ISTEP+: Grade 7
Mathematics
Released Items and Scoring Notes
Introduction
Indiana students in Grades 3-8 participated in the ISTEP+ Spring 2012 administration. The test
for ISTEP+ in Spring 2012 consisted of an Applied Skills section administered in March and a
Multiple-Choice section administered in late April and early May. For all grades, the Applied
Skills section of the assessment was handscored by trained evaluators. The Multiple-Choice
section was machine-scored. Scores for the Applied Skills and Multiple-Choice sections are
combined to generate a student’s total score.
Test results for both the Multiple-Choice and Applied Skills sections, as well as images of the
Applied Skills student responses, are available online. It is the expectation of the Indiana
Department of Education that schools will take this opportunity to have a conversation with
parents and students about the results. As a springboard for this conversation, the Indiana
Department of Education has created this document which outlines the released Applied Skills
questions and includes brief scoring notes that describe the given score points and explain the
scoring rules and expectations for the individual questions.
This document consists of:
• a brief description of the types of questions assessed
• a short summary of scoring rules utilized by the trained evaluators
• access to rubrics used to score student responses
• a copy of the released Applied Skills questions
• anchor papers used by evaluators to distinguish between rubric scores
NOTE: The Applied Skills operational questions are released at the end of each test
administration. It is important to keep in mind that a significant portion of a student’s score is
calculated from the Multiple-Choice section of the assessment, which is not addressed within this
document.
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QUESTION TYPES
This document addresses the Applied Skills section of ISTEP+, which allows students to
demonstrate their understanding of content in a variety of ways. The Applied Skills Assessment
consists of constructed-response (CR) and extended-response (ER) questions. CR and ER
questions are cognitively more demanding than multiple-choice (MC) questions. ER questions
are typically more complex and will likely require more steps to respond.
SCORING
For the Applied Skills Assessment, each question is scored according to a rubric. Rubrics clearly
define the requirements for each score point. Each student response is evaluated individually to
determine whether it is acceptable. This allows student scores to be reported as accurately as
possible. To ensure consistency when scoring the ISTEP+ questions, CTB/McGraw-Hill
works closely with assessment specialists at the Indiana Department of Education and teacher
committees to set guidelines for scoring student responses. Committees look at several student
papers and score them using the rubrics. Some of the student responses are selected as anchor
papers and are used as clear examples of specific score points. Samples of anchor papers
are presented within this document. Scoring supervisors then use anchor papers and approved,
scored student responses to ensure that responses are evaluated appropriately and consistently.
Individuals who evaluate and score ISTEP+ student responses must have a four-year college
degree and pass a series of qualifying tests on specific questions before they can evaluate any
student responses.
If a response is unscorable, it is assigned one of the following condition codes:
A
B
C
D
Blank/No Response/Refusal
Illegible
Written predominantly in a language other than English
Insufficient response/Copied from text
For additional information regarding ISTEP+ or other student assessments,
please contact the Indiana Department of Education by calling 317-232-9050
or writing via email: [email protected].
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The chart below summarizes the question types used to measure a student’s mastery of content,
the assessment that contains the particular question type, the standards assessed in each
assessment, and the scoring method used to evaluate a student’s response given the question
type.
Scoring Note: All student responses to questions found in each Applied Skills Assessment are
handscored using the specific rubric(s) outlined in the column labeled “Scoring Method.” As
indicated in the chart, all multiple-choice questions are machine scored.
Standards
Assessed
Question Type
Assessment
Constructed-Response (CR)
Applied Skills
Assessment
1,2,3,5,7
Extended-Response (ER)
Applied Skills
Assessment
1,2,3,5,7
Multiple-Choice (MC)
Multiple-Choice
Assessment
All
Scoring Method
4-pt. CR Rubric
(2-pts. Content and
2-pts. Problem
Solving)
6-pt. ER Rubric
(3-pts. Content and
3-pts. Problem
Solving)
Machine-Scored
More information is available regarding these assessment topics on the Office of Student
Assessment homepage at http://www.doe.in.gov/achievement/assessment.
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Constructed Response Rubric
2
1
0
2
1
0
Content Rubric
A score of two indicates a thorough understanding of the mathematical concepts embodied in
the task. The response
• shows algorithms, computations, and other content related work executed correctly and
completely.
A score of one indicates a partial understanding of the mathematical concepts embodied in the
task. The response
• contains errors in the execution of algorithms, computations, and/or other content related work.
A score of zero indicates limited or no understanding of the mathematical concepts embodied in
the task.
Problem-Solving Rubric
A score of two indicates a thorough understanding of the problem-solving concepts embodied in
the task. The response
• shows an appropriate strategy to solve the problem, and the strategy is executed correctly and
completely.
• identifies all important elements of the problem and shows a complete understanding of the
relationships among them.
