Additionproperties.pp
- 2. Three Properties of Addition 1. Commutative 2. Associative 3. Identity
- 3. The Commutative Property –The word commutative comes from the verb “to commute.” • Commuting means changing, replacing, or exchanging –People who travel back and forth to work are called commuters. • Traffic Reports given during rush hours are also called commuter reports.
- 4. Here are two families of commuters. Commuter A Commuter B Commuter A Commuter B Commuter A & Commuter B changed lanes. Remember… commute means to change.
- 5. Here is another example…
- 6. Think of this hypothetical situation: Every day you ride your bike to school. The distance from home to school is 2 miles. The distance from school to home is also 2 miles. How do we know this?
- 7. Home School The distance from Home to School is the same as the distance from school to home. Home + School = School + Home H + S = S + H A + B = B + A
- 8. The Commutative Property A + B = B + A
- 9. Three Properties of Addition 1. Commutative 2. Associative 3. Identity
- 10. The Associative Property –The word associative comes from the verb “to associate.” • Associate means connected, joined, or related –People who work together are called associates. • They are joined together by business, and they do talk to one another.
- 11. Let’s look at another example: Three people work together. Associate B needs to call Associates A and C to share some news. Does it matter who he calls first?
- 12. A C B Here are three associates. B calls A first He calls C last If he called C first, then called A, would it have made a difference? NO!
- 13. (The Role of Parentheses) • In math, we use parentheses to show groups. • In the order of operations, the numbers and operations in parentheses are done first. (PEMDAS) So….
- 14. The Associative Property (A + B) + C = A + (B + C) A C B A C B THEN THEN The parentheses identify which two associates talked first.
- 15. Three Properties of Addition 1. Commutative 2. Associative 3. Identity
- 16. The Identity Property of Addition I am me! You cannot change My identity!
- 17. Zero is the only number you can add to something and see no change.
- 18. Identity Property of Addition A + 0 = A + 0 =
- 19. Let’s practice ! Look at the problem. Identify which property it represents.
- 20. (9 + 8) + 7 = 9 + (8 + 7) The Associative Property of Addition It is the only addition property that has parentheses.
- 21. 12 + 0 = 12 The Identity Property of Addition It is the only addition property that has two addends and one of them is a zero.
- 22. 9 + 7 = 7 + 9 The Commutative Property of Addition It is the only addition property that has numbers that change places.
- 23. 4 + 6 = 6 + 4 The Commutative Property of Addition Numbers change places.
- 24. 3 + 0 = 3 The Identity Property of Addition See the zero?
- 25. (4 + 3) + 2 = 4 + (3 + 2) The Associative Property of Addition It has parentheses!
- 26. a + 0 = a The Identity Property of Addition Zero!
- 27. a + b = b + a The Commutative Property of Addition Moving numbers!
- 28. A (a + b) + c = a + (b + c) The Associative Property of Addition Parentheses! C B