Strand	Numbers and Operations
Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Topic	Numbers and Number Systems
Benchmark MA.6.1.1	Compare and order fractions, decimals, and percents
Sample Performance Assessment (SPA)	The student: Finds the approximate location of a fraction, decimal, and percent on a number line.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Compare and order fractions, decimals, and percents, with accuracy, and justify the comparisons	Compare and order fractions, decimals, and percents, with no significant errors	Compare and order fractions, decimals, and percents, with a few significant errors	Compare and order fractions, decimals, and percents, with a many significant errors

Topic	Numbers and Number Systems
Benchmark MA.6.1.2	Explain and give examples of number theory concepts (e.g., prime factorization, common factors, greatest common factor, common multiples, least common multiple, divisibility)
Sample Performance Assessment (SPA)	The student: Draws a factor tree to find the prime factorization of a number; shows a process for finding the greatest common factor and least common multiple of two or more numbers.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively explain and give examples of number theory concepts, with accuracy	Sufficiently explain and give examples of number theory concepts, with no significant errors	Minimally explain and give examples of number theory concepts, with a few significant errors	Have difficulty explaining and giving examples of number theory concepts

Strand	Numbers and Operations
Standard 2: Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other

Topic	Operation
Benchmark MA.6.2.1	Apply the order of operations when calculating with whole numbers
Sample Performance Assessment (SPA)	The student: Follows the rules for the order of operation when solving whole number problems.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the order of operations when calculating with whole numbers, with accuracy	Apply the order of operations when calculating with whole numbers, with no significant errors	Apply the order of operations when calculating with whole numbers, with a few significant errors	Apply the order of operations when calculating with whole numbers, with many significant errors

Topic	Operation Properties
Benchmark MA.6.2.2	Use the operation properties to simplify computations with fractions, decimals, and percents
Sample Performance Assessment (SPA)	The student: Decomposes (using the distributive property) and rearranges (using the commutative and/or associate properties) the numbers in order to put "friendly" numbers together to make it easier to perform the computations.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Strategically use the operation properties to simplify computations with fractions, decimals, and percents, with accuracy	Use the operation properties to simplify computations with fractions, decimals, and percents, with no significant errors	Use the operation properties to simplify computations with fractions, decimals, and percents, with a few significant errors	Use the operation properties to simplify computations with fractions, decimals, and percents, with many significant errors

Strand	Numbers and Operations
Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation

Topic	Estimation
Benchmark MA.6.3.1	Use estimation prior to computing with fractions and decimals and compare the estimation to the actual result
Sample Performance Assessment (SPA)	The student: Uses an appropriate estimation strategy to mentally determine an answer, then performs the actual computation and compares the result to the estimation.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently use estimation prior to computing with fractions and decimals and compare the estimation to the actual result	Usually use estimation prior to computing with fractions and decimals and compare the estimation to the actual result	Sometimes use estimation prior to computing with fractions and decimals and compare the estimation to the actual result	Rarely use estimation prior to computing with fractions and decimals and compare the estimation to the actual result

Topic	Estimation
Benchmark MA.6.3.2	Recognize situations in which it is more appropriate to estimate than to compute an exact answer
Sample Performance Assessment (SPA)	The student: Selects from a list problems that require an estimate or an accurate answer and solves the problem accordingly.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently determine situations in which it is more appropriate to estimate than to compute an exact answer, and provide justification	Usually determine situations in which it is more appropriate to estimate than to compute an exact answer	Sometimes determine situations in which it is more appropriate to estimate than to compute an exact answer	Rarely determine situations in which it is more appropriate to estimate than to compute an exact answer

Strand	Measurement
Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

Topic	Measurement Attributes and Units
Benchmark MA.6.4.1	Estimate the circumference and area of a circle (with no reference to a formula)
Sample Performance Assessment (SPA)	The student: Traces a circle onto centimeter grid paper and counts the squares and partial squares to estimate its area; places string along the circumference and measures it determine the circumference.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use and clearly explain a strategy to make reasonable estimates of the circumference and area of a circle (with no reference to a formula)	Use appropriate strategies to make reasonable estimates of the circumference and area of a circle (with no reference to a formula)	Incompletely or incorrectly apply appropriate strategies to make reasonable estimates of the circumference and area of a circle (with no reference to a formula)	Use inappropriate strategies to make reasonable estimates of the circumference and area of a circle (with no reference to a formula)

Topic	Measurement Attributes and Units
Benchmark MA.6.4.2	Construct angles with a given degree measure
Sample Performance Assessment (SPA)	The student: Uses a protractor (or angle ruler) to draw an angle with ±1° precision.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Construct angles with a given degree measure, with accuracy	Construct angles with a given degree measure, with no significant errors	Construct angles with a given degree measure, with a few significant errors	Construct angles with a given degree measure, with many significant errors

Topic	Measurement Formulas
Benchmark MA.6.4.3	Apply strategies and formulas to solve area and perimeter problems involving polygons (e.g., regular hexagons) and complex shapes (i.e., shapes composed of two or more common shapes)
Sample Performance Assessment (SPA)	The student: Decomposes complex shapes into common shapes, logically determines measurements that can be derived from the known measurements, and pieces together the area of each part to determine the total area.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply strategies and formulas to solve area and perimeter problems involving polygons and complex shapes, with accuracy	Apply strategies and formulas to solve area and perimeter problems involving polygons and complex shapes, with no significant errors	Apply strategies and formulas to solve area and perimeter problems involving polygons and complex shapes, with a few significant errors	Apply strategies and formulas to solve area and perimeter problems involving polygons and complex shapes, with many significant errors

Strand	Geometry and Spatial Sense
Standard 5: Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.6.5.1	Analyze and describe the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures
Sample Performance Assessment (SPA)	The student: Compares the ratio of side lengths to area of a variety of similar shapes (e.g., determines the ratio of the areas of two similar rectangles whose lengths have a 2:1 ratio).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Analyze and describe, in great detail, the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures	Analyze and describe, in sufficient detail, the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures	Analyze and describe, in some (but not enough) detail, the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures	Analyze and describe, in insufficient detail, the relationships among the angles, side lengths, perimeters, and areas of similar geometric figures

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.6.5.2	Create arguments for proving that two shapes are congruent
Sample Performance Assessment (SPA)	The student: States the measures that are needed to prove that two triangles are congruent.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Create compelling and logical arguments for proving that two shapes are congruent	Create convincing arguments for proving that two shapes are congruent	Create arguments that are generally on the right track for proving that two shapes are congruent	Create insufficient or incorrect arguments for proving that two shapes are congruent

Strand	Geometry and Spatial Sense
Standard 6: Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations

Topic	Symmetry
Benchmark MA.6.6.1	Use line symmetry and rotational symmetry to describe classifications of shapes (e.g., squares have 4 lines of symmetry and 90° rotational symmetry)
Sample Performance Assessment (SPA)	The student: Sorts shapes into separate groups based on line and/or rotational symmetry and describes the properties shared by each group's shapes.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use line symmetry and rotational symmetry to describe classifications of shapes, with accuracy	Use line symmetry and rotational symmetry to describe classifications of shapes, with no significant errors	Use line symmetry and rotational symmetry to describe classifications of shapes, with a few significant errors	Use line symmetry and rotational symmetry to describe classifications of shapes, with many significant errors

Strand	Geometry and Spatial Sense
Standard 7: Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics

Topic	Visualization and Spatial Reasoning
Benchmark MA.6.7.1	Construct a two-dimensional representation from different angles of a three-dimensional object
Sample Performance Assessment (SPA)	The student: Looks at an object from different views and draws a two-dimensional picture of the top, left, right, and front view.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Construct a two-dimensional representation from different angles of a three-dimensional object, with accuracy	Construct a two-dimensional representation from different angles of a three-dimensional object, with no significant errors	Construct a two-dimensional representation from different angles of a three-dimensional object, with a few significant errors	Construct a two-dimensional representation from different angles of a three-dimensional object, with many significant errors

Topic	Visualization and Spatial Reasoning
Benchmark MA.6.7.2	Draw two-dimensional shapes with specified properties
Sample Performance Assessment (SPA)	The student: Draws a shape from specific instructions (e.g., draws a quadrilateral that has two pairs of parallel sides).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Draw two-dimensional shapes with specified properties, with accuracy	Draw two-dimensional shapes with specified properties, with no significant errors	Draw two-dimensional shapes with specified properties, with a few significant errors	Draw two-dimensional shapes with specified properties, with many significant errors

Strand	Geometry and Spatial Sense
Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry

Topic	Coordinate Geometry
Benchmark MA.6.8.1	Predict the shape that is formed by connecting the points represented by given coordinates
Sample Performance Assessment (SPA)	The student: Predicts the shape that will form from a set of given coordinates and use the coordinates to justify the prediction.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Accurately identify the shape that is formed by connecting the points represented by given coordinates, and use the coordinates to justify the shape	Make reasonable predictions about the shape that is formed by connecting the points represented by given coordinates and use the coordinates to justify the prediction	Make somewhat reasonable predictions about the shape that is formed by connecting the points represented by given coordinates, but has difficulty justifying the prediction	Make unreasonable predictions about the shape that is formed by connecting the points represented by given coordinates

Topic	Coordinate Geometry
Benchmark MA.6.8.2	Use coordinate geometry to represent and analyze properties of geometric shapes
Sample Performance Assessment (SPA)	The student: Determines and justifies the coordinates of a vertex of a shape (e.g., parallelogram) when all but one of the vertices is given.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively and accurately use coordinate geometry to represent, analyze, and describe properties of geometric shapes	Use coordinate geometry to represent and analyze properties of geometric shapes, with no significant errors	Use coordinate geometry to represent and analyze properties of geometric shapes, with a few significant errors	Use coordinate geometry to represent and analyze properties of geometric shapes, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships

Topic	Patterns
Benchmark MA.6.9.1	Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols
Sample Performance Assessment (SPA)	The student: Expresses the rule for a numerical pattern in words and symbols.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols, with accuracy	Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols, with no significant errors	Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols, with a few significant errors	Represent visual and numerical patterns with tables and graphs and generalize the "rule" using words and symbols, with many significant errors

