1. Board work

2. Board work

3. Lesson 3: Properties of Operations
Chapter 5
Lesson 3: Properties of Operations

4. How can you use numbers and symbols to represent mathematical ideas?
Essential question!
How can you use numbers and symbols to represent mathematical ideas?

5. Today you will Learn… How to identify properties of operations
How to determine if conjectures are true or false and provide counterexamples for false conjectures
How to use properties to simplify algebraic expressions

6. Vocabulary Property: a statement that is true for any number
Commutative Property: the order in which numbers are added or multiplied does not change the sum or product

7. Vocabulary
Associative Property: the way in which numbers are grouped when they are added or multiplied does not change the sum or product
Additive Identity Property: when 0 is added to any number, the sum is the number

8. Vocabulary
Multiplicative Identity Property: when any # is multiplied by 1, the product is the #
Multiplicative Property of Zero: when any # is multiplied by 0, the product is 0

9. Vocabulary Conjecture: a statement that has not been proved
So it may or may not be true then.
Counterexample: an example that shows that a conjecture is false

10. Properties of Operations

11. Examples Name the property shown by each of the following statements:
2 · (5 · n) = (2 · 5) · n
(3 · m) · 2 = 2 · (3 · m)
4 + 0 = 4
Associative Property of Multiplication
Commutative Property of Multiplication
Additive Identity Property

12. Your Turn!
Got It?
pg. 368
a., b.

13. Conjectures And Counterexamples

14. Example

15. Example
Solution:

16. Your Turn!
Got It?
pg. 369 c.

17. Using the Properties of Operations

18. Example

19. Example
Solution:

20. Your Turn!
Got It?
pg. 369 d.

21. Simplifying Algebraic Expressions

22. Examples

23. Examples

24. Your Turn!
Got It?
pg. 370 e.

25. Homework
GP pg.370 (All)
IP pg (1-10, 13)

26. T.O.D. (Algebraic ExpressionS)
Evaluate the following algebraic expressions for x = 2, y = 3, and z = -5.
x + y – z =
xz + y2 =
3x2 + 4y2 =
z2 – 2xy =