Performance Level Descriptors. Mathematics

Transcription

1 Performance Level Descriptors

2 Grade 3 Well Students rarely, Understand that our number system is based on combinations of 1s, 10s, and 100s (place value, compare, order, decompose, and combine using addition) Understand fractions as parts of wholes Compare the size of common fractions using models including number lines Master addition and subtraction facts up to 20 Use strategies to estimate and compute addition and subtraction of whole numbers up to 100 Use models and strategies to solve multiplication problems Represent situations that involve addition, subtraction, multiplication, and division of whole numbers with pictures, objects, geometric models, and number sentences Understand numeric patterns in hundreds charts and those based on skip counting Name, describe, and sort solid and plane figures using several attributes (e.g., number of corners/sides and size) Measure length in standard units and area in non-standard units Tell time and determine elapsed time to the nearest half hour Collect, represent, and describe categorical and simple numerical data using tallies, tables, pictographs, bar graphs, and mode Page 2

3 Grade 4 Well demonstrate knowledge of grade-level level demonstrate gaps and misconceptions in content this level show evidence of solving Students rarely, incorrectly, and minimally understand the required content to advance to Understand whole numbers (1s, 10s, 100s, 1,000s) and decimals (tenths and hundredths), including place value, comparing, and ordering Understand fractions as parts of a whole and as division of whole numbers (3/5 also means 3 divided by 5) Compare and order fractions, recognize equivalent fractions (using physical models, benchmark fractions, or number line), and add and subtract benchmark fractions using models Estimate and compute sums and differences of multi-digit numbers, including money Master multiplication facts and related division facts, relate multiplication and division Estimate and compute products of multi-digit numbers using different strategies (including mental math and number operation properties) Represent situations that involve additions, subtraction, multiplication and division (with remainders), using pictures, geometric models, symbols, and number sentences Interpret tables, graphs, real-world events based on change over time Identify and classify two-dimensional and three-dimensional shapes, build three-dimensional object from two-dimensional representation Identify a combination of slides, flips, and turns to show that two shapes are congruent, and identify line and rotational symmetry Estimate and measure the length of objects to the nearest whole unit (inches or centimeters) and extend the precision to 1/2, 1/4, or 1/10 unit Find the perimeter of geometric figures and the area of rectangles by covering with unit squares Tell time to the nearest five minutes Collect, display, and describe numerical and categorical data (tables, scaled pictographs, bar graphs, line plots), noting important features such as concentration of values, spread of values, median, and mode Describe the likelihood of an experiment or event (e.g. possible or equally likely) Page 3

4 Grade 5 Well Students rarely, Understand whole numbers to 100,000 and decimals to thousandths, including place value, comparing, and ordering Describe numbers according to characteristics such as even, odd, factors, multiples, and squares Understand fractions as parts of a whole/set, division of whole numbers, and locations on a number line Generate equivalent forms of benchmark fractions, decimals, and percents Estimate answers (multiplication and division) and use a variety of strategies to multiply and divide whole numbers Add/subtract benchmark fractions and add/subtract decimals Use models or mental math to multiply fractions by whole numbers Find a given term in an arithmetic sequence, translate visual patterns into rules, and describe trends in patterns and graphs Model problem situations with objects, graphs, tables, or equations Analyze and classify two-dimensional shapes according to their properties and develop definitions for classes of shapes Measure and compare objects to the nearest 1/8 unit (U.S.) or to the nearest 1/10 (metric) and convert feet to inches and meters to centimeters Find the perimeter, area (covering with square units), and volume (filling with cubes) of a variety of shapes/objects Find elapsed time Collect, display, compare, and describe sets of data, noting important features such as concentration of values, spread of values, extreme values, typical values, median, mode, mean, and range (tables, scaled pictographs, bar graphs, line plots) Determine all the outcomes of an experiment and express probability as a number between 0 and 1 Page 4

5 Grade 6 Well Students rarely, Demonstrate equivalence of decimals, fractions, and percents Compare and order decimals, fractions, and percents Add, subtract, and multiply fractions and decimals, using models and in real-world settings Use proportional reasoning and/or benchmark percents to solve problems Describe and represent changes in patterns, tables, or graphs Use inverse operations to solve equations Estimate, measure, and classify angles Demonstrate the relationship between perimeter and area of rectangles (e.g., fixed perimeter, fixed area, doubling the area) Find the circumference of a circle in terms of π Understand and use the formulas for the area of triangles and parallelograms Use geometric properties of polygons to solve problems (e.g., sum of angles of a regular polygon) Construct and interpret a display of data (circle graphs, scatter plots, frequency counts) Compare two sets of data Analyze real-world data to calculate the chances of winning or losing a simple game Page 5

