Precalculus 

 

Precalculus, for me, is about helping students take the mathematics they have learned in previous courses and learn to apply it in new and different ways to solve unfamiliar problems.  It's about learning to recognize patterns in data and situations and refining the skills to describe those patterns mathematically, 

Functions

General Functions - Because my students have spent two years (in Algebra I and Algebra II) covering linear, quadratic and power functions, I combine them into one unit that focuses on the essential ideas of functions.  I typically begin by showing Dr. Seuss' Sneetches. I like the fact that the video allows us to talk about discrimination and stereotyping in a math class - and I think the Star On/Off machine is a wonderful model of a function in action.  It also helps remind students of the fact that particular functions "do" something - add, multiply, etc.  It also emphasizes that as machines are distinguished by the actions they perform, so too are functions. This discussion usually brings us to a discussion of how some functions behave similarly to one another while others behave very differently.

 

I follow this with some small group work in which students investigate and review different functions.  This worksheet worked well for me this year.  

 

Rational Functions - Typically, students study rational functions in Algebra II.  The focus of that study, more often than not, is more on learning to graph the functions without a calculator than on understanding the important ways in which these functions differ from others and their usefulness in modeling various phenomena in the world around us.  

 

Exponential Functions - I like to introduce exponential functions using this M&M Lab because it helps students to observe exponential decay in action.  I added the questions about comparing the decay rate of removing 10 M&Ms at a time to the decay rate they observed with the M&Ms a few years ago and found it helped me create conversations about how differently linear and exponential functions behave and particularly how quickly exponential functions decay.  I love this video by Professor Bartlett at the University of Colorado.  To be certain, the video is long and rapid-paced.  Using EdPuzzle, I have created a shorter version of it for my students, complete with reflection questions.

 

Logarithmic Functions

 

Trigonometric Functions

 

Probability

I like the book Probability Demystified by Allan Bluman.  My students find that it does a wondferful job explaining the important concepts in simple and concrete language. 

 

We cover the following topics:

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