Sample Items for End-of-Course Assessments

Transcription

Item Specifications: Algebra 1
WASHINGTON COMPREHENSIVE ASSESSMENT PROGRAM
Sample Items for
End-of-Course
Assessments
Algebra 1
2011-2012
OFFICE
OF
SUPERINTENDENT
OF
PUBLIC INSTRUCTION
Sample Items for End-of-Course Exams: Algebra 1
The purpose of this document is to identify sample items and previously released items that
align to the 2008 Mathematics Standards assessed on the End-of-Course Exams.
The performance expectations (PEs) in this document are identical to those in the Washington
State Test and Item Specifications. Performance expectations that will be assessed at the state
level appear in bold text. The remaining performance expectations, which appear in italicized
text, should be taught and assessed at the classroom level.
The information in the columns to the right of each performance expectation shows alignment
of each PE to other courses and item development parameters:




Integrated sequence shows the alignment of this PE to other courses. PEs that are
common to Algebra 1/Integrated Math 1 or Geometry/Integrated Math 2 are
labeled in green; PEs that align to other courses are labeled in yellow.
Cognitive complexity (C.C.) as Level 1, Level 2, Level 3, or Level 4 as defined by
Norman Webb.
Format may be Multiple-Choice (MC), Completion (CP), Short-Answer (SA), or not
assessed at the state level (NA).
Contextual Situation (Ctxt) may be required (Y), item dependent (I), or not allowed
(N).
Restrictions to cognitive complexity, item format and context are necessary to construct a valid
and reliable on-demand assessment; these restrictions are not necessary in classroom based
assessments. For more information regarding test organization, the types of items on the
exams, and considerations and procedures involved in item development, please refer to the
Test and Item Specifications.
Last Edited: 06/08/11
OSPI, Page 2
A1.1 Core Content: Solving Problems
(Algebra)
Items may ask students to:
Integrated
Sequence
C.C. Format Ctxt
A1.1.A Select and justify functions and equations to model and
solve problems.
M1.1.A
2
M2.1.A
MC,SA
Y
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 16
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, items 1 and 17
http://www.k12.wa.us/assessment/StateTesting/TestQuestions/WASLPractice-ParentStudent.aspx,
item 12
http://www.k12.wa.us/Mathematics/Assessment/ReleasedItems/2007/WARIDmathHS_WEB.pdf,
item 9
A1.1.B Solve problems that can be represented by linear
functions, equations, and inequalities.
M1.1.B
2
CP,SA
Y
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 10
item 27
items 10 and 19
A1.1.C Solve problems that can be represented by a system of
two linear equations or inequalities.
M1.1.C
2
CP,SA
Y
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf, pg 24-25
item 18
http://www.k12.wa.us/Mathematics/Assessment/ReleasedItems/2008/HSMathRIDFinal.pdf, item 6
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Pre-Season Football
OSPI, Page 3
A1.1.D Solve problems that can be represented by quadratic
functions and equations.
M2.1.C
2
CP
Y
item 34
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Marble Canyon, Safe Driving
A1.1.E Solve problems that can be represented by exponential
functions and equations.
M1.1.D
M2.1.D
2
MC,CP
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 21
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Best Interest
OSPI, Page 4
Y
A1.2 Core Content: Numbers, expressions, and operations
(Numbers, Operations, Algebra)
Integrated
Sequence
M1.6.A
C.C.
Format Ctxt
A1.2.A Know the relationship between real numbers and
1
the number line, and compare and order real
numbers with and without the number line.
MC
A1.2.B Recognize the multiple uses of variables,
M1.6.C
1,(2) MC,CP
determine all possible values of variables that
satisfy prescribed conditions, and evaluate
algebraic expressions that involve variables.
I
N
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Big Box, Skatepark
A1.2.C Interpret and use integer exponents and square M1.7.C
1
MC,CP
and cube roots, and apply the laws and properties of
exponents to simplify and evaluate exponential
expressions.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2011_EOC.pdf, pg 14 and 40
N
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Bacteria Growth
A1.2.E Use algebraic properties to factor and combine
M2.5.A 1
MC
like terms in polynomials.
N
item 25
OSPI, Page 5
A1.3 Core Content: Characteristics and behaviors of functions
(Algebra)
