Uses mathematical vocabulary to express ideas

Performance Descriptors
Basic / Proficient / Advanced
  • Use of math vocabulary is limitedor vocabulary and notation are used incorrectly
/
  • Usually uses appropriate math vocabulary and notation
/
  • Consistently uses math vocabulary and notation

  • Appropriate vocabulary: vocabulary addressed in your classroom instruction to date
  • Uses words, pictures or numbers to record and communicate mathematical reasoning

  • Performance Descriptors

Basic / Proficient / Advanced
  • Gives explanations that are essentially correct, but incomplete or difficult to understand
  • Presents supporting arguments that are incomplete or logically unsound
  • Uses pictures, symbols, tables, and graphs, that contain major errors or are irrelevant
/
  • Gives understandable explanations
  • Presents supporting arguments, that are logically sound, but may contain minor errors
  • Uses pictures, symbols, tables, and graphs that may contain minor errors or are somewhat irrelevant
/
  • Gives clear, concise, organized explanations
  • Presents supporting arguments that are strong and sound
  • Uses pictures, symbols, tables, and graphs that are correct and clearly relevant

  • Essentially correct: explanation contains no mathematical errors

Numbers/Number Concepts

Reads, writes, compares and orders whole numbers

Performance Descriptors
Basic / Proficient / Advanced
  • Reads, writes, orders and compares numbers to 1 million using appropriate words and symbols
/
  • Reads, writes, orders and compares numbers to 1 billion using appropriate words and symbols (5.N.1.1)
/
  • Reads, writes, orders and compares numbers beyond 1 billion using appropriate words and symbols

Reads, writes, compares and orders decimals, fractions and percents

Performance Descriptors
Basic / Proficient / Advanced
  • Compares fractions to the landmarks 0, ½, and 1
  • Compares decimals to the tenths place
/
  • Reads, writes, compares and orders decimals from .001 to 2
(5.N.1.1)
  • Reads, writes, compares and orders fractions (5.N.2.2)
  • Identifies and generates equivalent fractions, decimals and percents (5.N.1.3)
/
  • Compares and orders fractions and decimals beyond 2

Computation/Problem Solving

Demonstrates fluency with multiplication and related division facts

Performance Descriptors
Basic / Proficient / Advanced
  • Uses one quick relationship strategy or recalls multiplication facts
/
  • Uses one quick relationship strategy or recalls multiplication facts and demonstrates fluency with division problems related to the multiplication combinations (Rapid City 4TH grade)
  • Identifies numbers in the range of 1 to 50 as prime or composite and finds factors of numbers to 100 (5.N.1.2)
  • Determines the squares of numbers
1 – 12 (5.N.1.5) /
  • Identifies numbers between 51 and 100 as prime or composite and finds factors of numbers beyond 100

Makes reasonable computation estimates

Performance Descriptors
Basic / Proficient / Advanced
  • Uses landmarks/rounding to predict an answer or support the reasonableness of a solution to2-digit multiplication and division problems
/
  • Uses a variety of estimation strategies to predict an answer or support the reasonableness of a solution using whole numbers, decimals and fractions to the nearest whole (5.N.3.1)
/
  • Uses a variety of efficient estimation strategies to predict an answer or support the reasonableness of a solution using whole numbers, decimals, and fractions to the nearest half

  • 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 problems and check results

Performance Descriptors
Basic / Proficient / Advanced
  • Uses number strategies to accurately find the products and quotients of two-digit numbers and check results
  • Uses inefficient strategies to
  • accurately solve the four operations inword problems
/
  • Uses at least 2 number strategies flexibly to accurately find the products and quotients of multi-digit numbers and check results (5.N.2.1)
  • Solves multi-step word problems
(Rapid City Standard)
  • Multiply and divide decimal money amounts by numbers 1-9
(5.N.2.3) /
  • Uses a variety of strategies flexibly to accurately solve addition and subtraction problems with decimals and fractions and check results

Geometry

Classifies and identifies triangles and angles

Performance Descriptors
Basic / Proficient / Advanced
  • Identifies right and straight angles
  • Uses landmarks (90 and 180) to estimate angle measures between 0 and 180
/
  • Identifies and names isosceles, equilateral, right and scalene triangles (5.G.1.1)
  • Identifies and names acute, right, obtuse and straight angles (5.G.1.2)
  • Estimates and measures the size of angles and turns (5.G.1.2)
/
  • Constructs/draws angles and triangles that satisfy given attributes
  • Uses known angles to find measures of unknown angles

Solves problems involving shape, movement or location

(See journal tasks p. 23)

Basic / Proficient / Advanced
  • Sorts figures into polygons and non-polygons
  • Locates points on a coordinate grid
  • Recognizes and names polygons by number of sides
/
  • Determines multiple lines of symmetry in rectangles, squares and triangles (5.G.2.1)
  • Uses two-dimensional coordinate grids to find locations, represent points and simple figures and locate negative integers (5.G.2.3)
Analyzes and classifies plane (polygon) and solid (polyhedra) figures using attributes
(Rapid City Standard) /
  • Determines total lines of symmetry in regular polygons

Applies measurement concepts to solve problems

Performance Descriptors
Basic / Proficient / Advanced
  • Totals coins and makes change from $1.00
  • Chooses the appropriate U.S. standard units to measure length, weight, and capacity
/
  • Solves problems involving money including making change(5.M.1.2)
  • Develops and uses benchmarks for length, weight, volume and time to estimate, order and compare measurements (Rapid City Standard)
  • Uses appropriate tools to measure length, weight, temperature and area (5.M.1.4)
  • Converts U.S. standard units of length, weight and capacity(5.M.1.3)
/
  • Compares lengths expressed in different ways
  • meters and centimeters
  • meters and decimal fractions of a meter
  • meters and fractions of a meter

Algebra

Solves problems using patterns

Performance Descriptors
Basic / Proficient / Advanced
  • Identifies and extends patterns using one operation: addition, subtraction, multiplication or division
/
  • Solves problems using repeating and growing patterns involving more than one operation (5.A.4.1)
  • Represents and analyzes patterns and functions using words, tables and graphs (Rapid City Standard)
/
  • Uses patterns to make and explain generalizations

Identifies and uses mathematical symbols and properties

Performance Descriptors
Basic / Proficient / Advanced
  • Recognizes and uses the commutative property of addition and multiplication
  • Uses , =, or  to make number sentences true
/
  • Recognizes and uses the associative property of addition and multiplication (5.A.1.2)
  • Identifies relevant information in a word problem and applies it to a given formula (5.A.3.2)
Example: Area = length x width /
  • Recognizes and uses the distributive property of multiplication to solve computation problems

  • Writes and solves equations

  • Performance Descriptors

  • Basic
/
  • Proficient
/
  • Advanced

  • Represents a variable as an unknown using a letter or symbol
  • Simplifies whole number expressions using all four operations.
Example: 3(2+5)
  • Writes and solves number sentences that represent one-step word problems using whole numbers and all four operations.
/
  • Writes and solves number sentences that represent two-step word problems using whole numbers and all four operations (5.A.3.1)
/
  • Expresses mathematical relationships using equations
Example: 2x=y (student generated)

Data

Collects data, graphs data and describes important features of data sets

Performance Descriptors
Basic / Proficient / Advanced
  • Reads data from graphs and draws conclusions
  • Identifies the range, mode, and median in graphic information
/
  • Develops survey questions and collects data (5.S.1.1)
  • Represents data in line plots, bar graphs and line graphs using appropriate scales and labels (5.S.1.1)
  • Calculates and explains the mean for a whole number data set (5.S.1.2)
  • Identifies the range, mode and median of graphic information and uses them to interpret data (5.S.1.1)
/
  • Describes similarities and differences between data sets
  • Constructs representations that compare two data sets
  • Uses data sets as evidence for writing comparative statements

Uses probability to determine possible outcomes

Performance Descriptors
Basic / Proficient / Advanced
  • Records outcomes of probability experiments
  • Interprets the fairness of a game as equal probability to win
/
  • Describes events as certain, likely, unlikely or impossible (5.S.2.1)
  • Uses models to display possible outcomes and develops systematic ways to generate a list of all possibilities (5.S.2.2)
/
  • Represents probability as a fraction
  • Uses probability to predict how often an event will happen and selects events more or less likely to happen

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