Friday, August 23, 2013

Precalc Breakdown

Continuing with my Precalc brainstorm, I went through my new school's textbook (Functions Modeling Change, Fourth Edition, from John Wiley & Sons, Inc.), and pulled out specific content strands to correspond to each of the core topics I will need to teach. The current Precalc teachers don't all teach sequences as a topic in Precalc, but when I took it out, I found that no matter how I sequenced the basic algebra topics, they always seemed somewhat random and disconnected. So, I will still start off with a sequences discussion, in order to tie everything together for my own students. I also brainstormed a project for each Precalc unit during the year. If I end up throwing them out, it's ok! But, hopefully this gives me ideas to fall back on throughout the year. If they don't have references, either I have that project lying around from my own creation before or I think it'll be fairly straight-forward to pull one together this year.


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 2nd 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 RC-circuit
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 non-right 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 hand-drawn graphs to finding trig formulas (and thereafter, to finding GCD solutions for intersection points)

Non-right 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
Non-functions 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
Year-long, Ongoing Review

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

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