Topic	Functions
Benchmark MA.6.9.2	Describe simple one-step functions using words and symbols when given a table of "input" and "output" values
Sample Performance Assessment (SPA)	The student: Fills in missing data in a table of "input" and "output" values and describes a rule for the table using words or symbols. Example:
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe simple one-step functions using words and symbols when given a table of "input" and "output" values, with accuracy	Describe simple one-step functions using words and symbols when given a table of "input" and "output" values, with no significant errors	Have difficulty describing simple one-step functions using words and symbols when given a table of "input" and "output" values, but can determine other values in the table with no significant errors	Have difficulty describing simple one-step functions using words and symbols when given a table of "input" and "output" values, and determine other values in the table with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations

Topic	Numeric and Algebraic Representations
Benchmark MA.6.10.1	Interpret and solve problem situations involving two different variables
Sample Performance Assessment (SPA)	The student: Recognizes that a problem requires two variables (e.g., "What could be the dimensions of a rectangle with a perimeter of 36?"), finds several solutions for the two variables, and if possible, makes a general statement that describes all the possible solutions (e.g., the length and the width must be greater than zero and have a sum of 18).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Interpret and solve problem situations involving two different variables, with accuracy	Interpret and solve problem situations involving two different variables, with no significant errors	Interpret and solve problem situations involving two different variables, with a few significant errors	Interpret and solve problem situations involving two different variables, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.6.10.2	Use fact families to solve for an unknown in an open sentence
Sample Performance Assessment (SPA)	The student: Writes the fact family for an open sentence so that the variable is left alone on one side (e.g., to solve the equation x – 8 = 19, rewrite the equation as 19 + 8 = x).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use fact families to solve for an unknown in an open sentence, with accuracy	Use fact families to solve for an unknown in an open sentence, with no significant errors	Use fact families to solve for an unknown in an open sentence, with a few significant errors	Use fact families to solve for an unknown in an open sentence, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.6.10.3	Evaluate algebraic expressions
Sample Performance Assessment (SPA)	The student: Substitutes a variable in an algebraic expression for a given value, then simplifies the expression (e.g., evaluates 6x + 5 for x = 8 by substituting 8 in place of x, and finding the 6[8] + 5 simplifies to 53).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Evaluate algebraic expressions, with accuracy	Evaluate algebraic expressions, with no significant errors	Evaluate algebraic expressions, with a few significant errors	Evaluate algebraic expressions, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 11: Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions

Topic	Data Collection and Representation
Benchmark MA.6.11.1	Analyze how data collection methods and sample size can affect the results of data sets
Sample Performance Assessment (SPA)	The student: Compares the results of a survey where a small group of people were asked questions and the results of the same survey when a large number of people were asked the questions.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively explain, in great detail, how data collection methods and sample size can affect the results of data sets	Explain, in sufficient detail, how data collection methods and sample size can affect the results of data sets	Explain, in some (but not enough) detail, how data collection methods and sample size can affect the results of data sets	Explain, in insufficient detail, how data collection methods and sample size can affect the results of data sets

Strand	Data Analysis, Statistics, and Probability
Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis

Topic	Data Interpretation
Benchmark MA.6.12.1	Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set
Sample Performance Assessment (SPA)	The student: Determines the mean, median, and mode of a data set, compares these measures, and explains what the measures say about the data (e.g., when the mean, median and mode are the same, the student recognizes that the data is symmetrically distributed; when the mean is significantly greater than the median, the student recognizes that data is skewed toward the high end).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set, with accuracy	Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set, with no significant errors	Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set, with a few significant errors	Determine and interpret the measures of center (mean, median, mode) of a data set and explain what each measure indicates about the data set, with many significant errors

Topic	Data Interpretation
Benchmark MA.6.12.2	Use a stem-and-leaf plot to analyze a set of data
Sample Performance Assessment (SPA)	The student: Uses the shape of the data in a stem-and-leaf plot to describe the data, and determines the mean, median, and mode and uses these measures to describe the data.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use a stem-and-leaf plot to analyze a set of data, with accuracy	Use a stem-and-leaf plot to analyze a set of data, with no significant errors	Use a stem-and-leaf plot to analyze a set of data, with a few significant errors	Use a stem-and-leaf plot to analyze a set of data, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 13: Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data

Topic	Predictions and Inferences
Benchmark MA.6.13.1	Make inferences about a population based on the interpretation of a sample data set
Sample Performance Assessment (SPA)	The student: Analyzes a sample data set and uses that information to make a generalization that applies to the population.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently make reasonable inferences about a population based on the interpretation of a sample data set	Usually make reasonable inferences about a population based on the interpretation of a sample data set	Sometimes make reasonable inferences about a population based on the interpretation of a sample data set	Rarely make reasonable inferences about a population based on the interpretation of a sample data set

Strand	Data Analysis, Statistics, and Probability
Standard 14: Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability

Topic	Probability
Benchmark MA.6.14.1	Compute probabilities of simple compound events (e.g., rolling two dice, using two different spinners at the same time)
Sample Performance Assessment (SPA)	The student: Uses a strategy (e.g., tree diagram, organized list, area model) to systematically determine all of possibilities of two events occurring (e.g. two coins tossed, a spinner being spun twice), and states the probability of the outcomes occurring.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Accurately compute probabilities of simple compound events, and demonstrates an effective strategy	Compute probabilities of simple compound events, with no significant errors	Compute probabilities of simple compound events, with a few significant errors	Compute probabilities of simple compound events, with many significant errors

Strand	Numbers and Operations
Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Topic	Numbers and Number Systems
Benchmark MA.7.1.1	Solve problems using fractions, decimals, and percents
Sample Performance Assessment (SPA)	The student: Uses representations, models, equivalent forms, or other appropriate strategies to solve problems that involve fractions, decimals, or percents.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Follow and communicate appropriate strategies to solve problems using fractions, decimals, and percents, with accuracy	Solve problems using fractions, decimals, and percents, with no significant errors	Solve problems using fractions, decimals, and percents, with a few significant errors	Solve problems using fractions, decimals, and percents, with many significant errors

Topic	Numbers and Number Systems
Benchmark MA.7.1.2	Identify situations that require the use of large numbers and represent them using scientific notation
Sample Performance Assessment (SPA)	The student: Converts between standard notation and scientific notation when solving problems that involve large numbers.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Identify problem situations that require the use of large numbers, represent them using scientific notation, and accurately solve the situation	Identify situations that require the use of large numbers, and represent them using scientific notation, with no significant errors	Identify situations that require the use of large numbers, and represent them using scientific notation, with some significant errors	Identify situations that require the use of large numbers, and is unable to represent them using scientific notation

Topic	Numbers and Number Systems
Benchmark MA.7.1.3	Describe and solve situations represented by integers and absolute value
Sample Performance Assessment (SPA)	The student: Creates a problem involving integers in which the concept of absolute value is applied.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe and solve situations represented by integers and absolute value, with accuracy	Describe and solve situations represented by integers and absolute value, with no significant errors	Describe and solve situations represented by integers and absolute value, with a few significant errors	Describe and solve situations represented by integers and absolute value, with many significant errors

Topic	Numbers and Number Systems
Benchmark MA.7.1.4	Apply number theory concepts to solve problems
Sample Performance Assessment (SPA)	The student: Shows or explains how his or her understanding of a number theory concept helped to solve a problem (e.g., explains how the concept of least common multiples can be used to find out the fewest packages of 10 hotdogs and packages of 8 buns it would take to have exactly one hotdog for each bun with none left over).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Select and apply appropriate number theory concepts to accurately solve problems	Apply number theory concepts to solve problems, with no significant errors	Apply number theory concepts to solve problems, with a few significant errors	Apply number theory concepts to solve problems, with many significant errors

Strand	Numbers and Operations
Standard 2: Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other

Topic	Operations
Benchmark MA.7.2.1	Describe situations involving arithmetic operations with integers
Sample Performance Assessment (SPA)	The student: Creates a situation that involves calculating with positive and negative integers.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe situations involving arithmetic operations with integers, with accuracy	Describe situations involving arithmetic operations with integers, with no significant errors	Describe situations involving arithmetic operations with integers, with a few significant errors	Have difficulty describing situations involving arithmetic operations with integers

Topic	Operations
Benchmark MA.7.2.2	Apply the order of operations when calculating with rational number, excluding exponents
Sample Performance Assessment (SPA)	The student: Expands his or her use of the order of operations from whole numbers to rational numbers, excluding exponents and applies the order of operations in the correct sequence when simplifying numeric expressions that involve rational numbers (i.e., fractions, decimals, integers).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the order of operations when calculating with rational number, excluding exponents, with accuracy	Apply the order of operations when calculating with rational number, excluding exponents, with no significant errors	Apply the order of operations when calculating with rational number, excluding exponents, with a few significant errors	Apply the order of operations when calculating with rational number, excluding exponents, with many significant errors

Topic	Operations
Benchmark MA.7.2.3	Apply the inverse relationship between addition and subtraction, and between multiplication and division, to solve one-step equations
Sample Performance Assessment (SPA)	The student: Uses the inverse operation to isolate a variable on one side of an equation (e.g., [x + 8 = 15] can be changed by [x + 8 - 8 = 15 - 8] to become y = 7).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the inverse relationship between addition, and subtraction and between multiplication and division, to solve one-step equations, with accuracy	Apply the inverse relationship between addition, and subtraction and between multiplication and division, to solve one-step equations, with no significant errors	Apply the inverse relationship between addition, and subtraction and between multiplication and division, to solve one-step equations, with a few significant errors	Have difficulty applying the inverse relationship between addition, and subtraction and between multiplication and division, to solve one-step equations

Strand	Numbers and Operations
Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation

Topic	Computational Fluency
Benchmark MA.7.3.1	Add, subtract, multiply, and divide integers
Sample Performance Assessment (SPA)	The student: Uses a model (e.g., number line or red/black chips) to add (or subtract) integers; multiplies (or divides) integers and knows whether the answer is positive or negative.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Add, subtract, multiply, and divide integers, with accuracy	Add, subtract, multiply, and divide integers, with no significant errors	Add, subtract, multiply, and divide integers, with a few significant errors	Add, subtract, multiply, and divide integers, with many significant errors

