INCLUDES Pre-AP ® Approach to teaching and learning Geometry Course map Course framework Sample with Statistics assessment questions COURSE GUIDE Pre-AP ® Geometry with Statistics COURSE GUIDE Please visit Pre-AP online at preap.org for more information and updates about the course and program features. ABOUT COLLEGE BOARD College Board is a mission-driven not-for-profit organization that connects students to college success and opportunity. Founded in 1900, College Board was created to expand access to higher education. Today, the membership association is made up of over 6,000 of the world’s leading educational institutions and is dedicated to promoting excellence and equity in education.
Each year, College Board helps more than seven million students prepare for a successful transition to college through programs and services in college readiness and college success—including the SAT® and the Advanced Placement Program®. The organization also serves the education community through research and advocacy on behalf of students, educators, and schools. For further information, visit www. PRE-AP EQUITY AND ACCESS POLICY College Board believes that all students deserve engaging, relevant, and challenging grade- level 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 country to ensure all students have the supports to succeed in appropriately challenging classroom experiences that allow students to learn and grow. It is only through a sustained commitment to equitable 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 Merit Scholarship Corporation. 1 2 3 4 5 6 7 8 9 10 Contents v Acknowledgments ABOUT PRE-AP 3 Introduction to Pre-AP 3 Developing the Pre-AP Courses 3 Pre-AP Educator Network 4 How to Get Involved 5 Pre-AP Approach to Teaching and Learning 5 Focused Content 5 Horizontally and Vertically Aligned Instruction 8 Targeted Assessments for Learning 9 Pre-AP Professional Learning ABOUT PRE-AP GEOMETRY WITH STATISTICS 13 Introduction to Pre-AP Geometry with Statistics 13 Pre-AP Mathematics Areas of Focus 16 Pre-AP Geometry with Statistics and Career Readiness 18 Summary of Resources and Supports 20 Course Map 22 Pre-AP Geometry with Statistics Course Framework 22 Introduction 23 Course Framework Components 24 Big Ideas in Pre-AP Geometry with Statistics 25 Overview of Pre-AP Geometry with Statistics Units and Enduring Understandings 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 58 Learning Checkpoints 60 Performance Tasks 61 Sample Performance Task and Scoring Guidelines 70 Final Exam 71 Sample Assessment Questions 75 Pre-AP Geometry with Statistics Course Designation 77 Accessing the Digital Materials Acknowledgments College Board would like to acknowledge the following committee members, consultants, and reviewers for their assistance with and commitment to the development of this course. All individuals and their affiliations were current at the time of their contribution. Content Development Team Kathy L.
Heller, Trinity Valley School, Fort Worth, TX Kristin Frank, Towson University, Baltimore, MD James Middleton, Arizona State University, Tempe, AZ Roberto Pelayo, University of California, Irvine, Irvine, CA Paul Rodriguez, Troy High School, Fullerton, CA Allyson Tobias, Education Consultant, Los Altos, CA Alison Wright, Education Consultant, Georgetown, KY Jason Zimba, Student Achievement Partners, New York, NY Additional Geometry with Statistics Contributors and Reviewers James Choike, Oklahoma State University, Stillwater, OK Gita Dev, Education Consultant, Erie, PA Ashlee Kalauli, University of California, Santa Barbara, Santa Barbara, CA Joseph Krenetsky (retired), Bridgewater-Raritan School District, Bridgewater, NJ Yannabah Weiss, Waiakea High School, Hilo, HI COLLEGE BOARD STAFF Michael Manganello, Director, Pre-AP Mathematics Curriculum, Instruction, and Assessment Karen Lionberger, Senior Director, Pre-AP STEM Curriculum, Instruction, and Assessment Beth Hart, Senior Director, Pre-AP Assessment Mitch Price, Director, Pre-AP STEM Assessment Natasha Vasavada, Executive Director, Pre-AP Curriculum, Instruction, and Assessment About Pre-AP About Pre-AP Introduction to Pre-AP Every student deserves classroom opportunities to learn, grow, and succeed. College Board developed Pre-AP® to deliver on this simple premise. Pre-AP courses are designed to support all students across varying levels of readiness. They are not honors or advanced courses.
Participation in Pre-AP courses allows students to slow down and focus on the most essential and relevant concepts and skills. Students have frequent opportunities to engage deeply with texts, sources, and data as well as compelling higher-order questions and problems. Across Pre-AP courses, students experience shared instructional practices and routines that help them develop and strengthen the important critical thinking skills they will need to employ in high school, college, and life. Students and teachers can see progress and opportunities for growth through varied classroom assessments that provide clear and meaningful feedback at key checkpoints throughout each course.
DEVELOPING THE PRE-AP COURSES Pre-AP courses are carefully developed in partnership with experienced educators, including middle school, high school, and college faculty. Pre-AP educator committees work 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-AP partner schools from across the nation who have participated in multiyear pilots of select courses. Data and feedback from partner schools, educator committees, and advisory panels are carefully considered to ensure that Pre-AP courses provide all students with grade-level-appropriate learning experiences that place them on a path to college and career readiness.
PRE-AP EDUCATOR NETWORK Similar to the way in which teachers of Advanced Placement® (AP®) courses can become more deeply involved in the program by becoming AP Readers or workshop consultants, Pre-AP teachers also have opportunities to become active in their educator network. Each year, College Board expands and strengthens the Pre-AP National Faculty—the team of educators who facilitate Pre-AP Readiness Workshops and Pre-AP Summer Institutes. Pre-AP teachers can also become curriculum and assessment contributors by working with College Board to design, review, or pilot the course resources. Course Guide 3 Pre-AP Geometry with Statistics © 2021 College Board About Pre-AP Introduction to Pre-AP HOW TO GET INVOLVED Schools and districts interested in learning more about participating in Pre-AP should visit preap.org/join or contact us at preap@collegeboard.
