Algebra I: Lesson Plan * 8/25/2006

• Quickstart p.65 #47, 51
• Chapter 1 Test
• FCAT Practice: Reading Comprehension p.71: 1 - 9
  
• Lesson
  Chapter 2: Solving Equations
  (2-1) Solving One step equations
  
  1. Check Skills You'll Need p.74: 1 - 8
  2. Solving Equations Using Addition and Subtraction
     
     • Example 1 Using the Addition Property of Equality and Check Understanding #1
       
     • Example 2 Using the Subtraction Property of Equality and Check Understanding #2
     • Real-World Problem Solving with the Addition and Subtraction Properties of Equalities and Check Understanding #3
       
• HW p.77 - 80 # 1 - 20 x 3's, 57, 60, 69
  

PreCalculus: Lesson Plan * 8/25/2006

• Quickstart p.322 #121 - 124
• Lesson
  (4.5) Graphs of Sine and Cosine Functions p.323
  
  1. Complete a table of values for y = sin(x) and y = cos(x) using
     -2π, -3π/2, -π, -π/2, 0, π/6 (sine only), π/3 (cosine only) π/2, π, 3π/2, 2π as x values.
  2. Graph the sine and cosine functions using the table of values.
  3. Determine Max, min, and intercepts for sine and cosine functions
  4. Period for y = sin(x) and y = cos(x) is 2π
  5. y = sin(x) and y = cos(x) are a π/2 horizontal translation of each other so we get the cofunction relationships listed at the bottom of p.305
  6. Simplify Radicals Practice (Block I only)
     √27/√81 = √3
     √(25/4) = 5/2
     √(50/9) = 5√2/3
     √72/√50 = 6/5
     √75 - 4√75 = -15√3
     
• HW
  Read Section 4.5 - Graph of Sine and Cosine
  Complete notes for the section using the Student Success Organizer
  

PreCalculus: Lesson Plan * 8/23/2006

• Quickstart p.312 #66
• Quiz - (4.3) Right Angle Trig
  p.310 - 313 #4, 14, 20, 34, 44, 50, 58, 64
  
• Lesson
  (4.4) Trigonometric Functions of Any Angle
• HW Read Lesson p.314 - 315
  p. 320 - 321 #5 - 105 x 5's
  

Algebra I: Lesson Plan * 8/23/2006

• Quickstart FCAT Practice 1-4 and 1-5
• Lesson
  (1-8) Properties of Real Numbers
  
  1. Commutative (Moving) Property of + and x
     a + b = b + a
     2 + 3 = 3 + 2
     
     ab = ba
     (2)(3) = (3)(2)
  2. Associative (Grouping) Property of + and x
     (a + b) + c = a + (b + c)
     (2 + 3) + 5 = 2 + (3 + 5)
     
     (ab)c = a(bc)
     (2*3)5 = 2(3*5)
  3. Identity (who you are) Property of + and x
     a + 0 = a
     3 + 0 = 3
     
     a*1 = a
     3*1 = 3
     
  4. Inverse (opposite) Property of + and x
     a + (-a) = 0
     3 + -3 = 0
     
     a * (1/a) = 1
     3 * (1/3) = 1
     
  5. We use properties, definitions, or rules to justify our steps. This is called deductive reasoning.
     
• Checkpoint Quiz #2 p.58 # 1 - 10 with Quickstarts
  
• HW p.56 - 58 # 3 - 45 x 3's

Chapter 1 Test Friday, August 25
Omit Lesson 1-9: Graphing Data on the Coordinate Plane

PreCalculus: Lesson Plan * 8/22/2006

• Quickstart p.313 #81 - 88
• Lesson
  (4.3) Right Angle Trigonometry (cont.)
  
