| Code |
Description |
| MA.912.DP.4.1: | Describe events as subsets of a sample space using characteristics, or categories, of the outcomes, or as unions, intersections or complements of other events. |
| MA.912.DP.4.2: | Determine if events A and B are independent by calculating the product of their probabilities. |
| MA.912.DP.4.3: | Calculate the conditional probability of two events and interpret the result in terms of its context. |
| MA.912.DP.4.4: | Interpret the independence of two events using conditional probability. |
| MA.912.DP.4.5: | Given a two-way table containing data from a population, interpret the joint and marginal relative frequencies as empirical probabilities and the conditional relative frequencies as empirical conditional probabilities. Use those probabilities to determine whether characteristics in the population are approximately independent.Clarifications:
Clarification 1: Instruction includes the connection between mathematical probability and applied statistics. |
|
| MA.912.DP.4.6: | Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. |
| MA.912.DP.4.7: | Apply the addition rule for probability, taking into consideration whether the events are mutually exclusive, and interpret the result in terms of the model and its context. |
| MA.912.DP.4.8: | Apply the general multiplication rule for probability, taking into consideration whether the events are independent, and interpret the result in terms of the context. |
| MA.912.DP.4.9: | Apply the addition and multiplication rules for counting to solve mathematical and real-world problems, including problems involving probability. |
| MA.912.DP.4.10: | Given a mathematical or real-world situation, calculate the appropriate permutation or combination. |
This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| MA.912.DP.4.AP.1: | Given a sample space, select a subset of the sample space or given two sets, select the union, intersection, or complement of two sets. |
| MA.912.DP.4.AP.3: | Given the probability of two events, P(A and B) and P(A), in decimal form, select the conditional probability of the two events {[P(A and B))/(P(A)]}. |
| MA.912.DP.4.AP.6: | Recognize the concept of independence in everyday situations. |
| MA.912.DP.4.AP.7: | Given the probability of two mutually exclusive events in decimal form, use the addition rule for mutually exclusive probabilities: P(A or B)=P(A)+P(B). |
| MA.912.DP.4.AP.8: | Given the probability of two independent events in decimal form, use the multiplication rule for independent probabilities:
P(A and B)=P(A)P(B). |
| MA.912.DP.4.AP.2: | Given the probability of events A and B and the product of their probabilities, select whether the events are independent or not independent. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| Taxes using Venn Diagrams, Lesson 1: |
Students will review constructing and solving Venn diagrams with two and three data sets. Students will then convert text about the collection of taxes from the local, state, and federal governments into a Venn diagram. This is lesson 1 of a three-part integrated mathematics and civics mini-unit. |
| Taxes using Venn Diagrams, Lesson 2: | Students will discuss, recognize, and be challenged to list unions, intersections, and complements related to a Venn diagram created by three data sets. The data is the type of taxes assessed to citizens by the local, state, and federal governments. This is the second lesson in a 3-part integrated mathematics and civic mini-unit. |
| Dropping Out or Staying In: Two-Way Table Analysis: | This lesson will require students to calculate relative frequencies and determine if an association exists within a two-way table. The students will analyze the frequencies and write a response justifying the associations and trends found within the table. |
| Breakfast for Champions?: | Students will create and interpret two-way frequency tables using joint, marginal, and conditional frequencies in context. They will investigate whether breakfast is for champions. |
| Casino Royale: | Students examine games of chance to determine the difference between dependent and independent conditional probability. |
| What Are the Chances?: | Students will develop a program to simulate repeated rolls of a pair of dice in this lesson plan. They will program a realistic interaction between the user and the simulation as well as an analysis tool to identify the theoretical probability and track the observed probability for each outcome. |
| Name |
Description |
| Rain and Lightning: | This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions. |
| Return to Fred's Fun Factory (with 50 cents): | The task is intended to address sample space, independence, probability distributions and permutations/combinations. |
| Lucky Envelopes: | Students answer questions about the probabilities of independent and dependent events. |
| Cards and Independence: | This problem solving task lets students explore the concept of independence of events. |
| Alex, Mel, and Chelsea Play a Game: | This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events. |
| Coffee at Mom's Diner: | This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context. |
| Breakfast Before School: | The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context. |
| How Do You Get to School?: | This task requires students to use information in a two-way table to calculate a probability and a conditional probability. |
