1. science
2. mathematics

Illinois Standards Achievement Test
Mathematics Samples
Form LM
Grade 7
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
2
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Structure of the Grade 7 Mathematics ISAT
ISAT Mathematics testing in spring 2009 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 7 Mathematics ISAT
Students in grade 7 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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2009 ISAT Mathematics Form LM Sample Book - Grade 7
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 7 Mathematics ISAT
All students in grade 7 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 7 Mathematics ISAT
All students in grade 7 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 7 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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2009 ISAT Mathematics Form LM Sample Book - Grade 7
ISAT MATHEMATICS REFERENCE SHEET
Grades 7 and 8
5
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3484193
1
3528355
3
3528355_AR1
Use your inch ruler to help you
answer this question.
Seven students bought pencils
to share equally.
P
How many pencils did they buy?
2
27
38
A
B
≥
56
64
C
D
3484197
The ratio of the number of girls to
boys in a class is 3 to 2.
R
Q
There are 18 girls.
Which is the perimeter of
triangle PQR?
How many boys are in
the class?
A
23
12
3
2
A
≥B
C
D
B
C
≥D
7 inches
1
7 inches
2
8 inches
1
8 inches
2
GO ON
6
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3349238
4
3349238_AR1
3484199
6
9 feet
The area of the square below is
9 square yards.
3 feet
15 feet
3 yards
3 yards
27 feet
What is the area of the square
in square feet?
What is the area of the polygon?
≥
A
B
C
D
3484199_AR1
90 square feet
144 square feet
405 square feet
432 square feet
3484202
5
≥
A
B
C
D
12 square feet
27 square feet
54 square feet
81 square feet
3484202_AR1
What is the surface area of this
rectangular prism?
4 inches
2 inches
10 inches
≥A
B
C
D
136 square inches
120 square inches
80 square inches
16 square inches
GO ON
7
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3484208
7
3484208_AR1
The table shows the pattern between the number of squares made and the
number of toothpicks used.
Number of Squares
Number of Toothpicks
1
4
2
7
3
10
4
13
n
?
Picture
Which can be used to find the number of toothpicks needed for n squares?
4n
4n ⫺ 1
A
B
3n ⫹ 1
3n ⫺ 1
C
D
≥
3484211
8
Which is equal to
3x + 5 + x + 10 + 2y?
≥
A
B
C
D
6x ⫹ 15
3x ⫹ 2y ⫹ 15
4x ⫹ 2y ⫹ 15
9x ⫹ 12y
GO ON
8
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3484212
9
3484212_AR1
3484213
11
Points M, N, Q, Y, Z, and X are all
on circle P.
Which inequality
represents the graph?
M
-3
≥A
B
-2
-1
xⱕ2
x⬎2
0
1
C
D
3484213_AR1
2
N
3
Q
X
x⬍2
xⱖ2
P
Z
Y
3349277
10
Which represents the diameter
of circle P?
What values of x make the
inequality true?
≥
3x ⫺ 4 ⬎ 38
≥A
B
C
D
A
B
PM
ZN
C
D
XY
PQ
x ⬎ 14
x ⬍ 14
x ⬎ 11
x ⬍ 11
GO ON
9
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3349265
12
3349265_AR1
3484214
13
3484214_AR1
y
Points K, L, and M are vertices
on rectangle KLMN.
5
4
P
y
R
3
2
1
–5
–4
–3
–2
–1 0
–1
1
2
3
4
5
9
x
8
7
–2
Q
M (7, 10)
10
S
–3
6
5
–4
4
–5
3
2
L (7, 3)
K (1, 3)
1
Which point is at (3, -2)?
A
B
P
Q
≥
C
D
0
1
R
S
2
3
4
5
6
7
8
9
10
x
What are the coordinates of
vertex N?
≥
A
B
(7, 7)
(1, 10)
C
D
(10, 3)
(10, 1)
GO ON
10
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3484217
14
3484217_AR1
3484222
16
3484222_AR1 to AR5
The dimensions of rectangle N are
1
the dimensions of rectangle M.
2
N
M
Which must be true about
the two rectangles?
A The area of rectangle N is
1 the area of rectangle M.
2
Which set of bars represents
the data in the circle graph?
B The perimeter of rectangle N is equal
to the perimeter of rectangle M.
C The area of rectangle N is equal
to the area of rectangle M.
≥
D
≥A
The perimeter of rectangle N is
1
the perimeter of rectangle M.
2
B
3349226
15
3349226_AR1
Triangle PQT is similar to
triangle PRS.
C
S
T
D
4m
P
10 m
Q
R
10 m
What is the length of SR?
