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Common Core Math

High School Statistics & Probability Teaching and Learning Resources

Domain: CP: Conditional Probability and the Rules of Probability

Common Core Math

Select the cluster for resources on this page:

  • CP-A: Understand independence and conditional probability and use them to interpret data

  • CP-B: Use the rules of probability to compute probabilities of compound events.

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CP-A: Understand independence and conditional probability and use them to interpret data

Standards:

 

Technology-enhanced investigations:

Stattrek.com Statistics Dictionary contains the following key vocabulary for this domain.  Select the term from the Stattrek pull-down menu.  Use with CP-A, CP-B:

addition rule complement independent sample space
Bayes' theorem/rule conditional probablity intersection two-way table (frequency)
combination; permutation event multiplication rule union

 

Art of Problem Solving: Counting and Probability Videos: These are the videos that go with each of the sections within the 14-chapter textbook, Introduction to Counting & Probability.

Cut the Knot: Applet: Conditional Probability and Independent Events: This applet is an interactive tool that helps learners to grasp the definition and the significance of conditional probabilities and independent events.  Use with CP-A.3.

Data and Story Library (DASL): Use with CP-A.4.

LearnZillion:

Purple Math: Venn Diagrams: Introduction, Logic and set notation, Set notation exercises, Venn word problems.  Use with CP-A.1.

McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 10 Counting Methods and Probability for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook.  Use with CP-A.

MIT BLOSSOMS: Video lessons with additional teacher and learner resources.  Descriptions are from the video summaries.

  • Flu Math Games: "This video lesson shows students that math can play a role in understanding how an infectious disease spreads and how it can be controlled."  Additional simulations are included.  Aligns with Algebra standards SSE-B.3.c and REI-A.1; Function standards IF-C.8.b, BF-B.4.a, and LE-A-1.(a, c); and Statistics and Probability standards ID-B.6.a, IC-A.1, IC-B.4, CP-A.2, and MD-A.1.
  • The Monty Hall Problem or How to Outsmart a Game Show and Win a Car: "This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life."  Aligns with CP-A.2, CP-B.8, CP-B.9, MD-B.5.a, MD-B.6, and MD-B.7.

Stat Trek: Tutorials:

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 12 manipulatives addressing CP-A.1, 7 manipulatives for CP-A.2, 6 manipulatives for CP-A.3, 1 manipulative for CP-A.4, 7 manipulatives for CP-A.5.  Among those:

Wolfram MathWorld:

Zweigmedia.com: Tutorials and examples using fill-in or multiple choice to test understanding.  Learners can also choose to do game versions of some topics.  Use with CP-A:

Multiple Choice:

CK-12: Venn Diagrams: Use Venn diagrams to describe situations when problem solving. Practice questions with review content and video.  Aligns with CP-A.1.

Glencoe Online Learning Center, Algebra 2 (2010) self-check quiz: Ch. 12, Lesson 3: Conditional Probability

Glencoe Online Learning Center, Geometry (2010) self-check quizzes:

Khan Academy: Practice questions with videos.

MathsIsFun.com:

  • Probability: Complement Contains a concise explanation of the complement, outcomes that are "not" the event, with worked examples.  Following the explanation are ten multiple choice exercises.  Use with CP-A.1.
  • Probability: Independent Events Contains a concise explanation of the independent events with worked examples.  Following the explanation are ten multiple choice exercises.  Use with CP-A.2.
  • Dependent Events: Conditional Probability Contains a concise explanation of the conditional probability and dependent events with worked examples.  Following the explanation are ten multiple choice exercises.  Use with CP-A.3.

McDougal Littell ClassZone, Algebra 2, 2011:

McDougal Littell ClassZone, Geometry, 2011: Ch. 11.7 Quiz: Use Geometric Probability

OpenEd:

Constructed-response:

Khan Academy: Practice questions with videos.

OpenEd: Two way frequency tables: 3 free response questions.  Includes related review resources.  Aligns with CP-A.4.

Performance tasks:

Illustrative Mathematics:

  • The Titanic I: This task aligns with standards CP-A.1, CP-A.4, and CP-B.6.
  • The Titanic 2: This task aligns with standards CP-A.2, CP-A.3, CP-A.4, CP-A.5 and CP-B.6.

Mathematics Assessment Project: Standards: High School: Statistics & Probability: http://map.mathshell.org/stds.php?standardid=1233

Mathematics Vision Project, Secondary 2 Student Edition:

  • Module 9: Probability: This module contains 6 classroom tasks.  Standards CP-A.2, CP-A.3, CP-A.4, and CP-A.5 are found within task 2 and tasks 5-6.

