State Board of Education Topic Summary s21

STATE BOARD OF EDUCATION – TOPIC SUMMARY Topic: High School Math Achievement Level Descriptors Date: April 22, 2010 Staff/Office: Doug Kosty, Tony Alpert / Office of Assessment and Information Services Action Requested: Informational Only Adoption Later Adoption Adoption/Consent Agenda

ISSUE BEFORE THE BOARD: In preparation for this summer’s math Standards Setting and the fall submission for US Department of Education Peer Review, the State Board needs to adopt Mathematics Achievement Level Descriptors grades 3-8 and high school.

BACKGROUND: The State Board adopted new High School Mathematics Academic Content Standards in June of 2009. The Board had previously adopted new K-8 standards in December of 2007. Following the adoption of these Content Standards is a review of the Achievement Standards or cut scores. In order to ensure that Oregon’s state educational standards stay current and in line with national and international benchmarks, ODE staff and stakeholders will review the Achievement Standards (or cut scores) used to determine whether or not a student meets standards. In August 2010, ODE staff will convene stakeholders to set new Oregon Mathematics Achievement Standards. Achievement Standards were last set in 2006. In March, the Board adopted cross-subject, cross-grade General Policy Definitions and cross-grade Math Policy Definitions. Prior to the standards setting, the Board needs to adopt Mathematics Achievement Level Descriptors which are designed to provide a framework for this summer’s standards setting.

Math Standards Setting Timeline:

Date Topic Status December 2007 New K-8 Math Standards Adopted by State Board June 2009 New High School Math Standards Adopted by State Board January 2010 General Policy Definitions & Math Policy Reviewed by State Board Definitions March 2010 General Policy Definitions & Math Policy Adopted by State Board Definitions March 2010 High School Math Achievement Level Reviewed by State Board Descriptors April 2010 High School Math Achievement Level Adoption needed by State Descriptors Board April 2010 Grades 3-8 Math Achievement Level Review needed by State Board Descriptors May 2010 Grades 3-8 Math Achievement Level Descriptors Adoption needed by State Board May 2010 Grades 3-8 and High School Extended Math Review needed by State Board Achievement Level Descriptors June 2010 Grades 3-8 and High School Extended Math Adoption needed by State Board Achievement Level Descriptors August 2010 Math Standards Setting - Math Achievement Dependent on previous State Level Descriptors and Policy Definitions refined Board action October 2010 New Math Cuts Scores and refined Math Adoption needed by State Board Achievement Level Descriptors and Policy Definitions November 2010 Submission of new content standards, cut scores, and supporting data for US Department of Ed Peer Review approval for accountability purposes. 2010-11 school year Testing using new content standards and cut Dependent on previous State scores Board action

1 The timeline above places State Board adoption of the new cut scores in October, the same timeframe as the start of the 2010-11 testing year. This will minimize the need to retroactively apply cut scores to student tests.

If the Standards Setting is delayed past August, ODE will either have to:  Retroactively apply cut scores to student scores, or  Assess students on the previous math standards while teaching to the new standards for another year. For more information and background on the standards setting process, please see Appendix B.

Grade Specific Achievement Level Descriptors

Revision of the Achievement Level Descriptors is part of the implementation of the new mathematics assessments. The Achievement Level Descriptors (ALDs) at each grade will influence the upcoming achievement standards setting for mathematics, scheduled for August 2010. In order for Oregon’s standards to be accepted for federal accountability purposes, we must submit documentation to the U.S. Department of Education (U.S. DOE), and the ALDs are part of this required documentation. Achievement Level Descriptors are also used for school accountability purposes. Oregon’s new ALDs are being drafted by a team of Oregon math education experts. The new ALDs are being reviewed by education stakeholders with mathematics expertise. Below are the High School Achievement Level Descriptors. The Math ALDs for grades 3-8 are provided in Appendix A.

High School Achievement Level Descriptors

2 Proposed  InconsistentlyLevel 1  IdentifiesLevel and 2  UnderstandsLevel and3  UnderstandsLevel 4and MathematicsLevels applies properties of compares properties applies properties of applies properties of Achievement Studentstwo and threedo not Studentsof two and demonstrate three Studentsgeometric demonstrate figures and Studentsgeometric figures and LevelGeneral demonstratedimensional figures.mastery partialdimensional mastery figures. of masteryrelationships of grade-level between demonstrateanalyzes relationships DescriptorsPolicy of grade-level grade-level knowledgefigures in two and and skills three masterybetween offigures grade- in Definitions knowledge and skills knowledge and skills requireddimensions. for leveltwo and knowledge three and (ApplyHigh to all required for required for proficiency. skillsdimensions. exceeding the gradesSchool and proficiency. proficiency. requirement for allGeometry subjects)  Inconsistently  Determines area,  Determines area, proficiency. Determines area, determines area, surface area, and/or surface area, and/or surface area, and/or surface area, and/or volume given volume whether or not volume for non- Mathematics Studentsvolume given Studentsdimensions. demonstrate Studentsall dimensions demonstrate are Studentsroutine figures. Policy demonstratedimensions. Seldomlimited partialSometimes mastery solves of for masterygiven. Solves of related demonstrateSolves for missing Definitions masterysolves for of missing mathematicalmissing dimensions. mathematicalcontext-based masterydimensions of that (Apply to all mathematicaldimensions. knowledge and skills knowledgeproblems. and skills mathematicalrequire multiple grades) knowledge and skills through the direct through selecting from knowledgeequations. and through the direct application of an assortment of skills through the application Inconsistently of a uses concepts Uses some and theorems strategies Consistently and integrates use Consistently of multiple and concepttheorems or and procedure can proceduresand can solve in familiar integratingthe use of theorems concepts reasoningefficiently integrates strategies insometimes simplified solve and situationsproblems relatedwith regular to andand/or procedures algebraic in a andthe useapply of theoremsthem in familiarproblems situations related to success.congruent They and similar are varietyequations of situationsto solve newand/or and algebraic complex withcongruent occasional and similar ablefigures to explainin two and some withproblems consistent related to situationsequations towith solve success.figures in two and ofthree their dimensions. steps. success.congruent They and similarare able consistentand justify success. three dimensions. tofigures explain in two steps and and three Theyrelationships are able between to procedures.dimensions, including analyzecongruent their and similar right triangle strategiesfigures in two and and trigonometry. solutions.three dimensions.

 Sometimes justifies  Uses coordinate  Uses coordinate  Uses coordinate Mathematics  propertiesOften performs and solve geometry Performs to justify geometry Applies efficient to justify geometry Fluently appliesto justify Achievement computationsproblems using with propertiescomputations and with solve real properties,strategies forexplain properties,efficient strategies explain Level realcoordinate numbers geometry problemsnumbers accurately.involving two conjectures,performing and solve conjectures,for performing and Descriptors accurately.when the two dimensionalOrders or locates figures real problemscomputations involving with realtwo solvecomputations problems with Inconsistentlydimensional figures orders withnumbers numeric on a number dimensionalnumbers. Orders figures and involvingreal numbers. two Able High orhave locates numeric real coordinates.line. withlocates numeric real numbers on dimensionalto justify the figuresresult School numberscoordinates. on a number coordinates.a number line. withusing numeric mathematical and Algebra line. symbolicproperties. coordinates.

