Maine Through Year Assessment Summative Achievement Level Summaries - Math

Students who score at the Well Below State Expectations level can identify and compare multiplication statements and solve one- or two-step word problems involving multiplicative comparisons within 100. They can classify comparisons as multiplicative or additive and solve one- and two-step word problems with whole numbers without interpreting remainders. Additionally, they determine one-digit factors for composite numbers 4-20 and identify prime and composite numbers. The student continues number or shape patterns following given rules and determines the numeral for multi-digit whole numbers within 1,000 when performing addition and subtraction and within 100 when performing multiplication and division. They apply place value understanding to round whole numbers and add or subtract within 1,001 to 1,000,000 without regrouping. Furthermore, they multiply and divide within specified ranges and determine unit fractions on a number line. The student uses symbols to compare fractions and decimals, orders measurement units within one system, and solves one-step word problems involving various contexts. They apply area and perimeter formulas to rectangles and complete line plots for data measured to the nearest eighth-inch. Finally, they measure angles to the nearest degree, classify geometric objects, and identify lines of symmetry. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations level can identify multiplicative comparison statements that can be represented by multiplication expressions or equations. They solve one- or two-step word problems involving multiplicative comparisons using equations or visual diagrams. They determine factors for composite numbers between 12 and 30, identify multiples of one-digit factors, and distinguish between composite and prime numbers. They generate shape and number patterns based on given rules and interpret multiplication statements related to place value. They determine number names and expanded forms for multi-digit numbers, compare multi-digit numbers, and round whole numbers to the greatest place value. They perform addition and subtraction within 1,000,000, and multiply and divide multi-digit numbers by one-digit numbers without remainders. They determine and create equivalent fractions, compare and order fractions, and solve problems involving addition and subtraction of fractions with like denominators. They solve word problems involving multiplication of fractions by whole numbers and convert between fractions and decimals. Additionally, they solve measurement problems involving conversions and apply area formulas to rectangles. Finally, they complete and interpret line plots, understand angle measures, and classify geometric figures based on their properties. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can write multiplicative comparison statements to represent multiplication equations and solve related problems within 100. They solve one- or two-step word problems involving multiplicative comparisons using multiplication or division within 1,000 and represent these problems using equations or visual diagrams. They also tackle multi-step word problems with whole numbers and interpret remainders when necessary. Additionally, students determine factors for composite numbers between 21 and 100 and distinguish between composite and prime numbers. They interpret multiplication and division statements related to place value, determine expanded forms for multi-digit numbers, and apply place value understanding to round whole numbers. They perform addition and subtraction within 1,000,000, multiply and divide multi-digit numbers by one-digit numbers, determine and create equivalent fractions, and solve problems involving addition and subtraction of fractions with like denominators. They solve word problems involving multiplication of fractions by whole numbers and convert between fractions and decimals. Finally, they solve measurement problems involving conversions, apply perimeter and area formulas to squares and rectangles, and identify and classify geometric figures based on their properties. Mastery of the knowledge and skills of most grade level content is evident in students performing at this level.

Students who score at the Above State Expectations level can explain and analyze solutions to one- or two-step word problems involving multiplicative comparisons using multiplication or division within 101 to 1,000. They evaluate the reasonableness of solutions to multi-step word problems with whole numbers, especially when interpreting remainders. Additionally, they determine prime numbers from 37 through 97 and analyze statements about factors and multiples of whole numbers. These students can also identify and explain patterns using two operations and determine rules for number patterns. They interpret division statements related to place value and analyze place values in different numbers. Furthermore, they determine expanded notation for multi-digit numbers and justify rounding of whole numbers. They explain strategies used for addition, subtraction, multiplication, and division of multi-digit numbers. In terms of fractions, they determine equivalent fractions, explain fraction comparisons, and solve word problems involving addition, subtraction, and multiplication of fractions. They also analyze comparisons of decimals and solve measurement problems involving conversions. Additionally, they use data from line plots to solve problems and analyze how changes in dimensions affect perimeter and area. Finally, they identify and analyze properties of angles and geometric figures and draw and describe lines of symmetry. Students at this level demonstrate mastery of knowledge and skills on a range of complex grade level content.