8m
≥A
10 m
14 m
20 m
B
C
D
GO ON
11
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3356854
17
3356854.AR1 to .AR4
Which graph shows a line of best fit?
y
y
x
x
≥A
C
y
y
x
x
B
D
3349237
18
Jo needs an 85% average on her
five math tests. She earned
99%, 85%, 79%, and 88% on her
first four tests.
What score must she earn on
her fifth test in order to have an
average of exactly 85% for all
five tests?
74%
≥A
79%
85%
88%
B
C
D
GO ON
12
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
3349244
19
3484227
20
Mike has 2 red apples and 3 green
apples.
A restaurant has 5 different
hamburgers and 4 different
drinks.
He takes an apple without looking,
and gives it to his sister.
Then he takes an apple for himself.
What is the probability that
Mike and his sister will each
get a red apple?
10%
≥A
30%
40%
60%
B
C
D
How many different
combinations of one hamburger
and one drink are possible?
13
2
5
9
20
A
B
C
≥D
STOP
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Answer Key with Assessment Objectives Identified
Item
Number
Correct
Answer
1
C
6.7.07 Solve problems involving descriptions of numbers, including
characteristics and relationships (e.g., square numbers, prime/composite, prime
factorization, greatest common factor, least common multiple).
2
B
6.7.15 Use proportional reasoning to model and solve problems.
3
D
7.7.02 Solve problems involving the perimeter and the area of polygons and
composite figures using diagrams, models, and grids or by measuring or using
given formulas (may include sketching a figure from its description).
4
D
7.7.02 Solve problems involving the perimeter and the area of polygons and
composite figures using diagrams, models, and grids or by measuring or using
given formulas (may include sketching a figure from its description).
5
A
7.7.04 Determine the volume and surface area of a right rectangular prism
using an appropriate formula or strategy.
6
D
7.7.05 Solve problems involving unit conversions within the same
measurement system for length, weight/mass, capacity, and square units
(e.g., 1 ft2 = 144 in2).
7
C
8.7.01 Determine a missing term in a sequence, extend a sequence, and
construct and identify a rule that can generate the terms of an arithmetic or
geometric sequence.
8
C
8.7.03 Simplify algebraic expressions by identifying and combining like terms.
9
A
8.7.09 Identify, graph, and interpret inequalities on a number line.
10
A
8.7.11 Solve linear equations in one variable (e.g., 2x + 3 = 13) and inequalities
involving < or > (e.g., 2x < 6, x + 7 > 10).
11
B
9.7.04 Identify, describe, and determine the radius and diameter of a circle.
12
D
9.7.05 Graph points and identify coordinates of points on the Cartesian
coordinate plane (all four quadrants).
13
B
9.7.06 Represent and identify geometric figures using coordinate
geometry.
14
D
9.7.12 Recognize which attributes (such as shape, perimeter, and area)
change or don’t change when plane figures are composed, decomposed, or
rearranged.
15
A
9.7.14 Determine if figures are similar, and identify relationships between
corresponding parts of similar figures.
16
A
10.7.02 Compare different representations of the same data.
17
A
10.7.04 Identify a reasonable approximation of the line of best fit from a set
of data or a scatterplot.
Assessment Objective
14
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Item
Number
Correct
Answer
18
A
10.7.05 Determine and use the mode, range, median, and mean to
interpret data.
19
A
10.7.06 Solve problems involving the probability of a simple or compound
event, including representing the probability as a fraction, decimal, or
percent.
20
D
10.7.08 Solve simple problems involving the number of ways objects can
be arranged (permutations and combinations).
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.
15
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
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).
16
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Items Reactivos de Respuesta Corta
Plain English - Use pages 17 - 19
English and Spanish - Use pages 20 - 22
Inglés y Español - Usa las páginas 20 - 22
21
A submarine is 294 feet below sea level.
A helicopter is directly over the submarine.
The helicopter is 1,277 feet above sea level.
How far is it in feet from the helicopter to the submarine?
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 21.
17
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
22
On March 1, Jess has 1,000 minutes to use with her cell phone.
She uses 39 minutes per day.
On what date will Jess run out of minutes?
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 22.
18
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
23
Sam rolls a standard 6-sided number cube and flips a penny.
The six sides of the number cube are shown.
Both sides of the penny are also shown.
1
2
3 4
5
6
How many different outcomes are possible if Sam rolls the number cube and flips
the penny?
Show your work.
DO NOT WRITE HERE.
USE PAGE __ IN YOUR ANSWER
DOCUMENT TO ANSWER QUESTION 23.
19
STOP
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
21
A submarine is 294 feet below sea level. A helicopter is flying directly over the
submarine 1,277 feet above sea level.
What is the distance, in feet, from the helicopter to the submarine?
Show your work.
21
Un submarino se encuentra a 294 pies por debajo del nivel del mar. Un helicóptero vuela
directamente sobre el submarino, a 1,277 pies por encima del nivel del mar.