Topic	Estimation
Benchmark MA.7.3.2	Determine the reasonableness of a solution by comparing the answer to an estimate
Sample Performance Assessment (SPA)	The student: Rounds the answer, then compares it to his or her calculation to judge if it is correct (e.g., rounds the solution to "3,784 x 82 to 4,000 x 80").
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently determine the reasonableness of a solution by comparing the answer to an estimate	Usually determine the reasonableness of a solution by comparing the answer to an estimate	Sometimes determine the reasonableness of a solution by comparing the answer to an estimate	Rarely determine the reasonableness of a solution by comparing the answer to an estimate

Strand	Measurement
Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

Topic	Measurement Attributes and Units
Benchmark MA.7.4.1	Determine how measurements, such as perimeter and area, of common shapes (e.g., squares, rectangles, parallelograms, triangles, circles) are affected when one of the attributes is changed in some way
Sample Performance Assessment (SPA)	The student: Determines the new area and perimeter of a shape when one of its dimensions is doubled in length.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Explain and provide supporting examples of how measurements of common shapes are affected when one of the attributes is changed in some way	Determine how measurements of common shapes are affected when one of the attributes is changed in some way, with no significant errors	Determine how measurements of common shapes are affected when one of the attributes is changed in some way, with a few significant errors	Determine how measurements of common shapes are affected when one of the attributes is changed in some way, with many significant errors

Topic	Measurement Tools and Techniques
Benchmark MA.7.4.2	Uses ratios and proportions to relate a scale drawing to the actual object
Sample Performance Assessment (SPA)	The student: Selects an appropriate ratio and uses proportions to make a scale drawing of an object.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use known measurements to calculate desired measurements of circles, with accuracy	Use known measurements to calculate desired measurements of circles, with no significant errors	Use known measurements to calculate desired measurements of circles, with a few significant errors	Use known measurements to calculate desired measurements of circles, with many significant errors

Topic	Measurement Formulas
Benchmark MA.7.4.3	Use known measurements (e.g., radius) to calculate desired measurements (e.g., circumference and area) of circles
Sample Performance Assessment (SPA)	The student: Applies a formula to calculate the area of a circle when its radius is given; first determines the radius, then calculates the area when its diameter is given; determines the radius when the circumference is given.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use known measurements to calculate desired measurements of circles, with accuracy	Use known measurements to calculate desired measurements of circles, with no significant errors	Use known measurements to calculate desired measurements of circles, with a few significant errors	Use known measurements to calculate desired measurements of circles, with many significant errors

Strand	Geometry and Spatial Sense
Standard 5: Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.7.5.1	Apply the concept of similarity to solve problems
Sample Performance Assessment (SPA)	The student: Uses the concept of similarity to determine an unknown measurement (e.g., the height of a tall flagpole) using other known measurements (e.g., compares the length of the shadow of a small stick and the shadow of the flagpole and uses the ratio of the shadows to calculate the height of the flagpole from the height of the stick).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the concept of similarity to solve problems, with accuracy	Apply the concept of similarity to solve problems, with no significant errors	Apply the concept of similarity to solve problems, with a few significant errors	Apply the concept of similarity to solve problems, with many significant errors

Strand	Geometry and Spatial Sense
Standard 6: Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations

Topic	Transformation
Benchmark MA.7.6.1	Describe changes in size between a given figure and its dilation
Sample Performance Assessment (SPA)	The student: Provides examples of the application of the concept of dilation (e.g., overhead projectors, the enlargement feature on a copy machine).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe changes in size between a given figure and its dilation, with accuracy	Describe changes in size between a given figure and its dilation, with no significant errors	Describe changes in size between a given figure and its dilation, with a few significant errors	Describe changes in size between a given figure and its dilation, with many significant errors

Strand	Geometry and Spatial Sense
Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry

Topic	Coordinate Geometry
Benchmark MA.7.8.1	Use coordinate geometry to determine the change in size of a figure that is dilated by a scale factor
Sample Performance Assessment (SPA)	The student: Uses the differences in the ordered pair of the corresponding vertices of a figure to determine the scale factor by which the figure was dilated.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use coordinate geometry to determine the change in size of a figure that is dilated by a scale factor, with accuracy	Use coordinate geometry to determine the change in size of a figure that is dilated by a scale factor, with no significant errors	Use coordinate geometry to determine the change in size of a figure that is dilated by a scale factor, with a few significant errors	Use coordinate geometry to determine the change in size of a figure that is dilated by a scale factor, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships

Topic	Patterns
Benchmark MA.7.9.1	Create a pattern or function for a rule given in symbolic form
Sample Performance Assessment (SPA)	The student: Creates a table of values or draws a series of pictures that represents a given rule in symbolic form, such as N + 7.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Create a pattern or function for a rule given in symbolic form, with accuracy	Create a pattern or function for a rule given in symbolic form, with no significant errors	Create a pattern or function for a rule given in symbolic form, with a few significant errors	Create a pattern or function for a rule given in symbolic form, with many significant errors

Topic	Functions
Benchmark MA.7.9.2	Describe multi-step functions using words and symbols when given a table of "input" and "output" values and use the rule for the function to determine other input and output values
Sample Performance Assessment (SPA)	The student: Finds the rule for given table of values and uses the rule to find other missing values in the table. Example Describe the rule for this function and fill in the missing values:
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe multi-step functions using words and symbols when given a table of "input" and "output" values and use the rule for the function to determine other input and output values, with accuracy	Describe multi-step functions using words and symbols when given a table of "input" and "output" values and use the rule for the function to determine other input and output values, with no significant errors	Describe multi-step functions using words and symbols when given a table of "input" and "output" values and use the rule for the function to determine other input and output values, with a few significant errors	Describe multi-step functions using words and symbols when given a table of "input" and "output" values and use the rule for the function to determine other input and output values, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations

Topic	Numeric and Algebraic Representations
Benchmark MA.7.10.1	Analyze the relationship among tables, graphs (including graphing technology when available), and equations of linear functions, paying particular attention to the meaning of intercept and slope
Sample Performance Assessment (SPA)	The student: Shows or explains how slope and y-intercept are represented in a table, graph, and equation.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively explain, in great detail, the relationships among tables, graphs, and equations of linear functions, paying particular attention to the meaning of intercept and slope	Explain, in sufficient detail, the relationships among tables, graphs, and equations of linear functions, paying particular attention to the meaning of intercept and slope	Explain, in some (though not enough) detail, the relationships among tables, graphs, and equations of linear functions, paying particular attention to the meaning of intercept and slope	Explain, in insufficient detail, the relationships among tables, graphs, and equations of linear functions, paying particular attention to the meaning of intercept and slope

Topic	Numeric and Algebraic Representations
Benchmark MA.7.10.2	Use symbolic algebra to represent situations involving linear relationships
Sample Performance Assessment (SPA)	The student: Writes an equation to represent a linear relationship and defines what each variable represents.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use symbolic algebra to represent situations involving linear relationships, with accuracy	Use symbolic algebra to represent situations involving linear relationships, with no significant errors	Use symbolic algebra to represent situations involving linear relationships, with a few significant errors	Have difficulty using symbolic algebra to represent situations involving linear relationships

Topic	Numeric and Algebraic Representations
Benchmark MA.7.10.3	Solves linear equations and inequalities with one variable using algebraic methods, manipulatives, or models
Sample Performance Assessment (SPA)	The student: Solves a given equation or inequality for the unknown value and explains/shows how he or she determined the unknown value.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve linear equations and inequalities with one variable using algebraic methods, manipulatives, or models, with accuracy, and show/explain how to determine the unknown value	Solve linear equations and inequalities with one variable using algebraic methods, manipulatives, or models, with no significant errors	Solve linear equations and inequalities with one variable using algebraic methods, manipulatives, or models, with a few significant errors	Solves linear equations and inequalities with one variable using algebraic methods, manipulatives, or models, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 11: Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions

Topic	Data Collection and Representation
Benchmark MA.7.11.1	Design a study, collect data, and select the appropriate representation (line graph, bar graph, circle graph, histogram, stem and leaf plot, box and whisker plot) to display the data
Sample Performance Assessment (SPA)	The student: Selects a representation that supports the desired purpose of the study and is appropriate for the type of data being displayed (e.g., chooses to display data about what he or she spends his or her allowance on in a circle graph to emphasize the percentages that the data represents).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Design a meaningful and insightful study, collect data, and select the appropriate representation to display the data, with accuracy	Design a study, collect data, and select the appropriate representation to display the data, with no significant errors	Design a study, collect data, and select the appropriate representation to display the data, with a few significant errors	Design a study, collect data, and select the appropriate representation to display the data, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis

Topic	Data Interpretation
Benchmark MA.7.12.1	Relate the spread of a data set to a box-and-whisker plot
Sample Performance Assessment (SPA)	The student: Relates the distribution of data within each quartile to the shape of the box and the length of the whiskers in a box-and-whisker plot.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively and accurately explain how the spread of a data set is related to a box-and-whisker plot	Relate the spread of a data set to a box-and-whisker plot, with no significant errors	Relate the spread of a data set to a box-and-whisker plot, with a few significant errors	Relate the spread of a data set to a box-and-whisker plot, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 13: Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data

Topic	Predictions and Inferences
Benchmark MA.7.13.1	Formulate new questions that arise from previous conclusions or conjectures and plan a new study to answer them
Sample Performance Assessment (SPA)	The student: Plans a study to answer new questions that arise based on conjectures that he or she made from a previous study.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Formulate new questions that arise from previous conclusions or conjectures and plan a new study to answer them, with accuracy	Formulate new questions that arise from previous conclusions or conjectures and plan a new study to answer them, with no significant errors	Formulate new questions that arise from previous conclusions or conjectures and plan a new study to answer them, with a few significant errors	Formulate new questions that arise from previous conclusions or conjectures and plan a new study to answer them, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 14: Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability

Topic	Probability
Benchmark MA.7.14.1	Relate theoretical probability to experimental results
Sample Performance Assessment (SPA)	The student: Uses theoretical probability to support conjectures about the results of an experiment or simulation.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Effectively and accurately explain how theoretical probability relates to experimental results	Relate theoretical probability to experimental results, with no significant errors	Relate theoretical probability to experimental results, with a few significant errors	Relate theoretical probability to experimental results, with many significant errors

