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Pre-APGeometry with StatisticsCOURSE GUIDEINCLUDESApproach toteaching andlearningCourse mapCourse frameworkSampleassessmentquestions

Pre-APGeometrywith Statistics COURSE GUIDEPlease visit Pre-AP online at preap.collegeboard.org for more information and updates aboutthe course and program features.

ABOUT COLLEGE BOARDCollege Board is a mission-driven not-for-profit organization that connects students to collegesuccess and opportunity. Founded in 1900, College Board was created to expand accessto higher education. Today, the membership association is made up of over 6,000 of theworld’s leading educational institutions and is dedicated to promoting excellence and equityin education. Each year, College Board helps more than seven million students prepare fora successful transition to college through programs and services in college readiness andcollege success—including the SAT and the Advanced Placement Program . The organizationalso serves the education community through research and advocacy on behalf of students,educators, and schools.For further information, visit www.collegeboard.org.PRE-AP EQUITY AND ACCESS POLICYCollege Board believes that all students deserve engaging, relevant, and challenging gradelevel coursework. Access to this type of coursework increases opportunities for all students,including groups that have been traditionally underrepresented in AP and college classrooms.Therefore, the Pre-AP program is dedicated to collaborating with educators across the countryto ensure all students have the supports to succeed in appropriately challenging classroomexperiences that allow students to learn and grow. It is only through a sustained commitment toequitable preparation, access, and support that true excellence can be achieved for all students,and the Pre-AP course designation requires this commitment.ISBN: 978-1-4573-1495-7 2021 College Board. PSAT/NMSQT is a registered trademark of the College Board and National MeritScholarship Corporation.1 2 3 4 5 6 7 8 9 10

ContentsvAcknowledgmentsABOUT PRE-AP33Introduction to Pre-APDeveloping the Pre-AP Courses4How to Get Involved3Pre-AP Educator Network55Pre-AP Approach to Teaching and LearningFocused Content8Targeted Assessments for Learning59Horizontally and Vertically Aligned InstructionPre-AP Professional LearningABOUT PRE-AP GEOMETRY WITH STATISTICS1313Introduction to Pre-AP Geometry with StatisticsPre-AP Mathematics Areas of Focus18Summary of Resources and Supports1620Pre-AP Geometry with Statistics and Career ReadinessCourse Map2222Pre-AP Geometry with Statistics Course FrameworkIntroduction24Big Ideas in Pre-AP Geometry with Statistics232526354451Course Framework ComponentsOverview of Pre-AP Geometry with Statistics Units and EnduringUnderstandingsUnit 1: Measurement in DataUnit 2: Tools and Techniques of Geometric MeasurementUnit 3: Measurement in Congruent and Similar FiguresUnit 4: Measurement in Two and Three Dimensions5657Pre-AP Geometry with Statistics Model LessonsSupport Features in Model Lessons5858Pre-AP Geometry with Statistics Assessments for LearningLearning Checkpoints61Sample Performance Task and Scoring Guidelines6070717577Performance TasksFinal ExamSample Assessment QuestionsPre-AP Geometry with Statistics Course DesignationAccessing the Digital Materials

AcknowledgmentsCollege Board would like to acknowledge the following committee members, consultants, andreviewers for their assistance with and commitment to the development of this course. Allindividuals and their affiliations were current at the time of their contribution.Content Development TeamKathy L. Heller, Trinity Valley School, Fort Worth, TXKristin Frank, Towson University, Baltimore, MDJames Middleton, Arizona State University, Tempe, AZRoberto Pelayo, University of California, Irvine, Irvine, CAPaul Rodriguez, Troy High School, Fullerton, CAAllyson Tobias, Education Consultant, Los Altos, CAAlison Wright, Education Consultant, Georgetown, KYJason Zimba, Student Achievement Partners, New York, NYAdditional Geometry with Statistics Contributors and ReviewersJames Choike, Oklahoma State University, Stillwater, OKGita Dev, Education Consultant, Erie, PAAshlee Kalauli, University of California, Santa Barbara, Santa Barbara, CAJoseph Krenetsky (retired), Bridgewater-Raritan School District, Bridgewater, NJYannabah Weiss, Waiakea High School, Hilo, HICOLLEGE BOARD STAFFMichael Manganello, Director, Pre-AP Mathematics Curriculum, Instruction, and AssessmentKaren Lionberger, Senior Director, Pre-AP STEM Curriculum, Instruction, and AssessmentBeth Hart, Senior Director, Pre-AP AssessmentMitch Price, Director, Pre-AP STEM AssessmentNatasha Vasavada, Executive Director, Pre-AP Curriculum, Instruction, and Assessment