¿Cuál es la distancia, en pies, del helicóptero al submarino?
Demuestra tu trabajo.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 21.
20
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
22
On March 1, Jess had 1,000 monthly minutes to use with her cellular phone plan. She uses
39 minutes per day during March.
On what date will she run out of minutes?
Show your work.
22
El 1 de marzo, Jess tenía para usar 1,000 minutos mensuales en su celular. Durante ese mes,
ella usó 39 minutos diarios.
¿En qué día se quedó sin minutos?
Demuestra tu trabajo.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 22.
21
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
23
1
Sam rolls a standard 6-sided number cube (
) and flips a penny.
The six sides of the number cube and both sides of the penny are shown below.
4
1
2
5
3 4
5
6
How many different outcomes are possible if Sam rolls the number cube and flips
the penny?
Show your work.
23
1
Sam hace rodar un cubo numerado de seis lados (
) y arroja al aire una moneda de un
centavo. Los seis lados del cubo numerado y las dos caras de la moneda se muestran
abajo.
4
1
2
5
3 4
5
6
¿Cuántos resultados son posibles si Sam hace rodar el cubo numerado o voltea la
moneda?
Demuestra tu trabajo.
NO ESCRIBAS AQUÍ.
USA LA PÁGINA __ EN TU DOCUMENTO
DE RESPUESTAS PARA CONTESTAR
LA PREGUNTA 23.
22
STOP
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
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
23
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 21A
Short Response Student Sample 21A
Rubric Score Point = 2
Note: The student wrote the correct answer of 1,571 and showed correct work 1,277 + 294 to produce this
answer.
24
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 21B
Short Response Student Sample 21B
Rubric Score Point = 2
Note: The student wrote the correct answer of 1,571 and showed correct work 1,277– (-294) to produce
this answer.
25
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 21C
Short Response Student Sample 21C
Rubric Score Point = 1
Note: The student wrote an incorrect answer of 1,521 because of a number transfer error. The shown work
1,227 + 294 produces the answer given.
26
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 22A
Short Response Student Sample 22A
Rubric Score Point = 2
Note: The student correctly identified the 26 of March as the date on which she will use all her minutes
and showed supporting work.
27
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 22B
Short Response Student Sample 22B
Rubric Score Point = 2
Note: The student correctly identified the 26 of March as the date on which she will use all her minutes
and showed supporting work.
28
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 22C
Short Response Student Sample 22C
Rubric Score Point = 1
Note: The student did not identify the correct date but showed supporting work.
29
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 23A
Short Response Student Sample 23A
Rubric Score Point = 2
Note: The student correctly identified 12 possible outcomes and showed supporting work in a chart.
30
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 23B
Short Response Student Sample 23B
Rubric Score Point = 2
Note: The student correctly identified 12 possible outcomes and showed supporting work using
multiplication.
31
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Short-Response Student Sample 23C
Short Response Student Sample 23C
Rubric Score Point = 1
Note: The student showed work but miscounted and gave an incorrect answer of 14 different outcomes,
not 12.
32
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Sample Items
Followed by Scoring Rubric
and Student Samples
33
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
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).
34
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Items Reactivos de Respuesta Larga
Plain English - Use pages 35 - 36
English and Spanish - Use pages 37 - 39
Inglés y Español - Usa las páginas 37 - 39
24
Ben made $180 by selling 50 basketball tickets.
Each adult ticket cost $5.
Each student ticket cost $3.
He sold some adult tickets and some student tickets.
Student Ticket
$3
Adult Ticket
$5
1. How many adult tickets did he sell?
2. How many student tickets did he sell?
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 24.
35
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
25
The seventh-grade class is planning a pancake breakfast to raise money for a class trip.
Use the information below to answer the questions.
• Bags of pancake mix cost $10.00 each.
• Each bag makes 120 pancakes.
• Each person will be served 3 pancakes.
1. How many pancakes will the students need to make to serve 240 people?
2. What will be the total cost of the pancake mix needed to serve these 240
people?
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 25.
36
STOP
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
24
Ben sold some adult tickets and some student tickets for a basketball game.
• Each adult ticket cost $5.
• Each student ticket cost $3.
Ben collected $180 for the 50 tickets he sold.
Student Ticket
$3
Adult Ticket
$5
1. How many adult tickets did he sell?
2. How many student tickets did he sell?
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 24.
37
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
24
Ben vendió ingresos de adulto a algunos estudiantes para el juego de baloncesto.
• Cada ingreso de adulto cuesta $5.
• Cada ingreso de estudiante cuesta $3.
Ben recolectó $180 por los 50 ingresos vendidos.
Ingreso
Estudiante
Ingreso Adult
$5
$3
1. ¿Cuántos ingresos de adultos vendió?