Strand	Numbers and Operations
Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Topic	Numbers and Number Systems
Benchmark MA.8.1.1	Identify situations represented by square roots and cube roots
Sample Performance Assessment (SPA)	The student: Provides examples of situations that use square roots and cube roots (e.g., explains that the length of the hypotenuse of a right triangle may be represented by a square root).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe and provide examples of situations represented by square roots and cube roots	Identify situations represented by square roots and cube roots	Recognize whether situations involve square roots or cube roots	Have difficulty recognizing whether situations involve square roots or cube roots

Topic	Numbers and Number Systems
Benchmark MA.8.1.2	Compare and order rational numbers and square roots
Sample Performance Assessment (SPA)	The student: Orders a set of rational numbers and square roots on the number line.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Accurately order rational numbers and square roots, and justify the comparison	Compare and order rational numbers and square roots, with no significant errors	Compare and order rational numbers and square roots, with a few significant errors	Have difficulty comparing and ordering rational numbers and square roots

Topic	Numbers and Number Systems
Benchmark MA.8.1.3	Use ratios and proportions to represent the relationship between two quantities
Sample Performance Assessment (SPA)	The student: Describes a situation that involves two related quantities in the form of a ratio (e.g., if Katie shoots 3 baskets out of 8 attempts, represents her score:miss ratio as 3:5).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use ratios and proportions to represent the relationship between two quantities, with accuracy	Use ratios and proportions to represent the relationship between two quantities, with no significant errors	Use ratios and proportions to represent the relationship between two quantities, with a few significant errors	Use ratios and proportions to represent the relationship between two quantities, with many significant errors

Strand	Numbers and Operations
Standard 2: Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other

Topic	Operations
Benchmark MA.8.2.1	Apply the order of operations when calculating with rational numbers
Sample Performance Assessment (SPA)	The student: Expands his or her use of the order of operations to include exponents and applies the order of operations in the correct sequence when simplifying numeric expressions that involve rational numbers (i.e., fractions, decimals, integers).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the order of operations when calculating with rational numbers, with accuracy	Apply the order of operations when calculating with rational numbers, with no significant errors	Apply the order of operations when calculating with rational numbers, with a few significant errors	Apply the order of operations when calculating with rational numbers, with many significant errors

Topic	Operations
Benchmark MA.8.2.2	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots
Sample Performance Assessment (SPA)	The student: Finds the area of a square whose side length is a square root
Rubric
Advanced	Proficient	Partially Proficient	Novice
Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with accuracy	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with no significant errors	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with a few significant errors	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with many significant errors

Strand	Numbers and Operations
Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation

Topic	Computational Fluency
Benchmark MA.8.3.1	Add, subtract, multiply, and divide numbers with whole number exponents
Sample Performance Assessment (SPA)	The student: Uses arithmetic properties (e.g., associative, commutative, distribute, identity properties) and the Law of Exponents to calculate numbers that have whole number exponents (e.g., 42 x 44 = 46), and when appropriate, use the properties to make it easier to perform the calculations (e.g., instead of multiplying 3 x 3 x 3 x 3 to calculate 34, the student represents 34 as 32 x 32 which becomes 9 x 9 which can be more easily computed with mental math).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Add, subtract, multiply, and divide numbers with whole number exponents, with accuracy	Add, subtract, multiply, and divide numbers with whole number exponents, with no significant errors	Add, subtract, multiply, and divide numbers with whole number exponents, with a few significant errors	Add, subtract, multiply, and divide numbers with whole number exponents, with many significant errors

Topic	Estimation
Benchmark MA.8.3.2	Estimate a reasonable range (i.e., upper and lower limit) for the solution to a problem
Sample Performance Assessment (SPA)	The student: Uses appropriate estimation strategies to state upper and lower bounds of the estimated answer
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently estimate a reasonable range for the solution to a problem, and provide rationale	Usually estimate a reasonable range for the solution to a problem	Sometimes estimate a reasonable range for the solution to a problem	Rarely estimate a reasonable range for the solution to a problem

Strand	Measurement
Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

Topic	Measurement Attributes and Units
Benchmark MA.8.4.1	Select and use appropriate units to measure the surface area and volume of solids
Sample Performance Assessment (SPA)	The student: Selects a unit based on the desired level of precision, and explains why that unit was chosen rather than a different unit.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently select and use appropriate units to measure the surface area and volume of solids, and justify the choice of units	Usually select and use appropriate units to measure the surface area and volume of solids	Sometimes select and use appropriate units to measure the surface area and volume of solids	Rarely select and use appropriate units to measure the surface area and volume of solids

Topic	Measurement Tools and Techniques
Benchmark MA.8.4.2	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems
Sample Performance Assessment (SPA)	The student: Measures two quantities that are related (e.g., the capacity of water that comes out of a water fountain in 10 seconds), expresses the quantities as a ratio (rate), and uses it to solve a problem (e.g., "How long would it take to fill a gallon of water from a water fountain?").
Rubric
Advanced	Proficient	Partially Proficient	Novice
Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with accuracy	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with no significant errors	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with a few significant errors	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with many significant errors

Topic	Measurement Formulas
Benchmark MA.8.4.3	Use ratios and proportions to solve measurement problems
Sample Performance Assessment (SPA)	The student: Uses ratios and proportions to determine an unknown measurement when given known measurements (e.g., a student uses her height, the length of her shadow, and the length of a flagpole's shadow to determine the flagpole's height).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use ratios and proportions to solve measurement problems, with accuracy	Use ratios and proportions to solve measurement problems, with no significant errors	Use ratios and proportions to solve measurement problems, with a few significant errors	Use ratios and proportions to solve measurement problems, with many significant errors

Topic	Measurement Formulas
Benchmark MA.8.4.4	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids
Sample Performance Assessment (SPA)	The student: Applies the formula for the volume of prisms (or cylinders) when the necessary measurements are given; decomposes a prism (or cylinder or pyramid) into its different faces/bases, and applies strategies or formulas to determine their areas.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with accuracy	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with no significant errors	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with a few significant errors	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with many significant errors

Strand	Geometry and Spatial Sense
Standard 5: Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.8.5.1	Apply the Pythagorean theorem to solve problems involving right triangles
Sample Performance Assessment (SPA)	The student: Uses the Pythagorean theorem to find an unknown length in a problem involving a right triangle (e.g., finds the height of the ladder needed to wash a window that is 25 feet above the ground if the ladder is placed 4 feet from the side of the house).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the Pythagorean theorem to solve problems involving right triangles, with accuracy	Apply the Pythagorean theorem to solve problems involving right triangles, with no significant errors	Apply the Pythagorean theorem to solve problems involving right triangles, with a few significant errors	Apply the Pythagorean theorem to solve problems involving right triangles, with many significant errors

Strand	Geometry and Spatial Sense
Standard 6: Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations

Topic	Transformation
Benchmark MA.8.6.1	Perform a transformation (reflection, rotation, translation) when given a figure and necessary parameters
Sample Performance Assessment (SPA)	The student: Reflects a given figure over a given line of symmetry; rotates a given figure by a given angle around a given center of rotation; translates a given figure in a given direction by a given distance.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Perform a transformation when given a figure and necessary parameters, with precision and accuracy	Perform a transformation when given a figure and necessary parameters, with no significant errors	Perform a transformation when given a figure and necessary parameters, with a few significant errors	Perform a transformation when given a figure and necessary parameters, with many significant errors

Topic	Transformation
Benchmark MA.8.6.2	Describe the size, position, and orientation of shapes under transformations and compositions of transformations
Sample Performance Assessment (SPA)	The student: Describes the size, position, and orientation of a given shape after it has been reflected over one line of reflection, and the resulting image has been reflected over a second line of reflection.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe the size, position, and orientation of shapes under transformations and compositions of transformations, with accuracy	Describe the size, position, and orientation of shapes under transformations and compositions of transformations, with no significant errors	Describe the size, position, and orientation of shapes under transformations and compositions of transformations, with a few significant errors	Describe the size, position, and orientation of shapes under transformations and compositions of transformations, with many significant errors

Strand	Geometry and Spatial Sense
Standard 7: Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics

Topic	Visualization and Spatial Reasoning
Benchmark MA.8.7.1	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures
Sample Performance Assessment (SPA)	The student: Uses the two-dimensional net of a cylinder to determine its surface area.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Strategically use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with accuracy	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with no significant errors	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with a few significant errors	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with many significant errors

Strand	Geometry and Spatial Sense
Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry

Topic	Coordinate Geometry
Benchmark MA.8.8.1	Use coordinate geometry to represent transformations in the coordinate plane
Sample Performance Assessment (SPA)	The student: Determines the coordinates of a figure after it has been transformed (e.g., uses the coordinates of a given figure and its distance from the line of symmetry to locate the coordinates of its reflection).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use coordinate geometry to represent transformations in the coordinate plane, with accuracy	Use coordinate geometry to represent transformations in the coordinate plane, with no significant errors	Use coordinate geometry to represent transformations in the coordinate plane, with a few significant errors	Use coordinate geometry to represent transformations in the coordinate plane, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships

Topic	Patterns
Benchmark MA.8.9.1	Represent a variety of patterns (including recursive patterns) with tables, graphs (including graphing technology when available), words, and when possible, symbolic rules
Sample Performance Assessment (SPA)	The student: Identifies the rule that generates a recursive sequence, describes the pattern in words, and gives the next four numbers in the sequence (e.g., 1, 1, 2, 3, 5, 8, 13, __, __, __, __).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with accuracy	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with no significant errors	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with a few significant errors	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with many significant errors

Topic	Functions
Benchmark MA.8.9.2	Use linear relationships with two variables to solve problems
Sample Performance Assessment (SPA)	The student: Organizes data about the two variables into a table and/or graph, and uses the pattern or rule that defines the linear relationship to make predictions about data not in the original set.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use linear relationships with two variables to solve problems, with accuracy	Use linear relationships with two variables to solve problems, with no significant errors	Use linear relationships with two variables to solve problems, with a few significant errors	Use linear relationships with two variables to solve problems, with many significant errors

Topic	Functions
Benchmark MA.8.9.3	Identify functions as linear or nonlinear and contrast their properties from tables, graphs (including graphing technology when available), or equations
Sample Performance Assessment (SPA)	The student: Uses the data in a table to determine if the data represents a linear or nonlinear function, and justifies the decision.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Identify functions as linear or nonlinear, and explain and provide examples of how their properties are contrasted in tables, graphs, and equations	Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations	Identify functions as linear or nonlinear and attempt to contrast their properties	Have difficulty identifying functions as linear or nonlinear

