Warm-Up

1. Warm-Up • How do you balance your life? Section 2.5 (10/07/2013) Learning Target • I am learning the properties of algebra and geometry.

3. a = weighted blocks a a

4. Reflexive Property (Copy this) • Let “a” be a real number. • The property states that: • a = a • Example: • 5 = 5

5. a = weighted blocks b = weighted blocks Since the blocks are the same weight to start out with, no weight would change. What would happen to the scale if I were to switch the blocks to different sides? a b

6. Symmetric Properties (copy this down) • Let “a” and “b” be any real number. • The property say: • If a = b, then b = a. • Example: • 5x + 10 = 20 • 20 = 5x + 10

7. What would happen if I were to add an “c” block to the left hand side? a = weighted blocks c b = weighted blocks = weighted blocks a c b

8. Now, without removing any blocks. What can you do to make the scale balance? The scale would tip downward on the left hand side. You can add “c” block to the right hand side. a c b

9. a c c b

10. Addition (copy this down) • Let a, b, and c be any real number. • If a = b, then a + c = b + c • Example: • 2x = 10 • 2x + 5 = 10 + 5

11. What would happen to the scale if I replace two of “a” block with two “b” block? Nothing, since “b” block is equal weight with “a” block. b b a a a b b b

12. Substitution Property (copy this) • Let a, b, and c be any real number. • The property states: • If a = b, then b can replace a in any expression • Example: • Let a = b and 5a = 10 • Then we can say 5a = 5b = 10

13. What would happen if I take 2 “b” blocks away from the right hand side? b b a b b b

14. You can take away 2 “b” blocks on the left hand side. Without adding any blocks, how would you balance the scale? The scale would tip downward on the left hand side since it’s heavier. a b b b

15. a b

16. Subtraction Property (copy this) • Let a, b, and c be real numbers. • The property states that: • If a = b, then a – c = b – c. • Example: • 5x = 20 • 5x – 10 = 20 - 10

17. Let the weight of block “b” and the weight of block “a” be equal. Let the weight of block “b” and the weight of block “c” be equal. Using the substitution property, we didn’t do anything to change the weight. What would happen if replace “b” block with an “a” block? c a b a

18. Transitive Property • Let a, b, and c be real numbers. • The property states: • If a = b and b = c, then a = c • Example: • Let 3x = 5 and let 5 = 2y. • Then 3x = 2y

19. What would happen if I make the left hand side 3 times as heavy? b b b b a

20. It would tilt downward on the left hand side because it’s heavier. a b b b b

21. To balance out the scales, you multiply the weight on the right hand side by 3. b b b b a a a a

22. Multiplication Property (copy this down) • Let a, b, and c be real number. • The property states that: • If a = b, then . • Example: • 5x + 2 = 10

23. What would happen I divide the weight on the left hand side in half?? b b b b a a a a

24. Without adding blocks on the left hand side, what can I do to balance out the scale? It would tilt downward on the right hand side because it’s heavier. b b a a a a

25. To balance out the scale, divide the weight on the right hand side in half. b b a a

26. Division Property • Let “a” and “b” be real numbers. • The property states: • If a = b and c 0, then . • Example:

27. What is the area??? 4 6 3

28. Distributive Property • Let a, b, and c be any real numbers. • The property states: • Example: • 5(2 + 4) = 5(2) + 5(4) b c a

29. Properties of Congruence Reflexive Property: 1) Symmetric Property: 2) Transitive Property: 3)

30. Example: At each step, indicate the properties (congruence or algebraic) that was use. 1) 2) 3) 4) 5)

31. Recap • Properties of Equality (a.k.a. Algebraic Reasoning) • Additional • Subtraction • Multiplication • Division • Reflexive • Transitive • Symmetric • Substitution • Properties of Congruence (a.k.a. Geometric reasoning) • Reflexive • Symmetric • Transitive

32. Reflection • In your own words, what were the learning targets? • On a scale from 1-5 • 1 for not understanding the learning target at all. • 5 for completely understanding the learning target. • Explain