PARCC CAMPUS LEADERSHIP TEAM MATRIX TO HELP
1PARCC CAMPUS LEADERSHIP TEAMMATRIX TO HELP IDENTIFY ESSENTIAL CORE COMPETENICES & EVIDENCE FOR COLLEGE ALGEBRADIRECTIONS TO PARCC CAMPUS LEADERSHIP TEAMS:All two- and four- year colleges in Louisiana are currently addressing the following outcome, progress indicator, and activities as higher education works with PK-12education to successfully implement the Common Core State Standards and Partnership for Assessment of Readiness for College and Careers (PARCC) assessments in thefuture.Outcome:Statewide definition of “college readiness.”Progress Indicator: All two- and four-year institutions plus K-12 partners will reach consensus on a listing of competencies for a statewide definition of“college readiness” for English I and College Algebra by July 1, 2012.PARCC Campus Leadership Team Activities: Receive a matrix from the State Lead that contains a list of common Statewide Course Descriptors for College Algebra, a list of core competencies forPARCC assessments, and examples of evidence of mastery.Review the matrix and reach consensus on a set of core competencies and evidence in mathematics reflected in the CCSS that signal that a student ison-track to be college-ready.Submit a set of core competencies and types of evidence to the State Lead.Participate in a state meeting to reach consensus on core competencies and college-readiness standards (e.g., evidence) acceptable to all college anduniversities within Louisiana.This document contains a matrix for PARCC Campus Leadership Teams to use to start discussions about important core competencies that high school students shouldpossess as they exit high school and enter College Algebra courses. The matrix provides an overview of the Common Core State Standards and an overview of ACTexpectations in similar content areas. The matrix also identifies course descriptors that have been agreed upon by all technical colleges, community colleges, and universitiesin Louisiana that offer College Algebra courses. PARCC Campus Leadership Teams should do the following:First, use the matrix and the following two documents to identify important core competencies that a high school student should exhibit on a PARCC assessment that would indicatethat the high school student has a 75% likelihood of achieving a C or better (50% chance of a B or better) without need for remediation in a credit-bearing College Algebra course. The matrixcontains information found within the following two documents. CCSS Mathematics Document: Common Core State Standards for Mathematics (http://doe.louisiana.gov/topics/ccss math.html) ACT Document: College Readiness Standards for Explore, Plan, and ACT pdf)An additional document that teams may want to use is entitled: The Alignment of the Common Core State Standards and ACT’s College and Career Readiness System. Thedocument can be found at the following URL: ent.pdf. Teams may use also use other documents.Second, identify the 10-20 essential core competencies that would indicate that a high school student has a 75% likelihood of achieving a C or better (50% chance of a B or better) withoutneed for remediation in a credit-bearing College Algebra course. List the essential core competencies on the form found in Appendix A. In addition, identify evidence that could be found on aPARCC assessment that would indicate that the high school student exhibits the core competencies at the necessary proficiency level for success.Third, submit the form in Appendix A to Jeanne Burns (Jeanne.burns@la.gov) at the Louisiana Board of Regents by April 30, 2012. Documents from all campuses will be examined and a set of10-20 core competencies and evidence will be created for a discussion that will occur when all PARCC Campus Leadership Teams attend a statewide meeting during June 2012.
2DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsNumber and Quantity Overview(See pages 43-45 of CCSS MathematicsDocument)The Real Number System Extend the properties of exponents to rationalexponents. Use properties of rational and irrational numbers.Quantities Reason quantitatively and use units to solveproblems.The Complex Number System Perform arithmetic operations with complexnumbers. Represent complex numbers and their operations onthe complex plane. Use complex numbers in polynomial identities andequations.Vector and Matrix Quantities Represent and model with vector quantities. Perform operations on vectors Perform operations on matrices and use matrices inapplications.MATHEMATICAL PRACTICES:1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.ACT Standards(See pages 10-17 of ACT Document)Basic Applications and Operations &Numbers: Concepts and PropertiesACT 16-19Basic Applications and OperationsSolve routine one-step arithmetic problems (using wholenumbers, fractions, and decimals) such as single-step percentSolve some routine two-step arithmetic problemsNumbers: Concepts and PropertiesRecognize one-digit factors of a numberIdentify a digit’s place valueACT 20-23Basic Applications and OperationsSolve routine two-step or three step arithmetic problemsinvolving concepts such as rate and proportion, tax added,percentage off, and computing with a given averageNumbers: Concepts and PropertiesExhibit knowledge of elementary number concepts includingrounding, the ordering of decimals, pattern identification,absolute value, primes, and greatest common factorACT 24-27Basic Applications and OperationsSolve multistep arithmetic problems that involve planning orconverting units of measure (e.g., feet per second to miles perhour)Numbers: Concepts and PropertiesFind and use the least common multipleOrder fractions Work with numerical factorsWork with scientific notationWork with squares and square roots of numbersWork problems involving positive integer exponentsWork with cubes and cube roots of numbersDetermine when an expression is undefinedExhibit some knowledge of the complex numbersCore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
3DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsAlgebra Overview(See Pages 46-49 of CCSS MathematicsDocument)Seeing Structure in ExpressionsInterpret the structure of expressions.Write expressions in equivalent forms to solveproblems.Arithmetic with Polynomials and RationalExpressionsPerform arithmetic operations on polynomials.Understand the relationship between zeros andfactors of polynomials.Use polynomial identities to solve problems.Rewrite rational expressions.Creating EquationsCreate equations that describe numbers orrelationships.Reasoning with Equations and InequalitiesUnderstand solving equations as a process ofreasoning and explain the reasoning.Solve equations and inequalities in one variable.Solve systems of equations.Represent and solve equations and inequalitiesgraphically.MATHEMATICAL PRACTICES1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.ACT StandardsExpressions, Equations, & Inequalities(See pages 10-17 of ACT Document)ACT 16-19Substitute whole numbers for unknown quantities toevaluate expressions.Solve one-step equations having integer or decimalanswers.Combine like terms (e.g., 2x 5x).ACT 20-23Evaluate algebraic expressions by substituting integers forunknown quantities;Add and subtract simple algebraic expressions;Solve routine first-degree equations;Perform straightforward word-to-symbol translations;Multiply two binomials.ACT 24-27Solve real-world problems using first degree equationsWrite expressions, equations, or inequalities with a singlevariable for common pre-algebra settings (e.g., rate anddistance problems and problems that can be solved byusing proportions)Identify solutions to simple quadratic equationsAdd, subtract, and multiply polynomialsFactor simple quadratics (e.g., the difference of squaresand perfect square trinomials)Solve first-degree inequalities that do not requirereversing the inequality signCore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
4DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsFunctions Overview(See pages 50-53 of CCSS MathematicsDocument)Interpreting Functions Understand the concept of a function and usefunction notation. Interpret functions that arise in applications in termsof the context. Analyze functions using different representations.Building Functions Build a function that models a relationship betweentwo quantities. Build new functions from existing functions.Linear, Quadratic, and Exponential Models Construct and compare linear, quadratic, andexponential models and solve problems. Interpret expressions for functions in terms of thesituation they model.Trigonometric Functions Extend the domain of trigonometric functions usingthe unit circle. Model periodic phenomena with trigonometricfunctions. Prove and apply trigonometric identities.MATHEMATICAL PRACTICES:1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.ACT StandardsFunctions(See pages 10-17 of ACT Document)ACT 16-19NoneACT 20-23Evaluate quadratic functions, expressed in functionnotation, at integer valuesACT 24-27Evaluate polynomial functions, expressed in unctionnotation, at integer valuesExpress the sine, cosine, and tangent of an angle in a righttriangle as a ratio of given side lengthsCore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
5DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsModeling Overview(See pages 54-55 of CCSS MathematicsDocument)Modeling links classroom mathematics and statistics toeveryday life, work, and decision-making. Modeling isthe process of choosing and using appropriatemathematics and statistics to analyze empiricalsituations, to understand them better, and to improvedecisions. Quantities and their relationships in physical,economic, public policy, social, and everyday situationscan be modeled using mathematical and statisticalmethods. When making mathematical models,technology is valuable for varying assumptions,exploring consequences, and comparing predictionswith data.ACT StandardsN/ACore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
6DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsGeometry Overview(See pages 56-59 of CCSS MathematicsDocument)Congruence Experiment with transformations in the plane. Understand congruence in terms of rigid motions. Prove geometric theorems. Make geometric constructions.Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similaritytransformations. Prove theorems involving similarity. Define trigonometric ratios and solve problemsinvolving right triangles. Apply trigonometry to general triangles.Circles Understand and apply theorems about circles. Find arc lengths and areas of sectors of circles.Expressing Geometric Properties with Equations Translate between the geometric description and theequation for a conic section. Use coordinates to prove simple geometric theoremsalgebraically.Geometric Measurement and Dimension Explain volume formulas and use them to solveproblems. Visualize relationships between two-dimensional andthree-dimensional objects.Modeling with Geometry Apply geometric concepts in modeling situations.MATHEMATICSL PRACTICES1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.ACT StandardsGraphic Representations, Properties of Plane Figures,& Measurement(See pages 10-17 of ACT Document)ACT 16-19Graphic RepresentationsLocate points on the number line and in the first quadrantProperties of Plane FiguresExhibit some knowledge of the angles associated with parallel linesMeasurementCompute the perimeter of polygons when all side lengths aregivenCompute the area of rectangles when whole number dimensionsare givenACT 20-23Graphic RepresentationsLocate points in the coordinate planeComprehend the concept of length on the numberlineExhibit knowledge of slopeProperties of Plane FiguresFind the measure of an angle using properties of parallellinesExhibit knowledge of basic angle properties and specialsums of angle measures (e.g., 90 , 180 , and 360 )MeasurementCompute the area and perimeter of triangles and rectanglesin simple problemsUse geometric formulas when all necessary information isgivenACT 24-27Graphic RepresentationsIdentify the graph of a linear inequality on the numberlineCore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
76. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.Determine the slope of a line from points or equationsMatch linear graphs with their equationsFind the midpoint of a line segmentProperties of Plane FiguresUse several angle properties to find an unknown anglemeasureRecognize Pythagorean triplesUse properties of isosceles trianglesMeasurementCompute the area of triangles and rectangles when one ormore additional simple steps are requiredCompute the area and circumference of circles afteridentifying necessary informationCompute the perimeter of simple composite geometricfigures with unknown side lengths
8DISCUSSION DOCUMENT FOR PARCC CAMPUS LEADERSHIP TEAMS – CORE COMPETENCIES & EVIDENCE FOR SUCCESS IN COLLEGE ALBEBRAPotential Core Competencies for High School MathematicsCommon Core State StandardsStatistics and Probability Overview(See pages 60-63)Interpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a singlecount or measurement variable. Summarize, represent, and interpret data on twocategorical and quantitative variables. Interpret linear models.Making Inferences and Justifying Conclusions Understand and evaluate random processesunderlying statistical experiments. Make inferences and justify conclusions from samplesurveys, experiments and observational studies.Conditional Probability and the Rules ofProbability Understand independence and conditionalprobability and use them to interpret data. Use the rules of probability to compute probabilitiesof compound events in a uniform probability model.Using Probability to Make Decisions Calculate expected values and use them to solveproblems. Use probability to evaluate outcomes of decisions.MATHEMATICAL PRACTICES:1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique thereasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.ACT StandardsProbability, Statistics, & Data Analysis(See pages 10-17 of ACT Document)ACT 16-19Calculate the average of a list of numbersCalculate the average, given the number of data values andthe sum of the data valuesRead tables and graphsPerform computations on data from tables and graphsUse the relationship between the probability of an eventand the probability of its complementACT 20-23Calculate the missing data value, given the average and all datavalues but oneTranslate from one representation of data to another (e.g., a bargraph to a circle graph)Determine the probability of a simple eventExhibit knowledge of simple counting techniquesACT 24-27Calculate the average, given the frequency counts of all the dataValuesManipulate data from tables and graphsCompute straightforward probabilities for common situationsUse Venn diagrams in countingCore Competencies on a PARCC Assessmentthat Would Indicate that a High SchoolStudent has a 75% Likelihood of Achieving a Cor Better (50% Chance of a B or Better)Without Need for Remediation in a CreditBearing College Algebra CourseDraftBoR Statewide Descriptorsfor Credit-Bearing CollegeAlgebra CourseIn depth treatment of:Solving equations andinequalities;Function properties andgraphs;Inverse functions;Linear, quadratic,polynomial, rational,exponential and logarithmicfunctions with applications;andSystems of equations.