Strand	Patterns, Functions, and Algebra
Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations

Topic	Numeric and Algebraic Representations
Benchmark MA.8.10.1	Translate among tables, graphs (including graphing technology when available), and equations involving linear relationships
Sample Performance Assessment (SPA)	The student: Uses the information in a table to make a graph and equation; uses the information in a graph to make a table and equation; and uses a linear equation to make a table and graph.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Translate fluently among tables, graphs, and equations involving linear relationships, with accuracy	Translate among tables, graphs, and equations involving linear relationships, with no significant errors	Translate among tables, graphs, and equations involving linear relationships, with a few significant errors	Translate among tables, graphs, and equations involving linear relationships, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.8.10.2	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models
Sample Performance Assessment (SPA)	The student: Solves a given equation or inequality for the unknown values and shows/explains how he or she determined the unknown values.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with accuracy	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with no significant errors	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with a few significant errors	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.8.10.3	Use tables and graphs to represent and compare linear relationships
Sample Performance Assessment (SPA)	The student: Translates the information from a problem or equation into tables and graphs, and compares the tables (and graphs) of each relationship, paying particular attention to the point of intersection and the values leading up to the point of intersection and the values leading away from the point of intersection (e.g., Determine which is the better video rental plan if Plan A is represented by the equation C = 5V and Plan B is represented by the equation C = 2V + 20 where C is the cost in dollars and V is the number of videos rented).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use tables and graphs to represent and compare linear relationships, with accuracy	Use tables and graphs to represent and compare linear relationships, with no significant errors	Use tables and graphs to represent and compare linear relationships, with a few significant errors	Use tables and graphs to represent and compare linear relationships, with many significant errors

Topic	Rates of Change
Benchmark MA.8.10.4	Use the slope of a line to describe a constant rate of change
Sample Performance Assessment (SPA)	The student: Determines the slope of a line and uses that information to indicate the rate of change (e.g., finds the constant speed of a train by determining the slope of a distance-time graph of the train's movement).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use the slope of a line to describe a constant rate of change, with accuracy	Use the slope of a line to describe a constant rate of change, with no significant errors	Use the slope of a line to describe a constant rate of change, with a few significant errors	Use the slope of a line to describe a constant rate of change, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 11: Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions

Topic	Data Collection and Representation
Benchmark MA.8.11.1	Design a study that compares two samples, collect data, and select the appropriate representation (e.g., double bar graph, back-to-back stem and leaf plot, parallel box and whisker plots, scatter plot) to compare the sets of data
Sample Performance Assessment (SPA)	The student: Selects a representation that supports the desired purpose of the study and shows a visual comparison of the data sets (e.g., in studying the relationship between an 8th grader's height and arm span, the student displays chooses to represent the data in a scatter plot since scatter plots are designed to determine if correlations between two variables exist).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with accuracy	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with no significant errors	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with a few significant errors	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with many significant errors

Topic	Data Collection and Representation
Benchmark MA.8.11.2	Judge the validity of data based on the data collection method
Sample Performance Assessment (SPA)	The student: Explains that the results of an experiment or survey may be questionable because the data collection method or the way the sample was chosen is questionable.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently make reasonable judgments about the validity of data based on the data collection method	Usually make reasonable judgments about the validity of data based on the data collection method	Sometimes make reasonable judgments about the validity of data based on the data collection method	Rarely make reasonable judgments about the validity of data based on the data collection method

Strand	Data Analysis, Statistics, and Probability
Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis

Topic	Data Interpretation
Benchmark MA.8.12.1	Recognize situations appropriate for scatter plots
Sample Performance Assessment (SPA)	The student: Chooses to use a scatter plot when determining if a correlation exists between two variables (e.g., comparing the height of students to their arm spans).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently recognize situations appropriate for scatter plots, and create situations that involve using scatter plots	Usually recognize situations appropriate for scatter plots	Sometimes recognize situations appropriate for scatter plots	Rarely recognize situations appropriate for scatter plots

Topic	Data Interpretation
Benchmark MA.8.12.2	Analyze different representations of the same data to describe how representations can be used to skew a person's interpretation of the data
Sample Performance Assessment (SPA)	The student: Adjusts the intervals or scale on a graph to change the appearance of the graph and describes how the changes that were made affect a person's interpretation of the data.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Analyze different representations of the same data to describe, in great detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in sufficient detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in some (but not enough) detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in insufficient detail, how representations can be used to skew a person's interpretation of the data

Strand	Data Analysis, Statistics, and Probability
Standard 13: Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data

Topic	Predictions and Inferences
Benchmark MA.8.13.1	Make conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots
Sample Performance Assessment (SPA)	The student: Analyzes a scatter plot and makes a conjecture based on the presence or absence of an approximate line of best fit.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Make reasonable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots, and justify the conjecture	Make reasonable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots	Make questionable conjectures (though somewhat justifiable) about possible relationships between two characteristics of a sample based on interpretations of scatter plots	Make unjustifiable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots

Strand	Data Analysis, Statistics, and Probability
Standard 14: Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability

Topic	Probability
Benchmark MA.8.14.1	Judge the validity of conjectures that are based on experiments or simulations
Sample Performance Assessment (SPA)	The student: Refers to the theoretical probability, sample size, and data collection techniques to support the validity of a conjecture that is based on experiments or simulations with predictable outcomes.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Make reasonable judgments on the validity of conjectures that are based on experiments or simulations, and provides effective justification for the judgment	Make reasonable judgments on the validity of conjectures that are based on experiments or simulations	Make plausible judgments on the validity of conjectures that are based on experiments or simulations	Make unreasonable judgments on the validity of conjectures that are based on experiments or simulations

Strand	Numbers and Operations
Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Topic	Numbers and Number Systems
Benchmark MA.PA.1.1	Identify situations represented by square roots and cube roots
Sample Performance Assessment (SPA)	The student: Provides examples of situations that use square roots and cube roots (e.g., explains that the length of the hypotenuse of a right triangle may be represented by a square root).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe and provide examples of situations represented by square roots and cube roots	Identify situations represented by square roots and cube roots	Recognize whether situations involve square roots or cube roots	Have difficulty recognizing whether situations involve square roots or cube roots

Topic	Numbers and Number Systems
Benchmark MA.PA.1.2	Compare and order rational numbers and square roots
Sample Performance Assessment (SPA)	The student: Orders a set of rational numbers and square roots on the number line.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Accurately order rational numbers and square roots, and justify the comparison	Compare and order rational numbers and square roots, with no significant errors	Compare and order rational numbers and square roots, with a few significant errors	Have difficulty comparing and ordering rational numbers and square roots

Topic	Numbers and Number Systems
Benchmark MA.PA.1.3	Use ratios and proportions to represent the relationship between two quantities
Sample Performance Assessment (SPA)	The student: Describes a situation that involves two related quantities in the form of a ratio (e.g., if Katie shoots 3 baskets out of 8 attempts, represents her score:miss ratio as 3:5).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use ratios and proportions to represent the relationship between two quantities, with accuracy	Use ratios and proportions to represent the relationship between two quantities, with no significant errors	Use ratios and proportions to represent the relationship between two quantities, with a few significant errors	Use ratios and proportions to represent the relationship between two quantities, with many significant errors

Strand	Numbers and Operations
Standard 2: Numbers and Operations: OPERATION SENSE: Understand the meaning of operations and how they relate to each other

Topic	Operations
Benchmark MA.PA.2.1	Apply the order of operations when calculating with rational numbers
Sample Performance Assessment (SPA)	The student Expands his or her use of the order of operations to include exponents and applies the order of operations in the correct sequence when simplifying numeric expressions that involve rational numbers (i.e., fractions, decimals, integers).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the order of operations when calculating with rational numbers, with accuracy	Apply the order of operations when calculating with rational numbers, with no significant errors	Apply the order of operations when calculating with rational numbers, with a few significant errors	Apply the order of operations when calculating with rational numbers, with many significant errors

Topic	Operations
Benchmark MA.PA.2.2	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots
Sample Performance Assessment (SPA)	The student: Finds the area of a square whose side length is a square root
Rubric
Advanced	Proficient	Partially Proficient	Novice
Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with accuracy	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with no significant errors	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with a few significant errors	Demonstrate the inverse relationship between square numbers and square roots, and cubes and cubed roots, with many significant errors

Strand	Numbers and Operations
Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation

Topic	Computational Fluency
Benchmark MA.PA.3.1	Add, subtract, multiply, and divide numbers with whole number exponents
Sample Performance Assessment (SPA)	The student: Uses arithmetic properties (e.g., associative, commutative, distribute, identity properties) and the Law of Exponents to calculate numbers that have whole number exponents (e.g., 42 x 44 = 46), and when appropriate, use the properties to make it easier to perform the calculations (e.g., instead of multiplying 3 x 3 x 3 x 3 to calculate 34, the student represents 34 as 32 x 32 which becomes 9 x 9 which can be more easily computed with mental math).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Add, subtract, multiply, and divide numbers with whole number exponents, with accuracy	Add, subtract, multiply, and divide numbers with whole number exponents, with no significant errors	Add, subtract, multiply, and divide numbers with whole number exponents, with a few significant errors	Add, subtract, multiply, and divide numbers with whole number exponents, with many significant errors

Topic	Estimation
Benchmark MA.PA.3.2	Estimate a reasonable range (i.e., upper and lower limit) for the solution to a problem
Sample Performance Assessment (SPA)	The student: Uses appropriate estimation strategies to state upper and lower bounds of the estimated answer
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently estimate a reasonable range for the solution to a problem	Usually estimate a reasonable range for the solution to a problem	Sometimes estimate a reasonable range for the solution to a problem	Rarely estimate a reasonable range for the solution to a problem

Topic	Estimation
Benchmark MA.PA.3.3	Explain that rounding answers in certain real-world situations may lead to major problems
Sample Performance Assessment (SPA)	The student: Describes problems that could occur in real-world situations if answers were rounded (e.g., rocket missing the moon, a bridge collapsing, automobile brakes not working).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Explain, in great detail, that rounding answers in certain real-world situations may lead to major problems	Explain, in detail, that rounding answers in certain real-world situations may lead to major problems	Explain, in some detail, that rounding answers in certain real-world situations may lead to major problems	Explain, in minimal detail, that rounding answers in certain real-world situations may lead to major problems