• provides clear and complete explanations and/or interpretations when required.
A score of one indicates a partial understanding of the problem-solving concepts embodied in the
task. The response contains one or more of the following errors. The response
• shows an appropriate strategy to solve the problem. However, the execution of the strategy
contains errors and/or is incomplete.
• identifies some of the important elements of the problem and shows a general understanding of
the relationships among them.
• provides incomplete, partial, or unclear explanations and/or interpretations when required.
A score of zero indicates limited or no understanding of the problem-solving concepts embodied
in the task.
Clarification and Implementation Guidance
•
Correct answers ONLY, on all parts of the problem with no work shown, will receive a maximum
of 1 point in content and a maximum of 1 point in Problem Solving.
•
A student can receive the top score point in Problem Solving if the strategy used would result in a
correct answer even though the response contains computation errors.
•
A student can receive the top score point in Problem Solving if an error made in the “content”
portion is used with an appropriate strategy to solve the problem.
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Extended Response Rubric
3
2
1
0
3
2
1
0
Content Rubric
A score of three indicates a thorough understanding of the mathematical concepts embodied in
the task. The response
• shows algorithms, computations, and other content related work executed correctly and
completely.
A score of two indicates a partial understanding of the mathematical concepts embodied in the
task. The response
• shows an attempt to execute algorithms, computations, and other content related work correctly
and completely; computation errors or other minor errors in the content related work may be
present.
A score of one indicates a limited understanding of the mathematical concepts embodied in the
task. The response
• contains major errors, or only a partial process.
• contains algorithms, computations, and other content related work which may only be partially
correct.
A score of zero indicates no understanding of the mathematical concepts embodied in the task.
Problem-Solving Rubric
A score of three indicates a thorough understanding of the problem-solving concepts embodied
in the task. The response
• shows an appropriate strategy to solve the problem, and the strategy is executed correctly and
completely.
• identifies all important elements of the problem and shows a complete understanding of the
relationships among them.
• provides clear and complete explanations and/or interpretations when required.
A score of two indicates a partial understanding of the problem-solving concepts embodied in the
task. The response contains one or more of the following errors. The response
• shows an appropriate strategy to solve the problem. However, the execution of the strategy
lacks an essential element.
• identifies some of the important elements of the problem and shows a general understanding of
the relationships among them.
• provides incomplete or unclear explanations and/or interpretations when required.
A score of one indicates a limited understanding of the problem-solving concepts embodied in
the task. The response contains one or more of the following errors. The response
• shows an appropriate strategy to solve the problem. However, the execution of the strategy is
applied incorrectly and/or is incomplete.
• shows a limited understanding of the relationships among the elements of the problem.
• provides incomplete, unclear, or omitted explanations and/or interpretations when required.
A score of zero indicates no understanding of the problem-solving concepts embodied in the task.
Clarification and Implementation Guidance
•
Correct answers ONLY, on all parts of the problem with no work shown, will receive a maximum
of 2 points in content and a maximum of 2 points in Problem Solving.
•
A student can receive the top score point in Problem Solving if the strategy used would result in a
correct answer even though the response contains computation errors.
•
A student can receive the top score point in Problem Solving if an error made in the “content”
portion is used with an appropriate strategy to solve the problem.
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Constructed Response
Standard 3: Algebra & Functions
Standard 7: Problem Solving
Question 1
Michael bought a total of 42 pens and markers. He spent $24.50 on
markers and $1.25 for each pen. He spent a total of $59.50.
Write an equation that can be used to determine the number
of pens (p) Michael bought.
Equation_________________________
What is the cost of 1 marker?
Show All Work
Answer $__________
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Exemplary Response:
•
1.25p + 24.50 = 59.50
(Or other valid equation)
And
•
$1.75
Sample Process:
1.25p + 24.50 = 59.50
1.25p = 35
p = 28
42 – 28 = 14 markers
$24.50 ÷ 14 = $1.75
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Question 1, Sample A – Algebra & Functions Score Point 2; Problem Solving Score Point 1
Scoring Notes: This response shows a thorough understanding of the content skills
and a partial understanding of the problem-solving concepts within the question. The
written equation is correct. This student also determined the number of pens that
Michael bought (28) and followed through the entire process to solve this problem
with only one flaw. They should have used the number of pens (28) to determine the
number of markers Michael bought (42 – 28 = 14 instead of 42 – 35 = 7). This student
may have been confused with the meaning of the variable “p”, as they labeled the
value of 28 with a dollar sign instead of knowing that it represents the amount of pens.
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Question 1, Sample B – Algebra & Functions Score Point 1; Problem Solving Score Point 2
Scoring Notes: This response shows a partial understanding of the content skills and a
thorough understanding of the problem-solving concepts within the question. The
equation written is incorrect. However, the answer in part two and all other work
shown is correct. This student understood the process to determine the answer in part
two, however, they struggled to represent the situation algebraically as shown in part
one.