2. ¿Cuántos ingresos de estudiantes vendió?
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 24.
38
GO ON
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
25
The seventh-grade class is planning a pancake breakfast to raise money for their class trip.
All materials will be donated except the pancake mix. Based on the given information
below, answer the questions that follow.
• Bags of pancake mix cost $10.00 each.
• Each bag makes 120 pancakes.
• Each person will be served 3 pancakes.
1. How many pancakes would the students need to make to serve 240 people?
2. How much will it cost for all the bags of pancake mix needed to serve these
240 people?
Show all your work. Explain in words how you found your answer. Tell why you took
the steps you did to solve the problem.
25
La clase de séptimo grado está organizando un desayuno con panqueques para recaudar
fondos para su viaje escolar.
Todos los materiales serán donados, con excepción de la mezcla de panqueque. Con base
a la información proporcionada, responda a las siguientes preguntas.
• Cada bolsa de mezcla de panqueque cuesta $10.00.
• Con una bolsa se hacen 120 panqueques.
• A cada persona se le servirán 3 panqueques.
1. ¿Cuántos panqueques tendrán que hacer los estudiantes para servir a 240 personas?
2. ¿Cuánto costarán las bolsas de mezcla necesarias para servir a las 240 personas?
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 25.
39
STOP
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
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
40
IL07-A1-7SB
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 24A
41
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
42
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 24B
43
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
44
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 24C
45
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
46
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Scoring Guide for “Basketball Tickets”
The correct answer to this extended-response problem is 15 adult tickets and 35 student tickets.
Extended-Response Student Sample 24A
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 15 adult tickets and 35 student
tickets is present.
The response reflects a systematic
strategy (using a system of two
equations and two unknowns)
that includes all important
elements of the problem.
The response addresses both
what was done and why (“…set up
two equations…combined to get
values for x and y…”).
Extended-Response Student Sample 24B
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 15 adult tickets and 35 student
tickets is present.
The response reflects a systematic
strategy (guessing and checking
using multiples of $5 and $3) that
includes all important elements of
the problem.
The response addresses both
what was done and why
(“…18 + 30 only equaled 48 so
I knew I had to raise the ticket
numbers…I used the numbers
20 and 30 because their sum is
50…”).
Extended-Response Student Sample 24C
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
2
3
4
This response shows some
understanding of the problem’s
mathematical concepts and
principles. An incorrect answer of
30 adult tickets and 10 student
tickets is present.
The response identifies most
of the important elements, and
the solution process is nearly
complete (dividing the total cost
by 5 and 3 and adjusting).
The response addresses both what
was done and why (“…going to see
how many times 5 can go into
$180 without reaching 50…it
goes in 60 times and that’s too
many tickets so I’m going to take
away 6 …”).
47
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 25A
48
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
49
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 25B
50
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
51
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Extended-Response Student Sample 25C
52
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
53
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2009 ISAT Mathematics Form LM Sample Book - Grade 7
Scoring Guide for “Pancake Breakfast”
There are two parts to this problem. The correct answers are that the students need to make 720 pancakes to feed
120 people and that the bags of pancake mix will cost $60. Most student responses included basic arithmetic as the
strategy used to solve this problem.
Extended-Response Student Sample 25A
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 answers
of 720 pancakes and $60 are
present.
The response reflects a
systematic strategy that includes
all important elements of the
problem.
The response addresses both what
was done and why (“multiply
3 times 240 because there are
240 people and each person
gets 3 pancakes; each bag costs
$10...I multiplied 6 times 10”).
Extended-Response Student Sample 25B
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
3
4
3
This response shows a nearly
complete understanding of the
problem’s mathematical concepts
and principles. The correct answer
of 720 pancakes is given, but a
calculation error caused the student
to give an incorrect cost for the
pancake mix ($50).
The response reflects a
systematic strategy that includes
all important elements of the
problem.
The response addresses both what
was done and begins to address
why (“everybody needs 3 pancakes
so I multiplied 240 by 3”).
Extended-Response Student Sample 25C
MATHEMATICAL KNOWLEDGE
STRATEGIC KNOWLEDGE
EXPLANATION
1
1
4
The response shows limited to no
understanding of the problem’s
mathematical concepts. The
student states that 28,803 pancakes
are needed to feed 240 people.
This calculation is unreasonable
and also has an arithmetic error.
Although the cost is computed in
relation to the first answer given, it
too is unreasonable.
The response reflects an
inappropriate strategy that would
not lead to a correct solution.
54
The response addresses both what
was done and why (“I took 240 and
multiplied it by 120 because it said
each bag makes 120 pancakes;
I added 3 to 28,800 because…
because it said each person will be
served 3 pancakes”).