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New Jersey Assessment of Skills and Knowledge (NJ ASK)
Performance Level Descriptors
Mathematics
Grade 4
Proficient
The student performing at the proficient level demonstrates evidence of conceptual understanding, and of procedural and analytic skills. The student applies mathematical skills and knowledge to theoretical and real-world situations. In addition, the student communicates the required skills and makes connections within and among the mathematical content areas.
The student at this level understands of basic arithmetic operations – an understanding sufficient for problem solving in practical situations. The student understands the connections between common fractions, decimals, and applies this understanding to other mathematical topics.
The student understands and applies basic geometric properties and spatial relationships; applies the principles of similarity, symmetry, and coordinate geometry; interprets data and graphs; determines probabilities; applies the concepts and methods of discrete mathematics, and uses basic algebraic concepts and processes.
Advanced Proficient
The student performing at the advanced level demonstrates clear and consistent evidence of thorough conceptual understanding, and of procedural and analytic skills. The student consistently demonstrates the qualities outlined for proficient performance. In addition, the student at the advanced level demonstrates the use of abstract thinking and provides explanations that are consistently clear and thorough.
Students performing at this level use both inductive and deductive reasoning. They continue to develop more formal and abstract notions of problem solving, communication, mathematical connections and reasoning, and are able to demonstrate this by solving a wider range of problems and by connecting mathematics to a greater variety of situations in other content areas and in life.