 InconsistentlyInconsistently  IdentifiesEvaluates and and  IdentifiesConsistently and evaluates, performs  Fluently Consistently identifies simplifiesidentifies expressionsand performssimplifies singleexpressions singlecreates, and and composite determines andevaluates, performs creates, single involvingperforms realsingle transformationsinvolving real numbers of transformationsequivalent expressions (2) of andjustifies, composite and numberstransformations and/or of geometricand/or algebraic figures on a geometricinvolving real figures numbers on a transformationsdetermines (more algebraicgeometric symbols. figures on coordinatesymbols. This plane. coordinateand /or algebraic plane. thanequivalent 2) of geometric a coordinate plane. excludes factoring and symbols. figuresexpressions on a complex expressions. coordinateinvolving real plane. numbers and/or  Analyzes survey  Analyzes the  Determines and  Determinesalgebraic symbols. and Mathematics methods and strengths and analyzes survey analyzes survey Achievement  evaluatesSometimes data-based solves limitations Solves problems of survey methods Represents and linear evaluates methods Represents, and solves, Level linearreports equations with gaps given in methodsinvolving andlinear data-basedrelationships reports. and solves evaluatesinterprets data-basedthe Descriptors theunderstanding. equation. evaluatesequations data-basedusing tables, problems involving reportsmeaning and of, is and able to Identifies slope from a reportsgraphs, lookingand symbols. at the systems of linear communicateconverts among High graph. Solves wayDetermines the data slope. was equations using tables, appropriaterepresentations of School systems of linear analyzedOften solves and linear graphs, and symbols. suggestionslinear equations for and Statistics equations using displayed.inequalities and Solves linear improvement.inequalities. Solves and tables and graphs. graphs the solution. inequalities and graphs problems involving Probability  Inconsistently  Compares and draws  theCompares, solution. analyzes, Able to  Compares,systems of linearanalyzes, compares and draws conclusions about drawswork with conclusions function drawsinequalities conclusions using conclusions about independent data sets about,notation. and interprets about,tables, and graphs, interprets and independent data and data in graphical independent data sets independentsymbols. data sets sets and data in displays, including and data in graphical and data in graphical Mathematics  graphical Identifies displays,and central Identifies tendencies, and graphs displays, Distinguishes including between, displays, Distinguishes including Achievement inconsistentlyincluding central graphs range,linear, quadratic,and line of and best centralmanipulates, tendencies, graphs, centralbetween, tendencies, Level linear,tendencies quadratic, and and fit,exponential when appropriate. functions range,and applies and line linear, of best range,manipulates, and line graphs, of Descriptors exponentialrange. functions using tables, graphs, fit,quadratic, when appropriate. and bestand fit,applies when linear, 3 using tables, graphs, and equations. exponential functions in appropriate,quadratic, and and is High and equations. Students identify the routine and non-routine ableexponential to explain how a School Students can domain and range situations using tables, changefunctions, in theincluding data set Statistics sometimes find the from a graph. graphs, and equations. wouldmaking alter inferences the or POLICY QUESTIONS:  Should Oregon raise its Achievement Standards to align more closely with national and international standards?  How high should the bar be set? What should we expect of students earning a high school diploma? What should be expected for the purpose of school and district accountability?  Should Oregon change the names of the achievement levels from Does Not Meet, Nearly Meets, Meets, Exceeds to something new?

STAFF RECOMMENDATION:

ODE staff recommend adoption of the High School Achievement Level Descriptors this month.

Please note: the Board is asked to adopt the current versions of the Achievement Level Descriptors which will be used in this summer’s Standards Setting. During Standards Setting and ongoing stakeholder engagement, revisions to these ALDs may be recommended. Any updates to these statements will be provided to the Board in October for review.

ODE staff recommend adoption of the Math Achievement Level Descriptors for grades 3-8 in May. (See Appendix A for draft grade 3-8 ALDs)

Adoption of Mathematics Achievement Level Descriptors (at all grades) is needed for agency work flow by May. The latest possible adoption date is June, 2010. Final adoption of ALDs and Achievement Standards (cut scores) is needed in October 2010.

4 Appendix A: Draft Oregon Mathematics Achievement Level Descriptors – Grades 3 - 8

Draft Oregon Mathematics Achievement Level Descriptors – Grade 3

Proposed Level 1 Level 2 Level 3 Level 4 Levels General Students do not Students Students Students demonstrate Policy demonstrate mastery demonstrate partial demonstrate mastery mastery of grade-level Definitions of grade-level mastery of grade- of the grade-level knowledge and skills (Apply to all knowledge and skills level knowledge knowledge and skills exceeding the grades not all required for and skills required required for requirement for subjects) proficiency. for proficiency. proficiency. proficiency.

Mathematics Students Students Students Students demonstrate Policy demonstrate limited demonstrate demonstrate mathematical Definitions mathematical mathematical mathematical knowledge and skills (Apply to all knowledge and skills knowledge and knowledge and skills through the use of grades) through the direct skills through the through selecting multiple reasoning application of a direct application of from an assortment strategies and apply concept or concepts and of strategies and them in new and procedure in procedures in integrating concepts complex situations with simplified and familiar situations and procedures in a consistent success. familiar situations with regular variety of situations They are able to analyze with occasional success. They are with consistent their strategies and success. able to explain their success. They are solutions. steps. able to explain steps and procedures.

Mathematics  Attempts to model  Represents halves  Represents common  Represents common Achievement fractions but parts or fourths as equal fractions (e.g., fractions (e.g., halves, Level may not be equal. parts of a whole or halves, thirds, thirds, fourths, tenths) Descriptors distances on a fourths, tenths) as as equal parts of a number line. equal parts of a whole, parts of a set, or Number and whole, parts of a set, points or distances on a Operations or points or number line and can distances on a justify their reasoning. Develop an number line. understanding of fractions  Using unequal parts  Identifies which  Recognizes and  Recognizes and of different wholes, fractional part is demonstrates that demonstrates that sizes misinterprets larger only if wholes sizes of fractional of fractional parts are fractional size. are the same size. parts are relative to relative to the size of Confusion around the size of the the whole and can thinking that whole. explain their thinking. denominators with bigger numbers mean fractions of greater size.

 Attempts to  Uses fractions with  Uses fractions to  Uses fractions to represent fractions common represent numbers represent numbers that that are equal to, denominators to that are equal to, are equal to, less than, less than, or greater represent numbers less than, or greater or greater than one and than one but that are equal to, than one. recognizes mixed confuses numerator less than, or greater numbers as greater and denominator. than one. than one.

5 Mathematics  Sometimes  Solves problems  Solves problems that  Solves problems that Achievement compares or orders that involve involve comparing involve comparing and Level fractions while using comparing or and ordering ordering fractions by Descriptors models. ordering fractions fractions by using using a variety of by using models, models, benchmarks methods (e.g., models, Number and benchmarks (0, 1/2, (0, 1/2, 1), or benchmarks (0, 1/2, 1), Operations 1), or common common numerators or common numerators numerators or or denominators. or denominators. Develop an denominators. understanding of fractions  Experiments to  Sometimes  Identifies equivalent  Identifies equivalent (cont.) inconsistently Identifies equivalent fractions using fractions using models, identify equivalent fractions using models, including including the number fractions using models or the the number line. line. concrete models or number line. the number line.

 Inappropriately adds  Using models or  Adds common  Adds common fractions common fractions manipulatives, fractions with like with like denominators with like inconsistently adds denominators. and explains their denominators. common fractions thinking. with like denominators.

