## Bivariate Data Analysis Common Core Algebra 1 Homework Practice

## Presentation on theme: "Algebra 1 - Statistics: Bivariate & Categorical Data Unit 3"— Presentation transcript:

1 **Algebra 1 - Statistics: Bivariate & Categorical Data Unit 3**

Facilitator notesTime: n/aHandouts/participant activity: n/aFocus points:Title Page

2 PurposeProvided is a lesson for teachers to use to help students understand and analyze bivariate data. Included are the following:StandardsStatistics and Probability Learning ProgressionLesson AgendaGetting Ready for the Lesson (Resources and Tips)Vocabulary ActivitiesLesson(Presentation and Video)Textbook ConnectionsAdditional ResourcesFacilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Review the components that this PD provides:StandardsLearning ProgressionsLesson AgendaResources & TipsVocabulary ActivitiesLessonTextbook ConnectionsAdditional Resources

3 Common Core StandardsS-ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data. Recognize possible associations and trends in the data.(Understand, 2) (Analyze, 2) (Analyze, 3)Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Identifying the standards for lesson and unwrapping them.

4 Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Yellow, Red, & Green circles indicate the appropriate levels of DOK as required by the standardsThe Blue circles fill in the instructional paths needed to assist students in reaching those DOK levels.

5 Math PracticesMP1Make sense of problems and persevere in solving them.MP2Reason abstractly and quantitatively.Facilitator notesTime: 1-2 minutesHandouts/participant activity: n/aFocus points:Review the math practices associated with the lesson being presented.

6 **Statistics & Probability Prerequisite Skills: CC Math 8**

Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:The CA Framework also describes how students may accelerate to prepare for higher mathematics courses by compacting courses (animate circles around “compacted” and “accelerated”).Compacting means to compress content, which may entail the teacher and students working at a faster pace to complete the content. There is no skipping of standards within the compacted courses to accelerate to higher mathematics courses.By compacting courses in the middle school grades, students can be allowed to enter Geometry by the time they enter high school.With the California standards, student would simply skip course to get ahead. With the Common Core standards, students can still get ahead, but can no longer skip courses or rather standards. Therefore they must move at a faster pace.

7 **Middle School Focus Grade 6 Grade 7**

Develop understanding of statistical variability.Summarize and describe distributions.Grade 7Use 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.Grade 8Investigate patterns of association in bivariate data.Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:What are those standards that you must focus on and which ones are not part of your course with the new shifts in standard under common core?Grade 6Develop understanding of statistical variability.Summarize and describe distributions.Grade 7Use 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.Grade 8Investigate patterns of association in bivariate data.Let the participants know that they will use this handout in a later activity.Source: California Framework

8 **High School Focus Algebra I Geometry Algebra II**

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.GeometryConditional Probability and the Rules of ProbabilityUnderstand independence and conditional probability and use them to interpret data.Use the rules of probability to compute probabilities of compound events in a uniform probability model.Using Probability to Make Decisions Use probability to evaluate outcomes of decisionsAlgebra IIInterpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable.Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments.Make inferences and justify conclusions from sample surveys, experiments, and observational studies.Using Probability to Make Decisions Use probability to evaluate outcomes of decisions.Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:What are those standards that you must focus on and which ones are not part of your course with the new shifts in standard under common core?Algebra ISummarize, 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.GeometryConditional Probability and the Rules of ProbabilityUnderstand independence and conditional probability and use them to interpret data.Use the rules of probability to compute probabilities of compound events in a uniform probability model.Using Probability to Make Decisions Use probability to evaluate outcomes of decisionsAlgebra IIInterpreting Categorical and Quantitative Data Summarize, represent, and interpret data on a single count or measurement variable.Making Inferences and Justifying Conclusions Understand and evaluate random processes underlying statistical experiments.Make inferences and justify conclusions from sample surveys, experiments, and observational studies.Using Probability to Make Decisions Use probability to evaluate outcomes of decisions.Source: California Framework

9 **Learning Progression: HS Statistics & Probability**

Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Let’s take closer look at the California Department of Education’s description of the CC Math 8 course.Read the highlighted portionThe state framework shows the importance of the Grade 8 Math Course and how it has became the new gateway course for higher level math, as well as how Algebra 1 had shifted to high school.

10 **Lesson Agenda Vocabulary**

Video: Calculate conditional probabilities for bivariate categorical data by using two-way tablesLesson: M&M TaskTextbook ConnectionsFacilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Review the lesson agenda prior to implementation

11 **Planning for Instruction with Analysis of Bivariate Data**

Sweet SuccessPlanning for Instruction with Analysis of Bivariate DataFacilitator notesTime: 1 minuteHandouts/participant activity: n/aFocus points:Title Page for lesson

12 Getting ReadyPre-assessment- used to determine understanding of prerequisite skillsPrerequisite skills include7 SP 1 – 8Use 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.8 SPInvestigate patterns of association in bivariate data.Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Review what standards should be covered in a pre-assessment activity. This shows what students should have already learned prior to your course. Using a pre-assessment activity will assist students in frontloading prior knowledge before beginning new learning.

