# Teacher Resources

## Prize Winner, Part 1

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

**Estimated Time: **90 minutes

### Lesson Objectives:

- The students will understand and find independent and dependent conditional probabilities.
- The students will recognize, explain and interpret conditional probabilities given everyday language and everyday situations.

**Key Common Core State Standards:**

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.

S.CP.3: Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*.

S.CP.5: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. *For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.*

S.CP.6: Find the conditional probability of *A* given *B* as the fraction of *B*’s outcomes that also belong to *A*, and interpret the answer in terms of the model.

**Supporting Common Core State Standards:**

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

7.SP.C.8a: 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.

7.SP.C.8b: 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.

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”).**Standards for Mathematical Practice Emphasized:**

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

## Instructional Notes:

In this lesson, the students find and interpret conditional probabilities. The students look at various simple carnival games, and determine the probabilities of winning. Winning the games involves conditional probabilities. The students should have knowledge of simple probability, including finding the probability of independent and dependent events. The students should be familiar with probability involving unions, intersections and complements, as well. These concepts can be studied and/or reviewed in Module 5, although Module 6 is independent of the lessons taught in the prior module.

Take time to read the Progressions for the Common Core State Standards in Mathematics , pp 14 – 17. These documents provide an overview of conditional probability, providing real-world applications as well as simulation and two-way table examples. The examples provided in these documents can be used as an assessment for learning as students work through the lesson.

It is important for the students to logically think about what probability they are looking for in terms of the given situation. It is far more critical for a student to have a contextual understanding of probability, rather than to simply memorize formulas. The games used in this lesson are simple to construct. Consider allowing the students the time to “act out” the games so they can get a feeling for what the probabilities are asking while developing an understanding of experimental probability.> Go to Prize Winner, Part 1 lesson

## Sample Responses

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

## Prize Winner, Part 1 - Page 8

If the students are having difficulty with the concept of independence and dependence, refer to Module 5. Select the activities to help refresh the students’ knowledge.

## Prize Winner, Part 1 - Page 9

The concept of independence and dependence with respect to conditional probabilities can be a difficult concept for students. Note that this concept will be more closely looked at in the subsequent lesson. Understanding conditional probabilities can be more easily understood with two-way tables, which is the focus of the next lesson.

## UDL Opportunities:

**Principle 1: Provide Multiple Means of Representation**

Checkpoint 1.1 Offer ways of customizing the display of information.

Checkpoint 1.3 Offer alternatives for visual information.

Checkpoint 2.1 Clarify vocabulary and symbols.

Checkpoint 2.2 Clarify syntax and structure.

Checkpoint 2.3 Support decoding text, mathematical notation, and symbols.

Checkpoint 3.1 Activate or supply background knowledge.

Checkpoint 3.2 Highlight patterns, critical features, big ideas, and relationships.

Checkpoint 3.4 Maximize transfer and generalization.

**Principle 2: Provide Multiple Means of Action and Expression**

Checkpoint 4.2 Optimize access to tools and assistive technologies.

Checkpoint 5.3 Build fluencies with graduated levels of support for practice and performance.

Checkpoint 6.2 Support planning and strategy development.

Checkpoint 6.3 Facilitate managing information and resources.

Checkpoint 6.4 Enhance capacity for monitoring progress.

**Principle 3: Provide Multiple Means of Engagement**

Checkpoint 7.2 Optimize relevance, value, and authenticity.

Checkpoint 7.3 Minimize threats and distractions.

Checkpoint 8.4 Increase mastery-oriented feedback.

Checkpoint 9.1 Promote expectations and beliefs that optimize motivation.

Checkpoint 9.3 Develop self-assessment and reflection.