Precalculus

Precalculus combines the trigonometric, geometric, and algebraic techniques needed to prepare students for the study of calculus, and strengthens students’ conceptual understanding of problems and mathematical reasoning in solving problems. Facility with these topics is especially important for students intending to study calculus, physics, and other sciences, and/or engineering in college. Because the standards for this course are (+) standards, students selecting this Model Precalculus course should have met the college and career ready standards outlined in the Algebra I, Geometry, and Algebra II courses.

For the high school Model Precalculus course, instructional time should focus on four critical areas:

  1. extend work with complex numbers;
  2. expand understanding of logarithms and exponential functions;
  3. use characteristics of polynomial and rational functions to sketch graphs of those functions; and
  4. perform operations with vectors.

Standards for Mathematical Practice
The 2011 framework introduces Standards for Mathematical Practice. These standards complement the content standards so that students increasingly engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle, and high school years. These standards are the same at all grades from Prekindergarten to 12th grade.

An explanation of how the standards can be highlighted in High School can be found here.

These eight practices can be clustered into the following categories as shown in the chart below:

Habits of Mind of a Productive Mathematical Thinker:
MP.1: Make sense of problems and persevere in solving them.
MP.6: Attend to precision.

Reasoning and Explaining
MP.2: Reason abstractly and quantitatively.
MP.3: Construct viable arguments and critique the reasoning of others

Modeling and Using Tools
MP.4: Model with mathematics.
MP.5: Use appropriate tools strategically.

Seeing Structure and Generalizing
MP.7: Look for and make use of structure.
MP.8: Look for and express regularity in repeated reasoning.

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