Comprehensive Overview of Statistics and Probability Education
This educational resource provides a structured lesson plan to help teachers guide students in understanding and analyzing statistics and probability. It covers learning progression, standards, lesson agenda, vocabulary activities, and additional resources. The focus spans from middle school to high school, emphasizing concepts like finding probabilities of compound events, representing sample spaces, statistical variability, inference drawing, and probability models. The content includes visual aids, Common Core standards alignment, and math practices to enhance problem-solving skills.
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Math 7 Statistics and Probability Unit 4
Purpose Provided is a lesson for teachers to use to help students understand and analyze Statistics and Probability. Included are the following: Statistics and Probability Learning Progression Standards Lesson Agenda Getting Ready for the Lesson (Resources and Tips) Lesson (Presentation and Video) Vocabulary Activities Textbook Connections Additional Resources
Common Core Standards O7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. O b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., rolling double sixes ), identify the outcomes in the sample space which compose the event. (Understand, 2) (Understand, 1)
Math Practices MP 1 Make sense of problems and persevere in solving them. MP 2 Reason abstractly and quantitatively. MP 4 Model with mathematics. MP 5 Use appropriate tools strategically.
Statistics and Probability Prerequisite Skills: CC Math 6 https://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf
Middle School Focus Grade 6 Grade 7 Grade 8 Develop understanding of statistical variability Summarize and describe distributions Use random sampling to draw inferences about a population Draw informal comparative inferences about two populations Investigate chance processes and develop, use, and evaluate probability models Investigate patterns of association in bivariate data Source: California Framework
High School Focus Algebra 1 Geometry Algebra 2 Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models Understand independence and conditional probability and use them in interpret data Use the rules of probability to compute probabilities of compound events in a uniform probability model Use probability to evaluate outcomes of decisions Summarize, represent, and interpret data on a single count or measurement variable Understand and evaluate random processes underlying statistical experiments Make inferences and justify conclusions from sample surveys, experiments, and observational studies Use probability to evaluate outcomes of decisions Source: California Framework
Learning Progression: HS Statistics and Probability https://commoncoretools.files.wordpress.com/2011/12/ccss_progression_sp_68_2011_12_26_bis.pdf CCSS Domain Progression
Lesson Agenda O Vocabulary O Video: Representing the probability of compound events using organized tree diagrams O Lesson: What s for Dinner? O Textbook Connections
Representing the Probability of Compound Events Using Organized Tree Diagrams Planning for Instruction
Getting Ready O Pre-assessment: Used to determine understanding of prerequisite skills O Prerequisite skills include: O 6.SP.4 to 6.SP.5 O Summarize and describe distributions O Display numerical data O Summarize numerical data sets in relation to their context
Misconceptions and Anticipated Issues Common Issues Common Issues Suggested Strategies/Resources Suggested Strategies/Resources a. Use the additional practice worksheets from LearnZillion lesson. b. Understand if the event is independent or dependent. c. Understand experimental probability vs. theoretical probability. Students may think that because an event continues to occur that the likelihood of a new event occurring increases. Students may believe that in random events involving selection, the results are dependent on numbers rather than on ratios between numbers. Students may believe that experimental probability and theoretical probability are always equal. a. b. c.
Required Resources Materials Required Materials Required Special Materials: O Frequency Table O Spinners Handouts: O LearnZillion presentation handouts O LearnZillion additional worksheets O https://learnzillion.com/lesson_plans/871- representing-the-probability-of-compound-events-using- organized-tree-diagrams
Needed Vocabulary O Independent Event O Dependent Event O Sample Space O Compound Events O Experimental Probability O Theoretical Probability Or you could use: Word Map, Frayer Model, etc. Layered Book Example
LearnZillion For this lesson you need to create an account to access the handouts from LearnZillion. This is a free account and you will have access to many more lessons.
Adding Rational Numbers Using a Number Line https://learnzillion.com/lesson_plans/871-representing-the-probability-of- compound-events-using-organized-tree-diagrams
Planning and Time Activities Activities Time Time Notes Notes Preparation 2 hours Includes creating a pre- assessment, making copies, obtaining materials Pre-lessons 1 hours Review of 6th and/or 7th grade SP standards Vocabulary 1 hour Defining Independent Event, Dependent Event, Sample Space, Compound Events, Experimental Probability, and Theoretical Event Task-Lesson 2 hours Explanation and completion of work Practice and Additional Tasks 2 hours Additional worksheets from LearnZillion, Textbook practice, Illustrative Mathematics Tasks Total Time Total Time 9 hours 9 hours
Textbook Connection California Math Course 2 O Textbook Inquiry Lab: Textbook Inquiry Lab: O How can one event impact a second event in a How can one event impact a second event in a probability experiment? Pages 773 probability experiment? Pages 773 - - 774 O Textbook Lesson: Textbook Lesson: O Lesson 9 Lesson 9- -7 Independent and Dependent Events 7 Independent and Dependent Events Pages 775 Pages 775 782 782 O On On- -line Resources: line Resources: O Videos: Dependent Events, Probability of Independent Videos: Dependent Events, Probability of Independent Events, Real Events, Real- -World Examples World Examples O eTool eTool Kit Kit O Online PD Online PD 774
Textbook Connection Go Math Course 2 O Textbook Explore Activity: O Exploring Compound Probability page 381 O Textbook Lesson: O Lesson 12.3 Experimental Probability of Compound Events pages 382 386 O Online Resources O Professional Development Video
Textbook Connection CPM Course 2 O Course 2: O 5.2.5 Probability Trees O 5.2.6 Compound Events O Online Technology: O Spinner Tool
Additional Resources Illustrative Mathematics Mathematics - - www.illustrativemathematics.org www.illustrativemathematics.org O Waiting Times O Sitting Across from Each Other O Rolling Twice O Tetrahedral Dice O Red, Green, or Blue? O Khan Academy Khan Academy - - www.khanacademy.org www.khanacademy.org O Engage NY: Grade 7 Mathematics Module 5, Topic A, Lesson 7 O Illustrative
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