Strand	Measurement
Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

Topic	Measurement Attributes and Units
Benchmark MA.PA.4.1	Select and use appropriate units to measure the surface area and volume of solids
Sample Performance Assessment (SPA)	The student: Selects a unit based on the desired level of precision, and explains why that unit was chosen rather than a different unit.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently select and use appropriate units to measure the surface area and volume of solids	Usually select and use appropriate units to measure the surface area and volume of solids	Sometimes select and use appropriate units to measure the surface area and volume of solids	Rarely select and use appropriate units to measure the surface area and volume of solids

Topic	Measurement Tools and Techniques
Benchmark MA.PA.4.2	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems
Sample Performance Assessment (SPA)	The student: Measures two quantities that are related (e.g., the capacity of water that comes out of a water fountain in 10 seconds), expresses the quantities as a ratio (rate), and uses it to solve a problem (e.g., "How long would it take to fill a gallon of water from a water fountain?").
Rubric
Advanced	Proficient	Partially Proficient	Novice
Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with accuracy	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with no significant errors	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with a few significant errors	Express rates of change as a ratio of two different measures, where units are included in the ratio, and use the derived rate to solve problems, with many significant errors

Topic	Measurement Formulas
Benchmark MA.PA.4.3	Use ratios and proportions to solve measurement problems
Sample Performance Assessment (SPA)	The student: Uses ratios and proportions to determine an unknown measurement when given known measurements (e.g., a student uses her height, the length of her shadow, and the length of a flagpole's shadow to determine the flagpole's height).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use ratios and proportions to solve measurement problems, with accuracy	Use ratios and proportions to solve measurement problems, with no significant errors	Use ratios and proportions to solve measurement problems, with a few significant errors	Use ratios and proportions to solve measurement problems, with many significant errors

Topic	Measurement Formulas
Benchmark MA.PA.4.4	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids
Sample Performance Assessment (SPA)	The student: Applies the formula for the volume of prisms (or cylinders) when the necessary measurements are given; decomposes a prism (or cylinder or pyramid) into its different faces/bases, and applies strategies or formulas to determine their areas.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with accuracy	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with no significant errors	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with a few significant errors	Use formulas to determine the surface area and volume of selected prisms, cylinders, and pyramids, with many significant errors

Topic	Measurement Formulas
Benchmark MA.PA.4.5	Use the right triangle relationships (e.g., trigonometric ratios: cosine, sine, and tangent) to solve problems
Sample Performance Assessment (SPA)	The student: Uses an angle measurement in a right triangle (other than the right angle) and the length of one of the sides to determine the lengths of the other two sides.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use the right triangle relationships to solve problems, with accuracy	Use the right triangle relationships to solve problems, with no significant errors	Use the right triangle relationships to solve problems, with a few significant errors	Use the right triangle relationships to solve problems, with many significant errors

Strand	Geometry and Spatial Sense
Standard 5: Geometry and Spatial Sense: PROPERTIES AND RELATIONSHIPS: Analyze properties of objects and relationships among the properties

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.PA.5.1	Apply the Pythagorean theorem to solve problems involving right triangles
Sample Performance Assessment (SPA)	The student: Uses the Pythagorean theorem to find an unknown length in a problem involving a right triangle (e.g., finds the height of the ladder needed to wash a window that is 25 feet above the ground if the ladder is placed 4 feet from the side of the house).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the Pythagorean theorem to solve problems involving right triangles, with accuracy	Apply the Pythagorean theorem to solve problems involving right triangles, with no significant errors	Apply the Pythagorean theorem to solve problems involving right triangles, with a few significant errors	Apply the Pythagorean theorem to solve problems involving right triangles, with many significant errors

Topic	Geometric Shapes and Their Properties and Relationships
Benchmark MA.PA.5.2	Evaluate conjectures about classes of two- and three-dimensional shapes/objects
Sample Performance Assessment (SPA)	The student: Provides examples and logical reasons that supports a conjecture that was made about two- and three-dimensional shapes/objects (e.g., all quadrilaterals with perpendicular diagonals are squares), or provides counterexamples that refutes the conjecture.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Evaluate conjectures about classes of two- and three-dimensional shapes/objects, with accuracy	Evaluate conjectures about classes of two- and three-dimensional shapes/objects, with no significant errors	Evaluate conjectures about classes of two- and three-dimensional shapes/objects, with a few significant errors	Evaluate conjectures about classes of two- and three-dimensional shapes/objects, with many significant errors

Strand	Geometry and Spatial Sense
Standard 6: Geometry and Spatial Sense: TRANSFORMATIONS AND SYMMETRY: Use transformations and symmetry to analyze mathematical situations

Topic	Transformation
Benchmark MA.PA.6.1	Perform a transformation (reflection, rotation, translation) when given a figure and necessary parameters
Sample Performance Assessment (SPA)	The student: Reflects a given figures over a given line of symmetry; rotates a given figure by a given angle around a given center of rotation; translates a given figure in a given direction by a given distance.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Perform a transformation when given a figure and necessary parameters, with precision and accuracy	Perform a transformation when given a figure and necessary parameters, with no significant errors	Perform a transformation when given a figure and necessary parameters, with a few significant errors	Perform a transformation when given a figure and necessary parameters, with many significant errors

Topic	Transformation
Benchmark MA.PA.6.2	Describe the size, position, and orientation of shapes under transformations and compositions of transformations
Sample Performance Assessment (SPA)	The student: Describes the size, position, and orientation of a given shape after it has been reflected over one line of reflection, and the resulting image has been reflected over a second line of reflection.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe, in great detail, the size, position, and orientation of shapes under transformations and compositions of transformations	Describe, in detail, the size, position, and orientation of shapes under transformations and compositions of transformations	Describe, in some detail, the size, position, and orientation of shapes under transformations and compositions of transformations	Describe, in minimal detail, the size, position, and orientation of shapes under transformations and compositions of transformations

Topic	Transformation
Benchmark MA.PA.6.3	Describe three-dimensional shapes that are formed by rotating two-dimensional figures about an axis
Sample Performance Assessment (SPA)	The student: Illustrates/shows/names the image that is formed when a two-dimensional figure is rotated (spun) quickly around an axis, and describes how features of the image correspond to the original figure.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Describe, in great detail, three-dimensional shapes that are formed by rotating two-dimensional figures about an axis	Describe, in detail, three-dimensional shapes that are formed by rotating two-dimensional figures about an axis	Describe, in some detail, three-dimensional shapes that are formed by rotating two-dimensional figures about an axis	Describe, in minimal detail, three-dimensional shapes that are formed by rotating two-dimensional figures about an axis

Strand	Geometry and Spatial Sense
Standard 7: Geometry and Spatial Sense: VISUAL AND SPATIAL SENSE: Use visualization and spatial reasoning to solve problems both within and outside of mathematics

Topic	Visualization and Spatial Reasoning
Benchmark MA.PA.7.1	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures
Sample Performance Assessment (SPA)	The student: Uses the two-dimensional net of a cylinder to determine its surface area.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Strategically use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with accuracy	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with no significant errors	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with a few significant errors	Use two-dimensional representations of pyramids, prisms, and cylinders to solve problems involving these figures, with many significant errors

Strand	Geometry and Spatial Sense
Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry

Topic	Coordinate Geometry
Benchmark MA.PA.8.1	Use coordinate geometry to represent transformations in the coordinate plane
Sample Performance Assessment (SPA)	The student: Determines the coordinates of a figure after it has been transformed (e.g., uses the coordinates of a given figure and its distance from the line of symmetry to locate the coordinates of its reflection).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use coordinate geometry to represent transformations in the coordinate plane, with accuracy	Use coordinate geometry to represent transformations in the coordinate plane, with no significant errors	Use coordinate geometry to represent transformations in the coordinate plane, with a few significant errors	Use coordinate geometry to represent transformations in the coordinate plane, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships

Topic	Patterns
Benchmark MA.PA.9.1	Represent a variety of patterns (including recursive patterns) with tables, graphs (including graphing technology when available), words, and when possible, symbolic rules
Sample Performance Assessment (SPA)	The student Identifies the rule that generates a recursive sequence, describes the pattern in words, and gives the next four numbers in the sequence (e.g., 1, 1, 2, 3, 5, 8, 13, __, __, __, __).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with accuracy	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with no significant errors	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with a few significant errors	Represent a variety of patterns with tables, graphs, words, and when possible, symbolic rules, with many significant errors

Topic	Functions
Benchmark MA.PA.9.2	Use linear relationships with two variables to solve problems
Sample Performance Assessment (SPA)	The student: Organizes data about the two variables into a table and/or graph, and uses the pattern or rule that defines the linear relationship to make predictions about data not in the original set.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use linear relationships with two variables to solve problems, with accuracy	Use linear relationships with two variables to solve problems, with no significant errors	Use linear relationships with two variables to solve problems, with a few significant errors	Use linear relationships with two variables to solve problems, with many significant errors

Topic	Functions
Benchmark MA.PA.9.3	Identify functions as linear or nonlinear and contrast their properties from tables, graphs (including graphing technology when available), or equations
Sample Performance Assessment (SPA)	The student: Uses the data in a table to determine if the data represents a linear or nonlinear function, and justifies the decision.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Identify functions as linear or nonlinear, and explain and provide examples of how their properties are contrasted in tables, graphs, and equations	Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations	Identify functions as linear or nonlinear and attempt to contrast their properties	Have difficulty identifying functions as linear or nonlinear

Strand	Patterns, Functions, and Algebra
Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations

