Description
Title of Lesson: Review on Probability -- Independent and Dependent Events
UFTeach students’ names: Richard Madolid, Thomas Wilkey
Teaching date and time: April 5th, 2011, 9:20 A.M.
School and Mentor Teacher name: Howard Bishop Middle School, Mrs. McDowell
Grade / Topic: 7th Grade / Probability
Length of Lesson: 50 minutes
Source of the Lesson:
Appropriateness for Middle School Students: Technology based lessons appeal to many students in the middle school age bracket because society has conditioned kids to spend much of their free time playing games. The interactive animations grab the students’ attention by placing the students in a game-like, mental environment different from their usual desk and note-taking environment. The activity provides the students with a hands-on experiment on the computer that would otherwise take too much time to set up, perform, and clean up in the regular classroom.
Concepts
In terms of probability, an event is a collection of one or more outcomes, which are the possible results of an experiment. A compound event consists of two or more events that are not mutually exclusive, which means that both outcomes cannot occur at the same time. Specifically, two events are independent events if the occurrence of one event does not affect the likelihood that the other event will occur. In contrast, two events are dependent events if the occurrence of one event does affect the likelihood that the other event will occur. (Big Ideas Math Grade 7 Textbook) When two events, A and B, are independent, the probability of both occurring can be solved using the equation: P(A and B) = P(A) · P(B). However, when solving a probability that involves two compound, dependent events, the probability is said to be a conditional probability. The conditional probability of an event B in relation to an event A is the probability that B occurs after A has already occurred. P(B|A) is the notation for conditional probability. Using this notation, an equation was derived to calculate the probability: P(A and B) = P(A) · P(B|A). ()
Performance Objectives
• Students will be able to identify independent and dependent events.
• Students will be able to calculate the probabilities of independent events.
• Students will be able to calculate the probabilities of dependent events.
Florida State Standards:
• Grade 7, MA.7.P.7.2, Supporting Idea: Determine, compare, and make predictions based on experimental or theoretical probability of independent or dependent events.
Materials List and Student Handouts
• 22 pre-test
• 22 post-test
• 22 Independent and Dependent Worksheets
Advance Preparations
• Prepare powerpoint with examples.
• Projector for walkthrough on on-line exercise.
• Computer lab required for technology lesson.
• Have student name tags ready.
Safety
• There are no significant safety precautions.
|ENGAGEMENT Time: ____5 mins_____ |
|What the Teacher Will Do |Probing Questions |Student Responses and Potential Misconceptions |
|As the students arrive in the class, the teacher |“What is this object called?” |[a spinner] |
|will refresh the students on what probability is | | |
|by presenting the students with a spinner that |“What are the possible outcomes when | |
|has 3 colors. |spinning the spinner?” |[red, blue, yellow] |
| | | |
| |“What are the favorable outcomes of NOT | |
| |spinning a yellow?” | |
| | |[red, blue] |
| |“How many outcomes are there?” | |
| | | |
| | | |
| |“Is this experiment considered to be |[3] |
| |fair?” | |
| | | |
| |“What is the theoretical probability of | |
| |spinning red?” |[Yes because all of its possible outcomes are |
| | |equally likely] |
| |Spin the spinner 10 times and record the| |
| |results. Next, ask the students what the|[33%] |
| |experimental probability is of spinning | |
| |red based on the data. | |
| | | |
| | |[Answer will vary] |
| | | |
| | | |
| | | |
| | | |
|After the short review of probability is over, | | |
|the teacher will tell the students that today is | | |
|a technology lesson and they are going to be | | |
|using the computer lab to finish the lesson. | | |
|EXPLORATION Time: ____20 mins_____ |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|The teacher will have the students log into the | | |
|computers. | | |
|After the students are logged into their own | | |
|respective computers, they will go to | | |
|. After they are logged in, | | |
|students will enroll in a class using the | | |
