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Title: Introduction to Probability
Description:
This lesson encourages the students to learn about probability within a group setting. It allows them to help each other gain a better understanding of how probability works. It teaches how to compute probability of basic problems and how to compute conditional probability.
Standard(s): [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7)
Title: Introduction to Probability
Description: This lesson encourages the students to learn about probability within a group setting. It allows them to help each other gain a better understanding of how probability works. It teaches how to compute probability of basic problems and how to compute conditional probability.
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Title: Don't Compound the Problem
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Students will be able to determine the probability of a compound event. Drawing on their knowledge of simple probability to find the probability of more complex outcomes. Students will create a poster, PowerPoint, booklet, or foldable to display the process of calculating a compound probability.
Standard(s): [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7)
Title: Don't Compound the Problem
Description: Students will be able to determine the probability of a compound event. Drawing on their knowledge of simple probability to find the probability of more complex outcomes. Students will create a poster, PowerPoint, booklet, or foldable to display the process of calculating a compound probability.
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Title: Maybe  Maybe Not (Probability Introduction)
Description:
This is a beginning lesson on the concept of probability. Through a series of informal comparisons, the student will explore the chances of various outcomes of an event. The student will use vocabulary associated with probability.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
Standard(s): [ELA2013] (3) 31: Engage effectively in a range of collaborative discussions (oneonone, in groups, and teacherled) with diverse partners on Grade 3 topics and texts, building on others' ideas and expressing their own clearly. [SL.3.1] [ELA2013] (3) 27: With guidance and support from adults, use technology to produce and publish writing (using keyboarding skills) as well as to interact and collaborate with others. [W.3.6] [TC2] (35) 9: Use technology tools to organize, interpret, and display data. [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 11: Use digital tools to analyze authentic problems. [TC2] (35) 9: Use technology tools to organize, interpret, and display data. [TC2] (35) 10: Use digital environments to collaborate and communicate. [TC2] (35) 11: Use digital tools to analyze authentic problems. [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: English Language Arts (3), or Mathematics (7), or Technology Education (3  5)
Title: Maybe  Maybe Not (Probability Introduction)
Description: This is a beginning lesson on the concept of probability. Through a series of informal comparisons, the student will explore the chances of various outcomes of an event. The student will use vocabulary associated with probability.This lesson plan was created as a result of the Girls Engaged in Math and Science University, GEMSU Project.
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Title: What Are the Chances?
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Students will use technology to investigate probability from basic terms to the theoretical probability of events.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [TC2] (68) 8: Identify safe uses of social networking and electronic communication. [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 8: Identify safe uses of social networking and electronic communication. [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7), or Technology Education (6  8)
Title: What Are the Chances?
Description: Students will use technology to investigate probability from basic terms to the theoretical probability of events.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: The Name Game (incorporates measures of central tendency and probability).
Description:
This Investigation is adapted from the Connected Math Unit "Data About Us". This investigation develops some introductory statistical and probability techniques. Students collect and organize data about the numbers of letters in their names. This openended problem will help you to assess the techniques your students have developed to organize, summarize and display data.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [AED] VA1 (712) 3: Apply steps artists use in the production of art, including conceptualizing ideas and forms, refining ideas and forms, and reflecting on and evaluating both the process of production and the product. [MA2013] (6) 26: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [6SP2] [MA2013] (6) 27: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [6SP3] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Arts Education (7  12), or Mathematics (6  7)
Title: The Name Game (incorporates measures of central tendency and probability).
Description: This Investigation is adapted from the Connected Math Unit "Data About Us". This investigation develops some introductory statistical and probability techniques. Students collect and organize data about the numbers of letters in their names. This openended problem will help you to assess the techniques your students have developed to organize, summarize and display data.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Can You Curl Your Tongue?
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This lesson is adapted from a Connected Mathematics Unit, How Likely is It? This investigation introduces biology as a source of applications for probability. In this lesson, Curling your Tongue, students determine how many students in the class can curl their tongues and use this data to make predictions about the probability of any one student being able to curl his or her tongue. Then they "Tracing Traitsthe experimental method is compared with the way in which geneticists study a person’s traits: by examining the genetic makeup of the person’s parents, grandparents, and other relatives. Students then gain experience with determining whether people have the tonguecurling trait based on the genetic probabilities. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [S1] (7) 8: Describe the function of chromosomes. [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7), or Science (7)
Title: Can You Curl Your Tongue?
