Algebra I: Lesson Plan * 9/08/2006

SUBSTITUTE

• PEP RALLY
  
• Red and Blue Workbook
  p.5 #1 - 3
  Problem Solving Using Models (MA.B.1.4.2, MA.B.2.4.2, MA.D.2.4.2)
  p.17 #1 - 15
  Solving Addition and Subtraction Equations (MA.A.3.4.1, MA.D.2.4.2)
  p.18 #1 - 15
  Multiplication and Division Equations (MA.B.1.4.3, MA.C.2.4.1, MA.D.2.4.2)
  

PreCalculus: Lesson Plan * 9/08/2006

SUBSTITUTE

• Prerequisite Chapter Review
  p.67 - 69 #1 - 139 odd
  Check answers in Solution manual
  
• Chapter 1 Review
  p.131 - 132 #1 - 79 odd
  Check answers in Solutin manual
  

Algebra I: Lesson Plan * 9/07/2006

• Quickstart
  Red and Blue Workbook
  p.12 #1 - 11 Multiplication of Real Numbers (MA.A.3.4.1, MA.A.3.4.2)
  p.13 #4 - 9 The Distributive Property (MA.A.3.4.2)
  p.14 #10 - 15 Division of Real Numbers (MA.A.2.4.2, MA.A.3.4.1, MA.A.3.4.2)
  
• Chapter 1 ReTest

Precalculus: Lesson Plan * 9/07/2006

• Quickstart: adding and subtracting fractions
• Lesson
  4.6 Graphing Cotangent
  
  1. Find vertical asymptotes
     Solve bx - c = 0 and bx - c = π
  2. Find intercepts
     Midpoint between asymptotes
  3. Determine whether graph is increasing or decreasing
     Opposite of tangent
     a > 0, decreasing
     a < 0, increasing
     
• Group Activity Lesson 4.5
  p.370 #116 - 124 even
  
• Homework p.341 - 343 #1-8 ALL, 9 - 30 x 3's (Check on Tuesday)
  

Algebra I: Lesson Plan * 9/6/2006

• DBHS FCAT PreTest
• (2-1 and 2-2) Group Quiz
• Chapter 1 RE test postponed until tomorrow
  

PreCalculus: Lesson Plan * 9/06/2006

• Quickstart p.333 #95 (use pp. 191, 199 to help refresh your memory), 99, 101
• 4.5 Quiz - Graphing Sine and cosine functions [15 points]
  
  1. Determine the period, amplitude, and period-interval for
     y = (-1/2)sin[(3x/2) - (1/2)]
     [3 points]
     
  2. Sketch the graph of
     y = -2sin(2x + π)
     Show all work.
     [5 points]
  3. Sketch the graph of
     y = 2 + cos( x - π/4)
     Show all work.
     [5 points]
  4. Write a sine equation with a horizontal shift of π and an amplitude of 3.
     [2 points]
     
• Lesson
  (4.5) Mathematical Modeling
  
  1. Example: Find a trigonometric function to model the data in the following table
     x | 0 | π/2 | π | 3π/2 | 2π
     y | 2 | 4 | 2 | 0 | 2
     Solution: plot the 5 points. The graph starts at the intercept, so a sine function is a good choice. By examining the graph we see the amplitude is 2, the period is 2π, the graph is not shifted horizontally, and it is shifted up 2 units. So, a=2, b=1, c=0, d=2. So the equation is y = 2 + 2sinx
  2. (p.331 #75) Using a trig function to model real life data.
     Solution:
     a) amplitude is 0.85, period is 6, period-interval is [0,6], key points are (0,0), (3/2, 0.85), (3, 0), (9/2, -0.85), (6, 0). Sketch points and connect with a smooth curve.
     b) One full breath cycle is an inhale and an exhale. This corresponds to one period or 6 seconds.
     c) 60 seconds in a minute, divided by 6 seconds per cycle, that is 10 cycles per minute.
     
  (4.6) Graphs of Other Trig Functions
  
  1. tanx = sinx/cosx
     
     • undefined when cosx = 0, x = ...-π/2, π/2, 3π/2, 5π/2, ...
     • these undefined x values correspond to vertical asymptotes
     • Sketching y = a tan (bx - c)
       
       1. Find key points
          a) asymptotes
          Solve bx - c = π/2 AND bx - c = -π/2
          b) intercepts
          Midpoint between two consecutive asymptotes
          
       2. a > 0, increasing
          a < 0, decreasing
          
• Homework p.341: 9, 12, 24, 41 (checked on Monday)
  

Algebra I: Lesson Plan * 9/05/2006

• Quickstart Red and Blue WB p.11 #1 - 11
• Lesson
  (1-8) Using Properties to Justify your steps
  
  1. Review Properties
  2. Worksheet Signed Numbers Practice 14
     
  7 Simple Steps for Solving Equations
  
  1. Eliminate subtraction
  2. Eliminate Parentheses
  3. Eliminate Fractions
  4. Eliminate the variable from one side (if on two sides)
  5. Combine like terms
  6. Eliminate "add number"
  7. Eliminate "multiply number"
     
  (2-2) Solving two step equations
  
  1. Writing and solving equations to represent real life
  2. p.85 #58
     
• Homework Study for Chapter 1 Retest
  

PreCalculus: Lesson Plan * 9/05/2006

• Quickstart Green WB p.146 #66 - 82
  
• Lesson
  (4.5) Graphing Sine and Cosine Functions
  
  1. General Equation
     y = d + asin(bx - c) and y = d + acos(bx - c)
     Chart of the characteristics of a, b, c, d
  2. Examples
     p.331 #54
     y = -3cos(6x + π)
     a = -3, b = 6, c = -π, d = 0
     amplitude = |-3| = 3
     period = 2π/6 = π/3
     period - interval = [-π/6, -π/6 + π/3] = [-π/6, π/6]
     Five key points
     (-π/6, -3) Function is cosine and a < 1, so start at min = d - amplitude = 0 - 3 = -3
     (-π/12, 0) add period/4 = (π/3) /4 = π/12 to get x-coordinate
     (0, 3)
     (π/12, 0)
     (π/6, -3)
     Plot key points and connect with a smooth curve. Continue the pattern of one period-interval to get multiple periods.
     
     p.331 #50
     y = -4 + 5 cos πt/12
     a=5, b=π/12, c=0, d=-4
     amplitude = 5
     period = 2π/(π/12) = 24
     period - interval = [0/(π/12), 0/(π/12) + 24] = [0, 24]
     add 24/4 = 6 to x-coordinates
     (0, 1) cosine, a > 1, start at max = d + amp = -4 + 5 = 1
     (6, -4) add 6 to x-coordinate; y-coordinate goes to "intercept" at d=-4
     (12, -9) y-coordinate goes to min = d - amp = -4 - 5 = -9
     (18, -4) y-coordinate back to "intercept"
     (24, 1) y-coordinate back to max
     Plot five key points and connect with a smooth curve. Continue in either direction to plot more than one period.
  3. Practice p. 331 #39 - 53 Every Other Odd
     
• Homework p.331 #41 - 53 Every Other Odd
  

Labor Day

Enjoy your Labor Day weekend.
Come back to school refreshed and ready to work!
;-) Ms. L