| Musical Preferences: | This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table. |
| The Titanic 2: | This task lets students explore the concepts of probability as a fraction of outcomes using two-way tables. |
| The Titanic 1: | This task asks students to calculate probabilities using information presented in a two-way frequency table. |
| Random Walk III: | The task provides a context to calculate discrete probabilities and represent them on a bar graph. |
| Random Walk IV: | This problem solving task on probability combinations gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities. |
| The Titanic 3: | This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data. |
| Name |
Description |
| The Logic of Drug Testing: | This informational text resource is intended to support reading in the content area. This article explores the reliability of drug tests for athletes, using mathematics. The author attempts to address this issue by relating drug tests to conditional probability. Throughout the text, various numbers that affect the calculation of a reliable probability are discussed. Numbers such as test sensitivity, test specificity, and weight of evidence are related to Bayes' theorem, which is ultimately used to calculate the conditional probability. |
| Understanding Uncertainty: What Was the Probability of Obama Winning?: | This informational text resource is intended to support reading in the content area. The article examines various factors that changed the uncertainty of whether Barack Obama would win the 2008 election. Specifically,the article discusses probability, the science of quantifying uncertainty. The article questions common methods for assessing probability where symmetrical outcomes are assumed. Finally, the author explains how to use past evidence to assess the chances of future events. |
Vetted resources students can use to learn the concepts and skills in this topic.
| Title |
Description |
| Rain and Lightning: | This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions. |
| Return to Fred's Fun Factory (with 50 cents): | The task is intended to address sample space, independence, probability distributions and permutations/combinations. |
| Lucky Envelopes: | Students answer questions about the probabilities of independent and dependent events. |
| Cards and Independence: | This problem solving task lets students explore the concept of independence of events. |
| Alex, Mel, and Chelsea Play a Game: | This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events. |
| Coffee at Mom's Diner: | This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context. |
| Breakfast Before School: | The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context. |
| Musical Preferences: | This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table. |
| The Titanic 2: | This task lets students explore the concepts of probability as a fraction of outcomes using two-way tables. |
| The Titanic 1: | This task asks students to calculate probabilities using information presented in a two-way frequency table. |
| Random Walk III: | The task provides a context to calculate discrete probabilities and represent them on a bar graph. |
| Random Walk IV: | This problem solving task on probability combinations gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities. |
| The Titanic 3: | This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data. |
Vetted resources caregivers can use to help students learn the concepts and skills in this topic.
| Title |
Description |
| Rain and Lightning: | This problem solving task challenges students to determine if two weather events are independent, and use that conclusion to find the probability of having similar weather events under certain conditions. |
| Return to Fred's Fun Factory (with 50 cents): | The task is intended to address sample space, independence, probability distributions and permutations/combinations. |
| Lucky Envelopes: | Students answer questions about the probabilities of independent and dependent events. |
| Cards and Independence: | This problem solving task lets students explore the concept of independence of events. |
| Alex, Mel, and Chelsea Play a Game: | This task combines the concept of independent events with computational tools for counting combinations, requiring fluent understanding of probability in a series of independent events. |
| Coffee at Mom's Diner: | This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context. |
| Breakfast Before School: | The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context. |
| Musical Preferences: | This problem solving task asks students to make deductions about the kind of music students enjoy by examining data in a two-way table. |
| The Titanic 2: | This task lets students explore the concepts of probability as a fraction of outcomes using two-way tables. |
| The Titanic 1: | This task asks students to calculate probabilities using information presented in a two-way frequency table. |
| Random Walk III: | The task provides a context to calculate discrete probabilities and represent them on a bar graph. |
| Random Walk IV: | This problem solving task on probability combinations gives a situation where the numbers are too large to calculate, so abstract reasoning is required in order to compare the different probabilities. |
| The Titanic 3: | This problem solving task asks students to determine probabilities and draw conclusions about the survival rates on the Titanic using a table of data. |
