"This class, we got through a little more than one half page of the remaining vocabulary words and again created flashcards for them then went over the flashcards. The student got over half of the cards right this time.
We then kicked it into overdrive for the remaining topics on the math outline. We spent most of the time on the two most difficult topics: permutations vs. combinations and probability. We began by reviewing that some problems require you to determine the various different ways that things can be ordered or the various different ways things can be combined. I explained that these were two different but very similar topics called permutations and combinations. I explained that what he needed to know is that he needs to determine if what the problem is asking for is order specific or not. He understood this process, so I gave him a couple of practice problem to test his understanding.
We also discussed problems involving fractions of a whole. I gave him an example problem involving jellybeans. I gave him another problem involving the student body of sports players in order to test his knowledge.
We then moved on to probability. I explained that a lot of the time, questions involve both probability and permutations. I gave him a classic example, what is the probability of rolling a 7 on two dice? Just like the last process, he listed out all of the ways that someone could roll a seven: 1 and 6, 2 and 5, 3 and 4. I stated that he needed to also list out 6 and 1, 5 and 2, and 4 and 3. He then correctly told me that the probability of rolling a 7 is 6/36. I then tested his understanding by asking him the different probabilities of rolling a twelve, an eight, etc.
We finished probability with questions about cards. We reviewed that there are 52 cards in a deck with 4 different suits. I asked him questions involving cards drawn at random from the deck without replacement. I asked him what is the probability of drawing the ace of spades then another card that was not a spade? He correctly answered that it was (1/52)x(39/51). I finished the session by asking him another cards related question. If I draw three cards at random from the deck how many red cards should I EXPECT? The key word here is expect. Because you are drawing three cards and the probability of drawing a red card is _, you should expect to draw 1.5 red cards. Even though this is impossible, I explained that the question that he had gotten wrong on his practice test had asked him how many heads to EXPECT in a series of 3 coin flips, for which the correct answer was 3/2."