Gold Seal Lesson:
Evaluating Weather Data

Copernicus Education Gateway

Subject:

Science

Grade:

9-12

ICLE Standards:

Mathematics: Construct and draw inferences from charts, tables, and graphs that summarize data from real-world situations. Understand and apply measures of central tendency, variability, and correlation.

Science: Develop the abilities of scientific inquiry.

Performance Task:

Mr. McDonald owns a dairy farm. He earns a good living from the farm by using innovative practices. On an annual basis, he must evaluate the farm's production to determine if the income from the farm met his expectations. Often, Mr. McDonald must use data available from the farm extension service to help him make decisions. His farm is in a temperate climatic region consisting of hills and valleys. The last frost for the season usually occurs near the end of April, but occasionally will come in the first ten days of May. Farmer McDonald is considering planting a new hybrid corn that is frost resistant but produces lower yields. Frost resistant corn would enable him to plan earlier. Before planting, he examined the accompanying table Low Temperatures (degrees Fahrenheit) - April 20 through May 10.

Materials Needed:  Scientific calculator

1. Using the data in the Low Temperatures table, determine the mean, median, mode, and range of the temperatures for each date from April 20 through May 10. Describe, in writing, how you found these scores and show any formulas and/or paper and pencil calculations used to determine them. Record these scores in the Data Collection Table.

2. Using scores entered in the Data Collection Table, carry out the following procedure for each date from April 20 through May 20.

1. Divide the range by 2

2. Add the value obtained in "a" to the mean and also subtract it from the mean
   This procedure gives you an adjusted range. What is the earliest date with the adjusted range above 30 degrees Fahrenheit (frost resistant)? Is this information helpful in deciding an appropriate date to plant the corn? Justify your response.

3. The standard deviation, s, for a set of data is a measure of variation of the scores about the mean. It is ordinarily more useful in making decisions than the measures of central tendency. The standard deviation is found using the formula where n is the number of scores in the sample. Compute the standard deviation for each set of data in the Data Collection Table from April 20 through May 10. Show or state how you obtained these values.

4. How does the standard deviation help you determine the earliest possible date for planting corn without it freezing? Explain your logic.

5. What recommendation would you give to Farmer McDonald? Justify your response.
   
   Note to the teacher: The purpose of this learning activity is to analyze data (temperatures) using statistical measures over a number of years and to draw conclusions from these data. This task provides an excellent example of how mathematics is related to making agricultural decisions. Students make use of the scientific calculator.

Knowledge / Skills:

Know and apply the principles of scientific inquiry.  (xs1)

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions.  (m1)

Understand the best procedures for statistical data collection, organization, and display.  (m5)

Understand the characteristics of measures of central tendency (i.e., mean, median, and mode).  (m15)

Understand the characteristics of measures of dispersion (i.e., range, mean deviation, variance, and standard deviation).  (m36)

Present information in well-organized fashion that will be clear to the target audience.  (ela11)

Rubric:

3 Points  =  The student completes all parts of the task without coaching. He/she performs all mathematical calculations correctly and demonstrates an understanding of both the measures of central tendency and variability. The student shows necessary formulas and computations. His/her work is neatly organized. All explanations are clear and logical. The student uses data analysis to make a recommendation to Mr. McDonald.

2 Points  =  The student needs some coaching to complete all parts of the task. He/she performs all necessary mathematical calculations, but some minor errors occur. The student has a good understanding of measures of central tendency, but has difficulty with the concept of  variability. Some, but not all, formulas or explanations of work are shown. The student's work is fairly well organized, but not particularly neat and orderly. Several errors occur in his/her computations. His/her explanations are not clear and logical. The student has difficulty using data analysis to make a recommendation to Mr. McDonald.

1 Point  =  Even with coaching, the student does not complete all parts of the task. His/her work is difficult to follow and he/she does not demonstrate a complete understanding of the measures of central tendency nor of the concept of variability. The student is unable to use the formula for standard deviation. Explanations are vague and difficult to follow. Very few computations are shown and major errors occur in those that are shown. The student does not make a meaningful recommendation to Mr. McDonald.

0 Points  =  The student completes very little of the task. He/she shows little interest or effort in producing quality work. The student has little, if any, understanding of the statistical terms in the task. He/she does not differentiate between central tendency and variability. Explanations, if included, are meaningless and illogical. The student is unable to use data analysis to make a recommendation to Mr. McDonald and makes no attempt to do so.

Keywords:

SCIENTIFIC INQUIRY
METEOROLOGY
EARTH SCIENCE
WEATHER

Grades:

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [X] - 10 [X] - 11 [X] - 12 [X]

ICLE Application:

D

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