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Overview

Pre-AP Geometry with Statistics has a central focus on measurement that provides students with a holistic and comprehensive view of geometry as the study of shape and space. This course leverages transformations to deepen students’ knowledge of similarity and congruence. Since transformations are functions, they afford students a rich opportunity to connect algebra and geometry meaningfully, leading to a more sophisticated understanding of functions specifically and mathematics more broadly. To address concerns of disjointed conceptual development and lack of sophisticated knowledge of statistics and probability, this course includes a unit that provides time for a sustained and focused examination of topics that are essential for quantitative literacy.

Areas of Focus

Each Pre-AP course focuses on a small set of discipline-specific instructional priorities that support both teacher practice and student learning within the discipline. These areas of focus reflect research-supported reasoning practices that should receive greater emphasis in instructional materials and assessments than they often do. Pre-AP recognizes that many teachers and schools already embrace these disciplinary practices, and now we are offering resources that specifically emphasize these areas of focus.

Pre-AP Geometry with Statistics Areas of Focus:

  • Connecting Among Multiple Representations: Students represent mathematical concepts in a variety of forms and move fluently among the forms.
  • Authenticity of applications and modeling:Students create and use mathematical models to understand and explain authentic scenarios.
  • Engagement in mathematical argumentation: Students use evidence to craft mathematical conjectures and prove or disprove them with logical reasoning.

Underlying Unit Foundations

These big ideas are addressed across units:

  • Measurement
  • Transformations
  • Comparing Parts and Wholes

Course at a Glance

The table below shows the four main units in Pre-AP Geometry with Statistics, the recommended length for each unit, and the key topics in each.

Unit 1: Statistics and Probability
Timeframe: 7 weeks

Key concepts:

  • Describing the shape of data
  • Quantifying the chance of discrete data
  • Making inferences from variable data
Unit 2: Tools and Techniques of Measurement
Timeframe: 7 weeks

Key concepts:

  • Introducing measurement in geometry
  • Investigating when lines intersect
  • Using similarity and trigonometry to measure right triangles
Unit 3: Measurement of Similar and Congruent Figures
Timeframe: 7 weeks

Key concepts:

  • Transforming figures in the plane
  • Using similarity and congruence to compare polygons
  • Measuring lengths and angles in circles
Unit 4: Measurement in Two and Three Dimensions
Timeframe: 7 weeks

Key concepts:

  • Understanding area as two-dimensional measurement
  • Understanding volume as three-dimensional measurement
  • Exploring measurement in spheres

Instructional Resources

Schools that officially implement a Pre-AP course will receive access to instructional resources for each unit. These resources don’t constitute a full day-by-day curriculum. Instead, they provide support and model lessons as teachers design instruction for each unit.

Pre-AP Geometry with Statistics instructional resources include:

  • A course framework and model lessons for key concepts within each unit that provide guidance and support for teaching the course.
  • One or two practice performance tasks with scoring guidelines and instructional support suggestions for each unit.

Formative Assessments

Each unit contains:

  • Short, open-ended formative assessment problems or questions are embedded in some model lesson to show the targeted content and skills, related to the lesson’s learning objectives, that students should master in throughout the lesson.
  • Two online learning checkpoints per unit that feature multiple-choice and technology-enhanced questions modeled closely after the types of questions students encounter on SAT tests and AP exams. Learning checkpoints require students to examine graphs, data, and short texts— often set in authentic contexts—to respond to a targeted set of questions that measure student understanding of concepts and skills from the unit.
  • One performance task per unit that engage students in sustained problem solving and ask them to synthesize skills and concepts from across the unit to answer questions about a novel context.