Activity Overview
In this Derive™ activity, students apply the concept of definite integration and decide when a farmer should plant and harvest a crop of clover.
Before the Activity
See the attached DFW file for detailed instructions for this activity
Print pages from the attached DFW file for your class
During the Activity
Distribute the pages to the class.
Follow the Activity Procedures:
Set up a 2D plot window
Determine the latitude and longitude for the location and calculate the hours of sunlight during each day of the year for that location
Plot the data and observe that the graph is a sinusoidal curve
Determine the latitude and longitude of your position and write an expression for the number of daylight hours on spring equinox, autumn equinox, winter solstice, and summer solstice
Write an expression for the hours of daylight on day, t
Sum the values of the function over an interval of days
Take a representative value for the hours of daylight for each day, and add the values
Represent this sum graphically and plot the data about the tops of rectangles
Realize that the sum of the areas of the rectangles is the same as the area under the curve
Understand that the area under the curve is the total number of hours of daylight
Recognize the fact that the value of the definite integral and the value of the sum is the same
Complete the farmer's schedule and determine the dates for the first and second cuttings of clover
After the Activity
Students answer questions listed on the activity sheet.
Review student results:
As a class, discuss questions that appeared to be more challenging
Re-teach concepts as necessary