Description: This lesson is adapted from a Connected Mathematics Unit, How Likely is It? This investigation introduces biology as a source of applications for probability. In this lesson, Curling your Tongue, students determine how many students in the class can curl their tongues and use this data to make predictions about the probability of any one student being able to curl his or her tongue. Then they "Tracing Traitsthe experimental method is compared with the way in which geneticists study a person’s traits: by examining the genetic makeup of the person’s parents, grandparents, and other relatives. Students then gain experience with determining whether people have the tonguecurling trait based on the genetic probabilities. This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Probability with Tree Diagrams
Description:
Following an Illuminations lesson on tree diagrams and probability, students work independently using a PowerPoint tutorial. The PowerPoint tutorial attachment provides review and practice problems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7), or Technology Education (6  8)
Title: Probability with Tree Diagrams
Description: Following an Illuminations lesson on tree diagrams and probability, students work independently using a PowerPoint tutorial. The PowerPoint tutorial attachment provides review and practice problems.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Making Compound Probability Simple
Description:
Students will determine the probability of a compound event. Students will draw on their knowledge of simple probability to find the probability of more complex outcomes. Students will create a poster, PowerPoint, booklet, or foldable to display the process of calculating a compound probability.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics (7)
Title: Making Compound Probability Simple
Description: Students will determine the probability of a compound event. Students will draw on their knowledge of simple probability to find the probability of more complex outcomes. Students will create a poster, PowerPoint, booklet, or foldable to display the process of calculating a compound probability.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Probability What Are The Odds?
Description:
This lesson introduces the student to the concept of probability. Students will explore the meaning of theoretical and experimental probability by viewing interactive websites. A lab activity will be performed using cooperative learning groups to allow the students to determine experimental and theoretical probability.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [S1] (8) 1: Identify steps within the scientific process. [TC2] (35) 8: Collect information from a variety of digital sources. [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5]
Subject: Mathematics (7), or Science (8), or Technology Education (3  5)
Title: Probability What Are The Odds?
Description: This lesson introduces the student to the concept of probability. Students will explore the meaning of theoretical and experimental probability by viewing interactive websites. A lab activity will be performed using cooperative learning groups to allow the students to determine experimental and theoretical probability.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: Determining Fairness in Games of Chance
Description:
This activity reviews and incorporates the laws of probability. Students will analyze various games of chance to determine their "fairness". Students will also view a United Streaming video on gaming and do a math journaling activity to show understanding of probability and fairness in games of chance.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
Standard(s): [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5]
Subject: Mathematics (7)
Title: Determining Fairness in Games of Chance
Description: This activity reviews and incorporates the laws of probability. Students will analyze various games of chance to determine their "fairness". Students will also view a United Streaming video on gaming and do a math journaling activity to show understanding of probability and fairness in games of chance.This lesson plan was created as a result of the Girls Engaged in Math and Science, GEMS Project funded by the Malone Family Foundation.
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Title: New York with $1200
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CONGRATULATIONS!!! You are Demopolis Middle School’s first –place winner of the annual MATHATHON!!!!!!!!!! You and three of your classmates have been awarded an exciting trip to NEW YORK CITY! You will each be given $1200 to cover all your expenses during your three day stay. You must use only your $1200 prize to cover all expenses (transportation costs, hotel accommodations, food, gratuities (tips), souvenirs, and entertainment). Please budget your money carefully – decide which purchases are most important and budget these first. Don’t forget to have fun!!
Standard(s): [TC2] (68) 2: Publish digital products that communicate curriculum concepts. [TC2] (68) 5: Use basic features of word processing, spreadsheets, databases, and presentation software. [TC2] (68) 6: Select specific digital tools for completing curriculumrelated tasks. [TC2] (68) 8: Identify safe uses of social networking and electronic communication. [TC2] (68) 9: Practice responsible and legal use of technology systems and digital content. [TC2] (68) 11: Use digital tools and strategies to locate, collect, organize, evaluate, and synthesize
information. [MA2013] (7) 4: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. [7NS1] [MA2013] (7) 8: Understand that rewriting an expression in different forms in a problem context can shed light on the problem, and how the quantities in it are related. [7EE2] [MA2013] (7) 9: Solve multistep reallife and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form, convert between forms as appropriate, and assess the reasonableness of answers using mental computation and estimation strategies. [7EE3] [MA2013] (7) 10: Use variables to represent quantities in a realworld or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. [7EE4] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [SS2010] CIV (7) 9: Apply principles of money management to the preparation of a personal budget that addresses housing, transportation, food, clothing, medical expenses, insurance, checking and savings accounts, loans, investments, credit, and comparison shopping.