Integrated
Sequence
M1.2.A
C.C. Format Ctxt
A1.3.A Determine whether a relationship is a function
1,2
and identify the domain, range, roots, and independent
and dependent variables.
MC,SA
I
MC,SA
I
A1.3.B Represent a function with a symbolic expression, M1.2.B
2
as a graph, in a table, and using words, and make
connections among these representations.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 26-27
items 10 and 33
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Mass and Force, Big Box, Costs of
Essentials, Safe Driving
A1.3.C Evaluate f(x) at a (i.e., f(a)) and solve for x in the
M1.2.C
1
MC,CP N
equation f(x) = b.
item 14
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Building a House, CD Recording
Contract, Cell Phones, Football Kickoff, How Close is Lightning
OSPI, Page 6
A1.4 Core Content: Linear functions, equations, and inequalities
(Algebra)
Integrated
Sequence
M1.3.A
A1.4.A Write and solve linear equations and inequalities in
one variable.
C.C.
Format Ctxt
1,2
MC,CP
N
1
MC
N
1
MC
I
A1.4.B Write and graph an equation for a line given the
M1.3.D
slope and the y-intercept, the slope and a point on the line,
or two points on the line, and translate between forms of
linear equations.
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Building a House
A1.4.C Identify and interpret the slope and intercepts of a
M1.3.C
linear function, including equations for parallel and
perpendicular lines.
A1.4.D Write and solve systems of two linear equations and M1.3.E
1,2 MC,CP
inequalities in two variables.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 17 and 22
N
A1.4.E Describe how changes in the parameters of linear
M1.3.B
functions and functions containing an absolute
value of a linear expression affect their graphs and
the relationships they represent.
N
1,2
MC,SA
OSPI, Page 7
A1.5 Core Content: Quadratic functions and equations
(Algebra)
Integrated
C.C.
Sequence
M2.2.A 2
Format Ctxt
A1.5.A Represent a quadratic function with a symbolic
MC
I
expression, as a graph, in a table, and with a
description, and make connections among the
representations.
item 8
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Skatepark
A1.5.B Sketch the graph of a quadratic function, describe
M2.2.B 1,2
the effects that changes in the parameters have on
the graph, and interpret the x-intercepts as
solutions to a quadratic equation.
MC
I
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Football Kickoff
A1.5.C Solve quadratic equations that can be factored as
M2.2.D 1,2 MC,CP
(ax + b)(cx + d) where a, b, c, and d are integers.
N
A1.5.D Solve quadratic equations that have real roots by
M2.2.F 1,2
completing the square and by using the quadratic
formula.
N
MC,CP
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Hydraulophone
OSPI, Page 8
A1.6 Core Content: Data and distributions
(Data/Statistics/Probability)
Integrated
Sequence
M1.5.A
A1.6.A Use and evaluate the accuracy of summary statistics
to describe and compare data sets.
C.C.
Format Ctxt
2
MC,SA
Y
A1.6.B Make valid inferences and draw conclusions based
M1.5.C
2,3 MC,SA Y
on data.
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Mass and Force, Pre-Season
Football
A1.6.C Describe how linear transformations affect the
M1.5.B
center and spread of univariate data.
2
MC
Y
A1.6.D Find the equation of a linear function that best fits
M1.3.F
2
MC,SA
bivariate data that are linearly related, interpret the
slope and y-intercept of the line, and use the
equation to make predictions.
Y
item 8
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: CD Recording Contract, Costs of
Essentials, How Close is Lightning
A1.6.E Describe the correlation of data in scatterplots in
M1.3.G
terms of strong or weak and positive or negative.
2
MC
OSPI, Page 9
I
A1.7 Additional Key Content
(Algebra)
Integrated
Sequence
M1.7.A
A1.7.A Sketch the graph for an exponential function of the
form 𝒚 = 𝒂𝒃𝒏 where n is an integer, describe the
effects that changes in the parameters a and b have
on the graph, and answer questions that arise in
situations modeled by exponential functions.
C.C.
Format Ctxt
1,2
MC,SA
I
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Bacteria Growth, Best Interest, Cell
Phones
A1.7.B Find and approximate solutions to exponential
M1.7.B
equations.
2
MC
N
A1.7.C Express arithmetic and geometric sequences in both M1.7.D
1,2 MC,CP
explicit and recursive forms, translate between the
two forms, explain how rate of change is
represented in each form, and use the forms to find