Topic	Numeric and Algebraic Representations
Benchmark MA.PA.10.1	Translate among tables, graphs (including graphing technology when available), and equations involving linear relationships
Sample Performance Assessment (SPA)	The student: Uses the information in a table to make a graph and equation; uses the information in a graph to make a table and equation; and uses a linear equation to make a table and graph.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Translate fluently among tables, graphs, and equations involving linear relationships, with accuracy	Translate among tables, graphs, and equations involving linear relationships, with no significant errors	Translate among tables, graphs, and equations involving linear relationships, with a few significant errors	Translate among tables, graphs, and equations involving linear relationships, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.PA.10.2	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models
Sample Performance Assessment (SPA)	The student: Solves a given equation or inequality for the unknown values and shows/explains how he or she determined the unknown values.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with accuracy	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with no significant errors	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with a few significant errors	Solve linear equations and inequalities with two variables using algebraic methods, manipulatives, or models, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.PA.10.3	Use tables and graphs to represent and compare linear relationships
Sample Performance Assessment (SPA)	The student: Translates the information from a problem or equation into tables and graphs, and compares the tables (and graphs) of each relationship, paying particular attention to the point of intersection and the values leading up to the point of intersection and the values leading away from the point of intersection (e.g., Determine which is the better video rental plan if Plan A is represented by the equation C = 5V and Plan B is represented by the equation C = 2V + 20 where C is the cost in dollars and V is the number of videos rented).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use tables and graphs to represent and compare linear relationships, with accuracy	Use tables and graphs to represent and compare linear relationships, with no significant errors	Use tables and graphs to represent and compare linear relationships, with a few significant errors	Use tables and graphs to represent and compare linear relationships, with many significant errors

Topic	Rates of Change
Benchmark MA.PA.10.4	Use the slope of a line to describe a constant rate of change
Sample Performance Assessment (SPA)	The student: Determines the slope of a line and uses that information to indicate the rate of change (e.g., finds the constant speed of a train by determining the slope of a distance-time graph of the train's movement).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use the slope of a line to describe a constant rate of change, with accuracy	Use the slope of a line to describe a constant rate of change, with no significant errors	Use the slope of a line to describe a constant rate of change, with a few significant errors	Use the slope of a line to describe a constant rate of change, with many significant errors

Strand	Data Analysis, Statistics, and Probability
Standard 11: Data Analysis, Statistics, and Probability: FLUENCY WITH DATA: Pose questions and collect, organize, and represent data to answer those questions

Topic	Data Collection and Representation
Benchmark MA.PA.11.1	Design a study that compares two samples, collect data, and select the appropriate representation (double bar graph, back-to-back stem and leaf plot, parallel box and whisker plots, scatter plot) to compare the sets of data
Sample Performance Assessment (SPA)	The student: Selects a representation that supports the desired purpose of the study and shows a visual comparison of the data sets (e.g., in studying the relationship between an 8th grader's height and arm span, the student displays chooses to represent the data in a scatter plot since scatter plots are designed to determine if correlations between two variables exist).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with accuracy	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with no significant errors	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with a few significant errors	Design a study that compares two samples, collect data, and select the appropriate representation to compare the sets of data, with many significant errors

Topic	Data Collection and Representation
Benchmark MA.PA.11.2	Judge the validity of data based on the data collection method
Sample Performance Assessment (SPA)	The student: Explains that the results of an experiment or survey may be questionable because the data collection method or the way the sample was chosen is questionable.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently make reasonable judgments about the validity of data based on the data collection method	Usually make reasonable judgments about the validity of data based on the data collection method	Sometimes make reasonable judgments about the validity of data based on the data collection method	Rarely make reasonable judgments about the validity of data based on the data collection method

Strand	Data Analysis, Statistics, and Probability
Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis

Topic	Data Interpretation
Benchmark MA.PA.12.1	Recognize situations appropriate for scatter plots
Sample Performance Assessment (SPA)	The student: Chooses to use a scatter plot when determining if a correlation exists between two variables (e.g., comparing the height of students to their arm spans).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Analyze different representations of the same data to describe, in great detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in sufficient detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in some (but not enough) detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in insufficient detail, how representations can be used to skew a person's interpretation of the data

Topic	Data Interpretation
Benchmark MA.PA.12.2	Analyze different representations of the same data to describe how representations can be used to skew a person's interpretation of the data
Sample Performance Assessment (SPA)	The student: Adjusts the intervals or scale on a graph to change the appearance of the graph and describes how the changes that were made affect a person's interpretation of the data.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Analyze different representations of the same data to describe, in great detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in sufficient detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in some (but not enough) detail, how representations can be used to skew a person's interpretation of the data	Analyze different representations of the same data to describe, in insufficient detail, how representations can be used to skew a person's interpretation of the data

Strand	Data Analysis, Statistics, and Probability
Standard 13: Data Analysis, Statistics, and Probability: DATA ANALYSIS: Develop and evaluate inferences, predictions, and arguments that are based on data

Topic	Predictions and Inferences
Benchmark MA.PA.13.1	Make conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots
Sample Performance Assessment (SPA)	The student: Analyzes a scatter plot and makes a conjecture based on the presence or absence of an approximate line of best fit.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Make reasonable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots, and justify the conjecture	Make reasonable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots	Make questionable conjectures (though somewhat justifiable) about possible relationships between two characteristics of a sample based on interpretations of scatter plots	Make unjustifiable conjectures about possible relationships between two characteristics of a sample based on interpretations of scatter plots

Strand	Data Analysis, Statistics, and Probability
Standard 14: Data Analysis, Statistics, and Probability: PROBABILITY: Understand and apply basic notions of chance and probability

Topic	Probability
Benchmark MA.PA.14.1	Judge the validity of conjectures that are based on experiments or simulations
Sample Performance Assessment (SPA)	The student: Refers to the theoretical probability, sample size, and data collection techniques to support the validity of a conjecture that is based on experiments or simulations with predictable outcomes.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Make reasonable judgments on the validity of conjectures that are based on experiments or simulations, and provides effective justification for the judgment	Make reasonable judgments on the validity of conjectures that are based on experiments or simulations	Make plausible judgments on the validity of conjectures that are based on experiments or simulations	Make unreasonable judgments on the validity of conjectures that are based on experiments or simulations

Topic	Probability
Benchmark MA.PA.14.2	Calculate probabilities for simple events under different relationships (e.g., inclusion, disjoint, complementary, independent, dependent, with replacement, without replacement)
Sample Performance Assessment (SPA)	The student: Calculates the probability of an event (or a combination of events) and shows/explains how the probability was determined.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Calculate probabilities for simple events under different relationships, with accuracy	Calculate probabilities for simple events under different relationships, with no significant errors	Calculate probabilities for simple events under different relationships, with a few significant errors	Calculate probabilities for simple events under different relationships, with many significant errors

Topic	Probability
Benchmark MA.PA.14.3	Use the Fundamental Counting Principle to calculate combinations and permutations
Sample Performance Assessment (SPA)	The student: Shows/describes/determines all the possible combinations (or permutations) of events (e.g., uses an organized list, a tree diagram, chart, illustration).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use fundamental counting principles to calculate combinations and permutations, with accuracy	Use fundamental counting principles to calculate combinations and permutations, with no significant errors	Use fundamental counting principles to calculate combinations and permutations, with a few significant errors	Use fundamental counting principles to calculate combinations and permutations, with many significant errors

Strand	Numbers and Operations
Standard 1: Numbers and Operations: NUMBER SENSE: Understand numbers, ways of representing numbers, relationships among numbers, and number systems

Topic	Numbers and Number Systems
Benchmark MA.AI.1.1	Recognize situations that can be represented by matrices
Sample Performance Assessment (SPA)	The student: Decides if the information in a problem can be represented in a matrix, and if it can, shows how to input the data into a matrix.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Consistently recognize situations that can be represented by matrices, and create situations that involve using matrices	Usually recognize situations that can be represented by matrices	Sometimes recognize situations that can be represented by matrices	Rarely recognize situations that can be represented by matrices

Strand	Numbers and Operations
Standard 3: Numbers and Operations: COMPUTATION STRATEGIES: Use computational tools and strategies fluently and, when appropriate, use estimation

Topic	Computational Fluency
Benchmark MA.AI.3.1	Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers
Sample Performance Assessment (SPA)	The student: Applies one property, or a combination of properties, to simplify radical expressions (e.g.,
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers, with accuracy	Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers, with no significant errors	Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers, with a few significant errors	Apply arithmetic properties to operate on and simplify expressions that include radicals and other real numbers, with many significant errors

Topic	Computational Fluency
Benchmark MA.AI.3.2	Apply the laws of exponents to perform operations on expressions with integral exponents
Sample Performance Assessment (SPA)	The student: Applies the law of exponents to make it easier to simplify expressions that include integral exponents; in the case of negative exponents, the student rewrites the expression using positive exponents and simplifies (e.g., 3-2 = 1/32 = 1/9 ).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Apply the laws of exponents to perform operations on expressions with integral exponents, with accuracy	Apply the laws of exponents to perform operations on expressions with integral exponents, with no significant errors	Apply the laws of exponents to perform operations on expressions with integral exponents, with a few significant errors	Apply the laws of exponents to perform operations on expressions with integral exponents, with many significant errors

Topic	Computational Fluency
Benchmark MA.AI.3.3	Use addition, subtraction, and scalar multiplication of matrices to solve problems
Sample Performance Assessment (SPA)	The student: Represents the information in a problem with matrices, and then performs the appropriate operation on the matrices to solve the problem.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use addition, subtraction, and scalar multiplication of matrices to solve problems, with accuracy	Use addition, subtraction, and scalar multiplication of matrices to solve problems, with no significant errors	Use addition, subtraction, and scalar multiplication of matrices to solve problems, with a few significant errors	Use addition, subtraction, and scalar multiplication of matrices to solve problems, with many significant errors

Strand	Measurement
Standard 4: Measurement: FLUENCY WITH MEASUREMENT: Understand attributes, units, and systems of units in measurement; and develop and use techniques, tools, and formulas for measuring

Topic	Measurement Formulas
Benchmark MA.AI.4.1	Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement
Sample Performance Assessment (SPA)	The student: Evaluates a formula to solve for a specific measure (e.g. after finding the temperature in Celsius, uses the formula, F = 9/5C + 32 to convert the temperature into Fahrenheit).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement, with accuracy	Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement, with no significant errors	Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement, with a few significant errors	Use formulas, functions, or conversion equations to solve problems dealing with determining a measurement based on another derived or given measurement, with many significant errors

Strand	Geometry and Spatial Sense
Standard 8: Geometry and Spatial Sense: REPRESENTATIONAL SYSTEMS: Select and use different representational systems, including coordinate geometry

