Transcript Lesson 1
1-4 6th grade math Addition Properties Objective • To use addition properties and mental math strategies to compute mentally • Why? To help you add mentally and get a rounded estimate to an addition problem. California State Standards AF 1.3: Apply … the commutative, associative properties to evaluate expressions … MR 2.0: Use strategies, skills, and concepts in finding solutions. Vocabulary • Mental Math - The process of producing an exact answer without pencil and paper or other computational aids. • Commutative Property – The order in which numbers are added does NOT affect the sum. (Just which the order.) • 8 + 12 = 12 + 8 • Associative Property – The way in which addends are grouped does NOT affect the sum. (Keep the same order, but switch around the parentheses.) • 7 + (11 + 5) = (7 + 11) + 5 • Identity Property – The sum of any number and zero (0) is that number. • 45 + 0 = 45 • • • Vocabulary Compatible Numbers Method – Group together numbers that are easily computed mentally • 76 + 68 + 14 = (76 + 14) + 68 = 90 + 68 = 158 Break-Apart Method – Break-apart numbers to have easier numbers to work with. • 128 + 64 = (128 + 60) + 4 = 188 + 4 = 192 Compensation Method – Change one number to make it easy to use. Then change the other number to compensate (adjust). Imagine a balance. • 173 + 16 = (173 + 7) + (16 – 7) = 180 + 9 = 189 How to Use Addition Properties 1) Decide whether to use the Compatible Number Method, or Break-Apart Method or Compensation Method 2) Apply the rules to solve either one. 3) Check your work. Choose a strategy and compute mentally. A) 54 + 29 Use the break-apart strategy. = (54 + 20) + 9 = 74 + 9 = 83 B) 41 + 55 + 9 Use the compatible numbers strategy. = (41 + 9) + 55 = 50 + 55 = 105 Try It! Choose a strategy and compute mentally. 1) 28 + 74 + 32 2) 325 + 225 3) 88 + 64 4) 124 - 79 1) Compatible Numbers = (28 + 32) + 74 = 60 + 74 = 134 2) Compensation Method = (325 – 5) + (225 + 5) = 320 + 230 = 550 3) Break-Apart Method = (88 + 60) + 4 = 148 + 4 = 152 4) Compatible Numbers = (124 - 4) – (79 – 4) = 120 – 75 = 45 Objective Review • To use addition properties and mental math strategies to compute mentally • Why? You can now add mentally and get a rounded estimate to an addition problem. Addition properties and mental math strategies can be used to find exact answers without using pencil and paper. Independent Practice • Complete problems 617 • Copy original problem first. • Show all work! • If time, complete Mixed Review: 18-23 • If still more time, work on Accelerated Math.