Mathematics  Inconsistently  Represents the  Represents and  Represents and applies Achievement represents the concept of applies the the concept of Level concept of multiplication as concept of multiplication as Descriptors multiplication as repeated addition multiplication as repeated addition in a repeated addition. in a routine repeated addition. variety of situations and Number and situation. justifies their thinking. Operations, Algebra, and  Inconsistently  Partially represents  Consistently  Represents and applies Data Analysis represents the the concept of represents and the concept of division concept of division division as applies the as repeated subtraction Develop as repeated repeated concept of division and forming equal understanding subtraction or subtraction or as repeated groups in a variety of of multiplication forming equal forming equal subtraction and situations and justifies and division groups. groups. forming equal their thinking. groups.

 Inconsistently  Applies models of  Consistently applies  Applies models of attempts to use multiplication models of multiplication (e.g., models of (e.g., equal-sized multiplication (e.g., equal-sized groups, multiplication (e.g., groups, arrays, equal-sized arrays, area models, equal-sized area models, groups, arrays, equal “jumps” on groups, arrays, equal “jumps” on area models, number lines and area models, equal number lines and equal “jumps” on hundreds charts) and “jumps” on number hundreds charts) number lines and division (e.g., repeated lines and hundreds or division (e.g., hundreds charts) subtraction, partitioning, charts) or division repeated and division (e.g., and sharing) to solve (e.g., repeated subtraction, repeated non-routine problems subtraction, partitioning, and subtraction, and justify their thinking. partitioning, and sharing). partitioning, and sharing) to solve sharing) to solve problems. problems.  Applies increasingly  Inconsistently uses  Applies some  Applies increasingly sophisticated a strategy based strategies based sophisticated strategies based on Mathematics

6 Achievement on the number on the number strategies based the number properties Level properties (e.g., properties (e.g., on the number (e.g., place value, Descriptors place value, place value, properties (e.g., commutative, commutative, commutative, place value, associative, Number and associative, associative, commutative, distributive, identity, Operations, distributive, distributive, associative, and zero) to solve Algebra, and identity, and zero) identity, and zero) distributive, complex multiplication Data Analysis to attempt to to determine identity, and zero) and division problems determine multiplication or to solve involving basic facts. Develop multiplication or division involving multiplication and understanding division involving basic facts. division involving of multiplication basic facts. basic facts. and division  Applies the inverse (cont.)  Inconsistently uses  Partially uses the  Applies the inverse relationship between the inverse inverse relationship multiplication and relationship relationship between division (e.g., 5 x 6 = between between multiplication and 30, 30 ÷ 6 = 5) and multiplication and multiplication and division (e.g., 5 x 6 the relationship division (e.g., 5 x 6 division (e.g., 5 x = 30, 30 ÷ 6 = 5) between multiples = 30, 30 ÷ 6 = 5) or 6 = 30, 30 ÷ 6 = and the and factors in non- the relationship 5) or the relationship routine situations. between multiples relationship between multiples and factors with between multiples and factors in concrete models. and factors. routine situations.  Represents, analyzes  Inconsistently  Represents or  Represents, and extends number represents number extends number analyzes and patterns using rules patterns using patterns using extends number that involve rules that involve rules that involve patterns using multiplication and/or multiplication or multiplication or rules that involve addition (e.g., {3, 6, 9, addition (e.g., {3, addition (e.g., {3, multiplication 12, } .{1, 2, 4, 8,} ) to 6, 9, 12, }, .{1, 2, 6, 9, 12, }, .{1, 2, and/or addition the nth term. 4, 8, …} ) 4, 8, …} ) (e.g., {3, 6, 9, 12, }, .{1, 2, 4, 8, …})  Analyzes frequency  Inconsistently  Analyzes tables, bar graphs, interprets frequency tables,  Analyzes frequency picture graphs, and frequency tables, bar graphs, tables, bar graphs, line plots; and uses bar graphs, picture picture graphs, or picture graphs, them to solve graphs, or line line plots and and line plots; and complex problems plots involving uses them to uses them to solve involving addition, addition, solve problems problems involving subtraction, subtraction, involving addition, addition, multiplication, and multiplication, or subtraction, subtraction, division. division. multiplication, or multiplication, and division. division.

 Inconsistently  Identifies right  Consistently  Identifies right angles in identifies right angles in two- identifies right nonroutine two- angles in two- dimensional angles in two- dimensional shapes dimensional shapes shapes or dimensional shapes and determines if or determines if determines if and determines if angles are greater than angles are greater angles are greater angles are greater or less than a right than or less than a than or less than a than or less than a angle (obtuse and right angle (obtuse right angle (obtuse right angle (obtuse acute). and acute). and acute). and acute).

Mathematics  Sometimes identifies  Identifies,  Identifies, describes,  Identifies, describes,

7 Achievement describes or describes, compares, analyzes, compares, analyzes, Level informally classifies compares, or and informally and informally classify Descriptors triangles by their informally classifies classifies triangles triangles by their sides sides and angles. triangles by their by their sides and and angles and Geometry and sides and angles. angles. explains their thinking. Measurement  Inconsistently  Partially identifies,  Consistently  Identifies, describes Analyze 2- identifies, describes, describes, identifies, describes compares, analyzes, dimensional compares, or compares, and/or compares, analyzes, and classifies shapes, classifies classifies and classifies quadrilaterals (square, including quadrilaterals quadrilaterals quadrilaterals rectangle, perimeter (square, rectangle, (square, rectangle, (square, rectangle, parallelogram, parallelogram, parallelogram, parallelogram, rhombus, and rhombus, and rhombus, and rhombus, and trapezoid) by their sides trapezoid) by their trapezoid) by their trapezoid) by their and angles and sides and angles. sides and angles sides and angles. explains their thinking.

 Inconsistently  Identifies,  Identifies, describes,  Identifies, describes, identifies or describes, or and compares and compares describes compares pentagons, pentagons, hexagons, pentagons, pentagons, hexagons, and and octagons by the hexagons, and hexagons, and octagons by the number of sides or octagons by the octagons by the number of sides or angles and explains number of sides or number of sides or angles. their thinking. angles. angles.

 Attempts to  Decomposes,  Investigates and  Investigates, describes, decompose, combines, or describes the results and predicts the results combine, or transforms of decomposing, of decomposing, transform polygons polygons to make combining, and combining, and to make other other polygons. transforming transforming polygons polygons. polygons to make to make other other polygons. polygons.

 Builds or draws two-  Builds or draws  Builds, draws, and  Builds, draws, and dimensional shapes two-dimensional analyzes two- analyzes two- to understand shapes to dimensional shapes dimensional shapes to minimal attributes understand to understand understand attributes and properties of attributes and attributes and and properties of two- two-dimensional properties of two- properties of two- dimensional space and space. dimensional space. dimensional space. justifies their thinking.

 Inconsistently  Partially determines  Determines an  Determines an determines an an appropriate unit appropriate unit, appropriate unit, tool, appropriate unit or or tool to tool, or strategy to and strategy to find the tool to find the inconsistently find find the perimeter of perimeter of polygons perimeter of the perimeter of polygons. and justifies their polygons. polygons. thinking.

 Uses attributes or  Uses attributes or  Uses attributes and  Uses attributes and properties of two- properties of two- properties of two- properties of two- dimensional shapes dimensional dimensional shapes dimensional shapes to to inconsistently shapes to to solve problems solve non-routine identify parallel and consistently identify including problems including perpendicular lines, parallel and applications applications involving congruence, perpendicular lines, involving parallel parallel and symmetry, and congruence, and perpendicular perpendicular lines, perimeter. symmetry, and lines, congruence, congruence, symmetry, perimeter. symmetry, and and perimeter.