Students who score at the Well Below State Expectations level can add or subtract decimals to the tenths or hundredths place using visual models. They can multiply or divide decimals to the tenths or hundredths with visual aids. They can continue patterns multiplying whole numbers by 10 and determine equivalent expressions using exponents for 10, 100, and 1,000. They can find equivalent fractions and determine common denominators for fractions with unlike denominators. They understand place value in decimals to the thousandths place and can round decimal numbers to the nearest whole number. They can divide two-digit whole numbers by two-digit whole numbers with remainders and rewrite fractions as division problems and vice versa. They can solve one-step real-world problems involving multiplying a fraction by a whole number using fraction models. These students can create diagrams of packed right rectangular prisms given the volume and represent the volume using length × width × height. They use appropriate units for volume such as cubic centimeters and cubic inches. They can represent the volume of composite figures made up of right rectangular prisms as the sum of the volumes of its non-overlapping parts. In geometry, students can classify triangles and quadrilaterals based on side lengths. They can determine the x-axis, y-axis, and origin in the first quadrant of the coordinate plane and identify coordinates with whole numbers. They can determine the calculations represented by numerical expressions involving two or more different operations without grouping symbols. They can evaluate numerical expressions using addition, subtraction, multiplication, or division. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations Level can add fractions and mixed numbers with unlike denominators without regrouping. They can add or subtract decimals to the hundredths place without a model, and multiply or divide decimals by multiples of 10 using place value strategies. They are able to compare and order products by interpreting multiplication as scaling and continue patterns involving dividing whole numbers by 10 up to the thousandths place. Students at this level can interpret multiplicative comparison statements that represent the value of digits in decimal numbers as ten times the value in the place to its right. They can determine number names or expanded forms for decimal numbers to the thousandths place. These students can apply volume formulas to find the volume of right rectangular prisms when dimensions are given and calculate volume by counting unit cubes. They can determine missing side lengths given the volume and other dimensions. In geometry, students can classify triangles and quadrilaterals into specific categories using multiple properties. They can identify appropriate coordinate planes to represent real-world problems by selecting suitable axes labels and scales. They can determine corresponding terms of two numerical patterns, including when presented as ordered pairs, and evaluate numerical expressions with a mix of addition, subtraction, multiplication, and division without grouping symbols. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can add and subtract fractions and mixed numbers with unlike denominators, including regrouping and subtracting from whole numbers. They can compare and order products by interpreting multiplication as scaling when involving fractions and whole numbers. They understand place value and can determine and interpret multiplicative comparison statements for digits in whole numbers and decimals, recognizing that a digit in one place represents one-tenth of what it represents in the place to its left. They can determine the expanded form and notation for decimal numbers to the thousandths. They can multiply multi-digit whole numbers using the standard algorithm and multiply and divide decimals to the hundredths using strategies based on place value and properties of operations. They can solve real-world problems involving the multiplication and division of fractions and whole numbers, including interpreting the results. They can round decimal numbers to the nearest hundredth or thousandth and compare and order decimals to the thousandths place. They use whole-number exponents to denote powers of ten and explain patterns when multiplying by powers of ten. They can calculate the volume of right rectangular prisms with whole-number side lengths, determine missing side lengths given volume, and solve problems involving volume of composite figures made up of right rectangular prisms. They can solve multi-step problems involving units such as distances, time, volume, mass, and money, involving decimals and fractions. They can create and interpret numerical expressions with grouping symbols and evaluate them correctly. They can generate two numerical patterns using given rules and identify relationships between corresponding terms. In geometry, they can classify polygons with five or more sides using multiple properties, determine coordinates of points plotted in the first quadrant of the coordinate plane, and represent and solve problems by plotting points. Mastery of the knowledge and skills of most grade level content is evident in students performing at this level.

