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Performance Task:
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Use a moisture tester on corn that you bring from the same field each day starting on the first day of school and continuing until the field is harvested. Graph moisture in relation to date.
Each fall, farmers must decide when to start harvesting corn. Many factors affect this decision. The only component of this problem you are asked to consider is the moisture content of the grain. You will need the following information: (note - the teacher may prefer to have students do this research.)
| Date |
%
Water |
|
| 8/25 |
35% |
The corn must be sold at 15% moisture |
| 9/15 |
30% |
level, or else the farmer takes a cut in |
| 9/30 |
25% |
price that is higher than drying the corn |
| 10/15 |
20% |
himself |
| 11/1 |
|
15% |
Corn still standing in the field will continue to dry and will shatter during harvesting if it is too dry. Figure in a 2% loss for every percent of moisture that the corn loses after 16%.
The cost of drying the corn is $0.02 per bushel for each one percent of moisture content. Corn will sell at harvest at $2.50 per bushel. Average yield is 125 bushels per acre.
The farmer can harvest 5 bushels per hour and the dryer can dry 250 bushels per hour. Assume that both the farmer and the dryer can work only 12 hours per day because of weather and breakdowns
Model appropriate parts of the preceding information with functions, graph them, and predict the best date to begin harvest, ignoring all other conditions that affect this decision. Enter your functions in a spreadsheet to reach the same conclusion numerically.
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Knowledge / Skills:
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Perform operations with signed (positive and
negative) numbers, including decimals, ratios, percents, and
fractions. M.1
Understand the best procedures for statistical
data collection, organization, and display. M.5
Understand the use of variables in expressions
such as 4x, x+2, and 2x-1, solve for the variable, and know how to
represent expressions such as
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Rubric:
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4 POINTS: Student is able to determine optimum date to start harvest and support his conclusion numerically, graphically, and algebraically.
3 POINTS: Student determines an acceptable date to start harvest, but lacks good support in one area of the analysis.
2 POINTS: Student is able to analyze the problem with only one method.
1 POINT: Student provides very little justification for his/her
answers.
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