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#### New Jersey Core Curriculum Content Standards

May 1996

Mathematics Standards And Progress Indicators
Standard 4.14:
All Students Will Apply The Concepts And Methods Of Discrete Mathematics To Model And Explore A Variety Of Practical Situations.

Descriptive Statement: Discrete mathematics is the branch of mathematics that deals with arrangements of distinct objects. It includes a wide variety of topics and techniques that arise in everyday life, such as how to find the best route from one city to another, where the objects are cities arranged on a map. It also includes how to count the number of different combinations of toppings for pizzas, how best to schedule a list of tasks to be done, and how computers store and retrieve arrangements of information on a screen. Discrete mathematics is the mathematics used by decision-makers in our society, from workers in government to those in health care, transportation, and telecommunications. Its various applications help students see the relevance of mathematics in the real world.

Cumulative Progress Indicators

By the end of Grade 4, students:

 1 Explore a variety of puzzles, games, and counting problems 2 Use networks and tree diagrams to represent everyday situations. 3 Identify and investigate sequences and patterns found in nature, art, and music. 4 Investigate ways to represent and classify data according to attributes, such as shape or color, and relationships, and discuss the purpose and usefulness of such classification. 5 Follow, devise, and describe practical lists of instructions.

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

 6 Use systematic listing, counting, and reasoning in a variety of different contexts. 7 Recognize common discrete mathematical models, explore their properties, and design them for specific situations. 8 Experiment with iterative and recursive processes, with the aid of calculators and computers. 9 Explore methods for storing, processing, and communicating information. 10 Devise, describe, and test algorithms for solving optimization and search problems.

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

 11 Understand the basic principles of iteration, recursion, and mathematical induction. 12 Use basic principles to solve combinatorial and algorithmic problems. 13 Use discrete models to represent and solve problems. 14 Analyze iterative processes with the aid of calculators and computers. 15 Apply discrete methods to storing, processing, and communicating information. 16 Apply discrete methods to problems of voting, apportionment, and allocations, and use fundamental strategies of optimization to solve problems.

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