Keystone Exams: Algebra I - Mtlsd
Keystone Exams: Algebra IAssessment Anchors and Eligible ContentPennsylvania Department of Educationwww.education.state.pa.usApril 2014
PENNSYLVANIA DEPARTMENT OF EDUCATIONGeneral Introduction to the Keystone Exam Assessment AnchorsIntroductionSince the introduction of the Keystone Exams, the Pennsylvania Department of Education (PDE) has been working to create a set of tools designed to helpeducators improve instructional practices and better understand the Keystone Exams. The Assessment Anchors, as defined by the Eligible Content, are one of themany tools the Department believes will better align curriculum, instruction, and assessment practices throughout the Commonwealth. Without this alignment, itwill not be possible to significantly improve student achievement across the Commonwealth.How were Keystone Exam Assessment Anchors developed?Prior to the development of the Assessment Anchors, multiple groups of PA educators convened to create a set of standards for each of the Keystone Exams.Enhanced Standards, derived from a review of existing standards, focused on what students need to know and be able to do in order to be college and careerready. (Note: Since that time, PA Core Standards have replaced the Enhanced Standards and reflect the college- and career-ready focus.) Additionally, theAssessment Anchors and Eligible Content statements were created by other groups of educators charged with the task of clarifying the standards assessed on theKeystone Exams. The Assessment Anchors, as defined by the Eligible Content, have been designed to hold together, or anchor, the state assessment system andthe curriculum/instructional practices in schools.Assessment Anchors, as defined by the Eligible Content, were created with the following design parameters: Clear: The Assessment Anchors are easy to read and are user friendly; they clearly detail which standards are assessed on the KeystoneExams. Focused: The Assessment Anchors identify a core set of standards that could be reasonably assessed on a large-scale assessment; this willkeep educators from having to guess which standards are critical. Rigorous: The Assessment Anchors support the rigor of the state standards by assessing higher-order and reasoning skills. Manageable: The Assessment Anchors define the standards in a way that can be easily incorporated into a course to prepare students forsuccess.How can teachers, administrators, schools, and districts use these Assessment Anchors?The Assessment Anchors, as defined by the Eligible Content, can help focus teaching and learning because they are clear, manageable, and closely aligned with theKeystone Exams. Teachers and administrators will be better informed about which standards will be assessed. The Assessment Anchors and Eligible Contentshould be used along with the Standards and the Curriculum Framework of the Standards Aligned System (SAS) to build curriculum, design lessons, and supportstudent achievement.The Assessment Anchors and Eligible Content are designed to enable educators to determine when they feel students are prepared to be successful in theKeystone Exams. An evaluation of current course offerings, through the lens of what is assessed on those particular Keystone Exams, may provide an opportunityfor an alignment to ensure student preparedness.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 2Final—April 2014
How are the Assessment Anchors organized?The Assessment Anchors, as defined by the Eligible Content, are organized into cohesive blueprints, each structured with a common labeling system that can beread like an outline. This framework is organized first by module, then by Assessment Anchor, followed by Anchor Descriptor, and then finally, at the greatest levelof detail, by an Eligible Content statement. The common format of this outline is followed across the Keystone Exams.Here is a description of each level in the labeling system for the Keystone Exams: Module: The Assessment Anchors are organized into two thematic modules for each of the Keystone Exams. The module title appears at the top of eachpage. The module level is important because the Keystone Exams are built using a module format, with each of the Keystone Exams divided into twoequal-size test modules. Each module is made up of two or more Assessment Anchors. Assessment Anchor: The Assessment Anchor appears in the shaded bar across the top of each Assessment Anchor table. The Assessment Anchorsrepresent categories of subject matter that anchor the content of the Keystone Exams. Each Assessment Anchor is part of a module and has one or moreAnchor Descriptors unified under it. Anchor Descriptor: Below each Assessment Anchor is a specific Anchor Descriptor. The Anchor Descriptor