Created on: September 21, 2007

Website Address: https://www.curriki.org/oer/Grades-7-8--Patterns-Relations-and-Algebra

Mathematics Curriculum Framework

November 2000## Learning Standards by Strand

### Patterns, Relations, and Algebra

for Grades 7-8

#### Learning Standards

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

#### Exploratory Concepts and Skill

for Grades 7-8 and Single-Subject Courses

November 2000

for Grades 7-8

Understand patterns, relations, and functions | |

Represent and analyze mathematical situations and structures using algebraic symbols | |

Use mathematical models to represent and understand quantitative relationships | |

Analyze change in various contexts |

8.P.1 | Extend, represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic expressions. Include arithmetic and geometric progressions, e.g., compounding. |

8.P.2 | Evaluate simple algebraic expressions for given variable values, e.g., 3a2 - b for a = 3 and b = 7. |

8.P.3 | Demonstrate an understanding of the identity (-x)(-y) = xy. Use this identity to simplify algebraic expressions, e.g., (-2)(-x+2) = 2x - 4. |

8.P.4 | Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations. |

8.P.5 | Identify the slope of a line as a measure of its steepness and as a constant rate of change from its table of values, equation, or graph. Apply the concept of slope to the solution of problems. |

8.P.6 | Identify the roles of variables within an equation, e.g., y = mx + b, expressing y as a function of x with parameters m and b. |

8.P.7 | Set up and solve linear equations and inequalities with one or two variables, using algebraic methods, models, and/or graphs. |

8.P.8 | Explain and analyze-both quantitatively and qualitatively, using pictures, graphs, charts, or equations-how a change in one variable results in a change in another variable in functional relationships, e.g., C = ?d, A = ?r^{2} (A as a function of r), Arectangle = lw (Arectangle as a function of l and w). |

8.P.9 | Use linear equations to model and analyze problems involving proportional relationships. Use technology as appropriate. |

8.P.10 | Use tables and graphs to represent and compare linear growth patterns. In particular, compare rates of change and x- and y-intercepts of different linear patterns. |

for Grades 7-8 and Single-Subject Courses

- Describe, complete, extend, analyze, generalize, and create a wide variety of patterns, including iterative and recursive (e.g., Pascal's triangle), and linear functional relationships.
- Use tables, graphs, and appropriate technology to explore quadratic and exponential growth patterns.
- Investigate the use of systems of equations, tables, and graphs to represent mathematical relationships.
- Identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations.