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New Jersey Assessment of Skills and Knowledge (NJ ASK)
Performance Level Descriptors

Mathematics

(February 2009)

Grade 4 Math

Partially Proficient

Students performing at the partially proficient level generally require prompting to demonstrate knowledge of number sense, coordinate geometry, properties of operations and use of symbols, and systematic listing and counting, at a limited level of performance.

In general, partially proficient students:

  • Identify numbers as being large or small
  • Recognize that numbers apply to their daily life
  • Match corresponding whole numbers, decimals, and fractions to models
  • Use a number line to count and order numbers
  • Identify the commutative property of addition and multiplication
  • Identify <, >, or = symbols
  • Sort objects by attributes
  • List some possibilities for a counting situation

Proficient

Students performing at the proficient level may require prompting to demonstrate a basic knowledge of number sense, coordinate geometry, properties of operations and use of symbols, and systematic listing and counting at a moderate level of performance.

In general, proficient students:

  • Order and compare fractions and decimals
  • Apply numbers to real world situations
  • Model fraction/decimal/whole number equivalents
  • Use coordinates to locate and label points in the first quadrant
  • Identify the commutative, associative, identity and zero properties
  • Use symbols (<, >, =) to compare numbers
  • Organize objects in a Venn diagram according to attributes
  • List all possibilities for a counting situation

Advanced Proficient

Students performing at the advanced proficient level generally require minimal prompting to demonstrate knowledge of number sense, coordinate geometry, properties of operations and use of symbols, and systematic listing and counting at a high level of performance.

In general, advanced proficient students:

  • Explain how numbers represent specific information in the real world
  • Illustrate equivalent forms of whole numbers, decimals, and fractions
  • Count the horizontal and vertical units moved between two points in the first quadrant
  • Demonstrate an understanding of the commutative, associative, identity and zero properties
  • Create sentences using symbols
  • Analyze information using a Venn diagram
  • Represents in an organized way all possibilities of a counting situation