# MAFS.912.S-CP.1.1

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”).
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability: Conditional Probability & the Rules of Probability
Cluster: Level 1: Recall
Cluster: Understand independence and conditional probability and use them to interpret data. (Algebra 2 - Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date of Last Rating: 02/14
Status: State Board Approved

## Related Courses

This benchmark is part of these courses.
1200330: Algebra 2 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1200340: Algebra 2 Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1210300: Probability and Statistics Honors (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022 (current), 2022 and beyond)
1200335: Algebra 2 for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2019 (course terminated))
7912095: Access Algebra 2 (Specifically in versions: 2016 - 2018, 2018 - 2019, 2019 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.S-CP.1.AP.1a: Describe events as subsets of a sample space using characteristics or categories. For example: When rolling a die the sample space is 1, 2, 3, 4, 5, 6. The even numbers would be a subset of the sample space.
MAFS.912.S-CP.1.AP.1b: Describe the union of events in a sample space. For example: Event A contains soccer players, event B contains football players. The union of the sets is football players and soccer players all together.
MAFS.912.S-CP.1.AP.1c: Describe the intersection of events in a sample space. For example: Event A contains soccer players, event B contains football players. Intersection of the sets is players that participate in both soccer and football.
MAFS.912.S-CP.1.AP.1d: Describe the complement of events in a sample space. For example: Event A contains soccer players, event B contains football players. The complement of Event B is all players that are not football players.

## Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

## Assessments

Sample 2 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 3 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 1 - High School Algebra 2 State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

## Lesson Plans

Modeling Conditional Probabilities 1: Lucky Dip:

This lesson unit is intended to help you assess how well students are able to understand conditional probability, represent events as a subset of a sample space using tables and tree diagrams, and communicate their reasoning clearly.

Type: Lesson Plan

Modeling Conditional Probabilities 2:

This lesson unit is intended to help you assess how well students understand conditional probability, and, in particular, to help you identify and assist students who have the following difficulties representing events as a subset of a sample space using tables and tree diagrams and understanding when conditional probabilities are equal for particular and general situations.

Type: Lesson Plan

Medical Testing:

This lesson unit is intended to help you assess how well students are able to:

• make sense of a real life situation and decide what math to apply to the problem
• understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model
• represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams
• interpret the results and communicate their reasoning clearly

Type: Lesson Plan

Human Venn Diagram:

This activity is to strengthen students understanding of Venn diagrams, where the class becomes the problem. The class will be able to physically move and see how and why elements belong in each section of the Venn diagram.

Type: Lesson Plan

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

## Tutorials

Intersection of Two Subsets:

This tutorial will help the learners in learning how to determine the intersection of two subsets of a sample space by examining some particular examples.

Type: Tutorial

An event as a subsets of a sample space using tables and diagrams:

This tutorial will help the learners with their understanding of describing events as subsets of a sample space by using tables and tree diagrams.

Type: Tutorial

An Event as a Subset of a Sample Space:

This tutorial will help the learners with their understanding of describing events as a subsets of a sample space by focusing on some particular examples.

Type: Tutorial

## Video/Audio/Animation

MIT BLOSSOMS - Taking Walks, Delivering Mail: An Introduction to Graph Theory:

This learning video presents an introduction to graph theory through two fun, puzzle-like problems:"The Seven Bridges of Königsberg" and "The Chinese Postman Problem". Any high school student in a college-preparatory math class should be able to participate in this lesson. Materials needed include: pen and paper for the students; if possible, printed-out copies of the graphs and image that are used in the module; and a blackboard or equivalent. During this video lesson, students will learn graph theory by finding a route through a city/town/village without crossing the same path twice. They will also learn to determine the length of the shortest route that covers all the roads in a city/town/village. To achieve these two learning objectives, they will use nodes and arcs to create a graph and represent a real problem. This video lesson cannot be completed in one usual class period of approximately 55 minutes. It is suggested that the lesson be presented over two class sessions.

Type: Video/Audio/Animation

## Virtual Manipulative

Venn Diagrams for Set Operations:

This manipulative can be used to explore the set operations of unions, intersections, complements, and differences.

Type: Virtual Manipulative

## Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.

## Virtual Manipulative

Venn Diagrams for Set Operations:

This manipulative can be used to explore the set operations of unions, intersections, complements, and differences.

Type: Virtual Manipulative

## Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

The task is intended to address sample space, independence, probability distributions and permutations/combinations.

The Titanic 1:

This task asks students to calculate probabilities using information presented in a two-way frequency table.