Lesson Plan: Properties of Operations over the Real Numbers Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to solve problems involving operations and properties of operations on real numbers.


Students will be able to

  • understand and apply the following properties of addition and multiplication of real numbers:
    • closure (𝑎+𝑏 and 𝑎𝑏),
    • commutativity (𝑎+𝑏=𝑏+𝑎 and 𝑎𝑏=𝑏𝑎),
    • associativity ((𝑎+𝑏)+𝑐=𝑎+(𝑏+𝑐) and (𝑎𝑏)𝑐=𝑎(𝑏𝑐)),
    • identity (or neutral) elements (𝑎+0=𝑎 and 𝑎1=𝑎),
    • inverse elements (𝑎𝑎=0 and 𝑎1𝑎=1 for 𝑎0),
  • understand that subtraction and division are neither associative nor commutative.


Students should already be familiar with

  • the set of real numbers.


Students will not cover

  • simplifying the addition, subtraction, multiplication, and division of radical expressions (including rationalizing denominators).

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