Students who score at the Above State Expectations level can add and subtract fractions and mixed numbers with unlike denominators, including multiple terms and whole numbers. They can evaluate and justify solutions to real-world problems involving multiplication and division of fractions and mixed numbers using various methods. They explain strategies used to multiply and divide multi-digit numbers and perform operations with decimals to the hundredths, including multiple operations. They determine the expanded notation for decimal numbers to the thousandths and explain patterns when dividing by powers of ten. They solve complex measurement problems involving distances, time intervals, volumes, masses, and money with decimals and fractions. They analyze and compare volumes of right rectangular prisms, understanding how changing dimensions affects volume. In geometry, they create two-dimensional shapes based on classifications and plot points in the first quadrant of the coordinate plane, including with scale breaks. They explain the classification of regular polygons based on their properties. They evaluate numerical expressions with nested grouping symbols and analyze calculations to create true expressions. They explain relationships between corresponding terms in numerical patterns and determine rules from function tables or graphs. Students at this level demonstrate mastery of knowledge and skills on a range of complex grade level content.

Students who score at the Well Below State Expectations level can solve division problems with fractions and mixed numbers using fraction models, divide large whole numbers by one-digit numbers without remainders, and add or subtract decimals to the thousandths place. They can find common factors of whole numbers up to 50 and recognize contexts using positive and negative numbers. They understand opposite numbers, locate negative numbers on number lines, compare and order integers, and understand absolute value as distance from zero. They can identify coordinates and quadrants of points on the coordinate plane and find distances between points with the same x or y coordinate. These students can write and evaluate exponential expressions with whole-number exponents and identify expressions representing one-operation statements. They can evaluate one-variable expressions and identify equivalent expressions using properties of operations. They can determine if an inequality is true for a given value, solve simple equations, and identify independent and dependent variables. They can find the area of right triangles, represent the volume of right rectangular prisms, identify polygons on the coordinate plane, determine coordinates to complete polygons, identify three-dimensional figures from descriptions or nets, and interpret diagrams of prisms with unit-fraction cubes. In statistics, they can identify statistical questions, distinguish between measures of center and variation, determine the range of data sets, represent data on line or dot plots, and determine the number of observations in a data set. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations Level can evaluate expressions involving fractions with whole-number exponents. They can represent whole numbers less than 100 in exponential form by determining exponents or bases. They can create and identify expressions with positive rational numbers and variables to represent mathematical statements. They can solve problems involving division of fractions and mixed numbers, with or without models. They can divide large whole numbers, interpret remainders as decimals or fractions, and operate with decimals to the thousandths place. They determine greatest common factors and least common multiples of whole numbers. They understand positive and negative integers on number lines, find opposites, and evaluate absolute values. They determine coordinates and quadrants on the coordinate plane, including reflections. They compare and order integers, understand ratios and unit rates to solve real-world problems, calculate percentages, and convert between measurement systems. Students can determine areas of triangles and parallelograms, find unknown dimensions of right triangles, apply volume formulas for right rectangular prisms, identify polygons and side lengths using coordinates, and recognize nets of prisms and pyramids. They can turn non-statistical questions into statistical ones, make general statements about measures of center from data displays, determine mean or median, identify histograms and box plots from data, and describe outliers in context. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can solve problems involving division of fractions and mixed numbers, including multi-step word problems. They can divide large whole numbers by multi-digit numbers and interpret remainders as decimals or fractions and perform operations with decimals to the thousandths place. They determine the greatest common factor of two whole numbers up to 100 and the least common multiple of two whole numbers up to 12. They represent positive and negative values in context, compare and order integers and rational numbers, including negatives and non-integral values, using number lines and symbols. They understand and use absolute value and can plot and interpret points with rational coordinates in all quadrants of the coordinate plane. They evaluate numerical expressions with exponents and apply the order of operations, represent numbers in exponential form, and create expressions using appropriate operation terminology. They evaluate one-variable expressions and create equivalent expressions using properties of operations. They determine whether values satisfy equations or inequalities and solve them involving positive rational numbers. They determine areas of quadrilaterals, find unknown dimensions of triangles and parallelograms, calculate missing side lengths of right rectangular prisms with fractional or decimal measurements, and solve problems involving surface area of prisms and pyramids. They formulate statistical questions for real-world situations, describe data distributions using measures of center and variability, create and interpret line plots, histograms, and box plots, and draw conclusions about the data. Mastery of the knowledge and skills of most grade level content is evident in students performing at this level.

