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Fan Appreciation Night, Part 3

On this page you will find lesson objectives, standards, instructional notes and UDL opportunities.

Instructional Notes:

In this lesson, students will interpret data by constructing and interpreting a two-way frequency table.  This task will be a continuation of the “Fan Appreciation Night” (but the current task is independent of this previous task).

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Sample Responses

For sample responses to the Algebra II Journal questions, visit the Algebra II Journal in the Teacher Resources.

Fan Appreciation Night, Part 3 - Page 2

In Module 6, students will be introduced to conditional probability.  Consider revisiting this two-way table to have students calculate conditional probabilities.

Seating Sections	Number of Ticket Winners	Number of People who did not win	Total
100-Level Seats	60	2240	2300
200-Level Seats	20	1080	1100
General Admission	18	1532	1550
Skyboxes	2	48	50
Total	100	4900	5000

Sample Conditional Probability Questions:

• If the grand prize winner is selected from the 100-level seats, what is the probability that the grand prize winner has already won free tickets to an upcoming game?  (Answer: ${\displaystyle \frac{60}{2300}}$ )
• If the grand prize winner is a fan that did not win free tickets to an upcoming game, what is the probability that the winner is sitting in general admission seats?  (Answer: ${\displaystyle \frac{1532}{4900}}$ )
• Determine if the following events are independent or dependent:  a grand prize winner selected from 100-level seats and a grand prize winner selected from fans that did not win tickets to an upcoming game.  Use conditional probability to verify your conclusion.  (Answer: Event A:  winner selected from 100-level seats, Event B: winner selected from fans that did not win tickets to an upcoming game.  P(A) = ${\displaystyle \frac{2300}{5000}}$ , P(B) = ${\displaystyle \frac{4900}{5000}}$, P(A and B) = ${\displaystyle \frac{2240}{5000}}$.  If the events are independent, P(A|B) = P(A and B)/P(B) = P(A) and P(B|A) = P(A and B)/P(A) = P(B).  So P(A|B)= ${\displaystyle \left(\frac{2240}{5000}\right)/\left(\frac{4900}{5000}\right)=\left(\frac{2240}{4900}\right)}$ .  But P(B) = ${\displaystyle \frac{4900}{5000}}$, so these events are dependent.

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Fan Appreciation Night, Part 3 - Page 5

The first journal prompt can be modified to include more or less categories.  Depending on the interests of your students, consider modifying the data collection to allow student choice and opportunities for students to gather data for something that is of interest to them.

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Fan Appreciation Night, Part 3 - Page 6

Use the module reflection to formatively assess student understanding and determine what additional supports may be needed.

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UDL Opportunities:

Checkpoint 2.1 Clarify vocabulary and symbols.
Checkpoint 2.2 Clarify syntax and structure.
Checkpoint 2.3 Support decoding of text, mathematical notation, and symbols.
The Student Resources section includes key vocabulary clarifications that will support the decoding of text and mathematical language.  It may be helpful to introduce some of the key terms prior to the start of this lesson.  Students will also need to be comfortable using a graphing calculator.  A quick reference guide will also be available in the Student Resources section.  In addition, students will need to interpret the structure of a two-way table in order extrapolate key information.

Checkpoint 3.4 Maximize transfer and generalization.
Checkpoint 4.1 Vary the methods for response and navigation.
Checkpoint 6.3 Facilitate managing information and resources.
Checkpoint 7.1 Optimize individual choice and autonomy.
Checkpoint 7.2 Optimize relevance, value, and authenticity.

The lesson activities are set in real-world contexts in order to optimize relevance and authenticity.  Students may have choice for what data to collect.  Students should have choices as to how to present final findings to the class, which may include formal presentations, visual displays, or presentations using technology.