About Pre-AP

About Pre-APIntroduction to Pre-APEvery student deserves classroom opportunities to learn, grow, and succeed. CollegeBoard developed Pre-AP to deliver on this simple premise. Pre-AP courses aredesigned to support all students across varying levels of readiness. They are not honorsor advanced courses.Participation in Pre-AP courses allows students to slow down and focus on the mostessential and relevant concepts and skills. Students have frequent opportunitiesto engage deeply with texts, sources, and data as well as compelling higher-orderquestions and problems. Across Pre-AP courses, students experience sharedinstructional practices and routines that help them develop and strengthen theimportant critical thinking skills they will need to employ in high school, college, andlife. Students and teachers can see progress and opportunities for growth throughvaried classroom assessments that provide clear and meaningful feedback at keycheckpoints throughout each course.DEVELOPING THE PRE-AP COURSESPre-AP courses are carefully developed in partnership with experienced educators,including middle school, high school, and college faculty. Pre-AP educator committeeswork closely with College Board to ensure that the course resources define, illustrate,and measure grade-level-appropriate learning in a clear, accessible, and engaging way.College Board also gathers feedback from a variety of stakeholders, including Pre-APpartner schools from across the nation who have participated in multiyear pilots ofselect courses. Data and feedback from partner schools, educator committees, andadvisory panels are carefully considered to ensure that Pre-AP courses provide allstudents with grade-level-appropriate learning experiences that place them on a path tocollege and career readiness.PRE-AP EDUCATOR NETWORKSimilar to the way in which teachers of Advanced Placement (AP ) courses canbecome more deeply involved in the program by becoming AP Readers or workshopconsultants, Pre-AP teachers also have opportunities to become active in theireducator network. Each year, College Board expands and strengthens the Pre-APNational Faculty—the team of educators who facilitate Pre-AP Readiness Workshopsand Pre-AP Summer Institutes. Pre-AP teachers can also become curriculum andassessment contributors by working with College Board to design, review, or pilot thecourse resources.Course Guide 2021 College Board3Pre-AP Geometry with Statistics

About Pre-APIntroduction to Pre-APHOW TO GET INVOLVEDSchools and districts interested in learning more about participating in Pre-AP shouldvisit preap.collegeboard.org/join or contact us at preap@collegeboard.org.Teachers interested in becoming members of Pre-AP National Faculty or participatingin content development should visit preap.collegeboard.org/national-faculty orcontact us at preap@collegeboard.org.Pre-AP Geometry with Statistics4Course Guide 2021 College Board

About Pre-APPre-AP Approach to Teaching and LearningPre-AP courses invite all students to learn, grow, and succeed through focused content,horizontally and vertically aligned instruction, and targeted assessments for learning.The Pre-AP approach to teaching and learning, as described below, is not overlycomplex, yet the combined strength results in powerful and lasting benefits for bothteachers and students. This is our theory of action.Horizontally andVertically AlignedInstructionShared Principles,Areas of FocusFocused ContentCourse Frameworks,Model LessonsTargeted Assessmentsand FeedbackLearning Checkpoints,Performance Tasks,Final ExamFOCUSED CONTENTPre-AP courses focus deeply on a limited number of concepts and skills with thebroadest relevance for high school coursework and college and career success. Thecourse framework serves as the foundation of the course and defines these prioritizedconcepts and skills. Pre-AP model lessons and assessments are based directly on thisfocused framework. The course design provides students and teachers with intentionalpermission to slow down and focus.HORIZONTALLY AND VERTICALLY ALIGNED INSTRUCTIONShared principles cut across all Pre-AP courses and disciplines. Each course is alsoaligned to discipline-specific areas of focus that prioritize the critical reasoning skillsand practices central to that discipline.Course Guide 2021 College Board5Pre-AP Geometry with Statistics

About Pre-APPre-AP Approach to Teaching and LearningSHARED PRINCIPLESAll Pre-AP courses share the following set of research-supported instructionalprinciples. Classrooms that regularly focus on these cross-disciplinary principles allowstudents to effectively extend their content knowledge while strengthening their criticalthinking skills. When students are enrolled in multiple Pre-AP courses, the horizontalalignment of the shared principles provides students and teachers across disciplineswith a shared language for their learning and investigation, and multiple opportunitiesto practice and grow. The critical reasoning and problem-solving tools studentsdevelop through these shared principles are highly valued in college coursework and inthe workplace.Close Observationand ngSHAREDPRINCIPLESAcademicConversationClose Observation and AnalysisStudents are provided time to carefully observe one data set, text image, performancepiece, or problem before being asked to explain, analyze, or evaluate. This creates a safeentry point to simply express what they notice and what they wonder. It also encouragesstudents to slow down and capture relevant details with intentionality to support moremeaningful analysis, rather than rush to completion at the expense of understanding.Higher-Order QuestioningStudents engage with questions designed to encourage thinking that is elevatedbeyond simple memorization and recall. Higher-order questions require students tomake predictions, synthesize, evaluate, and compare. As students grapple with thesequestions, they learn that being inquisitive promotes extended thinking and leads todeeper understanding.Pre-AP Geometry with Statistics6Course Guide 2021 College Board

About Pre-APPre-AP Approach to Teaching and LearningEvidence-Based WritingWith strategic support, students frequently engage in writing coherent argumentsfrom relevant and valid sources of evidence. Pre-AP courses embrace a purposefuland scaffolded approach to writing that begins with a focus on precise and effectivesentences before progressing to longer forms of writing.Academic ConversationThrough peer-to-peer dialogue, students’ ideas are explored, challenged, and refined.As students engage in academic conversation, they come to see the value in beingopen to new ideas and modifying their own ideas based on new information. Studentsgrow as they frequently practice this type of respectful dialogue and critique and learnto recognize that all voices, including their own, deserve to be heard.AREAS OF FOCUSSocial StudiesScienceMathematicsArtsEnglishThe areas of focus are discipline-specific reasoning skills that students developand leverage as they engage with content. Whereas the shared principles promotehorizontal alignment across disciplines, the areas of focus provide vertical alignmentwithin a discipline, giving students the opportunity to strengthen and deepen theirwork with these skills in subsequent courses in the same discipline.Areas of FocusAlign Vertically Within Disciplines(Grades 6-12)Academic ConversationHigher-Order QuestioningEvidence-Based WritingClose Observation and AnalysisShared PrinciplesAlign Horizontally Across All CoursesFor information about the Pre-AP mathematics areas of focus, see page 13.Course Guide 2021 College Board7Pre-AP Geometry with Statistics

About Pre-APPre-AP Approach to Teaching and LearningTARGETED ASSESSMENTS FOR LEARNINGPre-AP courses include strategically designed classroom assessments that serve astools for understanding progress and identifying areas that need more support. Theassessments provide frequent and meaningful feedback for both teachers and studentsacross each unit of the course and for the course as a whole. For more informationabout assessments in Pre-AP Geometry with Statistics, see page 58.Pre-AP Geometry with Statistics8Course Guide 2021 College Board

About Pre-APPre-AP Professional LearningThe summer before their first year teaching a Pre-AP course, teachers are requiredto engage in professional learning offered by College Board. There are two optionsto meet this requirement: the Pre-AP Summer Institute (Pre-APSI) and the OnlineFoundational Module Series. Both options provide continuing education units toeducators who complete the training. The Pre-AP Summer Institute is a four-day collaborative experience that empowersparticipants to prepare and plan for their Pre-AP course. While attending, teachersengage with Pre-AP course frameworks, shared principles, areas of focus, andsample model lessons. Participants are given supportive planning time where theywork with peers to begin to build their Pre-AP course plan. The Online Foundational Module Series will be available beginning July 2020 toall teachers of Pre-AP courses. These 12- to 20-hour courses will support teachersin preparing for their Pre-AP course. Teachers will explore course materials andexperience model lessons from the student’s point of view. They will also beginto plan and build their own course materials, so they are ready on day one ofinstruction.Pre-AP teachers also have access to the Online Performance Task Scoring Modules,which offer guidance and practice applying Pre-AP scoring guidelines to student work.Course Guide 2021 College Board9Pre-AP Geometry with Statistics

