Algebra I: Lesson Plan * 9/01/2006

• Quickstart: SSS SB p. 9 # 1 - 8
• Reteach:
  (1-5) Subtracting Real Numbers
  
  1. Review Workbook Lesson 1-5
  2. Small Groups - Signed Numbers Practice 11 - Add or Subtract
     
  (1-6) Multiplying and Dividing Real Numbers
  
  1. Review Workbook Lesson 1-6
  2. Small Groups - Signed Numbers Practice 12 - Add, Subtract, Multiply or Divide
     
• Mini-Bat Quiz - Strand A, Standard 1, Form A

PreCalculus: Lesson Plan * 9/01/2006

• Quickstart p.146 of Algebra I Workbook #51 - 65
  
• Quiz on internet - Lesson 4.5 - E-mail instructor
  colleen.lynch@browardschools.com
  as text
  
• Student Success Organizer - Lesson 4.6 - Print and complete
• Turn in Quickstarts from 8/28, 8/31, and 9/1 and Homework from 8/28 and 8/31
  

Algebra I: Lesson Plan * 8/31/2006

• Quickstart
  SSS SB p.2 # 1 - 8 Exponents and Powers MA.A.1.4.4, MA.A.3.4.1, MA.B.1.4.1
  p.3 # 1 - 5 Order of Operations MA.A.3.4.2, MA.A.3.4.3
• Reteach
  (1-4) Adding Real Numbers
  
  1. Rule for Adding Numbers with the Same Sign
  2. Rule for Adding Numbers with Different Signs
     
  3. Review Workbook Lesson 1-4
  4. Small Groups - Signed Numbers Practice 10 - Addition
  5. Review Workbook Lesson 1-5
     

PreCalculus: Lesson Plan * 8/31/2006

• Quickstart: Algebra I Workbook p.145 #26 - 50 Simplifying Radicals
• Lesson
  (4.5) Graphing Sine and Cosine Functions
  
  1. Translations of Sine and Cosine Curves (p.327 - 328)
     The graphs of y=asin( bx - c) and y = acos( bx - c) have a horizontal shift of c/b.
     
     • Example: Sketch the graph of the following
       a) y = cos(x - π/2)
       Remember the five key points for y = cosx are
       (0, 1) [max]
       (π/2, 0) [int]
       (π, -1) [min]
       (3π/2, 0) [int]
       (2π, 1) [max]
       c/b = π/2 / 1 = π/2
       The graph shifts π/2 to the right. The key points become
       (π/2, 1) [max]
       (π, 0) [int]
       (3π/2, -1) [min]
       (2π, 0) [int]
       (5π/2, 1) [max]
       
       b) y = 2sin (2x + π/2)
       Remember the key points for y = sinx are
       (0, 0) [int]
       (π/2, 1) [max]
       (π, 0) [int]
       (3π/2, -1) [min]
       (2π, 0) [int]
       c/b = π/2 / 2 = π
       The graph shifts to the left π and the amplitude is 2 so the max has its y-coordinate at 2 and the min has its y-coordinate at -2. The five key points become
       (-π/4, 0) [int]
       (0, 2) [max]
       (π/4, 0) [int]
       (π/2, -2) [min]
       (3π/4, 0) [int]
     • Adding or subtracting onto the entire trig function results in a vertical shift.
       y = 1 - 0.5sin(0.5x - π)
       will have a vertical shift UP of 1 unit.
       
  2. Practice p. 330 #20, 22, 26, 34
     
• Homework
  p.330 - 331 #15 - 33 x 3's, #39 - 54 x 3's
  

Algebra I: Lesson Plan * 8/28/2006

• Quickstart Sunshine State Standards Support Book p.1 #1 - 6
  Variables in Algebra
  MA.B.1.4.2, MA.B.2.4.2, MA.D.2.4.2
  
• Lesson
  (2-1) Solving One-step Equations
  
  1. Solving equations using multiplication and division
     Examples 4, 5, 6 similar to textbook
     
  2. Critical Thinking: p.79 #74, 75
     Peer Buddies
  3. Geometry Integration
     p.79 #78. Given that a triangle is isosceles AND the measurement of one of its base angles, solve for the variable used to describe the other base angle.
     5x = 70, divide by 5 on each side, x = 14
     
  (2-2) Solving two-step Equations
  
  1. Example 1
     Solve 13 = y/3 + 5
     What has been done to y? Divided by 3, add 5. Undo each of these steps in reverse order. Subtract 5, multiply by 3.
     13 - 5 = y/3 +5 - 5
     8 = y/3
     3(8) = 3 (y/3)
     24 = y
  2. Real-World Problem Solving
     Example: You order iris bulbs from a catalog. Iris bulbs cost $0.90 each. The shipping charge is $2.50. If you have $18.50 to spend, how many iris bulbs can you order?
     Solution: Define a variable. b = number of iris bulbs
     Write an equation $18.50 = $0.90b + $2.50 [you only get charged the shipping fee once]
     b has been multiplied by 0.90 and then added to 2.50.
     To solve subtract 2.50, divide by 0.90
     18.50 - 2.50 = 0.90b + 2.50 - 2.50
     16 = 0.90b
     16/0.9 = 0.9b/0.9
     17.777... = b
     Do not have enough money for 18 bulbs, so you will purchase 17 bulbs.
     
  
  
• Homework
  p.77 - 80 #21 - 51 x 3's, 63, 66, 77, 79
  p.84 - 86 # 1 - 35 x 3's, 40 - 51 x 3's, 56, 67
  

PreCalculus: Lesson Plan * 8/28/2006

• Quickstart Algebra I Workbook p.145 #1-25, no calculator
• Lesson
  (4.5) Graphs of Sine and Cosine Functions
  
  1. Exploration with Graphing Calculators
     Graph y = sinx, y = 4 sinx, and y = sin(2x)
     Notice similarities and differences.
     Where are the intercepts, max, and min?
     What is the period, the distance on the x-axis until the graph repeats?
     What is the amplitude, the "height" of the graph?
     
  2. Amplitude and Period (p.325 - 326)
     
     • Amplitude = |a|
       y = a sinx
       vertical stretching when |a| > 1
       vertical shrinking when 0 < |a| < 1
       changes the y-coordinate of the minimum and maximum
       intercepts remain the same
       
     • Period = 2π/b
       y = sin( bx )
       horizontal stretching when 0 < b < 1
       horizontal shrinking when 1 < b
       changes the x-coordinate of the minimum and maximum and the intercepts
     • Find the amplitude and the period of y = -4cos(3x)
       Amplitude = |a| = |-4| = 4
       Period = 2π/b = 2π/3
       
• Homework
  p. 330 - 331 #1 - 12 x 3's