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Uses mathematical vocabulary to express ideas Performance Descriptors Proficient Usually uses appropriate math vocabulary and notation Basic Advanced Use of math vocabulary is limited Consistently uses correct math or vocabulary and notation is used vocabulary and notation incorrectly Appropriate: vocabulary and notation addressed in classroom instruction to date Uses words, pictures or numbers to record and communicate mathematical thinking Performance Descriptors Basic Proficient Advanced Gives explanations that are Gives understandable, organized Gives explanations that are clear, incomplete or confusing and explanations complete and explicit difficult to understand Presents supporting arguments, Presents supporting arguments Presents supporting arguments that are logically sound, but may that are strong, sound and contain that are incomplete or logically contain minor errors no errors unsound Uses pictures, symbols, tables, Uses pictures, symbols, tables, Uses pictures, symbols, tables, and graphs that may contain and graphs that are correct and and graphs that contain major minor errors or are somewhat clearly relevant errors or are irrelevant irrelevant Minor errors: Explanation is mathematically correct. Errors do not reflect mathematical misconceptions Numbers/Number Concepts Reads, writes, orders and compares whole numbers Basic Reads, writes, orders and compares numbers to 1,000 using appropriate words and symbols Performance Descriptors Proficient Reads, writes, orders and compares numbers to 10,000 using appropriate words and symbols Advanced Reads, writes, orders and compares numbers beyond 10,000 using appropriate words and symbols (3.N.1.1) Names, writes and compares fractions from visual representations Basic Identifies and represents unit fractions as parts of a group or parts of a whole (1/2, 1/3, 1/4) but records or labels fractions incorrectly Performance Descriptors Proficient Names and writes fractions from visual representations (pictures or models) (3.N.1.3) Compares fractions with like denominators (3.N.1.3) Advanced Relates notations for fractions (1/2, 1/4, 3/4, 1/5, 1/10)with decimal notations on the calculator Unit fraction: A fraction with a numerator of 1 Computation/Problem Solving Demonstrates fluency with multiplication facts Basic Performance Descriptors Proficient 1 Advanced Figures out multiplication facts through 5 x 10 using skip counting or other counting strategies Uses one quick relationship strategy or recalls multiplication facts through 6 x 12 (Rapid City Standard) Uses one quick relationship strategy or recalls multiplication facts beyond 6 x 12 Makes reasonable estimates Performance Descriptors Proficient Basic Sometimes uses landmarks/rounding to support the reasonableness of solutions Advanced Consistently uses estimation to support the reasonableness of solutions Rounds two-digit numbers to the nearest ten and 3-digit numbers to the nearest hundred(3.N.3.1) Uses a variety of estimation strategies to support the reasonableness of solutions Estimation can be assessed whenever students are working with computation activities, by asking students to estimate the solution before solving the problem. Uses multiple strategies to accurately and efficiently solve computation and story problems and check results Performance Descriptors Proficient Basic Uses 1 number strategy to solve addition and subtraction computation and story problems Uses pictures or counting and direct modeling to solve multiplication and division computation and story problems Advanced Uses 1 number strategy to solve addition and subtraction problems and at least 1 number strategy to check. (using numbers of up to 3 digits) (3.N.2.1) Uses 1 number strategy to solve multiplication problems and one counting or picture strategy to check (numbers up to 2 digits by 1 digit) (3.N.2.1) Uses direct modeling and number strategies to solve division problems (Rapid City Standard) Uses a variety of number strategies to solve addition, subtraction, multiplication and division problems and check results Recognizes, identifies and compares shapes and lines Performance Descriptors Basic Proficient Advanced Names squares, rectangles, triangles, cubes, spheres and cylinders Draws 2-dimensional pattern block figures Recognizes, identifies and compares: square, rectangle, triangle, cube, sphere and cylinder (3.G.1.1) Constructs geometric figures that satisfy given attributes Recognizes and names at least 3 of the following polygons and polyhedra: Polygons: hexagon, pentagon Polyhedra: square prism, octagonal prism, triangular prism, rectangular prism, hexagonal prism, hemisphere, cone or square pyramid (Rapid City Standard) Identifies and names points, lines, line segments and rays (3.G.1.2) Recognize: Selects the correct shape from