| Code |
Description |
| 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”). ★ |
| MAFS.912.S-CP.1.2: | 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. ★ |
| MAFS.912.S-CP.1.3: | 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. ★ |
| MAFS.912.S-CP.1.4: | 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. ★ |
| MAFS.912.S-CP.1.5: | 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. ★ |
This cluster includes the following access points.
| Access Point Number |
Access Point Title |
| 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. |
| MAFS.912.S-CP.1.AP.2a: | Describe the characteristics that make events independent. |
| MAFS.912.S-CP.1.AP.2b: | Calculate the probability of events A and B occurring together.
P(A and B) = P(A) × P(B) |
| MAFS.912.S-CP.1.AP.3a: | Using a two-way table, find the conditional probability of A given B. |
| MAFS.912.S-CP.1.AP.3b: | Identify when two events are independent.
P(A and B) ÷ P(A) = P(B) |
| MAFS.912.S-CP.1.AP.4a: | Select or make an appropriate statement based on a two-way frequency table. |
| MAFS.912.S-CP.1.AP.5a: | Select or make an appropriate statement based on real-world examples of conditional probability. |
Vetted resources educators can use to teach the concepts and skills in this topic.
| Name |
Description |
| STEM Genetics Board Game: | This is a STEM challenge to assist in teaching the probability of traits being passed down from parents to offspring by creating and playing a board game.
|
| Comedy vs. Action Movies Frequency Interpretation: | Using a completed survey of male and female student interest in comedy vs. action movies, the students will create a two-way frequency table using actual data results, fraction results, and percent results. The students will then act as the movie producer and interpret the data to determine if it is in their best interest to make a comedy or action movie. As the Summative Assessment, the student will take on the job/role of an actor/actress and interpret the data to support their decision. |
| Casino Royale: | Students examine games of chance to determine the difference between dependent and independent conditional probability. |
| 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. |
| 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. |
| 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
|
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| Unexpected Answers: | This lesson is designed to introduce students to statistical situations where the probabilities or outcomes might not be what is first expected. The lesson provides links to discussions and activities motivated by the idea of unexpected answers. Finally, the lesson provides links to follow-up lessons designed for use in succession with an introduction to probability and unexpected answers in probability. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |
