Year 2 Lesson Plan 18 - Canceling, Factorials and Permutations

  1. (5 min) Mental Math
    1. Take 2/3 of 66, multiply by 2, then subtract 11 [77]
    2. What is 5/8 - 1/2 times 2? [1/4]
    3. Take 50% of 1/4 of 400 [50]
    4. If x is 4, and y is 3, what is 2x - y? [5]
    5. If x is 4, and y is 5, and z is 6, what is x + y - z? [3]

  2. (5 min)Review canceling

    When you are drawing cards out of a deck, you may have noticed that sometimes the denominator can get very big. You may find that it is 52 x 51 x 50 x 49 x 48 which is 311,875,200. Well this number might be too big to fit into your calculator, so you might get an error. Anyway, it is a nuisance to have such a big number and then try to reduce it. An easier way to do it is to cancel like factors in the numerator and denominator before you multiply, like this:

    This is the probability of drawing 3 spades in a row

    Remember that the factors you cancel don't need to be above each other in the same fraction. In the above fraction, you see that the 4 in the denominator of the first fraction can be canceled with the 4 in the numerator of the second fraction. Try this:

         3      5      11     18
    --- x  --- x  ---- x ---- = ? 
     11     18      5      2
  3. Factorials and Permutations
    A factorial is a number that is the result of multiplying a number by all the whole numbers below it. It is written with an exclamation mark (!) after it, like this: 5!. Here are two examples:
    5! = 5 x 4 x 3 x 2 x 1 = 120
    6! = 6 x 5 x 4 x 3 x 2 x 1 = 720
    For a discussion of permutations, you can follow the discussion in the handout.

  4. (Remainder of class) In-class exercise

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