Subject: Mathematics (7), or Social Studies (7), or Technology Education (6  8)
Title: New York with $1200
Description: CONGRATULATIONS!!! You are Demopolis Middle School’s first –place winner of the annual MATHATHON!!!!!!!!!! You and three of your classmates have been awarded an exciting trip to NEW YORK CITY! You will each be given $1200 to cover all your expenses during your three day stay. You must use only your $1200 prize to cover all expenses (transportation costs, hotel accommodations, food, gratuities (tips), souvenirs, and entertainment). Please budget your money carefully – decide which purchases are most important and budget these first. Don’t forget to have fun!!
Thinkfinity Lesson Plans
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Title: Combinations
Description:
This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probabilityandstatistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problemsolving skills (including elimination and collection of organized data) and drawing conclusions. The use of higherlevel thinking skills (synthesis, analysis, and evaluations) is the overall goal.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: 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. [SCP2] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama)
Subject: Mathematics Title: Combinations
Description: This unit of two lessons, from Illuminations, focuses on combinations, a subject related to the probabilityandstatistics strand of mathematics. Students are encouraged to discover all the combinations for a given situation using problemsolving skills (including elimination and collection of organized data) and drawing conclusions. The use of higherlevel thinking skills (synthesis, analysis, and evaluations) is the overall goal. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Boxing Up
Description:
In this lesson, from Illuminations, students explore the relationship between theoretical and experimental probabilities. They use an interactive box model that allows them to simulate standard probability experiments such as flipping a coin or rolling a die.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL2 (912) 40: 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. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: 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. [SCP6] [MA2013] AL2 (912) 44: 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. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Boxing Up
Description: In this lesson, from Illuminations, students explore the relationship between theoretical and experimental probabilities. They use an interactive box model that allows them to simulate standard probability experiments such as flipping a coin or rolling a die. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Birthday Paradox
Description:
This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthdayproblem function.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 26: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [6SP2] [MA2013] (6) 27: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [6SP3] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1] [MA2013] PRE (912) 51: (+) Calculate the expected value of a random variable; interpret it as the mean of the probability distribution. [SMD2]
Subject: Mathematics Title: Birthday Paradox
Description: This Illuminations lesson demonstrates the birthday paradox, using it as a springboard into a unit on probability. Students use the TI83 graphing calculator to run a Monte Carlo simulation with the birthday paradox and engage in a graphical analysis of the birthdayproblem function. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Explorations with Chance
Description:
In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: 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. [SCP2] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] PRE (912) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [SIC5] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6]
Subject: Mathematics Title: Explorations with Chance
Description: In this lesson, from Illuminations, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities for the learning phases of predicting results, playing the games, and calculating probability ratios. Thinkfinity Partner: Illuminations Grade Span: 9,10,11,12
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Title: Stick or Switch?
Description:
This lesson, from Illuminations, presents a version of a classic gameshow scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: 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. [SCP2] [MA2013] AL2 (912) 40: 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. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: 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. [SCP6] [MA2013] AL2 (912) 44: 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. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] PRE (912) 48: Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. [SIC5] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Stick or Switch?
Description: This lesson, from Illuminations, presents a version of a classic gameshow scenario. You pick one of three doors in hopes of winning the prize. The host opens one of the two remaining doors, which reveals no prize, and then asks if you wish to stick or switch. Which choice gives you the best chance to win? Students explore different approaches to this problem including guesses, experiments, computer simulations, and theoretical models. Thinkfinity Partner: Illuminations Grade Span: 6,7,8,9,10,11,12
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Title: Sticks and Stones Demo
Description:
This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 47: 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. [SCP2] [MA2013] AL2 (912) 40: 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. [SCP3] [MA2013] AL2 (912) 41: Construct and interpret twoway frequency tables of data when two categories are associated with each object being classified. Use the twoway table as a sample space to decide if events are independent and to approximate conditional probabilities. [SCP4] [MA2013] AL2 (912) 43: 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. [SCP6] [MA2013] AL2 (912) 44: 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. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] DM1 (912) 12: Use combinatorial reasoning and counting techniques to solve applicationbased problems. (Alabama) [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Sticks and Stones Demo
Description: This student interactive, from an Illuminations lesson, allows students to generate random throws for the game '' Sticks and Stones.'' In the game, three sticks are tossed and a player moves his or her marker according to how the sticks land. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: Sticks and Stones
Description:
In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multination celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game.