About Pre-APGeometry with Statistics

About Pre-AP Geometry with StatisticsIntroduction to Pre-AP Geometry with StatisticsPre-AP Geometry with Statistics is designed to provide students with a meaningfulconceptual bridge between algebra and geometry to deepen their understanding ofmathematics. Students often struggle to see the connections among their mathematicscourses. In this course, students are expected to use the mathematical knowledge andskills they have developed previously to problem solve across the domains of algebra,geometry, and statistics.Rather than seeking to cover all topics traditionally included in a standard geometry orintroductory statistics textbook, this course focuses on the foundational geometric andstatistical knowledge and skills that matter most for college and career readiness. ThePre-AP Geometry with Statistics Course Framework highlights how to guide studentsto connect core ideas within and across the units of the course, promoting a coherentunderstanding of measurement.The components of this course have been crafted to prepare not only the nextgeneration of mathematicians, scientists, programmers, statisticians, and engineers,but also a broader base of mathematically informed citizens who are well equipped torespond to the array of mathematics-related issues that impact our lives at the personal,local, and global levels.PRE-AP MATHEMATICS AREAS OF FOCUSThe Pre-AP mathematics areas of focus, shown below, are mathematical practicesthat students develop and leverage as they engage with content. They were identifiedthrough educator feedback and research about where students and teachers needthe most curriculum support. These areas of focus are vertically aligned to themathematical practices embedded in other mathematics courses in high school,including AP, and in college, giving students multiple opportunities to strengthenand deepen their work with these skills throughout their educational career. Theyalso support and align to the AP Calculus Mathematical Practices, the AP StatisticsCourse Skills, and the mathematical practices listed in various state standards.Engagement inMathematicalArgumentationGreaterAuthenticity ofApplicationsand ModelingCourse Guide 2021 College BoardMathematicsAreas of Focus13ConnectionsAmong MultipleRepresentationsPre-AP Geometry with Statistics

About Pre-AP Geometry with StatisticsIntroduction to Pre-AP Geometry with StatisticsGreater Authenticity of Applications and ModelingStudents create and use mathematical models to understand and explain authenticscenarios.Mathematical modeling is a process that helps people analyze and explain the world.In Pre-AP Geometry with Statistics, students explore real-world contexts wheremathematics can be used to make sense of a situation. They engage in the modelingprocess by making choices about what aspects of the situation to model, assessing howwell the model represents the available data, drawing conclusions from their model,justifying decisions they make through the process, and identifying what the modelhelps clarify and what it does not.In addition to mathematical modeling, Pre-AP Geometry with Statistics studentsengage in mathematics through authentic applications. Applications are similar tomodeling problems in that they are drawn from real-world phenomena, but theydiffer because the applications dictate the appropriate mathematics to use to solve theproblem. Pre-AP Geometry with Statistics balances these two types of real-world tasks.Engagement in Mathematical ArgumentationStudents use evidence to craft mathematical conjectures and prove or disprove them.Reasoning and proof lie at the heart of the discipline of mathematics. Mathematicsis both a way of thinking and a set of tools for solving problems. Pre-AP Geometrywith Statistics students gain proficiency in deductively reasoning with axioms andtheorems to reach logical conclusions. Students also develop skills in using statisticaland probabilistic reasoning to make sense of data and craft assertions using data asevidence and support. Students learn how to quantify chance and make inferencesabout populations. Through these two different types of mathematical argumentation,students learn how to be critical of their own reasoning and the reasoning of others.Pre-AP Geometry with Statistics14Course Guide 2021 College Board

About Pre-AP Geometry with StatisticsIntroduction to Pre-AP Geometry with StatisticsConnections Among Multiple RepresentationsStudents represent mathematical concepts in a variety of forms and move fluentlyamong the forms.Pre-AP Geometry with Statistics students explore how to weave togethermultiple representations of geometric and statistics concepts. Every mathematicalrepresentation illuminates certain characteristics of a concept while also obscuringother aspects. Often, geometric reasoning is used to make sense of algebraiccalculations. Likewise, algebraic techniques can be used to solve problems involvinggeometry. Patterns in data can emerge by depicting the data visually. Statisticalcalculations are important and valuable, but they make more sense to students whenthey are conceptually grounded in and related to graphical representations of data.With experience that continues to develop in Pre-AP Geometry with Statistics,students become equipped with a nuanced understanding of which representationsbest serve a particular purpose.Course Guide 2021 College Board15Pre-AP Geometry with Statistics

About Pre-

26 Unit 1: Measurement in Data 35 Unit 2: Tools and Techniques of Geometric Measurement 44 Unit 3: Measurement in Congruent and Similar Figures 51 Unit 4: Measurement in Two and Three Dimensions 56 Pre-AP Geometry with Statistics Model Lessons 57 Support Features in Model Lessons 58 Pre-AP Geometry with Statistics Assessments for Learning

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