Exploring Addition Patterns

Grade Levels: 3 - 5


This lesson provides students with an opportunity to learn and use addition patterns to find sums.


  • Students will use basic addition facts and place-value patterns to add greater numbers.
  • Students will understand and use the Order Property of Addition and the Zero Property of Addition.



  1. Introduce key vocabulary: addition, equal, sum, addends.

  2. Review place value. Write the numbers 70, 530, 4, and 2,691 on the chalkboard in the form of a chart like the one below. Ask students to name which number is in the thousands place, hundreds place, tens place, and ones place.





















2, 691





  1. Have students use mental math to find each sum.

    4 + 3 = (7)

    40 + 30 = (70)

    400 + 300 = (700)

    5 + 7 = (12)

    50 + 70 = (120)

    500 + 700 = (1,200)

    9 + 4 = (13)

    90 + 40 = (130)

    900 + 400 = (1,300)

  2. Discuss the patterns. Students should see the basic addition fact (4 + 3 = 7), and understand that greater sums are similar because the digits on the left are the same. Only the number of zeros to the right varies. (4 tens + 3 tens = 7 tens. 4 hundreds + 3 hundreds = 7 hundreds).

  3. Distribute the guided practice worksheet: Addition Patterns and assist students as they work.

  4. Have students look carefully at problems 4 and 8. Ask:
    • What is the same about the two equations? (They have the same sums.)
    • What is different? (The order of addends is different.)

  5. Help students postulate the Order Property of Addition: changing the order of the addends does not change the sum. Have students look carefully at Exercises 9 and 10. Ask:

    • What would happen if you added 0 ones to 8 ones? (You would still have 8 ones.)
    • What if you added 5 ones to 0 ones? (5 ones)
    • Ask students what effect adding zero has. (None -- the sum is the same as the non-zero addend.)

  6. Help students articulate the Property of Zero when you add zero to any number, that number is the sum.


  • Have students answer the Assessment Questions to gauge their understanding of patterns and properties of addition.
  • Students should be able to:
  • Use addition patterns in finding sums.
  • Recognize place-value patterns and know that basic addition facts can help when adding greater numbers.
  • Demonstrate how to use the Order Property and the Property of Zero.


  • Use the extension worksheet: Identifying Patterns, to build on the ideas presented in this lesson.
  • Distribute the homework worksheet: Patterns of Addition, and have students complete it. You may want to go over the answers as part of a class discussion.
  • Divide students into groups of two. Distribute the enrichment worksheet: Circus Logic, and have partners work together. Discuss the answers as a class. If time permits, challenge students to create their own logic puzzles.
  • Visit Funbrain for more Math games.

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