Teachers interested in becoming members of Pre-AP National Faculty or participating in content development should visit preap.org/national-faculty or contact us at preap@collegeboard. Pre-AP Geometry with Statistics 4 Course Guide © 2021 College Board About Pre-AP Pre-AP Approach to Teaching and Learning Pre-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 overly complex, yet the combined strength results in powerful and lasting benefits for both teachers and students. This is our theory of action.
Horizontally and Vertically Aligned Instruction Shared Principles, Areas of Focus Focused Content Course Frameworks, Model Lessons Targeted Assessments and Feedback Learning Checkpoints, Performance Tasks, Final Exam FOCUSED CONTENT Pre-AP courses focus deeply on a limited number of concepts and skills with the broadest relevance for high school coursework and college and career success. The course framework serves as the foundation of the course and defines these prioritized concepts and skills. Pre-AP model lessons and assessments are based directly on this focused framework. The course design provides students and teachers with intentional permission to slow down and focus.
HORIZONTALLY AND VERTICALLY ALIGNED INSTRUCTION Shared principles cut across all Pre-AP courses and disciplines. Each course is also aligned to discipline-specific areas of focus that prioritize the critical reasoning skills and practices central to that discipline. Course Guide 5 Pre-AP Geometry with Statistics © 2021 College Board About Pre-AP Pre-AP Approach to Teaching and Learning SHARED PRINCIPLES All Pre-AP courses share the following set of research-supported instructional principles. Classrooms that regularly focus on these cross-disciplinary principles allow students to effectively extend their content knowledge while strengthening their critical thinking skills.
When students are enrolled in multiple Pre-AP courses, the horizontal alignment of the shared principles provides students and teachers across disciplines with a shared language for their learning and investigation, and multiple opportunities to practice and grow. The critical reasoning and problem-solving tools students develop through these shared principles are highly valued in college coursework and in the workplace. Close Observation Higher-Order and Analysis Questioning SHARED Evidence-Based PRINCIPLES Academic Writing Conversation Close Observation and Analysis Students are provided time to carefully observe one data set, text image, performance piece, or problem before being asked to explain, analyze, or evaluate. This creates a safe entry point to simply express what they notice and what they wonder.
It also encourages students to slow down and capture relevant details with intentionality to support more meaningful analysis, rather than rush to completion at the expense of understanding. Higher-Order Questioning Students engage with questions designed to encourage thinking that is elevated beyond simple memorization and recall. Higher-order questions require students to make predictions, synthesize, evaluate, and compare. As students grapple with these questions, they learn that being inquisitive promotes extended thinking and leads to deeper understanding.
Pre-AP Geometry with Statistics 6 Course Guide © 2021 College Board About Pre-AP Pre-AP Approach to Teaching and Learning Evidence-Based Writing With strategic support, students frequently engage in writing coherent arguments from relevant and valid sources of evidence. Pre-AP courses embrace a purposeful and scaffolded approach to writing that begins with a focus on precise and effective sentences before progressing to longer forms of writing. Academic Conversation Through peer-to-peer dialogue, students’ ideas are explored, challenged, and refined. As students engage in academic conversation, they come to see the value in being open to new ideas and modifying their own ideas based on new information.
Students grow as they frequently practice this type of respectful dialogue and critique and learn to recognize that all voices, including their own, deserve to be heard. AREAS OF FOCUS The areas of focus are discipline-specific reasoning skills that students develop and leverage as they engage with content. Whereas the shared principles promote horizontal alignment across disciplines, the areas of focus provide vertical alignment within a discipline, giving students the opportunity to strengthen and deepen their work with these skills in subsequent courses in the same discipline. English Mathematics Social Studies Arts Science Areas of Focus Align Vertically Within Disciplines (Grades 6-12) Academic Conversation Higher-Order Questioning Evidence-Based Writing Close Observation and Analysis Shared Principles Align Horizontally Across All Courses For information about the Pre-AP mathematics areas of focus, see page 13.
Course Guide 7 Pre-AP Geometry with Statistics © 2021 College Board About Pre-AP Pre-AP Approach to Teaching and Learning TARGETED ASSESSMENTS FOR LEARNING Pre-AP courses include strategically designed classroom assessments that serve as tools for understanding progress and identifying areas that need more support. The assessments provide frequent and meaningful feedback for both teachers and students across each unit of the course and for the course as a whole. For more information about assessments in Pre-AP Geometry with Statistics, see page 58. Pre-AP Geometry with Statistics 8 Course Guide © 2021 College Board About Pre-AP Pre-AP Professional Learning The summer before their first year teaching a Pre-AP course, teachers are required to engage in professional learning offered by College Board.
There are two options to meet this requirement: the Pre-AP Summer Institute (Pre-APSI) and the Online Foundational Module Series. Both options provide continuing education units to educators who complete the training. The Pre-AP Summer Institute is a four-day collaborative experience that empowers participants to prepare and plan for their Pre-AP course. While attending, teachers engage with Pre-AP course frameworks, shared principles, areas of focus, and sample model lessons.
Participants are given supportive planning time where they work with peers to begin to build their Pre-AP course plan.