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Board work

Board work

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

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

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

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

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

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

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

Properties of Operations

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

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

Conjectures And Counterexamples

Example

Example Solution:

Your Turn! Got It? pg. 369 c.

Using the Properties of Operations

Example

Example Solution:

Your Turn! Got It? pg. 369 d.

Simplifying Algebraic Expressions

Examples

Examples

Your Turn! Got It? pg. 370 e.

Homework GP pg.370 (All) IP pg.371-372 (1-10, 13)

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 =