Identify and sketch parallel, perpendicular, and intersecting lines.
13
D
9.6.07 Identify and sketch parallel, perpendicular, and intersecting lines.
14
D
9.6.09 Identify a three–dimensional object from its net.
15
D
9.6.12 Determine if figures are similar, and identify relationships between
corresponding parts of similar figures.
16
D
10.6.01 Read, interpret, and make predictions from data represented in a bar
graph, line (dot) plot, Venn diagram (with two circles), chart/table, line graph,
or circle graph.
Assessment Objective
15
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Answer Key with Assessment Objective Identified
Item
Number
Correct
Answer
17
C
10.6.01 Read, interpret, and make predictions from data represented in a
bar graph, line (dot) plot, Venn diagram (with two circles), chart/table, line
graph, or circle graph.
18
B
10.6.02 Compare different representations of the same data.
19
A
10.6.04 Determine the mode, range, median, and mean, given a set of
data or a graph.
20
B
10.6.05 Solve problems involving the probability of a simple event,
including expressing the probability as a ratio, fraction, decimal, or percent.
21
D
6.6.14 Solve problems involving addition and subtraction of fractions and
mixed numbers, and express answers in simplest form.
22
D
7.6.03 Compare and estimate length (including perimeter), area, volume,
weight/mass, and angles (0° to 180°) using referents.
23
C
8.6.03 Evaluate algebraic expressions with up to two whole number
variable values (e.g., evaluate 3m + n + 3 when m = 4 and n = 2).
24
C
8.6.04 Determine a rule having two operations from an input–output table
(e.g., multiply by 3 and add 2).
25
C
8.6.05 Select a table of values that satisfies a linear equation, and
recognize the ordered pairs on a rectangular coordinate system.
Assessment Objective
To view all the mathematics assessment objectives, download the Illinois Mathematics Assessment
Framework for Grades 3–8 online at www.isbe.net/assessment/IAFindex.htm.
16
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Sample Items
Followed by Scoring Rubric
Student Samples
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¢ =each
day
for
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 2006 and 2007 ISAT sample books for additional short-response items and student
samples (online at www.isbe.net/assessment/htmls/sample_books.htm).
17
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Items
Reactivos de Respuesta Corta
Plain English - Use pages English and Spanish - Use pages - Inglés y Español - Usa las páginas - 3484241
1
3484241_AR1
What is the location of point A?
What is the location of point B?
A
0
B
1
2
3
Label your answers.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 1.
18
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349370
2
B
10 in.
A
1 in.
3 in.
C
8 in.
4 in.
5 in.
3349370_AR1
12 in.
12 in.
6 in.
D
6 in.
6 in.
3 in.
Which rectangular prism has the greatest volume?
Volume of a rectangular prism ⫽ length ⫻ width ⫻ height
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 2.
19
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349372
3
3349372_AR1
Julio made a pattern of equilateral triangles out of toothpicks.
Number of Triangles Made
1
2
3
4
5
Number of Toothpicks Used
3
5
7
9
11
How many toothpicks would Julio use to make a figure with 10 equilateral triangles?
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 3.
20
STOP
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
1
3484241
3484241_AR1
3484241
3484241_AR1
Use the number line below to answer the following questions.
What number best represents the location of point A?
What number best represents the location of point B?
A
0
B
1
2
3
Label your answers.
1
Usa la línea numerada de abajo para responder a las siguientes preguntas.
¿Qué número representa mejor la ubicación del punto A?
¿Qué número representa mejor la ubicación del punto B?
A
0
B
1
2
3
Marca tus respuestas.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 1.
21
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349370
2
B
10 in.
A
1 in.
3 in.
C
8 in.
4 in.
12 in.
6 in.
D
6 in.
12 in.
5 in.
3349370_AR1
6 in.
3 in.
Which rectangular prism has the greatest volume?
Volume of a rectangular prism ⫽ length ⫻ width ⫻ height
Show your work.
3349370
2
B
10 in.
A
1 in.
3 in.
C
8 in.
4 in.
5 in.
12 in.
12 in.
3349370_AR1
6 in.