Students who score at the Above State Expectations level can analyze and evaluate solutions to problems involving ratios, percents, unit rates, and unit conversions. They create real-world contexts with positive and negative quantities and explain their meanings, including zero. They determine and explain coordinates and quadrants of points reflected across axes. They explain strategies used to divide fractions, mixed numbers, and whole numbers, and perform operations with decimals to the thousandths place. They solve real-world problems involving least common multiples of whole numbers less than or equal to 12. They use symbols to represent comparisons of integers and non-integer rational numbers, and graph and write coordinates of points in Quadrants II to IV. Students analyze linear equations in two variables with positive rational coefficients, understanding the quantities they represent, and analyze the meaning of solutions on a number line within real-world contexts. They create and explain equivalent expressions using properties of operations and combining like terms. They represent whole numbers greater than 100 in exponential form and analyze and compare exponential expressions. Students analyze how changing dimensions affects the volume of right rectangular prisms in real-world problems and analyze solutions involving volume and surface area. They justify whether a specific net represents a given prism or pyramid and determine unknown dimensions to solve problems involving area. Students compare different representations of the same data set and draw conclusions. They determine missing values in data sets when given the mean or median, explain general statements about measures of center and variability presented in data displays, and recommend and justify the best measures for real-world contexts. Students at this level demonstrate mastery of knowledge and skills on a range of complex grade level content.

Students who score at the Well Below State Expectations level can add and subtract negative integers using a number line, identify integers that add to zero, and recognize that fractions with a denominator of zero are undefined. They can solve one- and two-step problems involving rational numbers and represent problems with expressions or equations involving negative integers. They can calculate unit rates with unit fractions and decimals, determine proportional relationships from tables, graphs, or descriptions, find missing values, determine the constant of proportionality, and identify equations modeling proportional relationships. They can identify equivalent linear expressions with positive rational coefficients, and solve one-step problems involving rational numbers, including equations like px + q = r. They can determine scale factors from corresponding lengths of shapes, identify two-dimensional figures from slicing right rectangular prisms, find the radius or diameter of a circle, identify types of angles from diagrams, and solve problems involving perimeter, area, and volume of irregular shapes when dimensions are given. They can determine event likelihoods, distinguish between relative frequency and theoretical probability, determine sample spaces, differentiate between dependent and independent events, identify sample populations, and draw conclusions about measures of center from data representations with similar variabilities. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations Level can identify contexts matching expressions that add to zero, add integers of opposite signs using a number line, and add two negative integers without a number line. They determine signs of sums and differences when adding or subtracting integers, model additive inverses on a number line, and identify distances between integers as absolute values of differences. They subtract negative integers from positive or negative integers, subtract positive integers from negative integers without a number line, and determine equivalent expressions using additive inverses. They determine equivalent forms and signs of products and quotients of integers and rational numbers, including non-integral values. They convert fractions to terminating decimals and solve multi-step problems involving rational numbers. They create and identify equivalent linear expressions using properties and combining like terms and solve multi-step mathematical problems involving rational numbers in various forms, including fractions, decimals, and negative numbers. They solve certain equations and inequalities and graph solutions on a number line. They determine scale factors and missing lengths in similar figures, identify cross-sectional shapes of solids, compute area and circumference of circles, determine missing angle measures involving angle relationships, and solve problems involving perimeter, area, and volume of irregular shapes. They determine event likelihoods based on probabilities, approximate probabilities from data, determine theoretical probabilities of simple and compound events, make inferences about populations from samples, and draw conclusions about measures of center from data. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can interpret sums of rational numbers that result in zero in real-world contexts. They add and subtract integers and rational numbers, including negatives and non-integer fractions, without a number line. They determine distances and signs when working with integers and rational numbers on the number line. They multiply and divide integers and rational numbers, involving negatives and absolute values. They solve multi-step mathematical and real-world problems using all four operations with rational numbers and convert fractions to repeating decimals. They create and identify equivalent expressions using properties of operations and combining like terms, even when coefficients are non-integer rational numbers. They solve equations and inequalities involving rational numbers, including negatives and non-integer fractions, and represent real-world problems with these equations and inequalities. They determine reasonable solutions to multi-step problems involving rational numbers in various forms. They determine scale factors and missing lengths in scale drawings and solve problems involving perimeter, area, and circumference of geometric figures, including composite shapes. They identify two-dimensional figures resulting from cross-sections of cones, cylinders, and spheres. They solve for angle measures involving vertical, adjacent, complementary, and supplementary angles using algebraic expressions. They determine appropriate probabilities based on descriptions of likelihood and predict relative frequencies, comparing them to given probabilities. They use observed data to create probability models, including for non-uniform chance processes, and compare them with theoretical models. They calculate theoretical probabilities of independent and dependent compound events and assess the validity of representative samples. Mastery of the knowledge and skills of most grade level content is evident in students performing at this level.