9APPENDIX ATEN TO TWENTY ESSENTIAL CORE COMPETENCIES AND EVIDENCE FOR COLLEGE ALGEBRADirections:Based upon your PARCC Campus Leadership Teams’ discussions about core competencies, please identify the 10-20 essential core competencies that shouldbe measured on a PARCC assessment that would indicate that a high school student has a 75% likelihood of achieving a C or better (50% chance of a B orbetter) without need for remediation in a credit-bearing College Algebra course. In addition, identify evidence that could be found on a PARCC assessmentthat would indicate that a high school student exhibits the core competencies at the necessary proficiency level for success.#1234567891011121314151617181920Essential core competencies that should be measured on a PARCCassessment that would indicate that a high school student has a 75%likelihood of achieving a C or better (50% chance of a B or better) withoutneed for remediation in a credit-bearing College Algebra courseEvidence that could be found on a PARCC assessment that wouldindicate that a high school student exhibits the core competencies atthe necessary proficiency level for success
10Once completed, a copy of this form should be submitted to Jeanne Burns (Jeanne.burns@la.gov) at the Louisiana Board of Regents by April 30, 2012.
“college readiness” for English I and College Algebra by July 1, 2012. PARCC Campus Leadership Team Activities: Receive a matrix from the State Lead that contains a list of common Statewide Course Descriptors for College Algebra, a list of core competencies for PARCC
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CONTENTS CONTENTS Notation and Nomenclature A Matrix A ij Matrix indexed for some purpose A i Matrix indexed for some purpose Aij Matrix indexed for some purpose An Matrix indexed for some purpose or The n.th power of a square matrix A 1 The inverse matrix of the matrix A A The pseudo inverse matrix of the matrix A (see Sec. 3.6) A1 2 The square root of a matrix (if unique), not elementwise
A Matrix A ij Matrix indexed for some purpose A i Matrix indexed for some purpose Aij Matrix indexed for some purpose An Matrix indexed for some purpose or The n.th power of a square matrix A 1 The inverse matrix of the matrix A A The pseudo inverse matrix of the matrix A (see Sec. 3.6) A1/2 The square root of a matrix (if unique), not .
CONTENTS CONTENTS Notation and Nomenclature A Matrix Aij Matrix indexed for some purpose Ai Matrix indexed for some purpose Aij Matrix indexed for some purpose An Matrix indexed for some purpose or The n.th power of a square matrix A 1 The inverse matrix of the matrix A A The pseudo inverse matrix of the matrix A (see Sec. 3.6) A1/2 The square root of a matrix (if unique), not elementwise
PARCC states developed Claims for Mathematics based on the CCSSM. PARCC states developed the Model Content Frameworks to provide guidance to key elements of excellent instruction aligned with the Standards. The blueprints for the PARCC Mathematics Assessments have been devel
from 650 to 850 for all tests. Additionally, PARCC English language arts/literacy reports provide separate scale scores for both Reading and Writing. PARCC Reading scale scores range from 10 to 90 and PARCC Writing scale scores range from 10 to 60. For example, a student who earns an overall scale score of 80
to evaluate the quality of items in preparation for PARCC’s operational assessments in 2014-2015. In order to get a sample of students that is demographically representative of each state and PARCC as a whole, the sampling design calls for : 1. PARCC
The American Revolution Part One: The events leading up the Revolutionary War (1750 – 1775) Background Historically speaking, right now “we” are British. The Colonies are an extension of Britain, so we share their government, their identity, their pride, and also their enemies. There is NO United States of America. Taunton Flag, flown by colonists to show unity with the British crown .