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Question 1, Sample C – Algebra & Functions Score Point 1; Problem Solving Score Point 1
Scoring Notes: This response shows a partial understanding of the content skills and a
partial understanding of the problem-solving concepts within the question. The
equation written in part one has a flaw. Parentheses are needed around the
expression (59.50 – 24.50) to indicate a proper order of operations in the equation. In
part two, a correct process to determine the number of pens and markers is shown, and
those values are determined correctly. However, this student should have divided
24.50 by 14 to determine the cost of one marker.
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Constructed Response
Standard 2: Computation
Standard 7: Problem Solving
Question 2
Last week, a supermarket sold bananas for $0.60 per pound.
This week, bananas are on sale for $0.45 per pound.
What is the percent of decrease in the price per pound of bananas
from last week to this week?
Show All Work
Answer__________%
A restaurant needs to purchase 13 pounds of bananas.
How much will the restaurant save purchasing the bananas from the
supermarket this week compared with last week? Do NOT include tax.
Show All Work
Answer $__________
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Exemplary Response:
•
25%
And
•
$1.95
Sample Process:
0.60 – 0.45 = 0.15
0.15 ÷ 0.60 = 0.25
13 x 0.15 = $1.95
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Question 2, Sample A – Computation Score Point 2; Problem Solving Score Point 1
Scoring Notes: This response shows a thorough understanding of the content skills
and a partial understanding of the problem-solving concepts within the question.
There is only one flaw in this response. This student should have used the cost savings
per pound ($0.15) to multiply by 13 in part two. Everything else is correct.
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Question 2, Sample B – Computation Score Point 1; Problem Solving Score Point 2
Scoring Notes: This response shows a partial understanding of the content skills and a
thorough understanding of the problem-solving concepts within the question. There is
only one flaw in this response. This student did not convert 0.25 to 25%. Everything else
is correct.
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Question 2, Sample C – Computation Score Point 1; Problem Solving Score Point 1
Scoring Notes: This response shows a partial understanding of the content skills and a
partial understanding of the problem-solving concepts within the question. In part
one, the student should have divided the difference in prices ($0.15) by the original
cost ($0.60) when calculating the percent of decrease. In part two, the student should
have used the cost savings per pound ($0.15) to multiply by 13. It appears that this
student may have mistaken the sale price ($0.45) as the cost savings ($0.15).
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Question 2, Sample D – Computation Score Point 2; Problem Solving Score Point 0
Scoring Notes: This response shows a thorough understanding of the content skills and
limited or no understanding of the problem-solving concepts within the question. The
answer and work in part one is correct which contributes mainly to the Computation
Standard. The answer and work in part two is incorrect which mainly contributes to the
Problem Solving Standard for this question.
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Question 2, Sample E – Computation Score Point 0; Problem Solving Score Point 2
Scoring Notes: This response shows limited or no understanding of the content skills
and a thorough understanding of the problem-solving concepts within the question.
The answer and work in part one is incorrect which mainly contributes to the
Computation Standard. The answer and work in part two are correct which mainly
contributes to the Problem Solving Standard for this question.
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Constructed Response
Standard 3: Algebra & Functions
Standard 7: Problem Solving
Question 3
Jamie made a practice schedule for next week to prepare for her
piano show. Jamie plans to:
• practice the same number of minutes each day, Monday
through Friday
• practice a total of 120 minutes on Saturday and Sunday
• practice no more than 300 minutes for the week
Write an inequality that represents the number of minutes, m, Jamie
can practice each day, Monday through Friday, for next week.
Inequality_________________________
Jamie claims that she could practice ½ HOUR each day, Monday
through Friday, for next week.
Is Jamie’s claim correct? Use words, numbers, and/or symbols to
support your answer.
Show All Work
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
____________________________________________________________________________________________
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Exemplary Response:
•
5m + 120 ≤ 300
(Or other valid inequality)
And
•
Yes, Jamie’s claim is correct. If she practices ½ hour each day, Monday through Friday, she
will practice for less than 300 minutes.
Sample Process:
5(30) + 120 ≤ 300
150 + 120 ≤ 300
270 ≤ 300
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Question 3, Sample A – Algebra & Functions Score Point 2; Problem Solving Score Point 1
Scoring Notes: This response shows a thorough understanding of the content skills
and a partial understanding of the problem-solving concepts within the question.
The written inequality is valid, and the calculations shown in the work space are
correct. However, it appears that this student mistakenly thinks that Jamie is trying
to practice 300 minutes for the week rather than practice no more than 300 minutes
for the week. This lack of utilizing 300 in the correct manneris the only flaw in this
response.