Students who score at the Above State Expectations level can create and interpret sums, differences, products, and quotients of rational numbers, including negatives and fractions, in real-world contexts. They can identify patterns when converting rational numbers to decimals and solve multi-step problems involving all operations with rational numbers. They can explain proportional relationships given tables, graphs, or descriptions, and solve percent change problems using proportional reasoning. These students can create equivalent linear expressions with rational coefficients, including fractions, by manipulating expressions. They can explain relationships in equivalent expressions and solve real-world problems using linear equations and inequalities in multiple ways. They can solve problems involving area and scale drawings, explaining why calculating area differs from perimeter when using scale factors. They can find measurements of circles and composite figures, solve problems involving perimeter and area of composite shapes, and find missing dimensions when not directly given. They can determine angle measurements from algebraic expressions and angle relationships. They can compare and order probabilities, explain why events are more or less likely, and analyze theoretical and experimental probabilities. They understand conditions affecting probabilities, the importance of random sampling, and use measures of center and variability to compare populations. Students at this level demonstrate mastery of knowledge and skills on a range of complex grade level content.

Students who score at the Well Below State Expectations level can identify fractions as rational numbers, recognize pi as irrational, and determine the rationality of square and cube roots of whole numbers. They apply properties of exponents when multiplying expressions with the same bases and evaluate numerical expressions with negative integer exponents. Additionally, they convert between scientific notation with positive exponents of 10 and decimals. These students graph proportional relationships, determine unit rates from graphs, and find slopes of non-vertical lines. They also solve two-step linear equations, identify the number of solutions for linear equations, solve systems of linear equations, and recognize relations as functions. Moreover, they distinguish between linear and nonlinear functions, determine rates of change, and interpret variables in context. These students identify geometric transformations, determine congruency and similarity among figures, and calculate hypotenuses in right triangles. They also determine the volumes of cones, cylinders, and spheres, identify scatter plots representing data, and make predictions based on lines of best fit. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations level can identify given decimals as rational or irrational numbers and convert common repeating decimals into fractions. They can determine the rationality of the cube root of both perfect and non-perfect cube integers and place irrational numbers on a number line. Additionally, they estimate the value of irrational numbers and apply properties of exponents when multiplying and dividing numerical expressions with integer exponents, including negative exponents. These students evaluate square and cube roots of rational numbers, convert between scientific notation with negative exponents and decimals, and perform operations with numbers in scientific notation. They make comparisons between proportional relationships, graph proportional relationships, and use points from graphs to explain linear equations. They solve multi-step linear equations, determine the number of solutions for linear equations, and solve systems of linear equations. Moreover, these students identify and compare linear and nonlinear functions, determine the rate of change and initial value of linear functions, and interpret functions that model linear relationships. They identify and perform geometric transformations and determine congruency and similarity among figures. Additionally, they calculate lengths in right triangles, determine the volume of cones, cylinders, and spheres, and analyze scatter plots. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can convert less common repeating decimals into fractions and compare and order both rational and irrational numbers, using mathematical notation for comparisons. They place irrational numbers on a number line between whole numbers and estimate their values to the nearest ± 0.5. Applying properties of exponents, they handle numerical expressions involving both multiplication and division with integer exponents and rational-number bases. These students solve equations of the form x² = p and x³ = p for both perfect square and cube rational numbers, using appropriate symbols for solutions, and identify exponential equations in various contexts. Moreover, they perform operations with numbers expressed in scientific and decimal notation, comparing and ordering values across these formats. They interpret and graph proportional relationships, explain slopes, and write linear equations with specified solution criteria. Multi-step linear equations and systems of linear equations are within their grasp, as well as recognizing functions and comparing linear functions in different representations. In geometry, they apply transformations to create congruent or similar figures and determine the effects on two-dimensional figures using coordinates. Students also understand the Pythagorean Theorem in multi-step problems, solve for missing dimensions in three-dimensional figures, and determine volumes of cones, cylinders, and spheres in complex problems. They create and analyze scatter plots, use lines of best fit, and construct frequency tables to summarize categorical data. Mastery of the knowledge and skills of most grade-level content is evident in students performing at this level.

Students who score at the Above State Expectations level can explain and justify classifications of numbers as rational and irrational. They place expressions involving irrational numbers on a number line, find better approximations of irrational numbers, and simplify and evaluate numerical expressions with exponents. They write exponential equations that result in given square or cube roots, and express comparisons of quantities using scientific notation. These students perform operations with numbers in scientific and decimal notation, choosing appropriate units for real-world contexts. Furthermore, they analyze proportional relationships, explain slopes using similar triangles, and justify solutions to multi-step linear equations. They write systems of linear equations for real-world problems, determine systems given solutions and parameters, and explain intersections of graphs as solutions. These students also represent and compare functions, explain their properties, and create real-world situations modeled by graphs. They understand and justify congruence properties of geometric figures after transformations, explain effects of multiple transformations, and compare congruence and similarity. In geometry, they determine missing angles using geometric properties, solve multi-step problems involving the Pythagorean Theorem in three-dimensional figures, and compare distances among points. They calculate volumes of composite shapes, justify methods for solving real-world problems, and make predictions based on bivariate data patterns. Additionally, they evaluate and explain scatter plots, write linear equations for data sets, and interpret frequency tables to describe associations. Students performing above state expectations demonstrate mastery of knowledge and skills on a range of complex grade-level content

Students who score at the Well Below State Expectations Level can identify zeros of quadratic functions in factored form and perform basic operations on polynomials with one variable, such as adding, subtracting, and multiplying monomials and binomials. They can create and interpret linear equations and inequalities in one variable, graph linear equations in two variables, and assess solutions in real-world contexts. These students are able to rearrange simple equations, justify steps in equation solving, and solve systems of linear equations using elimination and graphical methods. They understand function notation, identify inputs and outputs, determine rates of change of linear functions, and compare key features of quadratic functions. They can model contexts mathematically, combine functions, distinguish between arithmetic and geometric sequences, and identify function transformations. In geometry, they recognize basic figures and their properties, understand transformations and symmetry, apply properties of congruent and similar triangles, and use the Pythagorean Theorem. They recognize properties of circles, including inscribed angles and equations. They can solve coordinate geometry problems, determining slopes, midpoints, perimeters, and areas on the coordinate plane. They calculate volumes of pyramids and identify cross-sections of solids. In statistics, they interpret data displays, calculate measures of center and spread, identify outliers, represent data with scatterplots, and identify linear models. They can calculate basic probabilities. Students at this level need additional support to master the content knowledge and skills at their current grade.