8 perimeter.

Proposed Level 1 Level 2 Level 3 Level 4 Levels General Students do not Students Students Students demonstrate Policy demonstrate mastery demonstrate partial demonstrate mastery mastery of grade-level Definitions of grade-level mastery of grade- of the grade-level knowledge and skills (Apply to all knowledge and skills level knowledge knowledge and skills exceeding the grades not all required for and skills required required for requirement for subjects) proficiency. for proficiency. proficiency. proficiency.

Mathematics  Inconsistently reads,  Reads, writes, or  Reads, writes, and  Reads, writes, and Achievement writes, or represents represents represent decimal represents decimal Level decimal numbers (to decimal numbers numbers (to the numbers (to the Descriptors the hundredths) (to the hundredths) hundredths) in a hundredths) context. Number and Operations  Use of models to  Uses models to  Uses models to  Uses models to connect represent fractions connect equivalent connect and and compare equivalent Develop an and decimals fractions and compare equivalent fractions and decimals understanding demonstrates decimals. fractions and including mixed of Decimals inconsistent decimals. numbers or improper understanding of the fractions. relationship.

 Inconsistently  Determines decimal  Consistently  Determines decimal determines decimal equivalents or determines decimal equivalents or equivalents for approximations for equivalents or approximations for common fractions. some common approximations for common fractions and fractions. common fractions. can explain the relationship between them.

 Compares fractions  Compares and  Compares and  Compares and orders a or decimals. orders fractions or orders fractions and mixed group of fractions compares and decimals. and decimals. orders decimals.

9  Estimates decimal or  Inconsistently  Estimates decimal  Estimates decimal or fractional amounts in estimates decimal or or fractional fractional amounts in routine and non-routine fractional amounts in amounts in routine routine and non- situations and justifies routine situations. situations. routine situations. solutions.  Represents money  Occasionally  Represents money  Represents money amounts to $10.00 in represents money amounts to $10.00 amounts to $10.00 in dollars and cents and amounts to $10.00 in in dollar and cents. dollars and cents applies to situations dollar and cents. and applies to involving purchasing situations involving ability and making purchasing ability change with the fewest and making change. bills and coins.

Mathematics  Sometimes  Applies with fluency  Applies with fluency  Applies with fluency Achievement computes multiplication facts multiplication facts to multiplication facts to 10 Level multiplication facts to to 10 times 10. 10 times 10 and times 10 and related Descriptors 10 times 10. related division facts. division facts in complex situations. Number and Operations  Demonstrates  Demonstrates  Demonstrates  Demonstrates and Algebra inconsistent partial understanding of understanding of understanding of understanding of application of application of models Fluency with application of application of models for for multiplication (e.g., division of models for models for multiplication (e.g., equal-sized groups, whole numbers multiplication (e.g., multiplication (e.g., equal-sized groups, arrays, area models, equal-sized groups, equal-sized groups, arrays, area models, equal intervals on the arrays, area models, arrays, area equal intervals on number line), place equal intervals on models, equal the number line), value, and properties of the number line). intervals on the place value, and operations number line), place properties of (commutative, value, or properties operations associative, and of operations (commutative, distributive) in complex (commutative, associative, and situations. associative, and distributive). distributive).

 Sometimes uses an  Uses a partially  Selects and uses  Selects and uses inappropriate appropriate appropriate appropriate estimation estimation strategy estimation strategy estimation strategies for for multiplication for multiplication strategies for multiplication (e.g., use (e.g., use (e.g., use multiplication (e.g., benchmarks, benchmarks, benchmarks, use benchmarks, overestimate, overestimate, overestimate, overestimate, underestimate, round) underestimate, underestimate, underestimate, to calculate mentally round) when round) when round) to calculate based on the problem computing with computing with mentally based on situation when whole numbers. whole numbers. the problem computing with whole situation when numbers and explains computing with why a strategy was whole numbers. chosen.

 Occasionally uses  Uses accurate or  Develops and uses  Develops and uses accurate methods to generalizable accurate, efficient, accurate, efficient, and multiply multi-digit methods to multiply and generalizable generalizable methods whole numbers. multi-digit whole methods to multiply to multiply 3-digit by 3- numbers. multi-digit whole digit whole numbers or numbers. larger.

10  Develops fluency with  Inconsistently  Sometimes uses a  Develops fluency efficient procedures for multiplies multi-digit particular procedure with efficient multiplying multi-digit whole numbers. for multiplying multi- procedures for whole numbers and digit whole multiplying multi-digit justifies why the numbers. whole numbers. procedures work on the basis of place value and number properties.

Mathematics  Inappropriately  Partially recognizes  Consistently  Efficiently recognizes Achievement identifies area. area as an attribute recognizes area as area as an attribute of Level of two-dimensional an attribute of two- two-dimensional Descriptors regions. dimensional regions. regions.

Grade 4  Inconsistently  Partially recognizes  Recognizes a square  Recognizes a square Measurement identifies a standard a square that is one that is one unit on a that is one unit on a unit for measuring unit on a side as side as the standard side as the standard area. the standard unit for unit for measuring unit for measuring area measuring area. area. in complex situations.

 Inappropriately uses  Partially determines  Determines area by  Determines area by different-sized units area by finding the finding the total finding the total number of area to cover a total number of number of same- of same-sized units of shape with gaps same-sized units of sized units of area area that cover an and/or overlaps. area that cover a that cover a shape irregular shape without shape with gaps or without gaps or gaps or overlaps. overlaps. overlaps.

 Inconsistently  Determines the  Determines the  Determines and justifies determines the appropriate units, appropriate units, appropriate units, appropriate units, strategies, or tools strategies, and tools strategies, and tools to strategies, or tools to to solve problems to solving problems solve problems that estimate or measure that involve that involve involve estimating or area. estimating or estimating or measuring area. measuring area. measuring area.

 Begins to see the  Partially connects  Connects area  Connects area measure area model of area measure to measure to the area to the area model used multiplication or the area model. model used to to represent begins to observe represent multiplication and area measure as multiplication and explains how this multiplication. uses this to express justifies the formula for the formula for area area of a rectangle. of a rectangle.

 Inconsistently finds  Finds the areas of  Finds the areas of  Determines the areas of the area of simple common shapes complex shapes that complex shapes that shapes. that can be can be subdivided can be subdivided into subdivided into into rectangles. rectangles and can rectangles. explain their thinking.

 Misunderstands the  Solves problems  Solves problems  Solves problems concept of finding involving perimeters involving perimeters involving perimeters perimeters and or areas of and areas of and areas of rectangles finding areas of rectangles and rectangles and and squares and rectangles and squares. squares. justifies their thinking. squares.  Recognizes and

11  Inconsistently  Partially recognizes  Recognizes that generalizes that notices or may not that rectangles with rectangles with the rectangles with the notice that the same area can same area can have same area can have rectangles with the have different different perimeters different perimeters and same area can have perimeters or that and that rectangles that rectangles with the different perimeters rectangles with the with the same same perimeter can or that rectangles same perimeter can perimeter can have have different areas with the same have different different areas. and can explain their perimeter can have areas. thinking. different areas.

Proposed Level 1 Level 2 Level 3 Level 4 Levels General Students do not Students Students Students demonstrate Policy demonstrate mastery demonstrate partial demonstrate mastery mastery of grade-level Definitions of grade-level mastery of grade- of the grade-level knowledge and skills (Apply to all knowledge and skills level knowledge and knowledge and skills exceeding the grades not all required for skills required for required for requirement for subjects) proficiency. proficiency. proficiency. proficiency.