D
6 in.
6 in.
3 in.
¿Qué prisma rectangular tiene el mayor volumen?
Volumen de un prisma rectangular = largo x ancho x altura
Demuestra tu trabajo.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 2.
22
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349372
3
3349372_AR1
Using toothpicks, Julio made a pattern of equilateral triangles. He recorded the number of
triangles made and the number of toothpicks used in a chart.
Number of Triangles Made
1
2
3
4
5
Number of Toothpicks Used
3
5
7
9
11
Using this chart, how many toothpicks would Julio use to make a figure with
10 equilateral triangles?
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 3.
23
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349372
3
3349372_AR1
Usando escarbadientes, Julio hizo un patrón de triángulos equiláteros. En un gráfico,
registró la cantidad de triángulos hechos y la cantidad de escarbadientes utilizados.
Cantidad de triángulos hechos
1
2
3
4
5
Cantidad de escarbadientes
utilizados
3
5
7
9
11
¿Cuántas latas deben poner en cada caja?
Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué
seguiste esos pasos para solucionar el problema.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 3.
24
STOP
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
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
25
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 1A
Short Response Student Sample1A
Rubric Score Point = 2
Note: The student correctly identiﬁed the location of both points.
26
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 1B
Short Response Student Sample1B
Rubric Score Point = 2
Note: The student correctly identiﬁed the location of both points.
27
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 1C
Short Response Student Sample1C
Rubric Score Point = 1
Note: The student correctly identiﬁed the location of one point.
28
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 2A
Short Response Student Sample2A
Rubric Score Point = 2
Note: The student correctly chose “D” as having the most volume, and supporting work, including the
volumes of the other three rectangular prisms, is present.
29
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
30
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 2B
Short Response Student Sample 2B
Rubric Score Point = 2
Note: The student correctly chose “D” as having the most volume, and supporting work is present.
31
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 2C
Short Response Student Sample 2C
Rubric Score Point = 1
Note: The student correctly calculated the volume of each rectangular prism but incorrectly chose “C” as
their answer.
32
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 3A
Short Response Student Sample3A
Rubric Score Point = 2
Note: The student provided the correct answer of 21 toothpicks and showed supporting work
(counting by 2s).
33
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 3B
Short Response Student Sample3B
Rubric Score Point = 2
Note: The student provided the correct answer of 21 toothpicks and showed supporting work
(# of triangles ⫻ 2 ⫹ 1).
34
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Short-Response Student Sample 3C
Short Response Student Sample3C
Rubric Score Point = 1
Note: The student provided an incorrect answer (20) but showed supporting work (drawing
and counting).
35
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Sample Items
Followed by Scoring Rubric
and Student Samples
36
_____________________________________________________________
2010 ISAT Mathematics Form LM Sample Book - Grade 6
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 2006 and 2007 ISAT sample books for additional extended-response items and student
samples (online at www.isbe.net/assessment/htmls/sample_books.htm).
37
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Blank Extended-Response Template
Mathematics - Session 3
DIRECTIONS
Make sure you
– show all your work in solving the problem,
– clearly label your answer,
– write in words how you solved the problem,
– write in words why you took the steps you did to solve the problem, and
– write as clearly as you can.
38
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Mathematics - Session 3
39
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Items
Reactivos de Respuesta Larga
Plain English - Use pages - English and Spanish - Use pages - Inglés y Español - Usa las páginas - 3484244
3484244_AR1
Austin, Ben, Catina, and Darius bring cans from home.
The cans go in 4 boxes.
Each box gets the same number of cans.
Austin
Ben
18 cans
25 cans
8 cans
13 cans
Box 2
Box 3
Box 4
Box 1
Catina
Darius
How many cans go in each box?
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION .
40
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349092
2
Use your centimeter ruler to solve this problem.
Make a scale drawing of a straight road that is 24 miles long.
Use the scale 1 centimeter represents 3 miles.
You must include:
• A beginning point
• An ending point
• A stop sign that is 6 miles from the ending point of the road
Label all parts of the road.
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 2.
