Probability+Rules+and+Independence


 * Probability and Independence Unit:**

Unit Goal: Students will apply their earlier experience with probability to build a further understanding of the concepts of simple and compound probabilities and independence.

Students will be able to:

i.e. commercials, sports, percentages vs percents, margin of error
 * Identify independent events
 * Understand and interpret independence
 * Calculate single event probabilities
 * Calculate compound probabilities
 * Identify sets, union of sets, and intersections of sets
 * Apply the probability rules (addition, multiplication) {P (A or B) = P(A) + P(B) – P (A and B), P( A and B)= P(A)P(B/A)=P(B)P(A/B)
 * Connect to real world situations

//First Learning Cycle//:

The goal is to define probability as the outcome of repeated samplings over a period of time and the idea of independence. The objectives we will concentrate on are:


 * Identify independent events
 * Calculate single event probabilities
 * Connect to real world situations
 * Identify sample spaces and events


 * //__Develop Understanding Task__//**

Task #1: Greed game

Teacher will need access to a six-sided dice and/or 10-sided dice.


 * Launch:**

Introduce the reward for the winner of the game. Explain the rules to the game as follows: 1. All students start the game standing at their desks. 2. The dice is rolled for points. Face value is given for each number except 2. If a 2 is rolled the round is over. The total points are cumulatively added for each roll. i.e. a 6 and then a 4 is rolled, the student collects 10 points. This continues until the end of the round. 3. Students decide at what point they want to sit down. They must sit before the next roll of the dice. Once a student sits down, they no longer tally points. If a 2 is rolled, the round is over and anyone left standing loses all points for that round. The student with the most points wins the round. The student with the most points at the end of four rounds, wins the game.


 * Explore:**

Start with the first round of the game, making sure to keep a tally of how many rolls until a two is rolled.

At the end of each round, debrief the students on that round relating probabilities and vocabulary. Probability: Independence: Events: Outcomes; Complement


 * Discuss:**

1. After 2 rounds of the game, have student verbally (written) explain their current strategy for the game. Finish the game. 2. At the end of the game have them distinguish if their strategy worked, why or why not? 3. Then have them decide what their strategy would be if a 10-sided dice was used instead. Express this verbally (written). What would the new probability be of getting a 2 and of not getting a 2? 4. Either play one round or one new game with the 10-sided dice.

Extension Idea: Have the students figure the probability if both dice are rolled.


 * //__Solidify Understanding Lesson__//**

Task #2: SET cards

Teacher needs deck of SET cards for each group of students.


 * Launch:** We have been discussing probability with dice, now we are moving to a more complicated type of situation, cards.


 * Explore:**

1. Give students the SET lab. (see attached) 2. As the students are working, walk around and ask relevant questions.


 * Discuss:**

The main focus of the activity is to help the students realize how sets can be formed, how intersections and unions can be related.

After this activity and discussion a “worksheet” type homework assignment is appropriate.


 * //__Practice Understanding Lesson__//**

Task #3: High Low Game