a group of shapes Identifies: Names the shape when it is shown Solves problems involving shape, movement and location Performance Descriptors Basic Compares 2 objects and determines if they are congruent Identifies geometric figures regardless of how they are flipped, slid or turned Proficient Demonstrates relationships between figures using similarity and congruence (3.G.2.1) Predicts which figures would result from a flip, slide or turn of a given figure (Rapid City Standard) 2 Advanced Constructs figures that are congruent and justifies why the figures are congruent Measurement Measures accurately using appropriate units Basic Measures length to the nearest inch or foot Chooses the most appropriate metric unit (centimeter or meter) to measure length Performance Descriptors Proficient Advanced Selects and uses appropriate units Carries out unit conversions: and accurately measures length o inches to feet/yards (inches, feet), weight (pounds, o feet to yards ounces) and capacity (cups, pints, quarts) (3.M.1.3) (3.M.1.4) Estimates length and measures to the nearest half-inch (3.M.1.5) Reads and tells time Basic Tells time to the minute using digital and analog clocks and relates time to daily events Performance Descriptors Proficient Reads and tells time before and after the hour using 5-minute intervals on an analog clock Advanced Tells time using fractional parts of an hour (a quarter to, a quarter past, half past) (3.M.1.1) Uses money to solve problems Basic Determines the value of a collection of like and unlike coins with a value up to $1.00 Performance Descriptors Proficient Counts, compares and solves problems using a collection of coins and bills for amounts up to $10.00 (3.M.1.2) Advanced Makes change from $1.00 Algebra Describes and extends number patterns and uses number patterns to make predictions Basic Extends linear number patterns Example: 4, 8, 12, ___, ___, Performance Descriptors Proficient Identifies and explains the relationship between repeated addition and multiplication (3.A.1.1) Describes, extends, and makes generalizations about linear number patterns (3.A.4.1) Advanced Represents and analyzes patterns using words, tables and graphs Expresses the relationship between addition and multiplication using equations Uses mathematical symbols and properties Basic Applies the properties of 0 and 1 to addition and multiplication Performance Descriptors Proficient Recognizes and uses the commutative property of 3 Advanced Selects appropriate relational symbols (, , =) to compare multiplication to solve related numbers beyond 10,000 problems (Rapid City Standard) Identifies and applies the properties of 0 and 1 to multiplication, addition and subtraction (3.A.1.2) Selects appropriate relational symbols (, , =) to compare numbers less than 10,000 (3.A.2.1) Solves for the unknown in computation and story problems Basic Solves open addition and subtraction sentences with one unknown in any position using whole numbers equal to or less than 100 Writes number sentences from problem situations using + or – and = with numbers to 100 Performance Descriptors Proficient Solves open addition and subtraction sentences with one unknown in any position using whole numbers between 100 and 1,000 (3.A.2.2) Writes and solves number sentences from word problems using addition, subtraction, multiplication and division (3.A.2.2) Advanced Solves open multiplication and division sentences with one unknown in any position Example: 3 x = 24 3x8= x 8 = 24 24 ÷ = 3 24 ÷ 8 = ÷8=3 Data and Probability Collects, organizes and represents data Basic Uses interviews, surveys and observations to gather data Constructs accurate representations of data that clearly communicate information o Tally Charts o Pictographs Performance Descriptors Proficient Advanced Collects, organizes, and Represents data in more than one represents data in scaled and way labeled graphs (3.S.1.2) o Line graphs o Bar graphs Creates and labels a graph (Rapid City Standard) Presents data in a way that clearly communicates information Answers questions about data represented in graphs Basic Makes observations about displayed data Tally charts Pictographs Bar graphs Performance Descriptors Proficient Asks and answers questions from data represented in graphs (3.S.1.1) o Tally charts o Pictographs o Bar graphs Determines the range and mode of 4 Advanced Analyzes data by describing their shape and patterns Interprets what is typical in a data set data sets (Rapid City Standard) Uses probability to determine possible outcomes Basic Lists possible outcomes and makes predictions about which outcome is more or less likely to occur Performance Descriptors Proficient Describes events as certain, impossible or likely (3.S.2.1) 5 Advanced Uses probability to compare and order events from certain to impossible or impossible to certain