level provides further details that delineate thescope of content covered by the Assessment Anchor. Each Anchor Descriptor is part of an Assessment Anchor and has one or more Eligible Contentstatements unified under it. Eligible Content: The column to the right of the Anchor Descriptor contains the Eligible Content statements. The Eligible Content is the most specificdescription of the content that is assessed on the Keystone Exams. This level is considered the assessment limit and helps educators identify the range ofthe content covered on the Keystone Exams. PA Core Standards: In the column to the right of each Eligible Content statement is a code representing one or more Pennsylvania Core Standard thatcorrelate to the Eligible Content statement. Some Eligible Content statements include annotations that indicate certain clarifications about the scope of anEligible Content.o “e.g.” (“for example”)—sample approach, but not a limit to the Eligible Contento “i.e.” (“that is”)—specific limit to the Eligible Contento “Note”—content exclusions or definable range of the Eligible ContentHow do the K–12 Pennsylvania Core Standards affect this document?Assessment Anchors and Eligible Content statements are aligned to the PA Core Standards; thus, the former enhanced standards are no longer necessary. Withinthis document, all standard references reflect the PA Core Standards.Standards Aligned System — http://www.pdesas.org/Pennsylvania Department of Education — www.education.state.pa.usCover photo Hill Street Studios/Harmik Nazarian/Blend Images/Corbis.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 3Final—April 2014
Keystone Exams: Algebra IMODULE 1—Operations and Linear Equations & InequalitiesASSESSMENT ANCHORA1.1.1 Operations with Real Numbers and ExpressionsAnchor DescriptorEligible ContentA1.1.1.1Represent and/or use numbersin equivalent forms (e.g.,integers, fractions, decimals,percents, square roots, andexponents).A1.1.1.1.1A1.1.1.1.2Anchor DescriptorA1.1.1.2Apply number theory conceptsto show relationships betweenreal numbers in problemsolving settings.Compare and/or order any real numbers.Note: Rational and irrational may be mixed.Simplify square roots (e.g., 24 2 6).Eligible ContentA1.1.1.2.1FINAL—April 2014PA Core StandardsCC.2.1.8.E.1Distinguish between rational and irrational numbersusing their properties.CC.2.1.8.E.4Estimate irrational numbers by comparing them torational numbers.CC.2.1.HS.F.1Apply and extend the properties of exponents to solveproblems with rational exponents.CC.2.1.HS.F.2Apply properties of rational and irrational numbers tosolve real-world or mathematical problems.PA Core StandardsFind the Greatest Common Factor (GCF) and/or CC.2.1.6.E.3the Least Common Multiple (LCM) for sets ofDevelop and/or apply number theory concepts to findmonomials.common factors and multiples.CC.2.1.HS.F.2Apply properties of rational and irrational numbers tosolve real-world or mathematical problems.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 4Final—April 2014
Keystone Exams: Algebra IMODULE 1—Operations and Linear Equations & InequalitiesAnchor DescriptorA1.1.1.3Use exponents, roots, and/orabsolute values to solveproblems.Eligible ContentA1.1.1.3.1Anchor DescriptorA1.1.1.4Use estimation strategies inproblem-solving situations.Simplify expressions involvingpolynomials.PA Core StandardsCC.2.1.HS.F.1Apply and extend the properties of exponents to solveproblems with rational exponents.CC.2.1.HS.F.2Apply properties of rational and irrational numbers tosolve real-world or mathematical problems.CC.2.2.8.B.1Apply concepts of radicals and integer exponents togenerate equivalent expressions.Eligible ContentPA Core StandardsA1.1.1.4.1Use estimation to solve problems.CC.2.2.7.B.3Model and solve real-world and mathematical problemsby using and connecting numerical, algebraic, and/orgraphical representations.CC.2.2.HS.D.9Use reasoning to solve equations and justify the solutionmethod.A1.1.1.5.1Add, subtract, and/or multiply polynomialexpressions (express answers in simplestform).Note: Nothing larger than a binomialmultiplied by a trinomial.Factor algebraic expressions, includingdifference of squares and trinomials.Note: Trinomials are limited to the formax2 bx c where a is equal to 1 after factoringout all monomial factors.Simplify/reduce a rational algebraicexpression.Anchor DescriptorA1.1.1.5Simplify/evaluate expressions involvingproperties/laws of exponents, roots, and/orabsolute values to solve problems.Note: Exponents should be integers from –10to 10.FINAL—April 2014Eligible ContentA1.1.1.5.2A1.1.1.5.3PA Core StandardsCC.2.2.HS.D.1Interpret the structure of expressions to represent aquantity in terms of its context.CC.2.2.HS.D.2Write expressions in equivalent forms to solve problems.CC.2.2.HS.D.3Extend the knowledge of arithmetic operations andapply to polynomials.CC.2.2.HS.D.5Use polynomial identities to solve problems.CC.2.2.HS.D.6Extend the knowledge of rational functions to rewrite inequivalent forms.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 5Final—April 2014