13 **Misconceptions and Anticipated Issues**

Common IssuesSuggested Strategies/ResourcesUsing the wrong total from the frequency tableMisunderstanding between the connection of joint frequency, marginal frequency, conditional relative frequencyFinding the wrong probabilityIncorrect calculations when dividing and dividing the wrong valuesNot able to read the symbol for conditional probabilityUse the additional practice worksheets from learnzilllion lessonUse more than 1 vocabulary organizer to address key vocabularyHave students use manipulatives, such as the cups in the task to correctly identify the sample being used and use additional worksheets from learnzillion lessonAllow students to use a calculatorReview notation during the lessonFacilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:These are guided questions to improve our students’ learning when misconceptions may occur.

14 **Required Resources Materials Required Special Materials:**

6 cups (clear is preferable) per group1 regular serving size bag of candy-coated milk chocolates for each group1 regular serving size bag of candy-coated chocolates with peanuts for each group OR1 bag per group of candy-coated milk chocolates manipulatives cut and assembled in a baggie1 bag per group of candy-coated milk chocolates with peanuts manipulatives cut and assembled in a baggie (use standard cut-outs on colored paper to differentiate)Handouts:Learnzillion presentation handoutsLearnzillion additional worksheetshttps://learnzillion.com/lesson_plans/1030Facilitator notesTime: 2-3 minutesHandouts/participant activity: n/aFocus points:Review the list of resources needed for the lesson and where to find materials online.

15 **Or you could use: Word Map, Frayer Model, etc.**

Needed VocabularyProbabilityMarginal ProbabilityJoint ProbabilityBivariateConditional ProbabilityTwo-Way TableRelative ProbabilityOr you could use: Word Map, Frayer Model, etc.Layered Book ExampleFacilitator notesTime: 4-5 minutesHandouts/participant activity: n/aFocus points:This shows a list of required academic language vocabulary that is needed for the lesson. In addition, a strategy, “Layered Book” is shown with the suggestion that there are alternative strategies that can be used as well.

16 LearnzillionFor 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.Facilitator notesTime: 4-5 minutesHandouts/participant activity: n/aFocus points:This is an introduction to the Learnzillion.com website where today’s lesson was pulled from. Teachers can sign up for a free account and have full access.

17 **https://learnzillion.com/lesson_plans/1030**

Calculate conditional probabilities for bivariate categorical data by using two-way tablesFacilitator notesTime: minutesHandouts/participant activity: n/aFocus points:Click on the hyper link to take you to the lesson. Lesson includes: PowerPoint, Video, and handouts. As a department, we will explore this resources togetherhttps://learnzillion.com/lesson_plans/1030

18 **Planning and Time Activities Time Notes Preparation 2 hours**

Includes creating a pre-assessment, making copies, obtaining materialsPre-lessonsReview of 7th and/or 8th grade SP standardsVocabulary1 hourDefining Conditional Probability, including joint and marginal frequencyM&M Task-LessonExplanation and completion of workPractice and Additional TasksAdditional worksheets from LearnZillion, Textbook practice, Illustrative Mathematics TasksTotal Time10 hoursFacilitator notesTime: minutesHandouts/participant activity: n/aFocus points:Suggested pacing for this lesson

19 **Textbook Connection Big Ideas**

Textbook Algebra 1 Section 11.4Classwork: Page problems 1 – 5Homework: Page problemsExtra Practice: Algebra 1 Resources by Chapter Section 10.3Practice A and B pageEnrichment and Extension pagePuzzle Time Page 408Student Journal Algebra 1 Section 11.4Two-Way Tables and Probability PageAssessment Book Algebra 1 Section 10.3PageFacilitator notesTime: 1-2 minutesHandouts/participant activity: n/aFocus points:Connections to the Big Ideas textbook for this specific standard / concept. As a department we may want to review this as well to compare to the Learnzillion lesson.

20 **Textbook Connection Spring Board**

Lesson 40-1 Bivariate DataClasswork Page 595 – 598 Problems 1 – 7Homework Page 600 ProblemsFacilitator notesTime: 1-2 minutesHandouts/participant activity: n/aFocus points:Connections to the SpringBoard textbook for this specific standard / concept. As a department we may want to review this as well to compare to the Learnzillion lesson.

21 **Textbook Connection CPM**

S-ID 5 is not in CPMFacilitator notesTime: 1-2 minutesHandouts/participant activity: n/aFocus points:Connections to the CPM textbook for this specific standard / concept. Please note, CPM does not address this standard. This is when a resource such as Learnzillion comes in handy.

22 Additional ResourcesIllustrative Mathematics -Two-Way Tables and ProbabilityThe Titanic 1: S.CP.1,4, and 6The Titanic II: S.CP.2-6Fred's FactoryBut Mango is My Favorite…Khan Academy -Engage NY Common Core CurriculumAlgebra II Module 4https://www.engageny.org/resource/algebra-ii-module-4-topic-a-lesson-3-07th Grade StandardsModule 5 – Statistics and ProbabilityFacilitator notesTime: minutesHandouts/participant activity: n/aFocus points:This is a list of additional resources surrounding the standards that may be used. If time permits, as a department, explore these sites.

23 **Contact your Secondary Math Coordinator**

Need Help?Contact your Secondary Math Coordinator

Сьюзан помнила, что за последние двадцать минут вводила только свой персональный код, когда выходила переговорить со Стратмором. Невозможно представить, что машина могла спутать пароль с командой отключения «Следопыта».

Понимая, что теряет время, Сьюзан вызвала на экран регистр замка и проверила, верно ли был введен персональный код. Все было сделано как положено. «Тогда откуда же пришла команда на ручное отключение?» - рассердилась .

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