Climate Patterns

“An Exercise in Scientific Inquiry”

Grade Level: Juniors and Seniors (11th and 12th grade)

Topic: Seasonal changes in temperature are explored and
related to changes in the angle of the sun’s rays.

This topic fits well into both a science and a math curriculum. It can be integrated into the chemistry curriculum (or any other science curriculum) as an exercise in scientific inquiry. It would work well at the beginning of the course when the topic of scientific method of investigation is introduced. It can also be integrated into the advanced math (pre-calculus) curriculum as an exercise in gathering, organizing and analyzing data, mathematical modeling, or trigonometric relationships. It would probably work best after the students have had some exposure to trigonometry.

Related Science Concepts
* Scientific Method (all sciences)
* Making Tables and Graphs (general science)
* Climate and Weather (meteorology)
* Motion of the Earth (astronomy)
* Properties of Light (physics)

Related Math Concepts
* Modeling Data (all math)
* Sine Curves (trigonometry)
* Curve Fitting (statistics)

Linkage to Illinois Learning Standards For Science

This unit aligns well with State Goals

11 A “Know and apply the concepts, principles and processes of scientific
12 E “Know and apply concepts that describe the features and processes of
the Earth and its resources.”

Linkage to Illinois Learning Standards For Math

This unit aligns well with State Goals

8 B “Interpret and describe numerical relationships using tables, graphs
and symbols.
8 C “Solve problems using systems of numbers and their properties.
9 D “Use trigonometric ratios and circular functions to solve problems.”

10 A “Organize, describe and make predictions from existing data.”

10 B “Formulate questions, design data collection methods, gather and
analyze data and communicate findings.”

Linkage to NCTM Standards

This unit aligns well with the following standards;

Standard 1. Mathematics as Problem Solving
Standard 2. Mathematics as Communication
Standard 4. Mathematical Connections
Standard 9. Trigonometry
Standard 10. Statistics

Materials Needed:

Computer(s) with inter-net access
TI-83 graphing calculators, one per student
TI-GRAPH LINK (optional)
TI-CBL with light sensor probe, one per group

TI-83 Graph Link
Geometer's Sketchpad
CHEMBIO program for TI-83/CBL

Flashlight with fresh batteries, one per group
Polar graph paper or protractors
atlas (optional)

Special Requirements:
You will want to reserve the computer lab in advance for the first day.
You could get by with one Graph Link for downloading their graphs.
A darkened room works best for the CBL light intensity lab.

Subject Matter Notes:

Students often have the misconception that the earth is closer to the sun in the summer and further away in the winter when in fact it is actually the opposite! Some students know that the seasons are caused somehow by the tilt of the earth’s axis but are not sure just how it all works. (As an interesting exercise have the students draw a diagram of the earth’s position in relation to the sun for the different season). Some may actually come up with the idea that one hemisphere is tilted toward the sun and receives direct rays while the other hemisphere is tilted away from the sun and gets less direct radiation. While this is true and probably is the simplified version that most students are taught, it is still not the whole picture!
Weather is a very complex phenomenon and is affected by many variables. The temperature is affected by the number of hours of sunlight received. Summer ‘days’ are longer than winter ‘days’ because of the tilt of the axis so there is more total sunlight. Is it no wonder that warm weather coincides with the summer solstice; the longest ‘day’ of the year? The lakes and oceans also play a big role in determining weather. Even though maximum daily solar energy occurs on June 21st for a city like Chicago, the highest average temperature occurs about a month later in July! This is because large bodies of water are slow to warm up and then retain that heat for a long period.
Since the planets move and spin in somewhat circular motion it is not too difficult to find examples of circular functions in nature. Tides, phases of the moon, rainfall, to name a few examples of where one might expect to find a trigonometric relationship.

Instructional Notes:

The unit is designed to be covered in five class periods;

Session 1: Collecting the Data
Students will locate temperature data on an inter-net site, record it,
and describe what patterns they observe.

If your students are not comfortable with the inter-net you could bookmark the
address ahead of time. It might be a good idea to just let them explore the web site or search for their own sites. If students have trouble coming up with a city in the southern hemisphere you could provide them with an atlas.

Session 2: Modeling the Data
Students will transfer their data to a calculator, construct a scatter plot, find an equation that models the data, and graph the equation that best fits it.

Some students will whiz right through this exercise while others will find it a real challenge. Don’t be too quick to do it for them. The process can be as educational as the product. If you have only one Graph Link running have one of the early finishers
download the students graphs so they can print them out.

Session 3: Develop a Theory
Students will discuss theories for the different seasons, observe a demonstration on changing area with changing angles, and complete an exercise using geometers sketchpad that models this relationship.

Allow the students some time to discuss their different theories. Be careful not to ‘give out answers’. Part of science is revising theories in light of new evidence. The flashlight demonstration can be done on the chalkboard. Tie a string to the flashlight and the tape the other end to the chalkboard. This keeps the flashlight at a constant distance and you can trace the images with chalk to see relative area differences. If you don’t have Geometer’s Sketchpad you can do the exercise with paper and pencil.
Trace the outline of a protractor on a piece of paper, cut a long narrow strip of paper, then just pin the strip on the center of the protractor and measure the distance between the intersection points for the different angles.

Session 4: Test the Theory
Students will collect light intensity data using the CBL, graph it and find an equation that models it.

If you have only one CBL you can still do the experiment it will just take longer. Each student can link to the CBL, run the experiment then leave with their data stored in their calculator. For best results try to exclude any background light.

Session 5: Follow Up and Conclusions
Students will answer some open-ended questions that relate to the topic of climate changes.

See Subject Matter Notes from above.