Pacing Guide and Curriculum Map for Gemini Pre-Calculus Course

Unit Name / Essential Questions / Content / Skills / Assessments / Activities/Lessons
Sept / Intro to functions.
Exponential Functions / Why do we strive to fit data to types of curves or functions? /
  • Intro to date/graph/equation way of looking at linear, hyperbolic, parabolic, inverse and trigonometric fns.
  • Basic form of an Exp. Fn.
  • Comparison of exp. fn to a linear fn.
  • Rate, growth factors
/ Students will:
  • Collect and organize data
  • Pair data and graphs with equations and types of functions
  • Use equations with variable exponents to produce data.
/ 2 formal tests
1 project – The Turtle population / Gingerbread Man – Linear
Depreciation – Linear
Shaq O’Neill hands vs feet– Linear
Gingerbread Man in Reverse
The Perfect Rectangle – Parabolic and hyperbolic
A murder mystery – Trigonometric
Bugs! – Exponential Growth
M&M’s – Exponential Decay
Oct / Exponential fns.
Logarithms
Transformation of funs / Is there value in pursuing the limit of a function?
What is the purpose of an inverse?
What value is there in understanding transformations of fns? /
  • Graphs of exp. fns.
  • Compounding vs. continuous growth
  • APR vs Effective Rate
  • Transformations of funs.
  • Inside/Outside changes
  • Shifts
  • Reflections and Symmetry
/ Students will:
  • Compare compound rates with continuous growth and decide on situations when continuous growth is valuable.
  • Compare and understand APR vs Effective rate both for borrowing and saving.
  • Experiment with and be able to verbalize the effect of transformations on equations of functions.
  • View transformations of functions in artwork and animation.
/ 1 written test
1 quiz
2 projects
Possible speaker / A Purrfect exponential problem – the growth of cat populations
The Best Bank – compound interest, continuous interest, effective rate
Kaleidoscope – reflection and symmetry
Cancel me out – wave theory
Make it Move – using transformations in animation
Nov / More transformations
Combinations of fns.
Families of Quadratic fns
Trig Fns / What makes a family?
What is the value of combining functions? /

Vertical and Horizontal shifts

  • Compression of fns.
  • Combinations of fns. Sum, Differences, Products and Quotients of fns.
  • Families of Quadratic fns based on transformations.
  • Trig functions.
/ Students will:
  • Compare experimental shifts on graphing calculators to equations and generalize the effect of changing parameters.
  • Solve applications of functional shifts.
  • Apply transformations to physical phenomena.
  • Be exposed to applications of trig fns.
/ 1 written test
1 quiz
2 projects / What goes up, must come down – parabolic families
The Ferris Wheel
The Revolving Door
Unit Name / Essential Questions / Content / Skills / Assessments / Activities/Lessons
Dec / Sinusoidal Fns
Inverse Trig fns
Composition of fns.
Power Fns
Rational fns and asymptotes / Does nature conform to laws of mathematics, or do we write mathematics to follow the forms of nature?
What ethical responsibility does a the presentation of data impose? /
  • Alternating current and sinusoidal fns.
  • Natural rhythms described as mathematical fns.
  • Inverse trig fns.
  • Decreasing and increasing trig models
  • Polar Coordinates
  • Domain and Range of inverse and composition of fns.
  • Quadratics, cubic, quartics
  • Negative integer powers
  • General form for a polynomial fn
  • Odd and Evenness of a function
  • Long and Short Run behavior of rational fn
  • Comparing values of fns (power, exponential and log fns)
  • Using composition of functions to model real world applications
/ Students will:
  • Recognize sinusoidal fns and construct equations from graphs and vice versa.
  • Explore natural phenomena through sinusoidal fns.
  • Understand the nature and meaning of asymptotes for business and industry production.
  • Test their tolerance for limits and asymptotes with increasing and decreasing models.
  • Graph polar coordinates by hand and with their calculators, varying parameters.
  • Recognize the type of data and situations that produce data associated with fns with negative powers.
  • Recognize the general form of a polynomial, quadratic, cubic and quartic and be able to test for long and short run behavior, check for odd and evenness, and compare values to other fns.
/ 1 test
1 quiz
2 projects / The bouncing ball – sinusoidal models
A rose is a rose – polar coordinates
Take me to the Limit – asymptotes
Modeling Real World Problems, ethics and decision making – Rainforest deforestation and population growth (composite functions)
Textbook: Functions Modeling Change – A preparation for calculus
Connally, Hughes-Hallett, Gleason, et al. Abridged version for use with FLCC Gemini Pre-Calculus Course
Second Edition
Wiley Custom Services
John Wiley & Sons, Inc. Hoboken, NJ

Revised 11/7/2018