41
STOP
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484244
3484244_AR1
Austin, Ben, Catina, and Darius collected cans for a local food shelter. They will put
the same number of cans in each of 4 boxes. The number of cans each student
collected is shown.
Austin
Ben
Catina
Darius
18 cans
25 cans
8 cans
13 cans
Box 1
Box 2
Box 3
Box 4
How many cans should they put in each box?
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 1.
42
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3484244
3484244_AR1
Austin, Ben, Catina y Darius recogieron latas de alimentos para un refugio local.
En cada una de 4 cajas colocarán la misma cantidad de latas. Se muestra la
cantidad de latas recolectadas por cada estudiante
Austin
Ben
Catina
Darius
18 latas
25 latas
8 latas
13 latas
Caja 1
Caja 2
Caja 3
Caja 4
¿Cuántas latas deben poner en cada caja?
Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué
seguiste esos pasos para solucionar el problema.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA .
43
GO ON
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
3349092
2
Use your centimeter ruler to help you solve this problem.
Make a scale drawing of a straight bike path that is 24 miles long. Use the scale
1 centimeter represents 3 miles.
You must include:
• A beginning point.
• An ending point.
• A drinking fountain that is 6 miles from the ending point of the path.
Label all parts of the path.
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
3349092
2
Utiliza la regla de centímetros para ayudarte a resolver este problema.
Dibuja en escala el sendero de una bicicleta que tiene 24 millas de largo. Usa la escala,
1 centímetro representa 3 millas
Debes incluir:
•· Un punto de partida.
•· Un punto de llegada.
•· Un bebedero a 6 millas del punto de llegada.
Marca todas las partes del sendero.
Demuestra tu trabajo. Explica con palabras cómo llegaste al resultado. Relata por qué
seguiste esos pasos para solucionar el problema.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA .
44
STOP
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Mathematics Extended-Response Scoring Rubric
The following rubric is used to score the extended-response items for all grade levels. A student-friendly
version of this extended-response scoring rubric is available online at www.isbe.net/assessment/math.htm.
SCORE
LEVEL
MATHEMATICAL KNOWLEDGE:
Knowledge of mathematical principles and
concepts which result in a correct solution to
a problem.
STRATEGIC KNOWLEDGE:
Identification and use of important
elements of the problem that represent
and integrate concepts which yield the
solution (e.g., models, diagrams, symbols,
algorithms).
EXPLANATION:
Written explanation of the rationales and
steps of the solution process. A justification
of each step is provided. Though important,
the length of the response, grammar, and
syntax are not the critical elements of this
dimension.
4
• shows complete understanding of the
• identifies all important elements of
• gives a complete written explanation of the
problem’s mathematical concepts and
the problem and shows complete
solution process; clearly explains what was
principles
understanding of the relationships among
done and why it was done
elements
• uses appropriate mathematical terminology
• may include a diagram with a complete
and notations including labeling answer if • shows complete evidence of an appropriate
explanation of all its elements
appropriate
strategy that would correctly solve the
problem
• executes algorithms and computations
completely and correctly
3
• shows nearly complete understanding of
• identifies most of the important elements
the problem’s mathematical concepts and
of the problem and shows a general
principles
understanding of the relationships among
them
• uses mostly correct mathematical
terminology and notations
• shows nearly complete evidence of an
appropriate strategy for solving the
• executes algorithms completely;
problem
computations are generally correct but may
contain minor errors
• gives a nearly complete written explanation
of the solution process; clearly explains
what was done and begins to address why
it was done
• may include a diagram with most of its
elements explained
• shows some understanding of the
problem’s mathematical concepts and
principles
• uses some correct mathematical
terminology and notations
• may contain major algorithmic or
computational errors
• identifies some important elements
of the problem but shows only limited
understanding of the relationships among
them
• shows some evidence of a strategy for
solving the problem
• gives some written explanation of the
solution process; either explains what was
done or addresses why it was done
• explanation is vague, difficult to interpret,
or does not completely match the solution
process
• may include a diagram with some of its
elements explained
• shows limited to no understanding of the
problem’s mathematical concepts and
principles
• may misuse or fail to use mathematical
terminology and notations
• attempts an answer
• fails to identify important elements or
places too much emphasis on unrelated
elements
• reflects an inappropriate strategy for
solving the problem; strategy may be
difficult to identify
• gives minimal written explanation of the
solution process; may fail to explain what
was done and why it was done
• explanation does not match presented
solution process
• may include minimal discussion of the
elements in a diagram; explanation of
significant elements is unclear
• no answer attempted
• no apparent strategy
• no written explanation of the solution
process is provided
2
1
0
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 1A
46
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 1B
47
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
48
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 1C
49
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
50
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Scoring Guide for “Cans for Food Shelter”
The correct answer to this extended-response problem is 16 cans in each box.