specific terms in the sequence.
N
A1.7.D Solve an equation involving several variables by
M1.6.D
1,2 MC
expressing one variable in terms of the others.
N
item 30
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Safe Driving
OSPI, Page 10
A1.8 Core Processes: Reasoning, problem solving, and communication
Items assessing A1.8 Core Processes will use Core Content or Additional Key Content performance
expectations from Algebra 1, which are identified below for each sample item.
Integrated
Sequence
C.C.
Format Ctxt
A1.8.A Analyze a problem situation and represent it
mathematically.
M1.8.
A1.8.B Select and apply strategies to solve problems.
A-C
3
MC,SA
A1.8.C Evaluate a solution for reasonableness, verify its
accuracy, and interpret the solution in the context of the
original problem.
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 8 (A1.7.D)
Y
item 30 (A1.7.D) and item 34 (A1.1.D)
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE tasks: Best Interest (A1.1.E),
Hydraulophone (A1.5.D), Marble Canyon (A1.1.D)
A1.8.E Read and interpret diagrams, graphs, and text
M1.8.E
2,3
SA
Y
containing the symbols, language, and conventions
of mathematics.
http://www.k12.wa.us/Mathematics/pubdocs/EOCSampleBookletAnswerKey.pdf, item 10 (A1.1.B)
http://www.k12.wa.us/Mathematics/Assessment/ReleasedItems/2007/WARIDmathHS_WEB.pdf, item
10 (A1.1.B)
(A1.6.B)
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Cell Phones
A1.8.G Synthesize information to draw conclusions, and
M1.8.G
3
MC,SA
evaluate the arguments and conclusions of others.
http://www.k12.wa.us/Mathematics/pubdocs/Updatesfor2012_EOC.pdf , pg 28 (A1.6.A)
http://moodle.ospi.k12.wa.us/course/view.php?id=44, COE task: Best Interest (A1.7.A)
OSPI, Page 11
Y
Other Resources on the Web:
Many teachers and districts in Washington State have created resources to help prepare their
students for EOC Exams and EOC Makeup Exams. Other states and agencies have also created
and released resources aligned to their own state standards for mathematics or to the Common
Core State Standards. The resources below have not been thoroughly reviewed by OSPI staff,
but instead are the responsibility of the reader to analyze resources and determine if they suit
the needs of their own students.
Database of Teacher-Created Resources on the EOC Supports Moodle:
http://moodle.ospi.k12.wa.us/course/view.php?id=18
Mukilteo School District EOC Makeup Review for Algebra:
http://www.bsd405.org/portals/0/curriculum/MSPMath/EOC%20Algebra%201%20Master%20F
INAL.pdf
Snohomish School District Review packet for Algebra 1:
http://www.sno.wednet.edu/index.php/download_file/-/view/2429/
ESD123 Math Initiative Regional Mathematics Bank: http://www.esd123.org/mathitem
Resources compiled by Bellevue School District:
http://www.bsd405.org/portals/0/curriculum/MSPMath/
Interactive Quizzes for Algebra and Geometry Review:
http://www.iq.poquoson.org/hs.htm#math
National Center for Education Statistics NAEP Questions Tool:
http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics
Released items by Science & Mathematics Achievement Required for Tomorrow (SMART):
http://www.smartconsortium.org/index.php?id=122
Wisconsin Released Item Book for Grade 10 Mathematics:
http://dpi.wi.gov/oea/pdf/mathrelease10.pdf
TIMSS Released Set of 8th Grade Mathematics Items:
http://timss.bc.edu/PDF/T03_RELEASED_M8.pdf
Interactive Web Sample Items by North Carolina State University:
http://cuacs8.mck.ncsu.edu/mathsampleitems/main.html
Sample Items for the North Carolina EOC Test of Algebra I:
http://www.ncpublicschools.org/accountability/testing/eoc/sampleitems/2b
OSPI, Page 12
ADP Assessment Consortium Algebra I Resources:
http://www.achieve.org/AlgebraITestOverview
Virginia Department of Education:
EOC Practice Items:
http://www.doe.virginia.gov/testing/sol/practice_items/index.shtml
Released Exams:
http://www.doe.virginia.gov/testing/sol/released_tests/index.shtml
Georgia Algebra I EOC Released Test Booklet, Spring 2004:
http://www.doe.k12.ga.us/DMGetDocument.aspx/Released%20Algegra%201.pdf?p=4BE1EECF
99CD364EA5554055463F1FBBF5D074D5FB1F2CAEB3B63B3ECB220CDD26C2114F3C57D8D2F15
6E2D2DFFA2812&Type=D
Tennessee EOC Item Samplers and Practice Tests:
http://tennessee.gov/education/assessment/sec_samplers.shtml
Florida EOC Practice Tests:
http://www.pearsonaccess.com/cs/Satellite?c=Page&childpagename=Florida/flPALPLayout&ci
d=1205461226846&pagename=flPALPWrapper
OSPI, Page 13

Sample Items for End-of-Course Assessments

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