Precalculus Unit 1 – All About Alice

Course Overview:

This unit starts with a model based on Lewis Carroll’s Alice in Wonderland, a story in which Alice’s height is doubled or halved by eating or drinking certain foods she finds. Out of the discussion of this situation come the basic principles for working with exponents – positive, negative, zero, and even fractional – and an introduction to logarithms. Building on the work with exponents, the unit discusses scientific notation and manipulation of numbers written in scientific notation. The Problems of the Week (POWs) in this unit deal with students’ logical reasoning and the process of deduction.

Week One:
  • Who’s Alice
  • Graphing Exponents
  • Pow 1
Week Two and Three:
  • Extending Exponentiation
  • The exponential pattern
  • The additive law of exponents
  • Zero as an exponent
  • Negative exponents
Week Four:
  • "Curiouser and Curiouser!"
  • Defining fractional exponents
  • Defining negative fractional exponents
Week Five and Six:
  • Turning Exponents Around
  • Logarithms
  • Negative logarithms
  • Base 10
  • Scientific Notation
Week Seven:
  • Presentations and Portfolios
Week Eight:
  • Assessments
Active Learning:

Students’ roles as mathematical students will be to experiment, to investigate, to ask questions, to make and test conjectures, and to reflect, and then to communicate their ideas both orally and in writing. Students will often work in teams and sometimes work on their own.

Expectations – Class expectations are based on the 4 Ps:
  • Be Prepared
    Students are expected to be in class and on time.
    Students are expected to keep a math binder with work organized into appropriate categories.
  • Be Polite
    Students are expected to respect their fellow classmates.
    Maintain appropriate classroom behavior (language, feet on floor, cleanliness, etc.).
  • Be Positive
    Students are expected to MAKE MATH MISTAKES AND HAVE FUN!
    Students are expected to participate and do their best.
  • Be Productive
    Students are expected to complete all class work and homework.
    Students are expected to make up any class work and/or homework that they miss due to absences. You (students) are responsible for asking for and getting the work that you miss!
Portfolio Project:

The portfolio project for this unit will have three parts:

  1. A cover letter that describes the central ideas of the unit
  2. Select papers from the unit (homework, classwork, etc.) that reflect the essence of the unit as well as demonstrates your progress in problem solving and writing about math problems
  3. A personal growth statement that addresses how you feel you progressed in the unit and what you feel you might need to work on as well as other thoughts about your experiences this quarter
Classwork and Participation:30%
Portfolio Project, Assessments, and Graded Assignments30%
Problem of the Week (POWs):20%