Linear Functions - Fitting a model to data

Check out the Lesson Resource page for other Powerpoint, Sketchpad and PDF resources.

Using Logger Pro to Analyze Crash Test Video

A lesson plan designed to use crash test video to teach about math and physics concepts. Math concepts involve linear equations, parametric equations, vectors forming a right triangle, percent difference, piece-wise functions, Pythagorean theorem and trigonometry using real world examples.

When complete, all videos, data, instructions and solutions will be provided.



Urban Mobility Study

* The number of miles on the y-axis of both graphs is in 1,000's of miles.

The 2005 Urban Mobility study provides a variety of data regarding transportation in urban areas. The data from this study has been transferred to a variety of formats and is available for download as a TI-83 program, Excel spreadsheet, pdf, or Logger Pro file.

Source: 2005 Urban Mobility

The TI-83 Program contains the following data:


Linear Functions - Circular Object Lab

A powerpoint of the circular object lab which relates distance traveled on a circle to the radius of the circle.

Lab Activity - To help students understand the relationship between linear distance and arclength, we completed a "circle lab".

Students are given a circular object such as a plate, a can, or a lid from a butter dish. Groups of students measure and record the radius. After measuring the radius, the object is rolled one complete revolution. The distance the object moves is measured and recorded. All groups report their findings and a stat plot of the data is made. A discussion of the slope in which all units divide out occurs. We soon find the C = 2πr is a specific case of S = θr where the angle 2π is one complete revolution of a circle. The next activity helps to explain why the units of 2π are called radians.
A circle is drawn on the board. Two students measure and mark the radius on a piece of rope. The piece of rope is then placed around the circle and the length of the radius becomes the arclength around the circle. A line is placed at the end of each length of the rope. It is determined that it takes approximately 6-1/3 lengths of the radius to go around the circle. Hence, the term radian is the angle which has its radius equal to its arclength. It takes 2π radians to complete one revolution of the circle.
  The image at the left shows a circle with the radius measured and marked around the outside edge of the circle. Each of the blue numbers is the radian measure of the angle.

Quadratic Functions - Fitting a model to data

A ball is rolled up and down a ramp with a motion detector measuring the displacement versus time. A parabolic data set is collected, shared with students, and fit using factored, vertex and quadratic forms. The TI-83 programs used in this lesson to collect data are GENDIST and LINKCK. The data set is available as B1. Analysis requires the program CHOOSE.




Sinusoidal Functions - Fitting a model to data

Using a motion detector pointed toward the floor and revolving the motion detector around the wheel, the height of of the revolving wheel can be recorded with the time. Manual techniques are applied to find a mathematical model and the model is explained in terms of motion around the wheel. Data for this activity is available in the TI-83, Excel, and Logger Pro.

Additional data sets for a pendulum and oscillating spring are available. The Excel file contains all 3 data sets. Units of distance are meters and time is in seconds.



01 - Collecting Data (2:22)
02 - Finding the Extrema (4:28)
03 - Finding the Vertical Shift (5:04)
04 - Finding the Amplitude (1:42)
05 - Finding the Period and Angular Velocity (3:56)
06 - Finding the Horizontal Shift (8:55)
07 - Explaining the Vertical Shift (4:21)
08 - Explaining the Amplitude and Horizontal Stretch (2:09)
09 - Explaining the Horizontal Shift (3:55)

TI-83, Logger Pro, Excel
Other Sample Data Sets   The Excel data set contains all 3 sets.

TI-83, Logger Pro
TI-83, Logger Pro


Math 8 - EDU Online Materials

Online mastery and testing materials for 8th grade math intervention using the Brownstone EDU web-based learning system.

Staff Development Materials -

June 7-8, 2006

August 25, 2005


© 2004 - 2011, Jerel L. Welker
Page Updated: October 8, 2012