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Lesson Plan

The Commutative and Associative Properties of Addition by ECSDM


Math, Science & Technology

Grade Levels

Elementary, 2nd Grade, 3rd Grade


  • Addend: the digits in an addition problem
  • Sum: the result of or answer to an addition problem
  • Commutative: the order of the addends is changed, but the sum remains the same.
  • Commutative Property Examples: a + b = b + a
    2 + 3 = 3 + 2
  • Associative: grouping the addends differently does not change the sum (we use parentheses to illustrate the grouping)
  • Associative Property Examples: a + (b + c) = (a + b) + c
    1 + (2 + 3) = (1 + 2) + 3


The assessment of this lesson could be teacher observation as well as student demonstration of skills: interactively on SMART board and written work using included pages.

  • Commutative Property.doc
  • Associative Property.doc
  • Commutative and Associative Properties.doc
  • Description

    The properties of addition are important in understanding the types of changes that can be made in an equation without changing the equality or balance of the equation.

    The Commutative and Associative properties are two of the basic properties used in solving basic algebraic equations with real numbers.

    This lesson will engage the students by using the SMART Board and hands-on manipulatives to demonstrate understanding of the Commutative and Associative Properties of addition.
    (I use this lesson in my Special Education classroom.)


    Learning Wave
    Math League


    The time to complete this lesson will vary depending upon students' abilities. The average time should be about 60-minutes. This will include students working at their desks as well as hands-on time at the SMART Board. A follow- up lesson using the SMART Board interactive slides would be beneficial the following day to help assess the students' retention of the lesson. You may also choose to visit one of the linked sites to illustrate and reinforce the lesson. This will vary the time stated above.

    Learning Objectives

    Students will use properties and strategies to add.
    Students will demonstrate understanding of two of the basic properties of addition.


    • SMART Board set-up
    • colored chips
    • paper and pencil
    • internet connection
    • student math journals
  • properties.pdf
  • Properties[1].notebook
  • Step-by-Step Procedure

      1. Explain to the students that they will be copying notes from the SMART Board and using the colored chips to demonstrate understanding of the concepts. Let them know that they may also be called up to the SMART Board to demonstrate in front of the class their understanding of the lesson using the interactive slides.
      2. Allow the students to verbalize possible definitions of the commutative property.
      3. After clicking to reveal the definition (by touching the screen where it should be), have the students copy the title commutative property, it's definition, and the pictorial representation of the problem into their math journals.
      4. Do some examples with the chips on various students' desks around the room and have all students observe. Give some examples for the students to do using their colored chips. Randomly check for correctly illustrated problems.
      5. Move to the next slide when you feel the class is ready.
      6. Follow the directions on each slide to engage the students in the lesson. Pick students to come up to the SMART Board and demonstrate use of the property.
      7. Navigate forward or backward using the arrow buttons at the bottom of each slide, to review or advance with the lesson.
      8. When you finish one property, you can stop the lesson and assess with the specific property worksheet, or go on to the next property. Decide this based on student participation and attention to the lesson.
      9. At the end of the interactive lesson(s), you can use the included assessment worksheets, design your own, or pull assessments from the student textbook.


      Once you are finished with the lesson, the interactive pages can become a math center lesson for your students to use either on the SMART Board or at individual computers.

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