# Teacher Resources

## Fan Appreciation Night, Part 1

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

Estimated Time:  60 - 75 minutes

### Lesson Objectives:

• Students will review experimental and theoretical probability.
• Students will distinguish between independent and dependent events.
• Students will calculate probabilities of compound events, including probabilities of complements ("not" statements).

Key Common Core State Standards:

S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

Supporting Common Core State Standards:

7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.

1. Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
2. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

1. 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.
2. 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.
3. Design and use a simulation to generate frequencies for compound events.

8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables.

Standards for Mathematical Practice Emphasized:

MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.

## Instructional Notes:

In this lesson, the students will build on concepts that were first explored in 7th grade.  Students will find the probability of independent and dependent events. Students will explore whether or not events are independent, i.e., the events are independent if P(A and B) = P(A)P(B).  Students will then compute and interpret theoretical and experimental probabilities of compound events.   The students will explore a scenario of a sporting event randomly giving fans free tickets to an upcoming game.

> Go to Fan Appreciation Night, Part 1 lesson

## Sample Responses

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

## Fan Appreciation Night, Part 1 - Page 3

Most of the activities in this module will focus on strategies for calculating theoretical probabilities.  Consider having students run experiments or simulations to calculate compound probabilities for some of the scenarios, including the It’s Academic scenario.

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## Fan Appreciation Night, Part 1 - Page 4

In Module 6, students will be introduced to conditional probability.  In Module 6, Lesson 1 “Prize Winner,” students will learn that events are independent if P(A|B)=P(A).  Once students are able to calculate conditional probabilities, consider revisiting examples from this module to verify that the events are independent using conditional probabilities.

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## Fan Appreciation Night, Part 1 - Page 6

Students have had previous exposure to sample space in Grade 7.  Review this concept as needed to help build understanding of probabilities of compound events.  Consider including tree diagrams and other visual models.

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## Fan Appreciation Night, Part 1 - Page 7

If students need additional support, create additional compound events using the It’s Academic scenario.  Consider opportunities to work in groups to calculate probabilities or create additional problem scenarios.

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## Fan Appreciation Night, Part 1 - Page 9

This journal prompt is similar to the classic “Birthday Problem” in which a student has to determine the probability that two students in the class share the same birthday.  Encourage students to work in small groups to try to solve this problem.  Focus more on their thought process for solving the problem rather than the solution.

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## UDL Opportunities:

Checkpoint 2.1 Clarify vocabulary and symbols.
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.

Checkpoint 3.1:  Activate or supply background knowledge.
Students have had prior exposure to probability in Grade 7 Common Core.  Prior to this lesson assess the background knowledge of students informally or formally to determine readiness for this online module.

Checkpoint 3.2:  Highlight patterns, critical features, big ideas, and relationships.
Checkpoint 3.4:  Maximize transfer and generalization.
By the end of this lesson, students should be able to distinguish between independent and dependent events and calculate probabilities of compound events that involve intersections, i.e. P(A and B).

Checkpoint 6.2:  Support planning and strategy development.
Checkpoint 7.2:  Optimize relevance, value, and authenticity.
Checkpoint 8.3:  Foster collaboration and community.

The scenarios in this lesson are based on real-world scenarios in order to optimize relevance and authenticity.  The journal prompt offers students an opportunity to work independently or in small groups to solve a challenging problem.