Math Standards & Proficiencies


NJ Mathematic Standards   |   Core Proficiencies-HSPA 9
Core Proficiencies-HSPA 10   |   Core Proficiencies-HSPA 11

Page 2...Proficiciencies for Algebra & Geometry
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New Jersey Math Standards

  1. All students will develop facility with all types of numbers and will use them to perform standard numerical operations and estimations in a variety of ways.
    (Number and Numerical Operations)
  2. All students will develop spatial sense and the ability to use geometric properties, relationships, and measurement to model, describe and analyze phenomena.
    (Geometry and Measurement).
  3. All students will represent and analyze relationships among variable quantities and solve problems involving patterns, functions, and algebraic concepts and processes.
    (Patterns and Algebra)
  4. All students will develop an understanding of the concepts and techniques of data analysis, probability, and discrete mathematics, and will use them to model situations, solve problems, and analyze and draw appropriate inferences from data.
    (Data Analysis, Probability, and Discrete Mathematics.)
  5. All students will use mathematical processes of problem solving, communication , connections, reasoning representations, and technology to solve problems and communicate mathematical ideas.
    (Mathmatical Processes)

CORE PROFICIENCIES FOR HSPA Prep 9

Students will be able to use:
  1. Numerical Operations
    1. Estimate, approximate, and judge the reasonableness of answers in a variety of problem-solving situations.
    2. Read, write, and round numbers; and recognize place value concepts.
    3. Demonstrate an understanding of primes, factors, and multiples in the solution of problems.
    4. Apply ratio, proportion, and percents in a variety of situations.
    5. Apply order-of-operation rules for calculator and pencil calculations.
  2. Patterns and Functions
    1. Use patterns and relationships to represent and solve problems using a calculator.
    2. Recognize and appreciate the mathematical patterns found in nature, work place, and everyday life.
  3. Data Analysis
    1. Collect, organize, and describe sets of data.
    2. Explain orally and in writing results shown in tabular or graphic form.
    3. Find the probability of a simple event.
    4. Understand, compute, and apply the mean, median, mode, range, and rank.
  4. Measurement and Geometry
    1. Use the appropriate tool and units to estimate and measure distance, area, volume, mass, angles, and temperature.
    2. Visualize and represent two- and three-dimensional geometric figures.
    3. Estimate and find the perimeter and area of irregular polygons.
    4. Calculate the volume of a solid figure.
    5. Understand and apply geometric properties of plane figures, such as lines, quadrilaterals, triangles, angles, and polygons.
    6. Use coordinate geometry to represent relationships.
  5. Fundamentals of Algebra
    1. Set up a first-degree algebraic expression, given its equivalent literal statement and vice versa.
    2. Evaluate basic algebraic expressions.
    3. Solve linear equations.
  6. Problem Solving
    1. Select and use a variety of techniques to analyze and solve real-world and mathematical problems.
    2. Select and apply appropriate tools needed to solve problems.

CORE PROFICIENCIES HSPA Prep 10

Students will be able to use:
  1. Numerical Operations
    1. Estimate, approximate, and judge the reasonableness of answers in a variety of problem-solving situations.
    2. Apply ratio, proportion, and percents in a variety of situations.
    3. Understand real numbers.
  2. Patterns and Functions
    1. Use patterns and functions to represent and solve problems using a calculator.
    2. Determine a rule describing a given set of data.
  3. Data Analysis
    1. Construct and draw inferences from charts, tables, and graphs.
    2. Compare two interpretations for a given display of data with respect to completeness and validity of conclusion.
    3. Determine the probability of a simple event by relative frequency or experimental methods.
  4. Measurement and Geometry
    1. Use coordinate geometry to represent relationships.
    2. Understand transformations and their effects on geometric figures, and apply these ideas informally.
    3. Classify geometric figures in terms of congruence and similarity, and apply these relationships informally.
    4. Apply the Pythagorean Theorem.
  5. Fundamentals of Algebra
    1. Solve equations.
    2. Apply algebraic methods to solve a variety of problems.

CORE PROFICIENCIES FOR HSPA Prep 11

Students will be able to:
  1. Numerical Operations
    1. Estimate, approximate, and judge the reasonableness of answers in a variety of problem-solving situations.
    2. Apply ratio, proportion, and percents in a variety of situations.
    3. Understand and apply real numbers in solving problems.
  2. Patterns and Functions
    1. Use patterns and functions to represent and solve problems using appropriate technology.
    2. Describe a given set of data using a rule, verbal expression, or graph.
    3. Demonstrate an understanding of arithmetic and geometric sequences and series using an intuitive/non-algebraic approach.
  3. Data Analysis
    1. Create and test an argument using displays or tables, given a set of statistics.
    2. Compare displays and interpretations with an eye to possible misuse of statistics.
  4. Measurement and Geometry
    1. Use coordinate geometry to represent relationships.
    2. Select and use geometric models to represent and solve problems.
    3. Estimate and/or find perimeters, areas, and volumes of shapes.
  5. Fundamentals of Algebra
    1. Solve linear inequalities.
    2. Solve a system of linear equations in two variables.
    3. Apply algebraic methods to solve a variety of problems.


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