Download Independent and Dependent Events

Compound Probability – Independent and Dependent Events Application
Teacher: Renee Carpenter
Topic: Probability and Statistics
Date: April 15, 2015
Content Area: Math
Grade Level: 7
Duration: 50 minutes
Rationale: This lesson is designed to provide students with the opportunity to discover the rule
for independent and dependent events through hands on investigation. Therefore, they will
develop a more comprehensive understanding of how to find the probability of independent and
dependent events as they practice writing and solving their own.
Massachusetts Framework
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Mathematics: Probability and Statistics
o 7.SP.8. Find probabilities of compound events using organized lists, tables, tree
diagrams, and simulation.
a. Understand that, just as with simple events, the probability of a compound
event is the fraction of outcomes in the sample space for which the compound
event occurs.
b. Represent sample spaces for compound events using methods such as
organized lists, tables and tree diagrams. For an event described in everyday
language (e.g., "rolling double sixes"), identify the outcomes in the sample
space which compose the event.
Objectives
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After the lesson, students will be able to explain the difference between independent and
dependent events in their own words without any assistance.
Given a set of manipulatives, students will be able to write and solve an independent
probability problem with 90% accuracy.
Given a set of manipulatives, students will be able to write and solve a dependent
probability problem with 90% accuracy.
After creating an independent and dependent probability problem, students will be able to
teach the problem to their classmates by independently identifying the problem as an
independent or dependent event, explain why is classified as such, and demonstrating the
solution to their problems.
Materials
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Mimio Lesson
Paper bag and colored cubes
Notecards (2 per student)
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Colored chips
Dice
Coins
Spinners
Homework: Chapter 10 practice quiz
Lesson Procedure
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Activator: Bell Work.
o Have a bell work problem reviewing independent and dependent events displayed
on the board for students to work on as they come in. Provide students with 5
minutes to work on the problem before reviewing it as a class.
Activities: Independent/Dependent event review and creating independent and dependent
probability problems.
o Independent/Dependent event review – Quickly review the concept of compound
probability and ask students if they can identify the two types of compound
probability. Review the terms independent event and dependent event and ensure
that students can identify the difference between the two and the key words
associated with each. Work through an example of both an independent and
dependent probability problem as a class.
o Creating independent and dependent probability problems - Transition into the
application activity by passing out the manipulatives and two notecards to each
student. Explain that their challenge is to use the manipulatives to help them write
their own independent and dependent probability problems. After they have
written one of each on the front of each of their notecards, they are to solve them
on the back. When there is about 20 minutes of class time remaining, have
students come up to the board, present their problems, and explain why they are
independent or dependent in addition to explaining their solution to teach the
class.
 Have a review worksheet one independent and dependent probability
ready for early finishers or students who demonstrate behavior that shows
they cannot handle the activity.
Summarizer: Exit ticket.
o Work with the class to help them define independent and dependent events in
their own words and determine the formula for finding each kind of probability.
They must show that they have copied down these notes in their notebook as an
exit ticket.
Homework
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Practice quiz - The homework assignment will serve as a review for students of all the
concepts covered in this unit in preparation for the upcoming quiz at the end of the week.
Assessment
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Pre-Assessment: Bell work.
o The bell work will serve as review of the different kinds of compound events. The
students’ ability to identify the event in the problem as independent or dependent
will allow me to identify the extent to which I need to reteach the vocabulary and
concepts in class before moving on to the new material.
Informal Assessments: Classroom discussion, observation, Mimio lesson, exit ticket, and
homework assignment.
o The observation and discussion throughout the students’ participation in the
Mimio lesson and follow along worksheet help determine the students’
understand of independent and dependent events. These activities will informally
assess students’ ability to differentiate between the two kinds of compound
probability as well as their ability to find the probability of various compound
events.
Formal Assessments: creating independent and dependent probability problems.
o By creating their own independent and dependent events and explaining them to
the class, students will formally demonstrate the extent to which they understand
the difference between independent and dependent events in addition to their
ability to find the probability of these events. Students will be formally assessed
against the instructional objectives for the lesson.
Accommodations/Modifications/ELL
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Accommodations
o Use preferential seating.
o Provide additional wait time when asking questions.
o Provide students with verbal or physical warnings that they are about to be called
on.
o Provide student with verbal cues to stay on task.
o Provide students with fidget toys and frequent breaks as needed.
o Review vocabulary with students to enhance understanding.
o Seat students next to a model peer to encourage good behavior and participation.
o Use a classroom timer to help students with time management.
o Allow students to stand if feeling restless.
o Provide students with the opportunity to use manipulatives to help determine the
probability.
o Simplify word problems and read them out loud for students.
o Work with struggling students in a small group.
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Provide frequent checks for accuracy when students are doing classwork.
Keep sample math problems on the board.
Provide students with additional time to complete the assignments.
Allow students to work in collaborative groups to increase understanding.
Provide students with a list of what they need to be prepared to present to the
class while teaching their problems.
Modifications
o The content will be modified as needed and stated on students’ IEPs.
Teacher Reflections
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Were the instructional objectives met?
What were the strongest and weakest components of my lesson?
Were any additional accommodations needed?
Was the activity addressing too many concepts at once? Were the students overwhelmed
by the task?
What was the biggest struggle for the students during the lesson and how can I address it
in the next lesson?
Would the students benefit from working in partners next time?
Did the manipulatives help promote the students’ understand or were they distracting?
How did students respond to the challenge of creating their own problems?
How did students respond to the challenge of teaching their problems to the class?
Resources
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Big Ideas Math; A Common Core Curriculum – Green by Ron Larson & Lauri Boswell