## Year 2 Lesson Plan 18 - Canceling, Permutations and Factorials

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. Permutations and factorials
Follow the discussion in the handout. Use your own discretion as to whether you actually hand this explanation out. You may want to just use it for your own notes, or hand it out as class ends.

4. (Remainder of class) In-class exercise

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