Keystone Exams: Algebra IMODULE 1—Operations and Linear Equations & InequalitiesASSESSMENT ANCHORA1.1.2 Linear EquationsAnchor DescriptorA1.1.2.1Write, solve, and/or graphlinear equations using variousmethods.Eligible ContentA1.1.2.1.1A1.1.2.1.2A1.1.2.1.3Write, solve, and/or apply alinear equation (includingproblem situations).Use and/or identify an algebraicproperty to justify any step in anequation-solving process.Note: Linear equations only.Interpret solutions to problemsin the context of the problemsituation.Note: Linear equations only.FINAL—April 2014PA Core StandardsCC.2.1.HS.F.3Apply quantitative reasoning to choose and interpret units and scalesin formulas, graphs, and data displays.CC.2.1.HS.F.4Use units as a way to understand problems and to guide the solutionof multi-step problems.CC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations on measurementwhen reporting quantities.CC.2.2.8.B.3Analyze and solve linear equations and pairs of simultaneous linearequations.CC.2.2.8.C.1Define, evaluate, and compare functions.CC.2.2.8.C.2Use concepts of functions to model relationships between quantities.CC.2.2.HS.C.3Write functions or sequences that model relationships between twoquantities.CC.2.2.HS.D.7Create and graph equations or inequalities to describe numbers orrelationships.CC.2.2.HS.D.8Apply inverse operations to solve equations or formulas for a givenvariable.CC.2.2.HS.D.9Use reasoning to solve equations and justify the solution method.CC.2.2.HS.D.10Represent, solve, and interpret equations/inequalities and systems ofequations/inequalities algebraically and graphically.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 6Final—April 2014
Keystone Exams: Algebra IMODULE 1—Operations and Linear Equations & InequalitiesAnchor DescriptorA1.1.2.2Write, solve, and/or graphsystems of linear equationsusing various methods.Eligible ContentA1.1.2.2.1A1.1.2.2.2Write and/or solve a system of linearequations (including problem situations) usinggraphing, substitution, and/or elimination.Note: Limit systems to two linear equations.Interpret solutions to problems in the contextof the problem situation.Note: Limit systems to two linear equations.FINAL—April 2014PA Core StandardsCC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations onmeasurement when reporting quantities.CC.2.2.8.B.3Analyze and solve linear equations and pairs ofsimultaneous linear equations.CC.2.2.HS.D.7Create and graph equations or inequalities to describenumbers or relationships.CC.2.2.HS.D.9Use reasoning to solve equations and justify the solutionmethod.CC.2.2.HS.D.10Represent, solve, and interpret equations/inequalitiesand systems of equations/inequalities algebraically andgraphically.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 7Final—April 2014
Keystone Exams: Algebra IMODULE 1—Operations and Linear Equations & InequalitiesASSESSMENT ANCHORA1.1.3 Linear InequalitiesAnchor DescriptorA1.1.3.1Eligible ContentWrite, solve, and/or graphA1.1.3.1.1linear inequalities using variousmethods.A1.1.3.1.2A1.1.3.1.3Anchor DescriptorA1.1.3.2Write, solve, and/or graphsystems of linear inequalitiesusing various methods.Write or solve compound inequalities and/orgraph their solution sets on a number line (mayinclude absolute value inequalities).Identify or graph the solution set to a linearinequality on a number line.Interpret solutions to problems in the contextof the problem situation.Note: Linear inequalities only.Eligible ContentA1.1.3.2.1A1.1.3.2.2Write and/or solve a system of linearinequalities using graphing.Note: Limit systems to two linear inequalities.Interpret solutions to problems in the contextof the problem situation.Note: Limit systems to two linear inequalities.FINAL—April 2014PA Core StandardsCC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations onmeasurement when reporting quantities.CC.2.2.HS.D.7Create and graph equations or inequalities to describenumbers or relationships.CC.2.2.HS.D.9Use reasoning to solve equations and justify the solutionmethod.CC.2.2.HS.D.10Represent, solve, and interpret equations/inequalitiesand systems of equations/inequalities algebraically andgraphically.PA Core StandardsCC.2.1.HS.F.5Choose a level of accuracy appropriate to limitations onmeasurement when reporting quantities.CC.2.2.HS.D.7Create and graph equations or inequalities to describenumbers or relationships.CC.2.2.HS.D.10Represent, solve, and interpret equations/inequalitiesand systems of equations/inequalities algebraically andgraphically.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 8Final—April 2014