Mathematics  Uses a fraction  Uses a fraction  Uses fraction models  Constructs multiple Achievement model to represent model to represent to represent the fraction models to Level addition or addition or addition and represent addition and Descriptors subtraction with subtraction with subtraction of subtraction of fractions unlike denominators unlike fractions with unlike with unlike Number and that are multiples of denominators. denominators. denominators. Operations each other. and Data Analysis  Uses a decimal  Uses a decimal  Uses decimal  Uses decimal models, model to add or model, place value, models, place value, place value, and Fluency with subtract decimals or number and number number properties to addition and (to the tenths). properties to add properties to add add and subtract subtraction of and subtract and subtract decimals (to the fractions and decimals (to the decimals (to the thousandths) and can decimals thousandths). thousandths). explain their work. Mathematics Achievement  Inconsistently uses  Uses appropriate  Selects and uses  Selects and uses Level

12 Descriptors appropriate strategies to appropriate appropriate strategies strategies to estimate fraction or strategies to to estimate a mixture of Number and estimate decimal decimal sums estimate fraction and fraction and decimal Operations sums and and/or differences. decimal sums and sums and differences. and Data differences. differences. Analysis  Beginning to develop  Develops an  Develops fluency  Develops fluency with Fluency with an efficient efficient procedure with efficient efficient procedures for addition and procedure for adding for adding and procedures for adding and subtracting subtraction of and subtracting subtracting fractions adding and fractions and decimals fractions and decimals or adding or decimals. subtracting fractions and justify why the decimals and subtracting and decimals. procedures work. (cont.) fractions.

 Solves simple  Solves simple  Solves problems  Solves non-routine problems involving problems involving involving the addition problems involving the the addition or the addition and and subtraction of addition and subtraction subtraction of subtraction of fractions and of fractions and fractions or decimals. fractions or decimals. decimals. decimals.

 Inconsistently  Often uses ordered  Uses ordered pairs  Uses ordered pairs on confuses x and y in pairs on coordinate on coordinate coordinate graphs to an ordered pair. graphs to specify graphs to specify specify locations and locations. locations and describe paths in describe paths. context.

 Inconsistently  Constructs double  Constructs and  Constructs and constructs double bar, line, or circle analyzes double bar, analyzes double bar, bar graphs, line, or graphs to solve line, and circle line, and circle graphs circle graphs to problems involving graphs to solve to solve problems solve problems fractions or problems involving involving fractions and involving fractions or decimals. fractions and decimals, in context. decimals. decimals.

Mathematics  Inconsistently  Applies  Applies  Applies understanding Achievement applies understanding of understanding of of models for division Level understanding of models for division models for division and the relationship of Descriptors one model for or the relationship and the relationship division to multiplication division or the of division to of division to to solve non-routine Number and relationship of multiplication to multiplication to problems. Operations division to solve problems. solve problems. and Algebra multiplication to solve problems.

 Inconsistently  Applies properties  Applies concepts of  Applies concepts of Fluency with applies properties of of operations to place value and the place value and the division of operations to solve solve problems properties of properties of operations whole numbers problems involving involving division. operations to solve to solve problems division. problems involving involving division and division. explain why they work.

 Uses an estimation  Uses estimation  Selects and uses  Selects and uses strategy for division strategies for appropriate appropriate estimation to calculate mentally division to calculate estimation strategies strategies for division to when computing with mentally when for division to calculate mentally whole numbers. computing with calculate mentally based on the problem Mathematics whole numbers. based on the situation when Achievement computing with whole

13 Level problem situation numbers and can justify Descriptors when computing with why a strategy was whole numbers. chosen. Number and Operations  Inconsistently uses  Uses accurate,  Develops and uses  Develops and uses and Algebra accurate, efficient, or efficient, or accurate, efficient, accurate, efficient, and generalizable generalizable and generalizable generalizable methods method to find method to find methods to find to find quotients for quotients for multi- quotients for multi- quotients for multi- multi-digit division Fluency with digit division digit division digit division problems and can division of problems. problems. problems. explain why the method whole numbers works. (cont.)  Beginning to develop  Applies efficient  Develops fluency  Develops fluency with fluency with efficient procedures for with efficient efficient procedures for procedures for dividing whole procedures for dividing whole numbers dividing whole numbers. dividing whole and justifies why the numbers. numbers. procedures work on the basis of place value and number properties.

 Determines the most  Determines the most  Inconsistently  Determines an appropriate form of the determines an appropriate form of appropriate form of the quotient and quotient and interprets appropriate form of the quotient and/or the remainder in a the quotient in a interprets the interprets the remainder in a complex problem problem situation. remainder in a situation. problem situation. problem situation.

Mathematics  Identifies only partial  Identifies and  Identifies and  Identifies and classifies Achievement attributes (angles, classifies triangles classifies triangles triangles by their Level sides) to incorrectly by their angles or by their angles and angles and sides, in Descriptors name triangles. with lengths on sides. context. sides rather than Geometry, congruent marks. Measurement, and Algebra  Misinterprets height  Applies formulas for  Finds relationships  Finds and justifies length, length of the areas of among the formulas relationships among Analyze three- side, or length of the triangles and for the areas of the formulas for the dimensional base when applying parallelograms triangles and areas of triangles and shapes, formulas. without parallelograms. parallelograms and including understanding. can explain why. volume and surface area  Frequently does not  Usually describes  Describes three-  Describes three- count number of three-dimensional dimensional shapes dimensional shapes by edges, faces, or shapes by the by the number of the number of edges, vertices correctly number of edges, edges, faces, faces, and/or vertices and confuses faces, and/or and/or vertices as as well as types of edges, faces, and vertices. well as types of faces, from multiple vertices. faces. perspectives.

 Frequently confuses  Sometimes  Recognizes volume  Recognizes volume as volume with area or recognizes volume as an attribute of an attribute of three- perimeter. as an attribute of three-dimensional dimensional space, in three-dimensional space. context. space. Mathematics  Miscounts volume of  Determines volume  Determines volume  Determines volume by Achievement three-dimensional by finding the total by finding the total finding the total

14 Level space. number of same- number of same- number of same-sized Descriptors sized units of sized units of units of volume that fill volume that fill a volume that fill a a three-dimensional Geometry, three-dimensional three-dimensional shape without gaps or Measurement, shape without shape without gaps overlaps or makes a and Algebra gaps or overlaps, or overlaps. shape with given only when filled volume. Analyze three- with cubes. dimensional shapes,  Seldom recognizes  Sometimes  Recognizes a cube  Recognizes a cube that including a cube that is one recognizes a cube that is one unit on is one unit on an edge volume and unit on an edge as that is one unit on an edge as the as the standard unit for surface area the standard unit for an edge as the standard unit for measuring volume and (cont.) measuring volume. standard unit for measuring volume. can apply it. measuring volume.

 Inconsistently  Determines the  Determines the  Determines the determines the appropriate units, appropriate units, appropriate units, appropriate units, strategies, or tools strategies, and tools strategies, and tools strategies, or tools for solving for solving problems for solving complex for solving problems problems that that involve problems that involve that involve involve estimating estimating or estimating or measuring volume. or measuring measuring volume. measuring volume and volume. can explain why it was chosen.

 Inconsistently  Decomposes three-  Decomposes three-  Decomposes three- decomposes three- dimensional shapes dimensional shapes dimensional shapes dimensional shapes and finds volumes and finds surface and finds surface areas and finds volumes of of rectangular areas and volumes and volumes of rectangular prisms. prisms. of triangular and triangular and rectangular prisms. rectangular prisms, in context.

