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Middle Grades Math: The Distributive Property
by Texas Instruments - Action Consequence, TI-Nspire Navigator Lesson

Published on August 31, 2011

Objectives

  • Students will learn the distributive property of multiplication over addition for real numbers.
  • Students will verify that algebraic expressions involving the distributive property are equivalent both graphically and algebraically.
  • Apply the properties of operations to generate equivalent expressions (CCSS).
  • Identify when two expressions are equivalent (CCSS).
  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients (CCSS).
  • Reason abstractly and quantitatively (CCSSM Mathematical Practice).
  • Look for and make use of structure (CCSSM Mathematical Practice).

Vocabulary

  • Distributive Property of Multiplication over Addition
  • real numbers
  • equivalent expressions
  • coinciding lines

About the Lesson

This lesson involves using the graphs of two lines to create equivalent expressions.
As a result, students will:

  • Change the values of a and b in the second line until the graphs coincide and explain why this shows that they now have equivalent expressions.
  • Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule, i.e. a(x + c) = ax + ac.
  • Change the values of a and c so that the graph a(x + c)matches the graph of one of the form ax + b.
  • Generate several other examples and derive a rule for generating equivalent algebraic expressions using the distributive rule in reverse, i.e. ax + aca(x + c).

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