Background
Pre-Planning
Big Ideas
Whether in AP Stats class or in a career/job setting, students need to have a strong understanding how probability works as well as how it applies to their life. Probability is a topic within statistics that assists students in exploring real-world random phenomena through simulation. Then probabilities can be formed to make predictions for the future.
Essential Questions
What is probability?
What is random behavior?
How can the Law of Large numbers help with probability?
Objectives
SWBAT use the general addition rule to calculate the probability involving two events.
When appropriate, SWBAT use a tree diagram to describe chance behavior.
SWBAT use the general multiplication rule to solve probability questions.
Whether in AP Stats class or in a career/job setting, students need to have a strong understanding how probability works as well as how it applies to their life. Probability is a topic within statistics that assists students in exploring real-world random phenomena through simulation. Then probabilities can be formed to make predictions for the future.
Essential Questions
What is probability?
What is random behavior?
How can the Law of Large numbers help with probability?
Objectives
SWBAT use the general addition rule to calculate the probability involving two events.
When appropriate, SWBAT use a tree diagram to describe chance behavior.
SWBAT use the general multiplication rule to solve probability questions.
Summative Assessment
To asses students, the instructor can use the SAT Math Data Analysis App. This app has an excellent tracker for student progress by displaying a pie chart of correct, incorrect and non-attempted responses. When the app opens, students should choose the Probability option. There are six tests included within probability. Students should complete the first two of these six tests to demonstrate their knowledge as outlined by the objectives for this lesson. 1. Basic Probability 2. Independent Events Once students have completed the tests for this app, he/she should contact the instructor and report their results. |
Lesson Opening
The Hook
Have students download the app YatzyAddict. In groups of three or four students, play two rounds of Yahtzee. After the second round have the groups discuss what they think the probability is to roll a yahtzee! |
Lesson Body
Explanation
The instructor should have students download the Data 2 Probability App. Students should wear headphones while using this app. This is an excellent app to learn probability as it is an interactive book. Students can read information they need to learn and answer questions as they go to determine whether or not they understand each process. Each type of probability skill is called a benchmark. When the student has answered correctly, the app marks the benchmark with a green dot. A read dot means the benchmark has not yet been met. Once the app has downloaded, students (working individually) will need to open and complete the following benchmarks to meet the objectives of this lesson. Within the benchmark, if students cannot answer a particular question, then they can open the textbook link to read how to proceed and calculate that particular type of probability. |
3. Rules of Operation
- Find the probability of complementary events
- Apply the addition rule of probability in context
6. Probabilities
- Explore empirical law of large numbers
7. Tree Diagrams
- Represent two-stage random experiments in tree diagrams
- Represent three-stage random experiments in tree diagrams
- Apply the product and addition rules to tree diagrams: two-stage random experiment
- Apply the product and addition rules to tree diagrams: three-stage random experiment
- Find probabilities on a tree diagram
- Find probabilities by creating a tree diagram.
Once a student has completed these benchmarks, he/she should check in with the instructor.
This app is excellent as it also reteaches how to add and multiple fractions. If any student needs a refresher regarding the rules of fractions, then students can open the explanations available.
- Find the probability of complementary events
- Apply the addition rule of probability in context
6. Probabilities
- Explore empirical law of large numbers
7. Tree Diagrams
- Represent two-stage random experiments in tree diagrams
- Represent three-stage random experiments in tree diagrams
- Apply the product and addition rules to tree diagrams: two-stage random experiment
- Apply the product and addition rules to tree diagrams: three-stage random experiment
- Find probabilities on a tree diagram
- Find probabilities by creating a tree diagram.
Once a student has completed these benchmarks, he/she should check in with the instructor.
This app is excellent as it also reteaches how to add and multiple fractions. If any student needs a refresher regarding the rules of fractions, then students can open the explanations available.
Check for Understanding
To check for student understanding, there is an excellent app called Appzest EZ Probability . Students should download the Appzest EZ Probability App. By selecting skills/chapters 5 through 10, students would be able to receive a brief explanation as well as practice problems. Chapters 5-10 most resemble the objectives for this lesson, therefore students should be directed to the following topics to complete the questions. 5. Probability - Simple Events 6. Opposite, Mutually Exclusive and Overlapping Events 7. Dependent & Independent Events 8. Compound Events 9. Probability - Dependent and Independent Events 10. Predictions |
Extended Practice
For additional practice, students should use the Teacher's Probability Quiz App. Be sure to have students use headphones for this app as there are excellent verbal explanations that accompany the app. This app has a variety of topics to choose in the Lessons menu. Students can select the topics in which they need more assistance. Once they think they have all topics mastered, they can take the quiz. There is also a revision section where students can practice even more! |
Closing
To close the lesson, have students share what they have learned by assigning each student to be an expert for one subtopic in the probability unit. Have students download the Prezi App. Then they should proceed to a Prezi Presentation already started by the instructor. Here is the link to the example embedded below.
Materials
The Materials Needed For This Lesson are
- An iPhone or an iPad Tablet for each Student.
- Headphones for each Student
- Wireless Internet Access for each above
- iTunes Account