 Identifies or  Identifies and  Identifies and  Identifies and measures measures measures measures necessary necessary attributes necessary necessary attributes attributes of shapes to of shapes to use attributes of of shapes to use use area, surface area, area, surface area, shapes to use area, surface area, and volume formulas or volume formulas area, surface area, and volume to solve problems, to solve problems. or volume formulas formulas to solve when there are missing to solve problems, problems, when parts of the when given the given all dimensions. dimensions and dimensions. formula.

15 Proposed  BeginningLevel to 1 develop  AppliesLevel the 2  Develops,Level analyzes, 3  Develops,Level analyzes, 4 Levels and apply the meaning of ratio, and applies the and applies the Policy Studentsmeaning ofdo ratio, not rate, Studentsrate, or percent to Studentsmeaning of ratio, Studentsmeaning demonstrate of ratio, rate, a DefinitionsMathematics demonstrateor percent to masterysolve demonstratesolve problems. partial demonstraterate, and percent mastery to deepand knowledge percent to solve of (ApplyAchievement to all ofproblems. grade-level mastery of grade- ofsolve the grade-level problems. mathematicalnon-routine problems. concepts gradesLevel and all knowledge and skills level knowledge knowledge and skills and procedures beyond subjects)Descriptors required Inconsistently for and Sometimes skills required requiredDetermines for decimal the Determines proficient level.decimal proficiency.determines decimal fordetermines proficiency. decimal proficiency.and percent and percent Number and equivalents for and percent equivalents for equivalents for Probability Studentscommon fractions, equivalentsStudents for commonStudents fractions, Studentscommon fractions, demonstrate Math demonstrateincluding limited demonstratecommon fractions, partial demonstrateincluding mastery masteryincluding of DescriptorsRate, ratio and masteryapproximations. of masteryincluding of ofapproximations. mathematical mathematicalapproximations, and (Applyprobability to all mathematical mathematicalapproximations. knowledge and skills knowledgeexplains how and to skills grades) knowledge and skills knowledge and through selecting throughcalculate the them. use of through the direct skills through the from an assortment multiple reasoning application Starting to of a direct Understands application the of of Understands strategies and the strategies Uses the and meaning apply of conceptunderstand or the conceptsmeaning andof integratingmeaning of concepts themprobability in new andand proceduremeaning of in proceduresprobability and in andprobability procedures and in a complexrepresents situations probabilities with simplifiedprobability and and familiarsometimes situations is able varietyrepresents of situations consistentas ratios, success.decimals, and familiarrepresent situations withto represent regular withprobabilities consistent as Theypercents are able to solve to analyze non- withprobabilities occasional as ratios, success.probabilities They as are success.ratios, decimals, They are and theirroutine strategies problems. and success.decimals, or ableratios, to explaindecimals, or ablepercents. to explain steps solutions. percents. somepercents. of their steps. and procedures.

 Inconsistently  Determines simple  Determines simple  Determines simple determines Inconsistently simple uses  experimentalUses appropriate or  Selectsprobabilities, and uses both  Selectsprobabilities and uses with Mathematics experimentalappropriate strategies or strategiestheoretical to appropriateexperimental strategies and appropriateoutcomes notstrategies equally to Achievement theoreticalto estimate fraction estimateprobabilities. fraction and totheoretical. estimate fraction estimatelikely. fraction and Level probabilities.and decimal products decimal products and decimal products decimal products and Descriptors and quotients. and quotients. and quotients. quotients in context.  Beginning to develop  Partially develops  Develops the  Applies the concept of Number the Beginning concept to of use pi as  theUses concept strategies of pi for as  Usesconcept and of analyzes pi as the  Uses,pi as theanalyzes, ratio of and the thestrategies ratio of for the solving solvingthe ratio problems of the strategiesratio of the for solving justifiescircumference a variety of of a Fluency with circumferenceproblems with of a withcircumference multiplication of a problemscircumference with of a strategiescircle to its for diameter solving to multiplication circlemultiplication to its diameter. and andcircle division to its of multiplicationcircle to its diameter. and problemssolve problems. with and division of division of fractions fractionsdiameter. and division of fractions multiplication and fractions and and decimals. decimals. and decimals. division of fractions and decimals  Inconsistently uses  Often uses the  Uses the order of decimals. Uses the order of Mathematics the order of order of operations operations to operations to simplify Achievement  Beginningoperations to to apply  toDeveloping simplify efficient  Usessimplify efficient expressions  Usesexpressions efficient that Level efficientsimplify procedures proceduresexpressions for that proceduresthat may include for proceduresinclude both for exponents Descriptors forexpressions. multiplying and multiplyingmay include and multiplyingexponents and and/or multiplyingand grouping and symbols.dividing dividing fractions or dividingexponents fractions and/or or dividinggrouping fractions symbols. and fractions and decimals Algebra decimals. decimals.grouping symbols. decimals. and justifies why they work. Writing and  Developing an  Developing an  Understands the  Understands the using  Beginningunderstanding to apply of the  understandingSometimes applies of  Appliesmeanings the and inverse uses  Appliesmeanings the andinverse uses of mathematical themeaning inverse or use of thethe inversemeaning and relationshipof variables. between relationshipvariables to between solve non- expressions relationshipvariables. between relationshipuse of variables. between multiplication and multiplicationroutine problems. and and equations multiplication and multiplication and division of fractions. division of fractions and Mathematics division of fractions. division of fractions. justifies why it works. Achievement  Evaluates or uses  Evaluates and  Writes, evaluates,  Writes, evaluates, and Level  Inconsistentlyexpressions and  usesOften expressions applies the  Appliesand uses the  Appliesuses expressions the properties and of Descriptors appliesformulas the to properties solve propertiesand formulas of to propertiesexpressions of and operationsformulas toto solvesimplify more ofsimple operations problems. to operationssolve simple to operationsformulas to to solve simplify calculationscomplex problems. involving a Algebra simplify basic simplifyproblems. calculations. calculationsproblems. with combination of fractions calculations. fractions or decimals. and decimals. Writing and  Beginning Identifies to use the  Sometimes Generally able uses to  Uses Identifies the relationship and  Applies Identifies the andrelationship relationship between the relationship between common between common common decimals between common decimals and decimals and fractions to and fractions to solve decimals and fractions to solve solve non-routine problems. fractions to solve problems, including problems. 16 problems, including measurement. measurement. using equivalent identify and represents represents complex mathematical expressions. represent equivalent equivalent equivalent expressions. expressions expressions. expressions (e.g., and equations different ways to see (cont.) a pattern).

 Beginning to  Represents,  Represents,  Extends patterns to determine analyzes, and analyzes, and the nth term using relationships and determines determines tables, graphs, words patterns using relationships and relationships and and when possible, tables, graphs, patterns using patterns using symbols. words and, when tables, graphs, tables, graphs, possible, symbols. words and, when words and, when possible, symbols. possible, symbols.

 Developing the  Often recognizes  Recognizes that the  Applies the knowledge concept that the that the solutions of solutions of an that solutions of a solutions of an an equation are the equation are the complex equation are equation are the values of the values of the the values of the values of the variables that make variables that make variables that make the variables that make the equation true. the equation true. equation true. the equation true.  Solves one-step  Solves one-step  Inconsistently  Solves simple one- equations by using equations involving solves one-step step equations by number sense, fractions or decimals. equations by using using number properties of number sense sense, properties of operations, and the and/or properties of operations, or the idea of maintaining operations. idea of maintaining equality on both equality on both sides of an equation. sides of an equation.