Extended-Response Student Sample 1A
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
4
4
4
This response includes evidence of
a complete understanding of the
problem’s mathematical concepts
and principles. The correct answer
of 16 cans is present.
The response reflects a systematic
strategy (adding the total number
of cans and dividing by 4) that
includes all important elements
of the problem.
The response addresses both what
was done and why (“…added to
see how many cans there are…
divided 64 by 4…have to be put in
4 boxes…”).
Extended-Response Student Sample 1B
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
4
4
4
This response includes evidence of
a complete understanding of the
problem’s mathematical concepts
and principles. The correct answer
of 16 cans is present.
The response reflects a systematic
strategy (adding the total number
of cans and dividing by 4 then
checking with tally marks) that
includes all important elements of
the problem.
The response addresses both what
was done and why (“…added
to see how many there are all
together…divided 64 ÷ 4 because
there are 64 cans and 4 boxes…”).
Extended-Response Student Sample 1C
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
4
4
2
This response includes evidence of
a complete understanding of the
problem’s mathematical concepts
and principles. The correct answer
of 16 cans is present.
The response reflects a systematic
strategy (adding the total number
of cans and dividing by 4 and
drawing a picture) that includes
all important elements of the
problem.
51
The response addresses only what
was done (“…first I add…then
I divide…”).
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 2A
52
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 2B
53
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
54
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Extended-Response Student Sample 2C
55
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
56
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2010 ISAT Mathematics Form LM Sample Book - Grade 6
Scoring Guide for “Bike Path”
To solve this problem correctly, students must make a scale drawing of a bike path. Since the scale given is
1 cm=3 miles, their scale drawing must be 8 cm long and have a drinking fountain that is 2 cm from the ending
point on their drawing. The drinking fountain could be on the bike path itself or beyond it in any direction, as
long as its distance from the ending point is 2 cm.
Extended-Response Student Sample 2A
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
4
4
4
This response includes evidence of
a complete understanding of the
problem’s mathematical concepts
and principles. Both the path
length and fountain placement are
correct.
The response reflects a
systematic strategy that includes
all important elements of the
problem. The student divided
24 by 3 to find the correct path
length of 8 cm and then drew the
path with the fountain correctly
placed on the path.
The response addresses both what
was done and why (“divided
24 by 3 so I would know how many
centimeters would equal
24 miles. Next, I draw a line that
was 8 centimeters long because
that is how many centimeters
it takes for 24 miles…After that
I divided 6 by 3 to get 2. The
reason…to find were the drinking
fountain goes…”).
Extended-Response Student Sample 2B
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
4
4
3
This response includes evidence of
a complete understanding of the
problem’s mathematical concepts
and principles. Both the path length
and fountain placement are correct.
The response reflects a
systematic strategy that includes
all important elements of the
problem.
The response addresses what was
done and begins to address why
(“my path was 8 centimeters long
because every 3 centimeters was
a mile”).
Extended-Response Student Sample 2C
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
2
4
4
The response reflects a
systematic strategy that includes
all important elements of the
problem.
The response addresses both
what was done and why (“I drew
a line that was 8 cm long because
8х3=24. Then I… measured
2 centimeters higher and labeled
drinking fountain because I
knew 3х2=6”).
This response includes some
understanding of the problem’s
mathematical concepts and
principles. The path contains a
major error (1 cm off in length).
This was a measuring error.
57