Skymath National Weather Report Module

Objectives

• Direct observation of the phenomena
• Making and recording measurements of the phenomena using a variety of instruments and appropriate scales and units
• Reading and interpreting on-line weather maps and satellite photographs
• Representing and manipulating the data in a variety of formats and displays

Applying this knowledge and these skills in development of a product, a national weather report and an annotated guide, which will require:

• Integrating the data on the three phenomena
• analyzing the data by geographic region
• Deriving conjectures and hypotheses from the data
• Communicating the report to an audience in an appropriate format

Overview

In every activity, learning will occur between the concrete, immediate, and informal and the abstract, distant, and formal. Data collection will start with student observation, outside homes and schools, recorded in invented notation. As the unit progresses, students can examine different types of instruments (even constructing their own), look at their region, and report data in symbolic and numeric form. With the culminating activity, students will be accessing real-time data, using standard notation, and looking at the national and international scene.

Another critical dimension of the unit is the development of student skills in making conjectures and hypotheses, a precursor to prediction. In all activities we will ask students to guess and estimate (e.g., what do you think the range of temperature will be in a 24 hour period?) and then think about their estimates in relationship to actual data. We will also ask students to justify their answers and begin to build a bank of hypotheses and theories, supported by data, which can be used in more complex problems and settings (e.g., in fall, when there are no clouds or wind at night, temperatures are lower). This practice in the building of logic, conjecture, and proof will provide a foundation for their forecasting efforts in future units and more generally, for using data in scientific theory- making and evaluation.

Investigations/Activities

This is a broad outline of student investigations and activities. Each investigation is likely to last from 2 to 4 weeks depending on the teachers' goals and interests.

1. Formal observations, Measurements, and Displays

   Students will begin this unit by identifying what they know and what questions they may have about the weather and the phenomena of wind, temperature, and sky appearance. Their questions and their conceptions will guide and shape the study. (Materials to be developed will include common student questions and concepts gathered in the sites and strategies for incorporating and addressing them in the investigations.)

   In the prior unit, students will have collected data on the phenomena at school and at home (focused on the local community) and kept weather journals, repositories for observations, data, hypotheses, questions, and reflections. Record keeping, initiated with informal systems, will now focus on more formal and standard units and formats. Cloud cover, temperature, and wind provide a range of examples of units, scales, and symbol systems. A sample weather map commonly used by meteorologists can be seen by clicking on this icon. It contains the standard meteorological symbols. The data from each reporting site are printed on a map identifying the geographical location of the site. The National Weather Service collects the data and distributes it. Each map represents a 'snapshot" of the weather across the world at a given time (identified by the Universal or Greenwich Mean Time at which the observations were made). The cloud cover present, surface conditions, and wind velocity (speed and direction) are represented in symbolic terms and can be identified by clicking on the following two icons; temperature, dew point, and atmospheric pressure are presented in numerical form.

   Click on this icon to see a typical meteorological station model plot.

   The central circle describes the cloud cover; filled represents 100% cover, an open circle stands for clear skies. The line from the circle represents the wind direction, the smaller lines perpendicular to this line (making it look like a flag) define the wind speed. The direction defined by the line is the direction from which the wind is blowing, that is, the direction one faces if one is looking into the wind. Note on the weather map that the wind at Los Angeles is blowing out to sea (off-shore); this is the end of the "Santa Anas" that caused such damaging fires in that area a few days earlier. The weather conditions in Miami, Florida on 3 November 1993 at 18:00 Universal time are shown on the weather map and reproduced in the above drawing: Wind is from the north by west at a speed of 15- 20 mph; temperature is 81 degrees Fahrenheit; dew point, 59 F, and atmospheric pressure 221 millibars. The sky is 75% covered with clouds.

   The data from weather maps can be displayed in other forms. A contour plot, for example, is familiar from the newspaper's daily weather report. Click on this icon to see a contour plot of the temperatures across the nation at the time the symbolic weather map was made. On the other hand, the information can be displayed in tabular form. For example, temperatures may be put into spreadsheet format to simplify the construction of stem and leaf or box and whisker charts for comparisons with other variables.

   Once basic concepts and units are in place, students will begin working with on-line maps and data. They will start to read maps, decipher symbols and take and record data from on-line sources at different time intervals. They will begin looking for patterns in data, to experiment with different numerical and graphical display formats, and to develop conjectures about the phenomena from their data. Students will start to compare their data with that provided on-line, if available, or with weather maps secured from the newspaper or the site Universities if not, and be asked to define differences and similarities and to explain discrepancies. Issues of accuracy and precision will be discussed. Students might also examine the differences between data on surface maps and data from a variety of altitudes. Differences can be graphed and analyzed.

   Students will start with the local community and move out to the state, the region, and the country. Concepts such as mean, median, and range will enter the conversation. Students working in groups, for example, might look at temperature, on a given date and time, across the country. One might look at a table of data listed by state in alphabetical order. Another group might look at a national Weather service map and a third group might construct a stem and leaf plot. Each group will be asked to write a temperature analysis and present their findings to the class.

2. Relationships among the Phenomena,

   In this investigation, students will start to examine the relationship between the different phenomena -- first temperature and wind velocity (with the development of the concept of "wind chill"), then with atmospheric pressure (with the development of regions of high and low pressure, fronts, and accompanying changes in weather patterns). Again, we will start with the local phenomena to which students have immediate access and then move out geographically. Again students will seek patterns in the data and develop conjectures which will be discussed and critiqued in class. And again they will keep their data and reflections in their journals.

3. A National Weather Report and a Class Guide to the Wind, Temperature, and Cloud Cover

   In this final investigation of the unit, students will create a portrait of the weather across the United States (or another country if it is appropriate). This will be an integrating activity in which students can demonstrate and showcase their meteorological and mathematical understanding. This weather portrait will include: narrative descriptions of weather by region (including the "best" and the 'worst"); charts, graphs, stem and leaf plots, box and whisker plots, and maps identifying highs and lows, medians, means, and ranges of phenomena; identification of severe weather; and patterns of cloud cover, wind, and temperature using contours, symbols, numbers and direct satellite imaging.

   Although the data and the report construction will have a single day focus, the planning and preparation will be far more extensive. Students will examine weather reports from different sources; newspaper, TV, radio, weather service, on-line. The class will define the components of the report, deciding which data to display and in what formats. Responsibility for the collection and display of the data will be divided among small groups.

   Accompanying the report will be a series of annotations explaining the data and the relationships among the phenomena. These annotations will be derived from the conjectures and "proofs" in students' journals and discussed and accepted by the class as a whole.

   The report and the annotations will be presented to an audience: families, other classes, senior citizens, a panel of community members, a panel of experts on-line.

   The National Weather Report and the annotations will lay the foundations for introducing a unit on forecasting: And what will the weather be tomorrow?

Mathematical Focus

Extensions

Sources

It is possible for your students to enter data into a computer using the program to be found in Data Analysis: New Topics for Secondary School Mathematics, Department of Mathematics and Computer Science, North Carolina School of Science and Mathematics, NCTM 1988, ISBN 0-87353-263-5. With it, students can construct scatter plots, stem-and-leaf plots, and calculate means, medians, and standard deviations. a helpful reference for the boxplots can be found in Moore and McCabe Introduction to the Practice of Statistics, W. H. Freeman & Co. San Francisco 1989 ISBN 0-716- 71989-4.

One example of a classroom evaluation is given in the MSEB publication "Measuring Up - Prototypes of Mathematical Assessment" - chapter entitled "Lightning Strikes Again!"

Summary