Let the Sun Shine In


Overview:

This activity is for students enrolled in Integrated Math 3, Algebra 2, Trigonometry or any mathematics class above them. Students should have knowledge of the family of sine and cosine curves and be able to use the TI-83 graphing calculator.

Materials Needed:

  1. Worksheet #1

  2. Worksheet #2

Teacher Preparation:

  1. Students should be familiar with transformations of the sine and cosine functions. This activity is written to fit the data to the cosine curve. I chose that because it is easier for students to fit since cosine has its maximum value on the y-axis. You can have students transform to sine as an extension. The TI-83 will fit a sine regression but uses the form y = A sin (Bx + C) + D. I like the form y = A sin B (x - C) + D or y = A cos B(x - C). They seem to be able to find the equation much easier because the "C" value is the horizontal shift and once they trace over to the first maximum value they can store that "x" value in for "C" and be done with the horizontal shift.

  2. As a classroom demonstration, you could model tide data and have the students fit the curve.

  3. Groups should contain 4 students with 3 as a minimum.

  4. There are certainly other websites that will automatically give students the total daylight time when all they need is to enter the latitude and longitude. I personally like the site chosen because it has the students thinking about the times. They also are using some additional calculator skills.
Extension: A possible extension for Calculus students would be to look at the steepest parts of the curves. Does the daylight change by the same amount each day of the year or is there a period of time when the changes are more pronounced.

California Math Content Standards Addressed:

Trigonometry

2. Students know the definition of sine and cosine as y- and x-coordinates of points on the unit circle and are familiar with the graphs of the sine and cosine functions.
4. Students graph functions of the form f(t) = A sin (Bt + C) or f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift.
13. Students know the law of sines and the law of cosines and apply those laws to solve problems.
19. Students are adept at using trigonometry in a variety of applications and word problems.

Specific NCTM PSSM 2000 Content Standards:

In grades 9-12 all students should:

Analyze change in various contexts

2. approximate and interpret rates of change from graphical and numerical data.
3. analyze functions of one variable by investigating rates of change, intercepts, zeros, asymptotes, and local and global behavior;
4. understand and compare the properties of classes of functions, including exponential, polynomial, rational, logarithmic, and periodic functions;
5. generalize patterns using explicitly defined and recursively defined functions;

NETS Technology Standard:

5. Technology research tools

  •  
    		•  Students use technology to locate, evaluate, and collect information from a variety of sources.

  •  
    		•  Students use technology tools to process data and report results.

  •  
    		•  Students evaluate and select new information resources and technological innovations based on the appropriateness for specific tasks.


    The Integrating Technology into Math Instruction webpages project is partially funded by a grant from The Boeing Company. Integrating Technology into Math Instruction is a project of +PLUS+ and is displayed on the Los Angeles Educational Partnership Learning Exchange. +PLUS+ is an initiative of the Los Angeles Educational Partnership.
    Updated June 2000