Standard(s): [MA2013] (3) 18: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one and twostep "how many more" and "how many less" problems using information presented in scaled bar graphs. [3MD3] [MA2013] (5) 19: Make a line plot to display a data set of measurements in fractions of a unit (^{1}/_{2}, ^{1}/_{4}, ^{1}/_{8}).
Use operations on fractions for this grade to solve problems involving information presented in line plots. [5MD2] [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 26: Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape. [6SP2] [MA2013] (6) 27: Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number. [6SP3] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8] [MA2013] AL1 (912) 42: Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. [SID2] [MA2013] AL1 (912) 43: Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). [SID3] [MA2013] AL1 (912) 47: 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. [SCP2] [MA2013] AL2 (912) 40: 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. [SCP3] [MA2013] AL2 (912) 42: Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. [SCP5] [MA2013] AL2 (912) 43: 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. [SCP6] [MA2013] AL2 (912) 44: 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. [SCP7] [MA2013] AL2 (912) 45: (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(BA) = P(B)P(AB), and interpret the answer in terms of the model. [SCP8] [MA2013] AL2 (912) 46: (+) Use permutations and combinations to compute probabilities of compound events and solve problems. [SCP9] [MA2013] GEO (912) 42: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] AL2 (912) 33: Write a function that describes a relationship between two quantities.* [FBF1] [MA2013] AL2 (912) 37: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 44: Understand statistics as a process for making inferences about population parameters based on a random sample from that population. [SIC1] [MA2013] PRE (912) 45: Decide if a specified model is consistent with results from a given datagenerating process, e.g., using simulation. [SIC2] [MA2013] PRE (912) 46: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. [SIC3] [MA2013] PRE (912) 47: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. [SIC4] [MA2013] ALT (912) 41: (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). [SMD6] [MA2013] PRE (912) 50: (+) Define a random variable for a quantity of interest by assigning a numerical value to each event in a sample space; graph the corresponding probability distribution using the same graphical displays as for data distributions. [SMD1]
Subject: Mathematics Title: Sticks and Stones
Description: In this Illuminations lesson, students play Sticks and Stones, a game based on the Apache game Throw Sticks, which was played at multination celebrations. Students collect data, investigate the likelihood of various moves, and use basic ideas of expected value to determine the average number of turns needed to win a game. Thinkfinity Partner: Illuminations Grade Span: 3,4,5,6,7,8
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Title: The Game of SKUNK
Description:
In this lesson, from Illuminations, students practice decisionmaking skills while playing a dice game called Skunk. This allows them to develop a better understanding of mathematical probability and of the concept of choice versus chance.
Standard(s): [MA2013] (6) 25: Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. [6SP1] [MA2013] (6) 28: Display numerical data in plots on a number line, including dot plots, histograms, and box plots. [6SP4] [MA2013] (6) 29: Summarize numerical data sets in relation to their context, such as by: [6SP5] [MA2013] (7) 17: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences. [7SP1] [MA2013] (7) 18: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. [7SP2] [MA2013] (7) 21: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around ^{1}/_{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event. [7SP5] [MA2013] (7) 22: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its longrun relative frequency, and predict the approximate relative frequency given the probability. [7SP6] [MA2013] (7) 23: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy. [7SP7] [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Subject: Mathematics Title: The Game of SKUNK
Description: In this lesson, from Illuminations, students practice decisionmaking skills while playing a dice game called Skunk. This allows them to develop a better understanding of mathematical probability and of the concept of choice versus chance. Thinkfinity Partner: Illuminations Grade Span: 6,7,8
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Title: Probability of Rolling Doubles
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This Khan Academy video explains the probability of rolling doubles on a pair of dice.
Standard(s): [MA2013] (7) 24: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. [7SP8]
Probability of Rolling Doubles
https://www.khanacad...
This Khan Academy video explains the probability of rolling doubles on a pair of dice.

