Modeling in Mathematics: a series of lessons exploring functions : Modeling in Mathematics: a series of lessons exploring functions Valerie Olson
Evergreen Park High School
Teacher of Algebra, Geometry, Algebra 2
Motivation : Motivation Goal to maximize student ownership in class
Take mathematical concepts to new heights with technology
Explore future career opportunities
Abstract : Abstract 3-4 lessons
Each lesson focuses on different exploration, different function
Technology used will be added each lesson
Test on Geometry Honors class in January
Lesson 1: Jump Up! : Lesson 1: Jump Up! Method
Students will break into groups of 3: recorder, jumper, timer
Jumper student will jump for 1 minute
Timer will say how many jumps per 10 seconds
Recorder will record
Lesson 1: Jump Up! : Lesson 1: Jump Up! With the data students will:
Graph data on paper
Then graph on Geometer’s Sketchpad
Finally use TI 84 to find equation of functions
Draw conclusions & explore why this function is exponential
Lesson 2: Swinging Pendulum : Lesson 2: Swinging Pendulum Procedure:
Various lengths of string to measure and then attach a weight
Count & record how many full rotations occur in 2 minutes
Lesson 2: Swinging Pendulum : Lesson 2: Swinging Pendulum With the data students will:
Plot length of string vs. number of swings per minute
Feed this data into Matlab/Geometer’s Sketchpad
Lessons 3 & 4 : Lessons 3 & 4 Attempts
Cell phone noise-too many factors to isolate, complicated
Kraft-false data provided gives only 1 month, no correlation is then provided
About Kraft Data : About Kraft Data Alt Item represents bar code, think “Oreos” or “Crystal Light”
PRISM Qty means the quantity Kraft has on hand in that month
Selected Cost is cost per item
PRISM Cost represents the total dollar impact at that specific facility
Fake Data from Kraft : Fake Data from Kraft
More on…Kraft! : More on…Kraft! I was told, “Once again - these numbers are not real! It’s just for one month. What you can do, is pick 10 items, then use the rest of the data and assign then to those ten items and you can show how the quantity changed over the months and you can use it to forecast future quantity and cost.”
So Where Am I Now? : So Where Am I Now? Looking for ideas on a physical science modeling application
Talking of experience often, but difficult to make lesson on 1/f noise, especially since I came back with little data
Wondering how to get Matlab, most especially since my school does NOT offer programming
Acknowledgements : Acknowledgements Sure Microphones
Kraft
NSA
Franz-Josef Elmer http://monet.physik.unibas.ch/~elmer/pendulum/
NSF