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Overview

Pre-AP Geometry with Statistics provides students with a meaningful conceptual bridge between algebraic and geometric problem-solving methods that deepens their understanding of mathematics.  A central focus for this course will be on utilizing transformations to deepen students’ knowledge of similarity and congruence. Since transformations are functions because, they afford students a rich opportunity to connect algebra and geometry leading to a more sophisticated understanding of functions. Therefore, to empower student growth and confidence in their statistical reasoning skills, this course includes an instructional unit that allows 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:

  • 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.
  • Integration of algebra and geometry: Students utilize algebraic techniques to solve geometric problems.

Underlying Unit Foundations

These big ideas are addressed across units:

  • Complex objects are composed of, and can be compared to, simpler objects.
  • Measurements of objects allow us to draw meaningful conclusions about those objects.
  • When a mathematical object is transformed, some measurements change while other measurements do not change.

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, model lessons, and practice problem sets for key concepts within each unit that provide guidance and support for teaching the course.
  • 1 practice performance task with scoring guidelines for each unit.

Learning Checkpoints

Each unit includes many opportunities for meaningful feedback:

  • 8 online quizzes featuring multiple-choice questions modeled closely after the types of questions students encounter on SAT tests and AP exams, as well as technology-enhanced questions. Unit quizzes require students to examine data, models, graphs, diagrams, and short texts—often set in authentic contexts—in order to respond to a targeted set of questions that measure both the key concepts and skills from the unit.
  • 4 performance-based tasks and corresponding scoring guidelines. The Pre-AP Geometry with Statistics performance tasks are opportunities to evaluate the depth of student understanding of key concepts and skills that are not easily assessed in a multiple-choice format. Performance tasks will give students an opportunity to practice sustained problem solving in authentic contexts and apply skills and concepts from across the course units.