Keystone Exams: Algebra IMODULE 2—Linear Functions and Data OrganizationsASSESSMENT ANCHORA1.2.1 FunctionsAnchor DescriptorA1.2.1.1Analyze and/or use patterns orrelations.Eligible ContentA1.2.1.1.1A1.2.1.1.2A1.2.1.1.3Analyze a set of data for the existence of apattern and represent the pattern algebraicallyand/or graphically.Determine whether a relation is a function,given a set of points or a graph.Identify the domain or range of a relation (maybe presented as ordered pairs, a graph, or atable).FINAL—April 2014PA Core StandardsCC.2.2.8.C.1Define, evaluate, and compare functions.CC.2.2.8.C.2Use concepts of functions to model relationshipsbetween quantities.CC.2.2.HS.C.1Use the concept and notation of functions to interpretand apply them in terms of their context.CC.2.2.HS.C.2Graph and analyze functions and use their properties tomake connections between the differentrepresentations.CC.2.2.HS.C.3Write functions or sequences that model relationshipsbetween two quantities.CC.2.4.HS.B.2Summarize, represent, and interpret data on twocategorical and quantitative variables.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 9Final—April 2014
Keystone Exams: Algebra IMODULE 2—Linear Functions and Data OrganizationsAnchor DescriptorA1.2.1.2Interpret and/or use linearfunctions and their equations,graphs, or tables.Eligible ContentA1.2.1.2.1A1.2.1.2.2Create, interpret, and/or use the equation,graph, or table of a linear function.Translate from one representation of a linearfunction to another (i.e., graph, table, andequation).FINAL—April 2014PA Core StandardsCC.2.1.HS.F.3Apply quantitative reasoning to choose and interpretunits and scales in formulas, graphs, and data displays.CC.2.1.HS.F.4Use units as a way to understand problems and to guidethe solution of multi-step problems.CC.2.2.8.B.2Understand the connections between proportionalrelationships, lines, and linear equations.CC.2.2.8.C.1Define, evaluate, and compare functions.CC.2.2.8.C.2Use concepts of functions to model relationshipsbetween quantities.CC.2.2.HS.C.2Graph and analyze functions and use their propertiesto make connections between the differentrepresentations.CC.2.2.HS.C.3Write functions or sequences that model relationshipsbetween two quantities.CC.2.2.HS.C.4Interpret the effects transformations have on functionsand find the inverses of functions.CC.2.2.HS.C.6Interpret functions in terms of the situations they model.CC.2.4.HS.B.2Summarize, represent, and interpret data on twocategorical and quantitative variables.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 10Final—April 2014
Keystone Exams: Algebra IMODULE 2—Linear Functions and Data OrganizationsASSESSMENT ANCHORA1.2.2 Coordinate GeometryAnchor DescriptorA1.2.2.1Describe, compute, and/or usethe rate of change (slope) of aline.Eligible ntify, describe, and/or use constant rates ofchange.Apply the concept of linear rate of change(slope) to solve problems.Write or identify a linear equation when given the graph of the line, two points on the line, or the slope and a point on the line.Note: Linear equation may be in point-slope,standard, and/or slope-intercept form.Determine the slope and/or y-interceptrepresented by a linear equation or graph.FINAL—April 2014PA Core StandardsCC.2.2.8.C.2Use concepts of functions to model relationshipsbetween quantities.CC.2.2.HS.C.1Use the concept and notation of functions to interpretand apply them in terms of their context.CC.2.2.HS.C.2Graph and analyze functions and use their properties tomake connections between the differentrepresentations.CC.2.2.HS.C.3Write functions or sequences that model relationshipsbetween two quantities.CC.2.2.HS.C.5Construct and compare linear, quadratic, andexponential models to solve problems.CC.2.2.HS.C.6Interpret functions in terms of the situations they model.CC.2.4.HS.B.1Summarize, represent, and interpret data on a singlecount or measurement variable.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 11Final—April 2014
Keystone Exams: Algebra IMODULE 2—Linear Functions and Data OrganizationsAnchor DescriptorA1.2.2.2Analyze and/or interpret dataon a scatter plot.Eligible ContentA1.2.2.2.1Draw, identify, find, and/or write an equationfor a line of best fit for a scatter plot.FINAL—April 2014PA Core StandardsCC.2.2.HS.C.6Interpret functions in terms of the situations they model.CC.2.4.8.B.1Analyze and/or interpret bivariate data displayed inmultiple representations.CC.2.4.HS.B.2Summarize, represent, and interpret data on twocategorical and quantitative variables.CC.2.4.HS.B.3Analyze linear models to make interpretations basedon the data.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 12Final—April 2014
