Lesson Plan # 18 - Percents, Multiple Probabilities

  1. (5 min) Mental Math
    1. What is one third of one fourth? [1/12]
    2. What is the perimeter of a square whose side is 4 1/2 inches? [18 in]
    3. What is 600 times 800? [480000]
    4. What is 200 times 80 [16000]
    5. What is the area of a triangle whose base is 7 inches and whose height is 6 inches? [21 sq. in.]

  2. (5 min) Review of homework #16 (<= 3 problems)

  3. (5 min) Introduce percents:

    1. The general idea:
      • All = 100% = 1/1
      • Empty/none = 0% = 0
      • Half = 50% = 1/2
    2. Draw this scale on the board: 
        100% - +---+ -> 1   = full
         |   |
   75% - |   | -> 3/4
         |   |
   50% - |   | -> 1/2 = half
         |   | 
   25% - |   | -> 1/4 
         |   |
    0%   +---+ -> 0   = empty

    3. Use the above scale to contrast percents to fractions:
      • 25% = 25/100 = 1/4 = .25
      • 75% = 75/100 = 3/4 = .75

    4. Show that dividing the numerator by the denominator of a fraction produces a decimal, using 1/4 as an example
      Show that percent = decimal * 100 using this same example
      Have students convert 3/4 to a decimal, then to a percent by multiplying by 100.

    If time permits, have students convert the following fractions to percents:
    • 1/8
    • 1/5
    • 1/10

  4. (15 min) In-class exercise, part 1 only
  5. (10 min) Explain multiple probabilities:
    1. Handout "Multiple Probabilities" handout. Follow the discussion in the handout. Students usually readily see the multiple coin flip example but have problems with the card examples, especially constructing the second card probability when the first card is not replaced. Go over that example CAREFULLY!
    2. Emphasize again that they are to multiply (not add) probabilities of independent things together.
  6. (Remainder of class) In-class Exercise, part 2

  7. Hand out homework as students successfully complete the in-class exercise.
Note: This lesson does not explore the meaning of independence. It is assumed in all problems presented. The second year course will explore independence more fully.