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Question 3, Sample B – Algebra & Functions Score Point 1; Problem Solving Score Point 2
Scoring Notes: This response shows a partial understanding of the content skills and a
thorough understanding of the problem-solving concepts within the question. The
inequality written is incorrect; however, this student shows some understanding of
representing the situation algebraically. The flaw in the inequality is that the student
did not include all 5 days of the week to appropriately model the situation. This is the
only flaw in this response. In part two, the student shows a valid process, correct
calculations, and gives a valid explanation to prove Jamie’s claim correct.
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Question 3, Sample C – Algebra & Functions Score Point 1; Problem Solving Score Point 1
Scoring Notes: This response shows a partial understanding of the content skills and a
partial understanding of the problem-solving concepts within the question. The
answer written on the inequality line is incorrect. In part two, the student’s process is
valid, and the calculations are correct which support Jamie’s claim. However, the
explanation is incorrect as it appears that this student mistakenly thinks that Jamie is
trying to practice 300 minutes for the week rather than practice no more than 300
minutes for the week.
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Question 3, Sample D – Algebra & Functions Score Point 0; Problem Solving Score Point 1
Scoring Notes: This response shows limited or no understanding of the content skills
and a partial understanding of the problem-solving concepts within the question. The
inequality written is incorrect. In part two, this student determines the amount of
practice minutes for the 5 days during the week. However, this student mistakenly
thinks that Jamie is trying to practice 300 minutes for the week rather than practice no
more than 300 minutes for the week. This student also fails to incorporate the minutes
practiced on Saturday and Sunday.
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Extended Response
Standard 5: Measurement
Standard 7: Problem Solving
Question 4
Tasty Corn cereal is sold in a box with the dimensions shown below.
Length: 19 centimeters
Height: 27 centimeters
Width: 6 centimeters
The Tasty Corn company only fills 80% of its cereal boxes.
How much cereal, in cubic centimeters, is in 1 box?
Show All Work
Answer__________ cubic centimeters
The volume of 30 pieces of Tasty Corn cereal is 2 cubic centimeters.
The Perin family serves its cereal in bowls that can hold 4,050 pieces
of cereal.
How many full bowls of cereal will the Perin family be able to eat from
1 box of Tasty Corn?
Show All Work
Answer__________full bowls
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Exemplary Response:
•
2,462.4 cubic centimeters
And
•
9 full bowls
Sample Process:
V = 19 x 6 x 27
V = 3,078 cubic centimeters
3,078 x 0.80 = 2,462.4
2,462.4 ÷ 2 = 1,231.2
1,231.2 x 30 = 36,936 pieces of cereal
36,936 ÷ 4,050 = 9.12
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Question 4, Sample A – Measurement Score Point 3; Problem Solving Score Point 2
Scoring Notes: This response shows a thorough understanding of the content skills
and a partial understanding of the problem-solving concepts within the question. The
only flaw in this response is that the student needed to divide by 2 in the second part of
the problem to obtain the correct answer. The ratio aspect of this problem was
misunderstood. Since the volume of 30 pieces of cereal is equal to 2 cubic centimeters,
the volume of 15 pieces of cereal is equal to 1 cubic centimeter. Thus, the student
should have divided by two in the process, or multiplied 2,462.4 by 15 instead of by 30.
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Question 4, Sample B – Measurement Score Point 3; Problem Solving Score Point 1
Scoring Notes: This response shows a thorough understanding of the content skills
and a limited understanding of the problem-solving concepts within the question. The
answer and work in part one is correct. In part two, both computations shown could
serve as correct initial steps. However, there are no other steps shown to complete the
process and determine the answer.
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Question 4, Sample C – Measurement Score Point 3; Problem Solving Score Point 0
Scoring Notes: This response shows a thorough understanding of the content skills
and limited or no understanding of the problem-solving concepts within the question.
The answer and work in part one is correct which contributes mainly to the
Measurement Standard. There is nothing correct in part two.
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Question 4, Sample D – Measurement Score Point 2; Problem Solving Score Point 2
Scoring Notes: This response shows a partial understanding of the content skills and a
partial understanding of the problem-solving concepts within the question. In part
one, the volume of cereal in one box is found. However, this student wrote 20% of the
entire volume on the answer line instead of 80%. This is the only flaw in part one. In
part two, everything is correct except for the fact that the student used the entire
volume of cereal in one box (3,078) when solving the problem. They should have used
80% of the entire volume (2,462.4). It should be noted that if this student had used
their incorrect value from part one (615.6) correctly in part two, then this student
would have received 3 points for problem solving.
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Question 4, Sample E – Measurement Score Point 1; Problem Solving Score Point 0
Scoring Notes: This response shows a limited understanding of the content skills and
no understanding of the problem-solving concepts within the question. In part one,
this student shows a correct process to determine the volume of cereal in one box.
However, a computation error is made when doing this calculation. There is nothing
correct in part two.
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