Thoughts??
Topic

Key
Lessons

Project
or Lab

From Arithmetic Sequences to
Linear and Quadratic Functions 
1. Sum
of arithmetic sequences
2. Quadratic
patterns and quadratic formulas from applying sequence formulas to sum 2^{nd}
differences
Daily openers: Practice
linear and quadratic skills

Triangular Numbers and Stellar Numbers (past IB Portfolio topic)

From Geometric Sequences to Exponential Functions

1. Sum
of geometric sequences
2. Exponential
formulas from applying sequence formulas to geometric sequences
3. Recursive
vs. explicit formulas
Daily openers: Practice
basic exponent and log skills


Modeling and Visualizing Graphs of Basic Forms

1. Interpretation
of parameters within a formula, domain, range
2. Compare
and contrast linear vs. exponential word problem setups
3. Using
GCD to analyze word problems after proper setup
Daily openers:
Practice graph prediction from formula

Regression lab via RCcircuit

Transformations of Families of Functions

1. Review
function notation
2. Use
the studied functions to reinforce basic transformations knowledge
Daily openers:
Practice transformations, forwards and backwards to/from formulas

@Samjshah’s family of transformed functions art project

Mini Capstone Unit: Modeling with Functions

1. Go
over function forms and uses (including forms not yet studied in the course)
2. Give
students guidelines on modeling assignment
3. Do
one example during class and then provide time in class to complete
individual assignments
Daily openers: Adjust
as perceiving student needs.

Use old IB portfolio topics

Trigonometry of Circles and Waves

1. Review
nonright triangle trig with project from @KFouss
2. Motivate
circular trig using rollercoaster problem
3. Unit
Circle
4. Graphing
and transforming waves in both modes
5. Solving
trig equations (graphical and algebraic)
6. Trigonometric
identities
7. Tangent
function and GCD solutions
Daily openers:
Unit circle memorization; from handdrawn graphs to finding trig formulas (and
thereafter, to finding GCD solutions for intersection points)

Nonright triangle trig project from @KFouss
Building an animated rollercoaster in Geogebra

End Behaviors of Polynomial and Rational Functions

1. Start
with modeling problems to motivate the various forms of new functions
2. Fully
develop each function type completely, paying attention to Calculus
terminology
3. Graphical
analysis of instantaneous rates along a graph
Daily openers: Predictions
of graphs based on formulas; verify with GCD

Stocks modeling project
Field trip planning project / write proposal to principal

Logarithmic Functions

1. Function
inverses
2. Motivate
topic using exponential vs. log scales
3. Mixed
practice in interpreting log scale graphs
Daily openers:
Solving logarithm equations

Research/poster representing an exponential dataset using multiple
forms of graphs, discussing visual tradeoffs

Nonfunctions and Modeling Using Different Coordinate Systems

1. Circles
and Ellipses
2. Polar
coordinate system
3. Hyperbola
and the idea of Locus
Daily openers: From
Cartesian to Polar Coordinates, vice versa

Art project via Desmos

Yearlong, Ongoing Review

Create a Precalculus Magazine summarizing each unit that we have
learned.

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