Properties  Pages  Lesson 1-6

Essential Question  What properties do I need to understand in order to simplify and evaluate algebraic expressions?

Definitions of the Four Properties: (p 28)  Commutative Property- property that states that two or more numbers can be added or multiplied in any order without changing the sum or product  Associative Property- property that states that for all real numbers the sum/product is always the same regardless of their grouping  Identity Property- property that states that the product of 1 and any number is that number and that the sum of zero and any number is that number  Distributive Property- property that states if you multiply a sum by a number, you will get the same result if you multiply each addend by that number and then add the products.

Property Foldable pg. 28  Fold and label Cut your paper so it looks like the diagram below.  When you cut your paper it should have 4 flaps.  As we go through the notes for today, write down the information about each property under that flap. Commutative Property Associative Property Identity Property Distributive Property

Commutative Property of Addition and Multiplication p. 28 Addition: The order of adding does not change the sum. Ex: = = Order doesn’t matter!!!

Commutative Property of Addition and Multiplication p. 28 Multiplication: The order of Multiplying does not change the product. Ex: 3 x 9 = 9 x 3 4 x 1 = 1 x 4 Order doesn’t matter!!!

Commutative Property Brain-Pop  Commutative- the numbers are moving (like commuting to school- same mileage either way)  1 fact about the commutative property:

Associative Property of Addition and Multiplication p. 28 Addition: Grouping numbers differently does not change the sum. Ex: 2 + ( 3 + 4) = ( 2 + 3) + 4 (5 + 1) + 9 = 5 + (1 + 9) Groups don’t matter!!!

Associative Property of Addition and Multiplication p. 28 Multiplication: Grouping numbers differently does not change the Product. Ex: 2 ( 3 x 4) = ( 2 x 3) x 4 (5 x 1) x 9 = 5(1 x 9) Groups don’t matter!!! HINT: A number right outside a parenthesis is a math short-cut for saying multiply!

Associative Property Brain Pop  Associative- parentheses change what group the numbers are a part of (like one part of the day you are friends with one group and the other part of the day you are friends with a different group)  Write down 1 fact about the associative property.

Identity Properties Addition: Adding 0 to a number does not change its value. Ex: = = 17 It’s still the same!

Identity Properties Multiplication: Multiplyind a number by 1 does not change its value. Ex: 2 x 1 = 2 1 x 17 = 17 It’s still the same!

Practice Tell which property is represented. A. 7  1 = 7 B = C. (5  1)  2 = 5  (1  2) One of the factors is 1. Identity Property The order of the numbers is switched. Commutative Property The numbers are regrouped. Associative Property

Used when multiplication occurs upon a parenthesis. Multiply everything inside by the coefficient. (The coefficient is the number outside.) Ex. 2( 3 + 4) = = 14 5(10 – 2) = 50 – 10 = 40 YOU MUST BE FAIR! Distributive Property

Distributive Property Brain-Pop  Write down 1 fact about the distributive property.

Practice Together… Tell which property is represented  1 = ( ) + 5 = 12 + (14 + 5) 3. 2  16 = 16  ( 3+ 4) = = 14

Discovery School Video Clip-Properties 9EBD-7DE195A052B2&blnFromSearch=1&productcode=US 9EBD-7DE195A052B2&blnFromSearch=1&productcode=US

Closing  List each property that we have discussed and write down a trick to help you remember that property. Associative Commutative Identity Distributive