1. Properties of Numbers; Operations with Integers Presented by Mr. Laws 8 th Grade Math, JCMS

2. Essential Question:  How can the operations of integers and algebraic expressions be associated to the properties of numbers?

3. Properties of Numbers Commutative Property a + b = b + a a x b = b x a 8 +2 = 2 + 8 6 x 4 = 4 x 6 Associative Property a + (b + c) = (a + b) +c a x (b x c) = (a x b) x c 2 + (4+6) = (2 + 4) + 6 5 x (6 x 4) = (5 x 6) x 4 Distributive Property a(b + c) = ab + ac a(b – c) = ab - ac 3 (2 + 4) = 3(2) + 3(4) 3 (6 – 2) = 3(6) – 3 (2) Identity Propertya + 0 = a a x 1 = a 4 + 0 = 4 5 x 1 = 5

4. Algebraic Expression  What is a algebraic expression? It contains a variable, a number and at least one operation symbol. n + 5 or 5 – x When you evaluate an expression, you are finding the numerical value.

5. Orders of Operation  What is the orders of operation? A familiar acronym: Please Excuse My Dear Aunt Sally In Math we call it PEMDAS 1.Parenthesis 2.Exponents 3.Multiplications 4.Division 5.Addition 6.Subtraction.

6. Key Ideas to Remember  Do all operations within grouping symbol first; start with the innermost grouping symbols.  Evaluate all powers before other operations.  Multiply and divide in order from left to right.  Add and subtract in order from left to right.

7. For example  Evaluate the following expression.

8. Evaluate Algebraic Expressions  Sometimes you will have to evaluate algebraic expression:  Example: Evaluate each expression if a=5, b=4, and c=8.

9. Absolute Value  The absolute value of a number is the distance the number is from 0.  The absolute value of a number is always positive or zero.  For Example: Both absolute values are 4 units away from zero.

10. Absolute Value Expressions  Evaluate each expression:  Evaluate ea. expression if a= -5 and b = 3.

11. Questions and Review  Write at least four questions pertaining to this lesson.  What did you learn in the lesson?  What do you still need to learn in this lesson?  What are some important things to remember about this lesson?