 

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CP-B: Use the rules of probability to compute probabilities of compound events.

Standards:

Technology-enhanced investigations:

Art of Problem Solving: Counting and Probability Videos: These are the videos that go with each of the sections within the 14-chapter textbook, Introduction to Counting & Probability.

Cut the Knot: Bayes' Theorem: Bayes' Theorem is used as a direct application of conditional probability of A given B: P(A|B) = P(A∩B) / P(B).  Three practical examples are provided with solutions.  Use with CP-B.6.

Study.com: College Math: Probability and Statistics: 11 video lessons.  Each includes sample problems and a quiz.  View the probability lessons to "learn about types of events that express probability, including simple, compound, complementary, independent and dependent. You'll learn what the outcomes of these events are and how you can calculate said probability. Other topics covered include the 'at least one' rule of independent events, permutations, math combinations and more."  Use with CP-B.

LearnZillion:

  • Lesson set: Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A: Two video lessons: Understand conditional probability, calculate conditional probabilities using a two-way table.  Aligns with CP-B.6.
  • Lesson set: Apply the addition rule: Two video lessons: Use addition rule to calculate the probability of disjoint event A or B, non-disjoint events and the addition rule, solve word problems using the addition rule, calculate probabilities by using the complement and addition rule, use conditional probability, calculate different probabilities by working backward using the addition rule.  Aligns with CP-B.7.

McDougal Littell ClassZone, Algebra 2, 2011: Select resources in Ch. 10 Counting Methods and Probability for interactive practice: Animations (Virtual manipulatives), Games/Vocabulary Flashcards, and PowerPoint lesson examples, and interactive problems within the eWorkbook. See multiple choice below for related sections to use within the eWorkbook.  Use with CP-B.

MIT BLOSSOMS: Video lesson with additional teacher and learner resources.  Description is from the video summary.  The Monty Hall Problem or How to Outsmart a Game Show and Win a Car: "This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life."  Aligns with CP-A.2, CP-B.8, CP-B.9, MD-B.5.a, MD-B.6, and MD-B.7.

Wolfram Demonstrations Project: Download the free Wolfram CDF player to interact with the following manipulatives.  Note: Within the Wolfram Demonstration Project are 6 manipulatives addressing CP-B.6, 5 manipulatives for CP-B.7, 6 manipulatives for CP-B.8, 23 manipulatives for CP-B.9.  Among those:

Zweigmedia.com:  Tutorials and examples using fill-in or multiple choice to test understanding.  Learners can also choose to do game versions of some topics.  Use with CP-B:

Multiple Choice:

Glencoe Online Learning Center, Geometry (2010) self-check quizzes: Ch. 13, Lesson 2: Probability with Permutations and Combinations Aligns with CP-B.9.

MathsIsFun.com:

  • Mutually Exclusive Events: Contains a concise explanation of the Addition Rule with examples for events that are mutually exclusive and not mutually exclusive.  Following the explanation are ten multiple choice exercises.  Use with CP-B.7.
  • Probability Tree Diagrams: Contains explanation of the use of tree diagrams and the multiplication principle to calculate probabilities of independent and dependent events.  Following the explanation are ten multiple choice exercises.  Use with CP-B.8.
  • Permutations and Combinations: Contains a concise explanation of the concepts and formulas used to calculate permutations and combinations.  Following the explanation are ten multiple choice exercises.  There is a Permutations and Combinations Calculator.  Use with CP-B.9.

McDougal Littell ClassZone, Algebra 2, 2011:

OpenEd:

Constructed-response:

Khan Academy: Practice questions with videos.

L. Spector: The Math Page: Topics in Precalculus: Use with CP-B.9:

  • Factorials: The concept of factorials and working with those is needed for calculating permutations and combinations.
  • Permutations and Combinations: These lessons help learners to understand the concepts of permutations and combinations and include practice problems with answers provided.

OpenEd:

Performance tasks:

Georgia Standards of Excellence Framework: Pre-Calculus Unit 8: Probability.  This unit contains eight tasks, including a culminating task: Design a Lottery Game. Tasks align with CP-B.8, CP-B.9, all standards in MD-A and MD-B, and related standards CP-A.2, CP-A.3, CP-B.6, and CP-B.7.

Illustrative Mathematcs:

Mathematics Assessment Project: Standards: High School: Statistics & Probability: http://map.mathshell.org/stds.php?standardid=1233 Task 438: Medical Testing

Mathematics Vision Project, Secondary 2 Student Edition:

  • Module 9: Probability: This module contains 6 classroom tasks.  Standards CP-B.6 and CP-B.7 are found within tasks 1-4.

 

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