17 Proposed  InconsistentlyLevel 1  Often Levelidentifies 2 and  IdentifiesLevel and 3  IntegratesLevel knowledge 4 of LevelsMathematics identifies or represents represents proportional PolicyAchievement Studentsrepresents do not Studentsproportional Studentsproportional Studentsrelationships demonstrate (Including a DefinitionsLevel demonstrateproportional mastery demonstraterelationships partial with demonstraterelationships mastery deepinverse knowledge proportionality) of (ApplyDescriptors to all ofrelationships grade-level with masterycoordinate of grade- graphs of(including the grade-level inverse mathematicalwith coordinate concepts graphs grades and all knowledgecoordinate and graphs skills leveland knowledgetables and knowledgeproportionality) and skillswith andand procedures tables. Clearly beyond subjects)Number, requiredand tables for and lacks andsometimes skills required requiredcoordinate for graphs, theinterprets proficient unit level. rate as Algebra and proficiency.understanding that forunderstands proficiency. that proficiency.tables, and the slope of the related Geometry unit rate is the slope unit rate is the equations. line. Math Studentsof the related line. Studentsslope of the related StudentsInterprets unit rate Students demonstrate DescriptorsProportionality demonstrate limited demonstrateline. partial demonstrateas the slope masteryof the mastery of (Applyand similarity to all mastery of mastery of ofrelated mathematical line. mathematical grades) mathematical mathematical knowledge and skills knowledge and skills knowledge Inconsistently and solves skills knowledge Usually solves and through Understands selecting through Applies theproportionality use of throughproblems the involving direct skillsproblems through involving the fromproportionality an assortment and multiplestrategies reasoning and applicationratio, proportion, of a directratio, application proportion, of ofapplies strategies ratios and to strategiesintegrates and knowledge apply of conceptpercent, or simple conceptspercent, andsimple integratingwrite and solve concepts themratios in to new solve and problems procedureprobability, in scale proceduresprobability, inscale andproportions procedures and in a complexincluding situations percent, with simplifiedfactors, similarity and familiarfactors, situations similarity, or varietysolve problemsof situations consistentprobability, success. scale familiarand congruence. situations withcongruence. regular withincluding consistent percent, Theyfactors, are similarityable to analyze and with occasional success. They are success.simple probability, They are theircongruence strategies and and success. able to explain ablescale to factors,explain steps solutions.justifies thinking. some of their steps. andsimilarity procedures. and congruence.  Lacks strategies and  Generally computes  Models and  Computes with integers Mathematics  Inconsistentlyprocedures to  Frequentlywith integers converts and  Selectscomputes and with converts  Convertsand applies among efficient Achievement computeconverts amongwith appliesamong differentmodels (in integersamong different (in everyday units strategiesdifferent units to analyze to solve Level integersdifferent andunits is of everydayunits of contexts). contexts).of measurement to integersmulti-step (including problems Descriptors inconsistentmeasurement with to measurement to solve problems everydayincluding ratescontext). and can negativesolve problems. integers. solve problems. including rates. support results.

Number and  Inconsistently  FrequentlyGenerally  ExtendsApplies scale knowledge factor  Integrates knowledge of Algebra estimatesrecognizes and/or how estimatesrecognizes and/or how ofto integersanalyze howand the rationalmeasurement numbers (length, and solveschanges problems in one solveschanges problems in one positivechange inrational one integersarea, volume) to estimate and and Rational involvingmeasure (e.g., usingmeasure negative (e.g., numbersmeasure (e.g.,to estimate fluentlyefficiently solve analyzes problems how numbers and computationlength, area, with rationallength, area, numbers. andlength, solve area, problems andchanges can justifyin one linear equations negativevolume) affectrational volume) affect involvingvolume) affects negative technique.measure affect another. numbers.another. another. rationalanother. numbers.

Mathematics  LacksInconsistently ability to  NormallyUses models applies to  AppliesUses models properties to of  AppliesUse models properties to explain of Achievement appliesexplain theproperties of propertiesexplain the of rationalexplain thenumbers rationaland justify numbers the and Level rationalreasonableness numbers and rationalreasonableness numbers of andreasonableness algebra to write of algebrareasonableness to write andof Descriptors anduse ofalgebra formulas to write for andformulas algebra for tothe write andformulas solve for linear the solveformulas linear for equationsthe in andthe circumference solve linear andcircumference solve linear and equationscircumference in one and onecircumference variable. Can and area Measurement equationsand area of in circles; one equationsarea of circles; in one variablearea of circles; and can justifyof complex steps circles; clearly. and Geometry variable.formulas for surface variable.surface area of explainsurface steps.area of surface area of area of pyramids, pyramids and pyramids and pyramids, cylinders; Develop and cylinders or the cylinders or volume cylinders; and the and the volume of use formulas volume of pyramids of pyramids volume of pyramids; pyramids, cylinders and for surface area cylinders or cones. cylinders and/or cylinders and cones. cones. and volume cones.

 Inconsistently uses a  Uses a given  Selects and uses  Efficiently uses given estimate of π estimate of π and estimates of π to estimates of π and uses and uses this value uses this value to estimate or calculate these values to to estimate or estimate or the circumference estimate or calculate calculate the calculate the and area of circles. the circumference and circumference and circumference and area of circles and can

18 area of circles. area of circles. justify the appropriateness of the estimate.

 Shows gaps in  Demonstrates  Applies relationships  Applies and justifies understanding of understanding of among formulas for strategies utilizing relationships among relationships the areas of different relationships among formulas for the among formulas for polygons when formulas for the areas areas of different the areas of determining surface of different polygons polygons when different polygons area. when determining determining surface when determining surface area. area. surface area.

 Inconsistently solves  Frequently solves  Solves problems  Applies strategies to problems involving problems involving involving surface solve complex problems surface areas of surface areas of areas of pyramids involving surface areas pyramids and pyramids and and cylinders and of pyramids and cylinders or volumes cylinders and volumes of pyramids cylinders and volumes of pyramids, volumes of and their of pyramids. Fluently cylinders, and pyramids or may applications. computes area and cones. attempt to solve by Computes area and volume of complex or dividing compound volume of complex irregular shapes by shapes into basic or irregular shapes creating a general shapes. by dividing them into formula to represent the basic shapes. shape.

19 Proposed Level 1 Level 2 Level 3 Level 4 Levels Policy Students do not Students Students Students demonstrate a Definitions demonstrate mastery demonstrate partial demonstrate mastery deep knowledge of (Apply to all of grade-level mastery of grade- of the grade-level mathematical concepts grades and all knowledge and skills level knowledge knowledge and skills and procedures beyond subjects) required for and skills required required for the proficient level. proficiency. for proficiency. proficiency.

Math Students Students Students Students demonstrate Descriptors demonstrate limited demonstrate partial demonstrate mastery mastery of (Apply to all mastery of mastery of of mathematical mathematical grades) mathematical mathematical knowledge and skills knowledge and skills knowledge and skills knowledge and through selecting through the use of through the direct skills through the from an assortment multiple reasoning application of a direct application of of strategies and strategies and apply concept or concepts and integrating concepts them in new and procedure in procedures in and procedures in a complex situations with simplified and familiar situations variety of situations consistent success. familiar situations with regular with consistent They are able to analyze with occasional success. They are success. They are their strategies and success. able to explain able to explain steps solutions. some of their steps. and procedures.