|specified code given to them via the teacher. | | |
|Then the students will log in using the | | |
|pre-created student account given to them via the| | |
|teacher. The students will then search | | |
|independent events, and explore the lesson | | |
|compound independent and dependent events. The | | |
|students will click on the gizmo flash web | | |
|application that shows a bag with a blue and | | |
|green marble on the side. | | |
| | | |
|The teacher will do the first problem with the | | |
|students. | | |
| | | |
| | | |
| | | |
| | | |
| | | |
| |“Without using the computer, let’s |[Okay.] |
| |imagine if we have a bag that contains 3| |
| |blue and 2 green marbles, and you draw | |
| |two marbles from the bag, one at a | |
| |time.” | |
| | | |
| |“If the marble is replaced in the bag | |
| |after it is drawn out, what are some of | |
| |the possible outcomes?” |[We can grab a blue or a green, blue has a 3/5 |
| | |chance to be drawn, where a green has a 2/5 chance |
| |“Is every individual draw an independent|to be drawn.] |
| |event?” | |
| | |[Yes, they are independent because each draw is |
| | |separate and the marbles are replaced.] |
| |“Let’s say that the bag contains both 3 | |
|The teacher will circulate the room and monitor |blue and 3 green marbles, how do you |[This would give each marble a 50/50 chance to be |
|the students as they complete the activity. |think the probability would change? |drawn. This makes it easier to predict and guess a |
| | |marble.] |
|EXPLANATION Time: ____10 mins_____ |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Now that the teacher has the students thinking |“Alright class, using the simulator of | |
|and working on paper, they can use the simulator |the marbles and bag in front of you, | |
|to help answer a few new questions. |were going to walk you through a quick | |
|The teacher can use a projector with the same |problem. Let’s say we have a bag with 3 | |
|website up to show the students an easy example |green and 2 blue marbles in front of us.| |
|then set them free to work a few harder problems.|What would be the probability of drawing| |
| |a blue marble from the bag on the first | |
| |try? How about a green marble?” | |
| | | |
| |“Now what would happen if we drew these | |
| |marbles out and DIDN’T replace them and |2/5 for the blue and 3/5 for the green marbles. |
| |drew twice? Would that be an independent| |
| |or dependent event?” | |
| | |The answers would change a lot. There would be |
| | |chances of drawing 2 blues, 2 greens, green/blue, |
| |“Can anyone tell me what an independent |or blue/green. This would be dependent; the marbles|
| |event is? What about a dependent event?”|are removed at the same time. |
| | | |
|At this point, the teacher will address any |“Great, a definition is independent | |
|misconceptions and cover the vocabulary and |events are separate actions that are | |
|definitions of a few new words introduced. |created by always having a perfect and |Independent events are when we don’t take marbles |
| |unchanging environment.” |out leaving everything as a fixed chance. |
| | | |
| | | |
| | | |
| |“How can we define independent and | |
| |dependent events as a formula?” |Dependent events are when we remove marbles, it |
| | |changes our outcome for each draw! |
| | | |
| | | |
| | | |
| | |P(A and B) = P(A) * P(B) is dependent, where as |
| | |independent is equal to P(A) * P(A). |
|ELABORATION Time: ____5 mins_____ |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
| |“Now take a look at a bag of marbles you|[If we draw with the marbles being replaced, we |
| |created, make sure there are at least 3 |just multiply the chances of drawing any of the |
| |marbles in it. Take a look at how the |previous solutions because we keep the same amount |
| |fractions in the calculation column |of marbles in the bag at the same time.] |
| |change when you switch between yes or no| |
| |when replacing the marbles after each | |
| |draw. | |
| | | |
| |Why do some numerators change? |[The denominator and numerator change based on it |
| |What about the denominator?” |being an independent or dependent event.] |
|EVALUATION Time: ____5 – 10 mins_____ |
|What the Teacher Will Do |Probing/Eliciting Questions |Student Responses and Misconceptions |
|Have the students log off the computer, then pass| | |
|out the post exam. | | |
| | | |
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