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### DOE Archives

#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.13:
All Students Will Develop An Understanding Of Algebraic Concepts And Processes And Will Use Them To Represent And Analyze Relationships Among Variable Quantities And To Solve Problems

Descriptive Statement: Algebra is a language used to express mathematical relationships. Students need to understand how quantities are related to one another, and how algebra can be used to concisely express and analyze those relationships. Modern technology provides tools for supplementing the traditional focus on algebraic techniques, such as solving equations, with a more visual perspective, with graphs of equations displayed on a screen. Students can then focus on understanding the relationship between the equation and the graph, and on what the graph represents in a real-life situation.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Understand and represent numerical situations using variables, expressions, and number sentences. 2 Represent situations and number patterns with concrete materials, tables, graphs, verbal rules, and number sentences, and translate from one to another. 3 Understand and use properties of operations and numbers. 4 Construct and solve open sentences (example: 3 + ___ = 7) that describe real-life situations.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 8, students:

 5 Understand and use variables, expressions, equations, and inequalities. 6 Represent situations and number patterns with concrete materials, tables, graphs, verbal rules, and standard algebraic notation. 7 Use graphing techniques on a number line to model both absolute value and arithmetic operations. 8 Analyze tables and graphs to identify properties and relationships. 9 Understand and use the rectangular coordinate system. 10 Solve simple linear equations using concrete, informal, and graphical methods, as well as appropriate paper-and-pencil techniques. 11 Explore linear equations through the use of calculators, computers, and other technology. 12 Investigate inequalities and nonlinear equations informally. 13 Draw freehand sketches of, and interpret, graphs which model real phenomena.

Building upon knowledge and skills gained in the preceding grades, by the end of Grade 12, students:

 14 Model and solve problems that involve varying quantities using variables, expressions, equations, inequalities, absolute values, vectors, and matrices. 15 Use tables and graphs as tools to interpret expressions, equations, and inequalities. 16 Develop, explain, use, and analyze procedures for operating on algebraic expressions and matrices. 17 Solve equations and inequalities of varying degrees using graphing calculators and computers as well as appropriate paper-and-pencil techniques. 18 Understand the logic and purposes of algebraic procedures. 19 Interpret algebraic equations and inequalities geometrically, and describe geometric objects algebraically.

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