 # Common Core High School Statistics & Probability Teaching and Learning Resources

## Domain: CP: Conditional Probability and the Rules of Probability • 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. ### CP-A: Understand independence and conditional probability and use them to interpret data

Standards:

• CP-A.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”).
• CP-A.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.
• CP-A.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.
• CP-A.4. Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.
• CP-A.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.

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.

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

Constructed-response:

Khan Academy: Practice questions with videos.

Illustrative Mathematics: Statistics and Probability:

• 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: https://www.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.

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

Standards:

• CP-B.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.
• CP-B.7. Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
• CP-B.8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
• CP-B.9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

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.

Omnicalculator.com: Statistics calculators include a Probability Calculator and Bayes' Theorem Calculator.  Explanation of theory is included for each.

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:

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:

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.

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: Statistics and Probability:

Mathematics Assessment Project: Standards: High School: Statistics & Probability: https://www.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. Back to top Common Core Math: Intro | HS Statistics & Probability Domain: ID  |  IC  |  CP  |  MD  |