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Understanding Commutative and Associative Properties in Mathematics

This lesson enables students to recognize and apply the commutative and associative properties, along with the properties of equality. The commutative property indicates that the order of addition and multiplication does not affect the result, while the associative property shows that the grouping of numbers can change without influencing the outcome. Through various examples and participation opportunities, students will enhance their understanding of these foundational concepts in algebra. Activities include identifying and justifying properties using mathematical expressions.

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Understanding Commutative and Associative Properties in Mathematics

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  1. ObjectiveThe student will be able to: recognize and use the commutative and associative properties and the properties of equality. SOL: A.4b Designed by Skip Tyler, Varina High School

  2. Commutative Property Commutative means that the order does not make any difference. a + b = b + a a • b = b • a Examples 4 + 5 = 5 + 4 2 • 3 = 3 • 2 The commutative property does not work for subtraction or division.

  3. Please select a Team. • Boys • Girls

  4. Associative Property Associative means that the grouping does not make any difference. (a + b) + c = a + (b + c) (ab) c = a (bc) Examples (1 + 2) + 3 = 1 + (2 + 3) (2 • 3) • 4 = 2 • (3 • 4) The associative property does not work for subtraction or division.

  5. Name the property1) 5a + (6 + 2a) = 5a + (2a + 6) commutative (switching order) 2) 5a + (2a + 6) = (5a + 2a) + 6 associative (switching groups) 3) 2(3 + a) = 6 + 2a distributive

  6. Which property would justify rewriting the following expression without parentheses? 3(2x + 5y) • Associative property of multiplication • Distributive property • Addition property of zero • Commutative property of multiplication

  7. Which property would justify the following statement? 8x + 4 = 4 + 8x • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  8. Which property would justify the following statement?8 + (2 + 6) = (8 + 2) + 6 • Associative property of addition • Distributive property • Addition property of zero • Commutative property of addition

  9. Team Scores

  10. Participant Scores

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