Keystone Exams: Algebra IMODULE 2—Linear Functions and Data OrganizationsASSESSMENT ANCHORA1.2.3 Data AnalysisAnchor DescriptorA1.2.3.1Use measures of dispersion todescribe a set of data.Eligible ContentA1.2.3.1.1Anchor DescriptorA1.2.3.2A1.2.3.2.3Anchor DescriptorA1.2.3.3Apply probability to practicalsituations.Estimate or calculate to make predictionsbased on a circle, line, bar graph, measure ofcentral tendency, or other representation.Analyze data, make predictions, and/or answerquestions based on displayed data (box-andwhisker plots, stem-and-leaf plots, scatterplots, measures of central tendency, or otherrepresentations).Make predictions using the equations orgraphs of best-fit lines of scatter plots.Eligible ContentA1.2.3.3.1PA Core StandardsCalculate and/or interpret the range, quartiles, CC.2.4.HS.B.1and interquartile range of data.Summarize, represent, and interpret data on a singlecount or measurement variable.CC.2.4.HS.B.3Analyze linear models to make interpretations based onthe data.Eligible ContentUse data displays in problemA1.2.3.2.1solving settings and/or to makepredictions.A1.2.3.2.2FINAL—April 2014Find probabilities for compound events (e.g.,find probability of red and blue, find probabilityof red or blue) and represent as a fraction,decimal, or percent.PA Core StandardsCC.2.4.HS.B.1Summarize, represent, and interpret data on a singlecount or measurement variable.CC.2.4.HS.B.3Analyze linear models to make interpretations basedon the data.CC.2.4.HS.B.5Make inferences and justify conclusions based onsample surveys, experiments, and observationalstudies.PA Core StandardsCC.2.4.7.B.3Investigate chance processes and develop, use, andevaluate probability models.CC.2.4.HS.B.4Recognize and evaluate random processes underlyingstatistical experiments.CC.2.4.HS.B.7Apply the rules of probability to compute probabilitiesof compound events in a uniform probability model.Eligible Content may be assessed using problem-solving situations.Pennsylvania Department of EducationAssessment Anchors and Eligible ContentKeystone Exams: Algebra I—Page 13Final—April 2014
General Introduction to the Keystone Exam Assessment Anchors. Introduction . Since the introduction of the Keystone Exams, the Pennsylvania Department of Education (PDE) has been working to create a setof tools designed to help educators improve instructional practices and better understand the Keystone Exams.
Keystone Exams. The module title appears at the top of each page. The module level is important because the Keystone Exams are built using a module format, with each of the Keystone Exams divided into two equal-size test modules. Each module is made up of two or more Assessment Anchors.
Medical-Only HMO, Keystone 65 Select Medical-Only HMO, and Keystone 65 Select Rx HMO have networks of doctors, hospitals, pharmacies, and other providers. Keystone 65 Basic Rx HMO, Keystone 65 Liberty Medical-Only HMO, Keystone 65 Select Medical-Only HMO, and Keystone 65 Select Rx HMO: If you use providers that are not in
Texts of Wow Rosh Hashana II 5780 - Congregation Shearith Israel, Atlanta Georgia Wow ׳ג ׳א:׳א תישארב (א) ׃ץרֶָֽאָּהָּ תאֵֵ֥וְּ םִימִַׁ֖שַָּה תאֵֵ֥ םיקִִ֑לֹאֱ ארָָּ֣ Îָּ תישִִׁ֖ארֵ Îְּ(ב) חַורְָּ֣ו ם
Robert Gerver, Ph.D. North Shore High School 450 Glen Cove Avenue Glen Head, NY 11545 gerverr@northshoreschools.org Rob has been teaching at . Algebra 1 Financial Algebra Geometry Algebra 2 Algebra 1 Geometry Financial Algebra Algebra 2 Algebra 1 Geometry Algebra 2 Financial Algebra ! Concurrently with Geometry, Algebra 2, or Precalculus
Added KeyStone II specifics to SRTP examples (Page 3-8) Added mention of KeyStone II engine to Protocol Descriptions. (Page 2-5) Added Specifics for IPsec in KeyStone II devices at IPsec Examples. (Page 3-3) Included SRTP KeyStone II Updates (Page 2-21) Put KeyStone II specification in IPSEC Use (Page 2-11)
KE01053 Keystone Literature - English as a Second Language X KV01053 Keystone Literature - Visually Impaired X KH01053 Keystone Literature - Hearing Impaired X KAE01053 Keystone Literature - Alternative Education X K01005 Keystone – AP English Language and Composition X X X K01006 Keystone – AP Engl
Keystone First Keystone First . July 1, 2018 P.O. Box 7307 P.O. Box 7316 London, KY 40742 London, KY 40742 . Keystone First will send the Health Care Provider a letter acknowledging Keystone First's receipt of the request for a First Level Appeal Review within ten business days of Keystone .
AGMA American Gear Manufacturers Association AIA American Institute of Architects. AISI American Iron and Steel Institute ANSI American National Standards Institute, Inc. AREA American Railway Engineering Association ASCE American Society of Civil Engineers ASME American Society of Mechanical Engineers ASTM American Society for Testing and .