Topic	Coordinate Geometry
Benchmark MA.AI.8.1	Graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques
Sample Performance Assessment (SPA)	The student: Shows/explains how to graph a line when the slope and y-intercept are known; shows/explains how to graph a line using the slope and one point on the line; shows/explains how to graph a line using the x- and y-intercepts.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Show and explain how to graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques, with accuracy	Graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques, with no significant errors	Graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques, with a few errors	Graph linear equations using slope-intercept, point-slope, and x- and y-intercept techniques, with many significant errors

Topic	Coordinate Geometry
Benchmark MA.AI.8.2	Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line
Sample Performance Assessment (SPA)	The student: Shows/explains how to finds the slope of a line using two points on the line (or when given the graph of a line, or when given the equation of the line).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Show and explain how to determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line, with accuracy	Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line, with no significant errors	Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line, with a few significant errors	Determine the slope of a line when given the graph of a line, two points on the line, or the equation of the line, with many significant errors

Strand	Patterns, Functions, and Algebra
Standard 9: Patterns, Functions, and Algebra: PATTERNS AND FUNCTIONAL RELATIONSHIPS: Understand various types of patterns and functional relationships

Topic	Patterns
Benchmark MA.AI.9.1	Determine if a linear pattern exists in a set of data and represent the data algebraically and graphically
Sample Performance Assessment (SPA)	The student: Uses an organized table of the data and/or a graph of the data to justify whether a linear pattern exists or not.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Show and explain how to determine if a linear pattern exists in a set of data, and represent the data algebraically and graphically, with accuracy	Determine if a linear pattern exists in a set of data, and represent the data algebraically and graphically, with no significant errors	Determine if a linear pattern exists in a set of data, and represent the data algebraically and graphically, with a few significant errors	Have difficulty determining if a linear pattern exists in a set of data, and is unable to represent the data algebraically and graphically

Topic	Patterns
Benchmark MA.AI.9.2	Compare and contrast the concepts of direct and inverse variation of a relation
Sample Performance Assessment (SPA)	The student: Finds a relation that is a direct variation and represents it on a graph.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Compare and contrast, in great detail, the concepts of direct and inverse variation of a relation	Compare and contrast, in sufficient detail, the concepts of direct and inverse variation of a relation	Compare and contrast, in some (but not enough) detail, the concepts of direct and inverse variation of a relation	Compare and contrast, in insufficient detail, the concepts of direct and inverse variation of a relation

Topic	Functions
Benchmark MA.AI.9.3	Determine the zeros of a linear or quadratic function algebraically and graphically
Sample Performance Assessment (SPA)	The student: Shows/explains how to use an algebraic method (or graph, or graphing calculator) to find the zeros of a function.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Show and explain how to determine the zeros of a linear or quadratic function algebraically and graphically, with accuracy	Determine the zeros of a linear or quadratic function algebraically and graphically, with no significant errors	Determine the zeros of a linear or quadratic function algebraically and graphically, with a few significant errors	Determine the zeros of a linear or quadratic function algebraically and graphically, with many significant errors

Topic	Functions
Benchmark MA.AI.9.4	Compare and contrast the properties of linear functions and exponential functions
Sample Performance Assessment (SPA)	The student: Graphs several linear functions and several exponential functions to compare the shape of the graphs.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Compare and contrast, in great detail, the properties of linear functions and exponential functions	Compare and contrast, in sufficient detail, the properties of linear functions and exponential functions	Compare and contrast, in some (but not enough) detail, the properties of linear functions and exponential functions	Compare and contrast, in insufficient detail, the properties of linear functions and exponential functions

Strand	Patterns, Functions, and Algebra
Standard 10: Patterns, Functions, and Algebra: SYMBOLIC REPRESENTATION: Use symbolic forms to represent, model, and analyze mathematical situations

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.1	Solve linear equations and inequalities in one variable using a variety of strategies (e.g., algebraically, by graphing, by using a graphing calculator)
Sample Performance Assessment (SPA)	The student: Shows/explains how to solve for the variable in a linear equation or inequality using a selected strategy (e.g., algebraic method, graphing, or using graphing technology), and shows how find the solution using a different strategy.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve linear equations and inequalities in one variable using a variety of strategies, with accuracy	Solve linear equations and inequalities in one variable using a variety of strategies, with no significant errors	Solve linear equations and inequalities in one variable using a variety of strategies, with a few significant errors	Solve linear equations and inequalities in one variable using a variety of strategies, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.2	Translate between verbal mathematical situations and algebraic expressions and equations
Sample Performance Assessment (SPA)	The student: Represents mathematical situations algebraically and determines a situation that could be represented by an algebraic expression or equation.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Translate between verbal mathematical situations and algebraic expressions and equations, with accuracy	Translate between verbal mathematical situations and algebraic expressions and equations, with no significant errors	Translate between verbal mathematical situations and algebraic expressions and equations, with a few errors	Translate between verbal mathematical situations and algebraic expressions and equations, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.3	Justify the steps used in simplifying expressions and solving equations and inequalities
Sample Performance Assessment (SPA)	The student: Uses concrete objects, pictorial representations, and the properties of real numbers to justify the steps used to simplify expressions and solve equations and inequalities.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Justify, in great detail, the steps used in simplifying expressions and solving equations and inequalities	Justify, in sufficient detail, the steps used in simplifying expressions and solving equations and inequalities	Justify, in some (but not enough) detail, the steps used in simplifying expressions and solving equations and inequalities	Justify, in insufficient detail, the steps used in simplifying expressions and solving equations and inequalities

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.4	Determine the equation of a line when given the graph of the line, the slope and a point on the line, or two points on the line
Sample Performance Assessment (SPA)	The student: Shows/explains how to determine the equation of a line when given the graph of a line, the slope and a point on a line, or two points on a line.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Show and explain how to determine the equation of a line when given the graph of the line, the slope and a point on the line, or two points on the line, with accuracy	Determine the equation of a line when given: the graph of the line, the slope and a point on the line, or two points on the line, with no significant errors	Determine the equation of a line when given: the graph of the line, the slope and a point on the line, or two points on the line, with a few significant errors	Determine the equation of a line when given: the graph of the line, the slope and a point on the line, or two points on the line, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.5	Solve systems of two linear equations in two variables algebraically and graphically
Sample Performance Assessment (SPA)	The student: Uses an algebraic strategy (e.g., elimination, substitution), solve a system of two linear equations in two variables, and uses a graph or graphing technology to show how to find the solution graphically.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve systems of two linear equations in two variables algebraically and graphically, with accuracy	Solve systems of two linear equations in two variables algebraically and graphically, with no significant errors	Solve systems of two linear equations in two variables algebraically and graphically, with a few significant errors	Solve systems of two linear equations in two variables algebraically and graphically, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.6	Factor first- and second-degree binomials and trinomials in one or two variables
Sample Performance Assessment (SPA)	The student: Selects and applies an appropriate technique to completely factor polynomials (e.g., using techniques such as finding a common factor in all terms, the difference of two squares, and the perfect squares of binomials, reverse FOIL).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Factor first- and second-degree binomials and trinomials in one or two variables, with accuracy	Factor first- and second-degree binomials and trinomials in one or two variables, with no significant errors	Factor first- and second-degree binomials and trinomials in one or two variables, with a few significant errors	Factor first- and second-degree binomials and trinomials in one or two variables, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.7	Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology
Sample Performance Assessment (SPA)	The student: Solves quadratic equations by factoring algebraically (e.g., completing the square, using the quadratic formula), or by locating the intersection point(s) of the quadratic function and the x-axis on a graph.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology, with accuracy	Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology, with no significant errors	Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology, with a few significant errors	Solve quadratic equations in one variable algebraically, graphically, or by using graphing technology, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.8	Select and use a variety of strategies (e.g., concrete objects, pictorial representations, algebraic manipulation) to perform operations on polynomials
Sample Performance Assessment (SPA)	The student: Adds (or subtracts or multiplies) polynomials (or divides polynomials by monomials) by selecting and applying appropriate strategies.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Select and use a variety of strategies to perform operations on polynomials, with accuracy	Select and use a variety of strategies to perform operations on polynomials, with no significant errors	Select and use a variety of strategies to perform operations on polynomials, with a few significant errors	Select and use a variety of strategies to perform operations on polynomials, with many significant errors

Topic	Numeric and Algebraic Representations
Benchmark MA.AI.10.9	Analyze transformations of lines and understand how the transformation are represented in equations
Sample Performance Assessment (SPA)	The student: Writes the equation of a line before and after undergoing a transformation, and explains how the transformation is represented by the altered part of the equation.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Analyze transformation of lines and show how the transformations are represented in equations, with accuracy	Analyze transformations of lines and show how the transformations are represented in equations, with no significant errors	Analyze transformations of lines and show how the transformations are represented in equations, with a few significant errors	Analyze transformations of lines and show how the transformations are represented in equations, with many significant error

Strand	Data Analysis, Statistics, and Probability
Standard 12: Data Analysis, Statistics, and Probability: STATISTICS: Interpret data using methods of exploratory data analysis

Topic	Data Interpretation
Benchmark MA.AI.12.1	Compare data sets using statistical techniques (e.g., measures of central tendency, standard deviation, range, stem-and-leaf plots, and box-and-whisker graphs)
Sample Performance Assessment (SPA)	The student: Selects a representation that supports the desired purpose of the study and shows a visual comparison of the data sets (e.g., in studying the relationship between an 11th grader's height and arm span, the student displays chooses to represent the data in a scatter plot since scatter plots are designed to determine if correlations between two variables exist).
Rubric
Advanced	Proficient	Partially Proficient	Novice
Compare data sets selectively using appropriate statistical techniques, and justify the choice of technique	Compare data sets using appropriate statistical techniques	Compare data sets using suggested statistical techniques	Have difficulty comparing data sets using statistical techniques

Topic	Data Interpretation
Benchmark MA.AI.12.2	Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists)
Sample Performance Assessment (SPA)	The student: Sketches bivariate data in a scatter plot and determines the line of best fit.
Rubric
Advanced	Proficient	Partially Proficient	Novice
Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists), with accuracy	Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists), with no significant errors	Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists), with a few significant errors	Display bivariate data in a scatter plot, describe its shape, and determine the line of best fit that models a trend (if a trend exists), with many significant errors