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CRT 1 Notes 1 Name ______________________________________________________ Hour _____________ 1.1 Using Differences to Identify Patterns Number Sequence – _____________________________________________ Constant Difference – ___________________________________________ ____________________________________________________ Conjecture – ___________________________________________________ Examples: Find the next three terms of each sequence by using constant differences. a. 12.4, 10.7, 9, 7.3, 5.6, … b. 49, 64, 81, 100, 121, … The third and fourth terms of a sequence are 26 and 40. If the second differences are a constant 4, what are the first five terms of the sequence? Homework: p. 8 # 10-24 1.2 Variables, Expressions, and Equations Variable – _____________________________________________________ Algebraic Expression – __________________________________________ CRT 1 Notes 2 Name ______________________________________________________ Hour _____________ Evaluations – __________________________________________________ _____________________________________________________ Equations – ____________________________________________________ Solution – _____________________________________________________ Examples: 1. Make a table to show the value of the expression 4m – 10 when m is 8, 9, 10, and 11. 2. The cost to rent a set of jet skis is a $20 fee plus $50 per hour. Make a table to show the total cost to rent the skis for 1 hour through 5 hours. Write an equation for the situation. Use guess-and-check to solve the following equations. 3. 19x + 13 = 51 4. 7x – 12 = 44 Homework: p. 16 # 10 – 36 even, 37-39 all CRT 1 Notes 3 Name ______________________________________________________ Hour _____________ 1.3 The Algebraic Order of Operations ______________________________________________________________ ________________ ________________ ________________ ________________ ________________ ________________ Examples: Evaluate each expression. 1. 72 (98) + 12 3. 4 2 2 7 32 5 2. Homework: p. 21 # 18 – 64 even 91 7 6 CRT 1 Notes 4 Name ______________________________________________________ Hour _____________ 2.1 The Real Numbers and Absolute Value Real Numbers Rationals Irrationals Integers Whole Numbers Natural Numbers Natural Numbers – ______________________________________________ Whole Numbers – ______________________________________________ Integers – _____________________________________________________ Rationals – ____________________________________________________ Irrationals – ___________________________________________________ Absolute Value – _______________________________________________ Examples: Use division to write each rational number as a decimal. Indicate whether it is a terminating or repeating decimal. a. 13 40 b. 7 12 c. 5 9 CRT 1 Notes 5 Name ______________________________________________________ Hour _____________ Insert an ordering symbol to make each statement true. a. -3 ___ 6 b. -8.5 ___ -8.6 b. -(8.6 – 1.5) b. 16 c. 4 16 ___ 5 20 c. 72 Evaluate each expression. a. -(-10) Simplify 8 a. Homework: p. 58 # 20-60 even, 61-64 all 2.2-2.3 Adding and Subtracting Real Numbers Walking on a number line Steps: 1. _______________________________________________________ 2. _______________________________________________________ (______________________________________________________) 3. _______________________________________________________ (______________________________________________________) 4. _______________________________________________________ CRT 1 Notes 6 Name ______________________________________________________ Hour _____________ Examples: 1. 3–7 2. -5 + (-8) Homework: Number line worksheet 2.2 More adding and subtracting Rules: _________________________________________________________ _________________________________________________________ Adding Same Sign _________________________________________________________ Adding Opposite Signs _________________________________________________________ Examples: 1. (-7) + (-15) 3. 4 7 15 15 Homework: 2.2-2.3 wkst 2. 5.7 + (-3.2) CRT 1 Notes 7 Name ______________________________________________________ Hour _____________ 2.4 Multiplying and Dividing Real Numbers Rules: ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ ___________________________ = ___________________ Examples: 1. (-15) (2) 2. (-6.1)(-9) 3. 36 4 4. 3.8 19 Homework: p. 78 # 18 – 58 even CRT 1 Notes 8 Name ______________________________________________________ Hour _____________ 2.5 Properties and Mental Computation Commutative Property of Addition For all real numbers a and b: ________________ Commutative Property of Multiplication For all real numbers a and b: ________________ Associative Property of Addition For all real numbers a, b, and c: ___________________ Associative Property of Multiplication For all real numbers a, b, and c: ___________________ Distributive Property For all real numbers a, b, and c: ____________________ ____________________ Examples: Complete each step and name the property used. 1. (36 + 15) + 64 =(15 + ___) + 64 = 15 + (36 + ___) = 15 + ___ = _____ Find the opposite of each expression. 2. x+y Homework: p. 86 # 12-36 even CRT 1 Notes 9 Name ______________________________________________________ Hour _____________ 2.6 Adding and Subtracting Expressions Term – _______________________________________________________ Like Term – ___________________________________________________ Coefficient – __________________________________________________ Constant – ____________________________________________________ Simplify expressions – ___________________________________________ Examples: Simplify. 1. (4y – 5) + (-3y + 2) 2. (a + 9) – (-3a – 7) 3. (7x – 13y) – (8x + 6y) Homework: p. 92 # 22 – 46 even CRT 1 Notes 10 Name ______________________________________________________ Hour _____________ 2.7 Multiplying and Dividing Expressions Examples: Simplify. 1. 8x (-5x – 9) 2. (-3a – 4)(-5) 3. (4a – b + 3) + 2(5a + 2b – 1) 4. 10 x 2 5 5 Homework: p. 101 # 18 – 46 even Name ______________________________________________________ Hour _____________ Monday Labor Day 11 Tuesday Warm-ups for 9/1-9/5 Wednesday Thursday Friday Name ______________________________________________________ Hour _____________ 12 Monday Tuesday Warm-ups for 9/8-9/12 Wednesday Thursday Friday Name ______________________________________________________ Hour _____________ 13 Monday Tuesday Quiz 2.2-2.4 Warm-ups for 9/15-9/19 Wednesday Thursday Friday Name ______________________________________________________ Hour _____________ 14 Monday Tuesday CRT 1A Wednesday Warm-ups for 9/15-9/19 Test 1 Thursday Friday