1-5 Properties of Numbers Aim: How can we identify the properties of operations and use them to solve problems?

2 Warm up 1.True or False? (Explain): = Evaluate: 12 + (-12) + 12 = 3.True or False? (Explain): 7 x (-4) = (-4) x 7 4.Evaluate: 11 x (-4) x (-2) = 5.True or False? (Explain): 3(2+5) = 3 ⋅ 2+3 ⋅ 5 6.Evaluate: 2( ) =

3 Commutative Property of Addition and Multiplication The order in which items are added or multiplied do not effect the answer. Example: = Example: 4 x 2.5 = 2.5 x 4

4 Associative Property of Addition and Multiplication The order in which the same grouped items are added or multiplied do not effect the answer. Example: (5+7) + 9 = 9 + (5+7) Example: (3+2) x 4 = 4 x (3+2)

5 Distributive Property The ability to distribute the factor outside the set of parentheses to each item inside, and then add the results. Example: (8)(2 + 4) = (16) + (32) = 48 Example: (-5)(7 + 3) = (-35) + (-15) = (-50) 5

6 Using Mental Math Example 1: Simplify : = Example 2: Simplify: 5 ⋅ (-2) ⋅ 8 = Example 3: Simplify: (-2.5) ⋅ (-4) ⋅ (-10) =

Think, Turn and Talk (Part One) How can the following expressions be rewritten then evaluated? 13(2 + a) = (5 - b)(-3) = 1.4 ⋅ ⋅ 3 =

Think, Turn and Talk (Part Two) At Six Flags Great Adventures a roller coaster plunges down a vertical drop of 73.4 feet. At the beginning of the drop, the coaster was located at 95.5 feet above the ground. 1. Write an integer that represents this change in height. 2. Write an expression that represents the change in height for the roller coaster during the drop. 3. How high is the roller coaster when it reaches the bottom of the drop?

Think, Turn and Talk (Part Three) At a candy store, a child bought 4 pounds of chocolate at $3.76 per pound, 3 milkshakes at $1.25 each and 5 buckets of popcorn at $2.29 each. What is the total cost for all items purchased? (Hint: Think of how many variables you will need for your equation.)

10 Exit Ticket Error Analysis A student claims that: 7 ⋅ = 7 ⋅ 4 + 5, by the use of the Commutative Property of Addition. What is the error? How can the original equation be rewritten correctly?