  1. Proving Trig Identities
     
  2. Using Trig Identities
     Example: If θ is an acute angle such that cosθ = 0.3, then find the following
     a) sinθ
     Solution: Use the Pythagorean Identity (sinθ)^2 + (cosθ)^2 = 1
     (sinθ)^2 + (0.3)^2 = 1
     (sinθ)^2 = 1 - (3/10)^2
     (sinθ)^2 = 1 - (9/100)
     (sinθ)^2 = 91/100
     sinθ = √91/10
     b) tanθ
     Solution: Use the quotient identity tanθ = sinθ/cosθ
     c) cotθ
     Solution: Use the reciprocal identity cotθ = 1/tanθ
     d) secθ
     Solution: Use the reciprocal identity secθ = 1/cosθ
     e) cscθ
     Solution: Use the reciprocal identity cscθ = 1/sinθ
     
  3. Applications with Right Triangles
     Example: If the sun is 30° up from the horizon and shining on a tree forming a 50 foot shadow, how tall is the tree?
     Solution: Draw a picture
     h/50 = tan30°
     h = 50 tan30°
     h = 50(√3/3) ≈ 28.82 feet
     
  4. Evaluating Trig Functions with a calculator
     Make sure your calculator is in the correct mode, radians or degrees, when calculating trig values
     
• HW p.310 - 313 21 - 63 x 3's
  

Algebra I: Lesson Plan * 8/22/2006

• Quickstart: p.28 - 29 #39, 41, 78
  
• Classwork: Workbook p. 7 - 12 x 5's
  
• Lesson:
  (1-7) Distributive Property
  
  1. What is the distributive property?
  2. Simplifying an Expression
     Example: 3(4m - 7)
     Solution: 3(4m - 7) = 3(4m) - 3(7) = 12m - 21
     Using the multiplication property of -1
  3. Terms, like terms, coefficient
  4. Writing an expression
  5. Combining Like terms
• HW: p.50 - 51 #1 - 85 x 5's
  

PreCalculus: Lesson Plan * 8/21/2006

• Quickstart p.300 - 301 #3, 7, 15, 25, 33, 39, 51, 59
  
• Unit Circle Quiz
• Lesson
  (4.3) Right Angle Trigonometry
  
  1. Definition of six trig functions (p.303)SOH CAH TOA
     sin θ = opp / hyp
     cos θ = adj / hyp
     tan θ = opp / adj
     csc θ = hyp / opp
     sec θ = hyp / adj
     cot θ = adj / opp
  2. Unit Circle coordinates
     Where did the coordinates on the Unit Circle come from?
     • Let's start with 45 ° = π/4
       If we draw a right isosceles triangle, as above, and make one of the legs have a measurement of 1, then the other leg will also equal 1 because in an isosceles triangles the legs are congruent. Using the Pythagorean theorem we determine that the hypotenuse will equal √2. Then, using the definitions of the trig functions for right triangles, we find that when θ = 45°
       sin θ = opp / hyp = 1/√2 = √2/2
       cos θ = adj / hyp = 1/√2 = √2/2
       tan θ = opp / adj = 1/1 = 1
       The other three functions can be determined in a like manner.
       
     
     
     • Now let's investigate for 30° = π/6 and 60° = π/3
       In an equilateral triangle, each angle measures 60° (180°/3).
       Drawing a perpendicular bisector creates two triangles with angle measures 30°-60°-90°.
       
       If each side of the equilateral triangle measures 2, then the hypotenuse of our right triangle will measure 2 and the shortest leg (opposite the 30°angle) will measure 1 (half of 2). Using the Pythagorean Theorem, the length of the other leg (opposite the 60° angle) will equal √3.
       
       Then, using the definitions of the trig functions for right triangles, we find that
       when θ = 30° = π/6
       sin θ = opp / hyp = 1/2
       cos θ = adj / hyp = √3/2
       tan θ = opp / adj = 1/√3= √3/3
       The other three functions can be determined in a like manner.
       
       when θ = 60° = π/3
       sin θ = opp / hyp = √3/2
       cos θ = adj / hyp = 1/2
       tan θ = opp / adj = √3/1= √3
       The other three functions can be determined in a like manner.
     3. Trig Identities
     
     • Pythagorean Identities
     • Quotient Identities
     • Reciprocal Identities
       
• HW p.310 - 313: 3 - 18 x 3's