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

Mathematics
Grade 4

6/23/2009

Partially Proficient

Students performing at the Partially Proficient level have limited recall, recognition and application of basic mathematical concepts, skills, and vocabulary to solve problems involving real world situations.

  • Partially Proficient students understand and perform simple routine numerical operations of whole numbers. The students have limited ability to demonstrate number sense by using place value concepts, fractions and decimals.  Partially Proficient students can compute simple sums and differences of fractions and decimals.  These students have difficulty with determining the appropriate operation for a given situation and with estimating their results.

  • Partially proficient students understand and apply basic concepts of geometry and measurement.  These students demonstrate a basic working knowledge of spatial sense, geometric properties, and geometric relationships.  Partially Proficient students can use appropriate measurement tools accurately to solve simple problems involving perimeter, area, and volume.  These students have a basic understanding of coordinate geometry and lines of symmetry.

  • Partially Proficient students have a basic understanding of how quantities are related to one another and how to represent and analyze those relationships using algebraic concepts.  These students can recognize, describe, extend, and create simple patterns, as well as solve simple problems involving functions.

  • Partially Proficient students have a basic understanding of the concepts and methods of data analysis, probability, and discrete mathematics.  These students can read, interpret and construct simple graphs, tables, and/or charts, but often find it difficult to predict or make an informed decision based on information retrieved from a variety of sources. Partially Proficient students demonstrate limited skills using tools and strategies for representing, organizing, and interpreting data.  These students can solve simple problems involving mean, median, and mode.

  • Partially Proficient students can identify and use basic mathematical terms and apply some reasoning methods to solve simple problems.

Proficient

Students performing at the proficient level demonstrate recall, recognition and application of mathematical concepts, skills, and vocabulary to solve problems involving real world situations.

  • Proficient students understand and perform numerical operations of whole numbers and can use a specified procedure with accuracy. These students demonstrate number sense by using place value concepts, fractions, and decimals. Proficient students can compute sums and differences of fractions and decimals. These students determine the appropriate operation for a given situation and can use estimation appropriately.

  • Proficient students understand and apply concepts of geometry and measurement.  These students demonstrate a working knowledge of spatial sense, geometric properties and geometric relationships.  Proficient students can use appropriate measurement tools accurately to solve problems involving perimeter, area and volume.  These students understand and apply concepts of coordinate geometry as well as identify lines of symmetry.

  • Proficient students demonstrate an understanding how quantities are related to one another and how to represent and analyze those relationships using algebraic concepts.  These students can recognize, describe, extend, and create patterns as well as solve functions for a given variable, including inverse relationships.  Proficient students can understand, name, and apply properties of operations and numbers.

  • Proficient students have an understanding of how to apply the concepts and techniques of data analysis, probability, and discrete mathematics.  These students can read, interpret and construct graphs, tables and/or charts as well as predict or make an informed decision based on information retrieved from a variety of sources. Proficient students demonstrate skills using tools and strategies for representing, organizing, and interpreting data as well as solve problems involving mean, median, and mode.

  • Proficient students use various forms of representation to illustrate steps to a solution and effectively communicate a variety of reasoning methods to solve multi-step problems.  These students can explain steps and procedures for finding solutions as well as check the reasonableness of their results.

Advanced Proficient

Students performing at the Advanced Proficient level clearly and consistently demonstrate the qualities outlined for Proficient performance.  These students clearly and consistently demonstrate thorough conceptual understanding of procedural and analytical skills. In addition, Advanced Proficient students demonstrate the use of abstract thinking and provide explanations that are consistently clear and thorough. These students use both inductive and deductive reasoning to solve non-routine problems as well as consistently demonstrate the ability to abstract relevant information, use multiple strategies and/or reasoning methods, and use various forms of representations to solve complex problems. Advanced Proficient students demonstrate an understanding of the reasonableness of their answers.