# The NAEP Mathematics Achievement Levels by Grade

Specific definitions of the NAEP Basic, NAEP Proficient, and NAEP Advanced achievement levels for grades 4, 8, and 12 are presented in the tables that follow. Because of changes made to the NAEP mathematics framework in 2005, the NAEP achievement-level descriptions and cut points indicated below for grade 12 have been updated. To maintain trend, results for grades 4 and 8 are reported on a 0–500 scale while results for grade 12, beginning with the 2005 assessment, are reported on a 0–300 scale. View the grade 12 NAEP achievement-level descriptions and cut scores used prior to 2005.

The NAEP achievement levels are cumulative; therefore, students performing at the NAEP Proficient level also display the competencies associated with the NAEP Basic level, and students at the NAEP Advanced level also demonstrate the skills and knowledge associated with both the NAEP Basic and the NAEP Proficient levels. The cut score indicating the lower end of the score range for each level is noted in parentheses.

 NAEP Basic(262) Students performing at the NAEP Basic achievement level can likely simplify expressions involving integersuse operations to solve real-world problems involving integers or fractionsuse proportional relationships to find equivalent ratios and create fractions and fractional relationships, with or without modelsdemonstrate understanding of scientific notation  Students performing at the NAEP Basic achievement level can likely reason and determine measurements, including length, area, and volume, with descriptions, labeled diagrams, and units providedapply proportional reasoning to solve problems in context using scale factor, distance, unit conversion and quantitiesapply simple scale factor value to find unknown lengths of triangles and rectangles without setting up a proportion  Students performing at the NAEP Basic achievement level can likely find a missing angle in a triangle given two angles and understand that angles of a triangle add to 180 degreesrecognize quadrilaterals given a description of their shared attributes  Students performing at the NAEP Basic achievement level can likely interpret, create, and/or compare different data set representations to determine a specific set of values for mean, mode, and range while identifying errors and appropriateness  Students performing at the NAEP Basic achievement level can likely use a coordinate plane to identify and plot coordinate points preciselyfind the distance between pointsrecognize and extend patterns within an arithmetic or geometric sequence of numbers in a list or table (arithmetic, geometric) to solve problems in contextidentify, solve, and/or evaluate one- and two-step equations, and apply slope, given linear relationships Students performing at the NAEP Proficient achievement level can likely demonstrate an understanding of using and creating ratios to solve problems mathematically or in contextcalculate GCF and LCMperform basic operations with rational numbers to solve problems in context while applying proper units and converting between fractions, decimals, and percentcompare and order rational numbers with rational or common irrational numbers with or without a number lineapply problem-solving strategies to solve square roots and ratio and proportions  Students performing at the NAEP Proficient achievement level can likely demonstrate an understanding of solving problems that relate to comparing measures of two or three dimensions of spacedetermining possible dimensions given area and volume as well as selecting appropriate units of measure and applying scale factor to areareason abstractly using addition and subtraction in contextual situationssolve problems involving capacity, area, and weightclassify angle measurements using diagrams and protractors  Students performing at the NAEP Proficient achievement level can likely understand concepts of parallel and perpendicular linesuse angle relationships and/or measurements formed when parallel lines are cut by a transversal.apply concepts of corresponding parts between similar and congruent figures with some containing composite shapes in contextapply problem-solving strategies to solve Pythagorean Theorem problemssolve problems in context by creating a figure in the coordinate plane that satisfies area and perimeter criteriareflect a shape on the coordinate plane over the x- and y-axis and plot some of the corresponding pointsdetermine unknown side lengths by decomposing a polygon using given constraintsdetermine coordinates of missing endpoints of vertical or horizontal line segments on a coordinate plane Students performing at the NAEP Proficient achievement level can likely use problem solving skills to make calculations based on multiple representations of data sets in context to determine measures of central tendencies, theoretical probability, and basic probability conceptsestimate values along the line of best fitidentify sources of bias in a sample designcalculate the mean from tables of data in multiple sets of values  Students performing at the NAEP Proficient achievement level can likely create, model, identify, and solve one-step inequalities and multi-step equations with or without context and with or without constraintsevaluate and extend sequential and recursive patterns using tables, models, multiple steps or from translating a written descriptiongraph and identify key features of linear and nonlinear functionsrecognize the effects on a graph when the slope and y-intercept are changed Students performing at the NAEP Advanced achievement level can likely solve mathematical problems and problems in context with rational numbers including absolute values and variables by interpreting, creating and using diagramsengage with abstract situations and apply properties such as even and/or odd numbers, divisibility rules, and prime and composite numbers in mathematic situations  Students performing at the NAEP Advanced achievement level can likely create a proportion to represent scale in context and analyze number lines with fractional intervalsuse ratios and proportion to find and/or explain measurements in multi-step situations, including unit rate and speed/distancesolving problems involving area including composing and decomposing complex figuresreason abstractly using multiple steps of addition and subtraction in contextestimate length and measure using tools appropriately in context  Students performing at the NAEP Advanced achievement level can likely understand angle relationships formed when parallel lines are cut by a transversal(s) to solve complex problemsdetermine relative positions of points using the geometric ideas of midpoint involving directionality on the coordinate planeclassify geometric solids by their properties and recognize cross-sections of plane and solid figures predicting results of subdividing complex plane figures in a variety of waysperform a sequence of transformations in the coordinate plane and identify corresponding parts and pointsunderstand and apply relationships of circles and central anglesevaluate proportionality and similarity to find unknown valuesjustify the sum of interior angles of polygonsdemonstrate knowledge of the faces of geometric solidsdetermine unknown sides of triangles using Pythagorean Theorem or similar triangles Students performing at the NAEP Advanced achievement level can likely analyze and compare problems using problem-solving skills to make calculations and connections based on multiple representations of data sets to determine measures of central tendencies and their effect, theoretical and experimental probability, and basic probability conceptsuse a line of best fit or line graph to make predictions and interpretationsanalyze and critique graphical displays to justify appropriateness and solve problems  Students performing at the NAEP Advanced achievement level can likely interpret, analyze, apply, and justify mathematical or contextual linear and nonlinear relationships and their key features represented through equations, tables, and graphs of a line, including with scales other than 1evaluate, interpret, justify, solve, and write multiple-step equations and/or expressions and inequalities with fractions and/or multiple variables in contextual situations with or without constraints Note: The content descriptions represented within the reporting ALD statements are intended to reflect the content defined within the framework.