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New Jersey Core Curriculum Content Standards

May 1996

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All Students Will Understand, Select, And Apply Various Methods Of Performing Numerical Operations

**Descriptive Statement:** Numerical operations are an essential part
of the mathematics curriculum. Students must be able to select and apply
various computational methods, including mental math, estimation, paper-and-pencil
techniques, and the use of calculators. Students must understand how to
add, subtract, multiply, and divide whole numbers, fractions, and others
kinds of numbers. With calculators that perform these operations quickly
and accurately, however, the instructional emphasis now should be on understanding
the meanings and uses of the operations, and on estimation and mental
skills, rather than solely on developing paper-and-pencil skills.

**Cumulative Progress Indicators**

By the end of Grade 4, students:

1. |
Develop meaning for the four basic arithmetic operations by modeling and discussing a variety of problems. |

2. |
Develop proficiency with and memorize basic number facts using a variety of fact strategies (such as "counting on" and "doubles"). |

3. |
Construct, use, and explain procedures for performing whole number calculations in the various methods of computation. |

4. |
Use models to explore operations with fractions and decimals. |

5. |
Use a variety of mental computation and estimation techniques. |

6. |
Select and use appropriate computational methods from mental math, estimation, paper- and-pencil, and calculator methods, and check the reasonableness of results. |

7. |
Understand and use relationships among operations and properties of operations. |

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicator 6 above, by the end of Grade 8, students:

8. |
Extend their understanding and use of arithmetic operations to fractions, decimals, integers, and rational numbers. |

9. |
Extend their understanding of basic arithmetic operations on whole numbers to include powers and roots. |

10. |
Develop, apply, and explain procedures for computation and estimation with whole numbers, fractions, decimals, integers, and rational numbers. |

11. |
Develop, apply, and explain methods for solving problems involving proportions and percents. |

12. |
Understand and apply the standard algebraic order of operations. |

Building upon knowledge and skills gained in the preceding grades, and demonstrating continued progress in Indicator 6 above, by the end of Grade 12, students:

13. |
Extend their understanding and use of operations to real numbers and algebraic procedures. |

14. |
Develop, apply, and explain methods for solving problems involving factorials, exponents, and matrices. |

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