Lesson Plan #23 - Adding and subtracting like factors

  1. (5 min) Mental Math
    • What is the probability of flipping a coin 3 times
      and getting a 'heads' all 3 times? [1/8]
    • Start with 2400, divide by 100, then divide by 3 [8]
    • What is the probability of drawing a red 6
      out of a deck of 52 cards? [1/26]
    • What is 20% of 80? [16]
    • Multiply 1/4 by 4/5 and reduce [1/5]

  2. (5 min) Review of homework #22 (<= 3 problems)

  3. (10 min) Discuss adding and subtracting like factors:

    1. Use this example to introduce adding X's:

      X + 2X = 27

      Point out that 2X means that there are 2 X's there. So

      X + 2X = 3X, so

      3X = 27,

      Therefore X = 9, because 3 X 9 = 27.
    2. Key point: So 3X means 2 things:
      1. 3 X's
      2. 3 times X
      Point out that these mean the same thing.
    3. Use a subtraction example:

      4X - 2X = 18
    4. Applications in geometry:
      1. Draw a rectangle twice as wide as it is high and label 2 of the sides "X" and "2X". Construct the equation for the perimeter:
        X + 2X + X + 2X = 24 inches.
        What is the length of the short side?
        6X = 24
        X = 4.
      2. Draw a tall isosceles triangle with angles X, 2X, and 2X.
        Construct an equation for the sum of the angles:
        X + 2X + 2X = 180
        What is the smallest angle?
        5X = 180
        X = 36 degrees!
  4. (Remainder of class) In-class Exercise.

  5. Hand out homework as students successfully complete the in-class exercise.


Note: Biggest student problem with this lesson:
Understanding that for the equation:
2X + X = 9,
when you ask "How many X's are there? that the answer is not 2. This means understanding that 2X really means that there are 2 X's here.