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Course Guides and Frameworks

Overview

The Pre-AP Algebra 1 course is designed to deepen students’ understanding of linear relationships by emphasizing patterns of change, multiple representations of functions and equations, modeling real world scenarios with functions, and methods for finding and representing solutions of equations and inequalities. Taken together, these ideas provide a powerful set of conceptual tools that students can use to make sense of their world through mathematics.

Areas of Focus

The Pre-AP mathematics areas of focus, shown below, are mathematical practices that students develop and leverage as they engage with content. They were identified through educator feedback and research about where students and teachers need the most curriculum support. These areas of focus are vertically aligned to the mathematical practices embedded in other mathematics courses in high school, including AP, and in college, giving students multiple opportunities to strengthen and deepen their work with these skills throughout their educational career. They also support and align to the AP Calculus mathematical practices, the AP Statistics course skills, and the mathematical practices listed in various state standards.

Pre-AP Algebra 1 Areas of Focus:

  • Connections among multiple representations: Students represent mathematical concepts in a variety of forms and move fluently among the forms.
  • Greater 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.

Underlying Unit Foundations

These big ideas are addressed across units:

  • Patterns of change
  • Representations
  • Modeling with functions
  • Solutions

Course at a Glance

The tables below show the four main units in Pre-AP Algebra 1, the recommended length for each unit, and the key topics in each.

Unit 1: Linear Functions and Linear Equations 
Timeframe: ~9 weeks

Key concepts:

  • 1.1 Constant rate of change and slope
  • 1.2 Linear functions
  • 1.3 Linear equations
  • 1.4 Linear models of nonlinear scenarios
  • 1.5 Two-variable linear inequalities
Unit 2: Systems of Linear Equations and Inequalities
Timeframe:~5 weeks

Key concepts:

  • 2.1 The solution to a system of equations
  • 2.2 Solving a system of linear equations algebraically
  • 2.3 Modeling with systems of linear equations
  • 2.4 Systems of linear inequalities
Unit 3: Quadratic Functions
Timeframe:~9 weeks

Key concepts:

  • 3.1 Functions with a linear rate of change
  • 3.2 The algebra and geometry of quadratic functions
  • 3.3 Solving quadratic equations
  • 3.4 Modeling with quadratic functions
Unit 4: Exponent Properties and Exponential Functions
Timeframe:~5 weeks

Key concepts:

  • 4.1 Exponent rules and properties
  • 4.2 Roots of real numbers
  • 4.3 Sequences with multiplicative patterns
  • 4.4 Exponential growth and decay

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 for teachers as they design their instruction for each Pre-AP Algebra 1 unit.

Pre-AP Algebra 1 instructional resources include:

  • A course framework: the framework defines what students should know and be able to do by the end of the course. It serves as an anchor for model lessons and assessments, and it is the primary document teachers can use to align instruction to course content.
  • Teacher resources, available in print and online, include a robust set of model lessons that demonstrate how to translate the course framework, shared principles, and areas of focus into daily instruction.

Additional resources: All students need access to a graphing utility (such as graphing calculators or an app on a cellphone or a laptop with graphing software like Desmos) and don’t need to purchase any particular device or equipment.

Assessments for Learning

Each unit contains:

  • Short, open-ended formative assessment problems for each 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, mathematical expressions, 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 engages students in sustained problem solving and asks them to synthesize skills and concepts from across the unit to answer questions about a novel context.
  • One or two practice performance tasks with scoring guidelines and instructional support suggestions for each unit.
  • A final exam that allows students to demonstrate their mastery of the skills learned throughout the course. This exam is optional.