This lesson builds off of the basic probability work from the previous lesson. I like to start the class with a quick "check in." The concept is essentially the opposite of an exit ticket. I sometimes refer to these as "entrance tickets."
For this lesson, I use five questions focusing on the use of "and" or "or" in probability. I like the five questions listed here: http://www.regentsprep.org/regents/math/algebra/APR8/PracAND.htm
Because I want this portion of the class to pass relatively quickly, I give them up to ten minutes. When they are finished, they have 3 minutes to check their answers online (computers are already on their tables) and begin to fix their errors.
To help them move forward, we present out solutions on the board.
For this class, students show their work to the problems in this template:
Once students begin to work on the template, I check in with them on the work from the start up. I like to change the questions slightly and check for reasoning. For example, Question 4 asked, "A standard deck of cards is shuffled and one card is drawn. Find the probability that the card is red or a jack." I would follow up by swapping in the work "and" or changing the categories, perhaps "diamond or a jack." This lets me know how they are doing and forces them to confront their misconceptions.
Question 13 is often an issue for my students. This question involves a bit of reading and intimidates many students. So this is a good opportunity to talk about "breaking a question down" and identifying "what it is we need to solve."
The second part of the question is where they often get flustered. They ask "what is the least amount of marbles you would need to add to have a 50% chance of getting a green."
Students often answer the question for Hats A and C but are hesitant with Hat B, which contains 6 blue marbles and 5 red marbles (11 in total). The fact that their are 11 in total (an odd and prime number) as well as no green marbles tends to throw them a bit. So we discuss the idea of solving this problem backwards. Instead of asking how many marbles should we add, we can think, "how many marbles would there be so that the 11 in their represent 50%?" This helps students realize that they need to double the 11 marbles in the hat and add 11 green marbles. By doubling what we have with green marbles, the green marbles will represent half of the total. This brings out the reciprocal relationship between doubling and halving.