Mathematics  Translates among  Translates among  Translates among  Translates among Achievement simple contextual, many contextual, routine contextual, routine and non-routine Level verbal, tabular, verbal, tabular, verbal, tabular, contextual, verbal, Descriptors graphical, and graphical, and graphical, and tabular, graphical and algebraic algebraic algebraic algebraic Algebra representations of representations of representations of representations of linear functions. linear functions. linear functions. linear functions. Linear functions and equations  Inconsistently finds  Frequently finds  Routinely finds slope  Finds slope of a line the slope of a line slope of a line of a line given two given two points or a when presented in given two points or points or a graphical graph, and identifies 0 graphical form. a graphical representation and and undefined slope representation. identifies special without applying a slopes (0 or formula. undefined).

 Inconsistently find  Finds some  Finds intercepts,  Finds intercepts, intercepts when in intercepts in identifies slope and identifies slope, standard form, standard form and y-intercept in slope- converts from standard identify slope and y- slope-intercept intercept form, and form and slope-intercept intercept when in form and often recognizes a form fluently, and slope-intercept form, identifies slope and proportional recognizes a and recognizes a y-intercept when in relationship (y = kx). proportional relationship proportional slope-intercept (y = kx). relationship (y = kx). form and Mathematics recognizes a Achievement proportional Level relationship (y = Descriptors kx).

Algebra  Uses linear  Selects and uses  Uses linear equations to  Uses linear represent and analyze equations to solve equations to solve linear equations to Linear functions non-routine problems to familiar problems in routine problems represent and and equations make predictions and one variable. and uses them to analyze problems (cont.) make some and make inferences. predictions. predictions and inferences.

 Writes equations for  Uses graphs or  Uses graphs or  Writes equations for tables to solve problems in two problems in two tables to solve some variables, solves the problems in two problems in two variables and solves 20 variables involving the system using system using tables or variables involving a graphs, and applies basic system of a everyday system tables or graphs. of equations and Determines if lines understanding of equations and can equality to solve them determine parallel, can determine are parallel, Appendix B: Additional Information and Background on the Standards Setting Process and Achievement Level Descriptors.

The following information was presented to the State Board at their January meeting and is provided here as additional context.

What is Oregon’s Standards Setting Process? Large scale assessments such as the Oregon Assessment of Knowledge and Skills (OAKS) are designed to provide information to students, parents, educators, policymakers, and other stakeholders about what students know and can do in a particular content area. Scores are reported using two conventions: Achievement Levels and Scale Scores. Achievement Levels assist in describing to what degree students have met the expectations that Oregon policy makers establish for student achievement in regard to state content standards. Scale Scores describe student achievement in a systematic manner that can be used to describe student achievement and student growth in achievement

Over the coming months, Oregon will re-establish the achievement expectations we have for students on statewide assessments. Following best practices, ODE staff will engage Oregon educators and stakeholders to participate in a standards setting with attention focused on a reasonable cut score given external data about national and international benchmarks. During the standards setting, the participants will review the cut-scores that are best aligned with college-readiness, national and international benchmarks, and then give input as to whether or not these proposed scores are valid. Participants meet for two to three days and engage in structured conversations that include consideration of the following: Oregon content standards, the purpose of the achievement standards and their role in new graduation requirements, the General and Math Policy Definitions, the difficulty of the content as represented by the test items, and knowledge of Oregon students.

Prior to this standards setting, revised Achievement Level Descriptors are adopted by the State Board to help guide the discussion. This year, in alignment with Marianne Perie’s recommendations, ODE is also developing overarching Policy Definitions to help further align the standards across grades and subjects.

How Does This Work Relate to the Adoption of Common Core State Standards? ODE is working with other states around the country to ensure that the Common Core State Standards eventually adopted will be in the best interest of kids. At this time, ODE staff have some concerns about the current version under review. However, there is still much work to be done to finalize the Common Core State Standards, and once finalized these new standards will be implemented over a several year period. Additional work will be needed in the future to align these with Oregon’s standards and adjust cut scores as needed, but this work is still several years down the road. This summer, Oregon will submit a plan for adoption of the Common Core State Standards including details on how these standards will be adopted and phased-in.

Review of Achievement Levels Oregon currently has the following Achievement Levels: Does Not Yet Meet, Nearly Meets, Meets, and Exceeds. As we approach the adoption of new cut scores, we will determine the appropriate level of rigor at each of these levels. This is also a good time to reassess the number and names of our Achievement Levels. NCLB requires states to set a minimum of three achievement levels and Perie, in her article, recommends no more than four levels. It seems advisable, therefore, to maintain our current four-tiered system. Naming, however, takes more consideration. As Perie states, “The terms themselves carry meaning, even without further description; therefore, naming a level is the first step in defining performance…The words chosen express the values of the policymakers and thus should be selected carefully.” [Perie, 2008]

One question before the Board this winter/spring is whether Oregon should adopt new names for our Achievement Levels. New names may be particularly advisable if the Board decides to raise the rigor of the cut scores, as indicated by initial comparison of Oregon’s achievement levels with national benchmarks. For the purposes of this docket, the place holder names of Level 1, Level 2, Level 3, and Level 4 have been used. Level 3 would be considered a “Proficient” or “Meets” level.

21 In our outreach with the field, ODE staff have solicited feedback on several possible new names and that information is available in Appendix C.

Why Raise the Rigor? Comparisons to NAEP (National Assessment of Education Progress) indicate that at least at Elementary and Middle School, Oregon’s “Meets” is well below NAEP’s “Proficient.” The inclusion of NAEP (national) and PISA (international) test items in this spring’s OAKS field test will provide additional information as to how Oregon students do compared to their peers around the country and the world. This additional information could inform the standards setting in August and the resulting cut scores.

What are Achievement Level Descriptors (ALDs)? The Oregon Achievement Level Descriptors (ALDs) explain the knowledge and skills that students typically demonstrate at specific levels of the Oregon Assessment of Knowledge and Skills (OAKS) in each grade and in each subject. The ALDs define, for example, what a student is expected to know at the “Meets” level in 5th grade Mathematics. Marianne Perie of the National Center for the Improvement of Educational Assessment calls ALDs “the foundation of standard-setting activities as they provided the explanation for how student achievement differs from one level to the next.” [Perie, 2008]

Revision of Mathematics Achievement Level Descriptors Achievement Level Descriptors are based on excerpts of the larger set of content standards and generally represent the knowledge and skills assessed at each level. Students who score at or within a particular level of achievement possess the bulk of the abilities described at that level and generally have mastered the skills described in the preceding achievement levels. Educators can use the descriptors to explain the knowledge and skills a student is expected to possess to achieve the various achievement levels for each test. Descriptors are both grade and subject specific.

Revision of the Achievement Level Descriptors is part of the implementation of the new mathematics assessments that represent the content standards adopted in 2007 - 2009. The Achievement Level Descriptors will influence the upcoming achievement standards setting for mathematics, scheduled for August 2010. In order for Oregon’s standards to be accepted for federal accountability purposes, we must submit documentation to the U.S. Department of Education (U.S. DOE), and the Achievement Level Descriptors are part of this required documentation. Achievement Level Descriptors are also used for school accountability purposes.

In preparation for drafting the Mathematics Achievement Level Descriptors a team of math education experts has reviewed state and national resources including:  The new Oregon Mathematics Content Standards  Draft Common Core State Standards  Articles on national best practices  NAEP trends  ALDs from other key states

This team is developing Math Achievement Level Descriptors for all grades.