Created on: September 21, 2007

Website Address: https://www.curriki.org/oer/Grades-7-8--Number-Sense-and-Operations

Mathematics Curriculum Framework

November 2000## Learning Standards

### Number Sense and Operations

for Grades 7-8

#### Learning Standards

Students engage in problem solving, communicating, reasoning, connecting, and representing as they:

#### Exploratory Concepts and Skills

for Grades 7-8 and Single-Subject Courses

November 2000

for Grades 7-8

Understand numbers, ways of representing numbers, relationships among numbers, and number systems | |

Understand meanings of operations and how they relate to one another | |

Compute fluently and make reasonable estimates |

8.N.1 | Compare, order, estimate, and translate among integers, fractions and mixed numbers (i.e., rational numbers), decimals, and percents. |

8.N.2 | Define, compare, order, and apply frequently used irrational numbers, such as ?2 and ?. |

8.N.3 | Use ratios and proportions in the solution of problems, in particular, problems involving unit rates, scale factors, and rate of change. |

8.N.4 | Represent numbers in scientific notation, and use them in calculations and problem situations. |

8.N.5 | Apply number theory concepts, including prime factorization and relatively prime numbers, to the solution of problems. |

8.N.6 | Demonstrate an understanding of absolute value, e.g., |-3| = |3| = 3. |

8.N.7 | Apply the rules of powers and roots to the solution of problems. Extend the Order of Operations to include positive integer exponents and square roots. |

8.N.8 | Demonstrate an understanding of the properties of arithmetic operations on rational numbers. Use the associative, commutative, and distributive properties; properties of the identity and inverse elements (e.g., -7 + 7 = 0; 3/4 x 4/3 = 1); and the notion of closure of a subset of the rational numbers under an operation (e.g., the set of odd integers is closed under multiplication but not under addition). |

8.N.9 | Use the inverse relationships of addition and subtraction, multiplication and division, and squaring and finding square roots to simplify computations and solve problems, e.g. multiplying by 1/2 or 0.5 is the same as dividing by 2. |

8.N.10 | Estimate and compute with fractions (including simplification of fractions), integers, decimals, and percents (including those greater than 100 and less than 1). |

8.N.11 | Determine when an estimate rather than an exact answer is appropriate and apply in problem situations. |

8.N.12 | Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives). |

for Grades 7-8 and Single-Subject Courses

- Investigate the meaning of significant digits.
- Investigate negative integral exponents and their use in scientific and calculator notation.