Patterns, Relations, and Algebra

 

  • 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

 

Standard
Students engage in problem solving, communicating, reasoning, connecting and representing as they:
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.1)
Evaluate simple algebraic expressions for given variable values, e.g., 3a2 – b for a = 3 and b = 7. (8.P.2)
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.3)
Create and use symbolic expressions and relate them to verbal, tabular, and graphical representations (8.P.4)

 

Exploratory Concepts and Skills for Grades 7-8
Patterns, Relations and Algebra
  • 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.
  • Make predictions, conduct experiments, and discuss discrepancies to develop understanding of actual versus predicted outcomes
  • Conduct repetitive experiments (e.g., repeated throwing of three or more dice) and compare the outcomes to predicted probabilities

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