6 Grade 7 Well Students rarely, Apply proportional reasoning to solve problems that involve unit rates, ratios, similar figures, scale factors, and simple probability Compare and perform operations with fractions, decimals, and percents Compare and perform operations with integers and apply knowledge of integers to a coordinate plane Describe linear relationships in visual patterns, tables, graphs, and equations Use multiple representations to model the same situation (tables, graphs, and equations) Use variables in representing situations, evaluating expressions, and solving linear equations Make connections between perimeter/area and volume/surface area Find the area and circumference of circles Determine the volume and surface area of cylinders and prisms using models Recognize and make representations in two dimensions of a three-dimensional figure and vice versa Demonstrate and apply relationships between sides and angles of triangles and other polygons Construct and interpret displays of one- and two-variable data (scatter plot and stem and leaf plot) Choose an appropriate measure of center (mean, median, mode) and spread (range) to interpret data set(s) Construct a sample space to determine theoretical probabilities of an event Page 6

7 Grade 8 Well Students rarely, Use exponential notation to represent whole numbers; express numbers in scientific notation Understand and perform operations with rational numbers; use inverse operations, distributive properties, and order of operations when appropriate Use square numbers and square roots to reason about the relationship between the side of a square and its area Apply proportional reasoning strategies to those involving similar geometric figures Understand and use slope and y-intercept to write and interpret equations of a line Analyze relationships among tables, graphs, and equations of lines paying particular attention to the meaning of y-intercept and slope Create and solve equations based on situations that are linear Use an algebraic expression to represent any term in a numeric or geometric pattern Demonstrate equivalency of algebraic expressions requiring distributive property, inverse operations, or properties of equalities Compare tables and graphs to identify functions as linear or nonlinear Use properties of pairs of angles found in parallel lines, intersecting lines, and polygons to find angle measures Recognize exponential rates of growth and decay in tables and graphs Develop and evaluate mathematical arguments to demonstrate geometric relationships, such as similarity, congruence, or symmetry Apply the Pythagorean Theorem to solve problems involving right triangles Solve problems involving surface area and volumes of various prisms Page 7

8 Construct and interpret displays of single sets of data (histograms, box plots) and related sets of data (scatter plots) Construct and interpret scatter plots and associated lines of fit to make predictions Construct sample space to find the probability of a single or compound event Compare and make predictions from experimental and theoretical probabilities of the same event Page 8

9 Grade 9 Well Students rarely, Compare, order, estimate, and operate with real numbers, including exponents and square roots Demonstrate properties of the real number system and use them to evaluate expressions for given variables Generate the nth term of an arithmetic or geometric pattern using a variety of strategies (recursive thinking, visual models) Classify, compare, and model situations with functions that are linear or exponential by finding and using rates of change, graphs, tables, and equations Model and solve linear equations and inequalities; identify solutions to systems of equations and inequalities Make strategic selection of graphing calculator viewing window and scale to solve problems Write linear and exponential equations for given parameters and understand the effect of changing a parameter Use algebraic concepts such as slope to verify parallelism, perpendicularity, and geometric properties to construct triangles and rectangles in the coordinate plane Solve problems that require an understanding of the Pythagorean Theorem relationships Solve problems involving surface area and volume of prisms, pyramids, cylinders, cones, and spheres Draw and support conclusions for statistical data and describe the effects of outliers Determine sample spaces; compute and interpret probabilities Use and design simulations or experiments to determine probabilities of independent and dependent events Page 9

10 Grade 10 Well Students rarely, Demonstrate a comprehensive understanding of irrational numbers, absolute value, square roots, and exponents; solve problems that involve using operations Generate the nth term of linear, exponential, and quadratic patterns using a variety of strategies (recursive thinking, visual models) Compare, model, and solve situations involving linear, exponential, and quadratic functions by using tables, graphs, or equations Model and solve situations involving systems of equations and inequalities using tables, graphs, or algebraic methods Distinguish between situations involving direct and inverse variations Represent situations with matrices and use matrix operations with the aid of technology to solve problems Apply the Pythagorean Theorem (and its converse), including the distance formula, to various situations Apply right triangle trigonometry and properties of similarity to solve problems Use angle relationships created by intersecting and parallel lines and properties of polygons to solve problems Compare and classify polygons given properties and deduce properties given the polygon, using coordinate and/or Euclidean geometry Use partitioning and algebraic reasoning to solve area, volume, and surface area problems Reason deductively to justify a conclusion or to create a counterexample Understand how transformations affect functions, shapes, and data displays Compute and interpret probabilities of independent and dependent events using permutations, combinations, or counting techniques Compute and interpret expected value Page 10