Students who score at the Below State Expectations Level can perform basic operations with polynomials, such as adding, subtracting, and multiplying simple expressions. They are able to solve simple linear and quadratic equations and inequalities, and they can identify graphs of quadratic equations. They can rearrange equations with two variables using two steps and justify simple steps in solving equations. They understand how to evaluate functions for given inputs and can identify domains and ranges of functions presented in graphs or tables. They are able to interpret key features of functions, such as intercepts, maximums, and minimums, from graphs or tables. They can compare linear and exponential functions and describe their rates of change. They can solve systems of linear equations using tables and algebraic methods and can factor simple quadratic expressions to find zeros of functions. In geometry, these students can identify transformations such as rotations, reflections, and translations, and understand basic properties of congruence and similarity in figures. They can calculate volumes and perimeters of simple geometric shapes and solve problems involving right triangles using the Pythagorean Theorem. They can represent and analyze data using frequency tables, histograms, and scatterplots, and can interpret simple probability events. They can describe relationships between two variables on a scatterplot and identify linear models that best fit the data. Students at this level are approaching mastery of some grade-level content but have gaps in knowledge and skills.

Students who score at the At State Expectations level can multiply polynomials, including complex binomials and multiple polynomials with various variables. They use equations to solve problems from quadratic functions and create linear equations from descriptions, tables, or graphs. They represent relationships using equations in more than two variables and model situations with constraints using equations, inequalities, or systems. They rearrange complex equations and justify solution methods. They identify solutions of nonlinear equations, recognize graphs as solution sets, and explain intersections of y = f(x) and y = g(x) as solutions to f(x) = g(x). They find solutions using tables or graphs and understand linear inequalities in two variables as half-planes. They solve linear and compound inequalities with variable coefficients, factor quadratic equations to find real solutions, and manipulate systems of equations for equivalence. They solve real-world problems using linear systems and systems involving linear and quadratic equations using tables or graphs. They interpret quadratic and linear expressions, determine equivalent expressions, factor quadratics to find zeros, and create explicit or recursive expressions. They combine functions and write formulas for arithmetic or geometric sequences. They analyze function transformations, domains, and ranges, evaluate functions, and interpret function notation. They interpret key features of functions, determine average rates of change, and understand intercepts and extrema of functions. They compare linear and exponential functions, recognize contexts with constant rates of change, determine linear functions from data, interpret rates of change, and use units to guide problem-solving. Mastery of the knowledge and skills of most grade level content is evident in students performing at this level.

Students who score at the Above State Expectations level can determine expressions for real-world problems involving monomials and binomials. They solve equations and inequalities, including quadratic, rational, and exponential functions, and create equations in multiple variables to represent relationships. They analyze systems of equations or inequalities in real-world contexts, rearrange equations, and understand that graphs represent solutions. They solve quadratic equations, including complex solutions, justify methods, and solve systems involving linear and quadratic equations. They interpret and rewrite exponential and polynomial expressions, factor quadratics, and analyze sequences. They evaluate and analyze functions, understand transformations, and interpret average rates of change. They identify exponential and quadratic functions and determine equations of functions with specific properties. They understand units and accuracy in complex problems, perform operations with radicals and rational exponents, and comprehend rational and irrational numbers. In geometry, they analyze proofs and constructions, understand similarity and congruence through transformations, and apply trigonometry and the Pythagorean Theorem. They solve probability problems, interpret data, analyze variable relationships, and explain the suitability of functions for data sets, interpreting slopes and intercepts in linear models. Students at this level demonstrate mastery of knowledge and skills on a range of complex grade level content.