New Jersey Core Curriculum Content Standards

May 1996

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**Mathematics Standards And Progress Indicators**

**Standard 4.6:**

All Students Will Develop Number Sense And An Ability To Represent Numbers In A Variety Of Forms And Use Numbers In Diverse Situations

All Students Will Develop Number Sense And An Ability To Represent Numbers In A Variety Of Forms And Use Numbers In Diverse Situations

**Descriptive Statement:** Number sense is defined as an intuitive
feel for numbers and a common sense approach to using them. It is a comfort
with what numbers represent, coming from investigating their characteristics
and using them in diverse situations. It involves an understanding of
how different types of numbers, such as fractions and decimals, are related
to each other, and how they can best be used to describe a particular
situation. Number sense is an attribute of all successful users of mathematics.

**Cumulative Progress Indicators**

By the end of Grade 4, students:

1. |
Use real-life experiences, physical materials, and technology to construct meanings for whole numbers, commonly used fractions, and decimals. |

2. |
Develop an understanding of place value concepts and numeration in relationship to counting and grouping. |

3. |
See patterns in number sequences, and use pattern-based thinking to understand extensions of the number system. |

4. |
Develop a sense of the magnitudes of whole numbers, commonly used fractions, and decimals. |

5. |
Understand the various uses of numbers including counting, measuring, labeling, and indicating location. |

6. |
Count and perform simple computations with money. |

7. |
Use models to relate whole numbers, commonly used fractions, and decimals to each other, and to represent equivalent forms of the same number. |

8. |
Compare and order whole numbers, commonly used fractions, and decimals. |

9. |
Explore real-life settings which give rise to negative numbers. |

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

10. |
Understand money notations, count and compute money, and recognize the decimal nature of United States currency. |

11. |
Extend their understanding of the number system by constructing meanings for integers, rational numbers, percents, exponents, roots, absolute values, and numbers represented in scientific notation. |

12. |
Develop number sense necessary for estimation. |

13. |
Expand the sense of magnitudes of different number types to include integers, rational numbers, and roots. |

14. |
Understand and apply ratios, proportions, and percents in a variety of situations. |

15. |
Develop and use order relations for integers and rational numbers. |

16. |
Recognize and describe patterns in both finite and infinite number sequences involving whole numbers, rational numbers, and integers. |

17. |
Develop and apply number theory concepts, such as primes, factors, and multiples, in real-world and mathematical problem situations. |

18. |
Investigate the relationships among fractions, decimals, and percents, and use all of them appropriately. |

19. |
Identify, derive, and compare properties of numbers. |

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

20. |
Extend their understanding of the number system to include real numbers and an awareness of other number systems. |

21. |
Develop conjectures and informal proofs of properties of number systems and sets of numbers. |

22. |
Extend their intuitive grasp of number relationships, uses, and interpretations, and develop an ability to work with rational and irrational numbers. |

23. |
Explore a variety of infinite sequences and informally evaluate their limits. |

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