Note: This activity has many intersections with the National and State Science Education Standards.

NATIONAL SCIENCE EDUCATION STANDARDS, Grades 5-8 (NRC, 1996)

SCIENCE AND INQUIRY STANDARDS:

• Design and conduct scientific investigations.

• Use appropriate tools and techniques to gather, analyze and interpret data.

• Answer questions that can be solved by scientific investigations.

• Think critically and logically to make relationships between evidence and explanations.

EARTH SCIENCE STANDARDS:

• Compare and contrast properties and conditions of objects in the solar system to those on Earth.

• Explain how the tilt of the Earth and its revolution around the Sun results in uneven heating of the Earth, which in turn causes the seasons. Those motions explain such phenomena as the day, the year, phases of the moon and eclipses.

• Understand that seasons result from variations in the amount of the sun's energy hitting the surface, due to the tilt of the earth's rotation on it axis and the length of the day.

MASSACHUSETTS STATE SCIENCE STANDARDS, Grades 6-8 (11/00)

EARTH SCIENCE STANDARDS:

• Compare and contrast properties and conditions of objects in the solar system to those on Earth.

• Explain how the tilt of the Earth and its revolution around the Sun results in uneven heating of the Earth, which in turn causes the seasons.

 

A. Learning objectives:

• Identify the North, South, East and West directions using shadows during the course of the day.

• Collect shadow data in a systematic manner.

• Note and describe how shadows change throughout the day, and how noontime shadow lengths change with the seasons.

 

B. Materials:

• Gnomon (pencil, tinker toy, etc) -- stick to use for casting a shadow

• Compass

• Ruler

• Large protractor

• Pencil

• Large piece of paper

• Time Required: At least one full-day to collect data and one or two additional days to process, and interpret the results.

 

C. Background:

This lesson addresses many common misunderstandings and misconceptions that students have about the Earth's orbit around the Sun. In this lesson, students can gather enough empirical data using the Sun's shadow to: establish the four directions, track the daily rotation of the Earth on its axis, prove that the Sun is never "straight up" or directly overhead at our latitude of 42°, and understand that the Sun does not necessarily reach its highest point in the sky at exactly 12:00 noon. Additionally, students will gain knowledge of the four directions, which will enable them to accurately describe objects related to astronomy, navigation, map reading and orienteering.

Once the directions are established, an additional avenue of inquiry involves measuring shadow lengths when the Sun is due south (around noon). These shadow lengths will change regularly throughout the year, and careful analysis of the noon-time shadow repeated throughout the year, then students can graph data that proves the Earth's axis is tilted at 23°.

You might begin this lesson by asking some pre-assessment questions. For example:

• Find out if your students can estimate the location of the four directions. Do any students still think that north is up and south is down?
• What environmental clues can your students use to find the four directions? For example, moss growing on the north side of a tree or observing the position of the Sun or moon rising in the east and setting in the west.
• What clues can they use to find the four directions during the day versus at night? Ex. Position of the Sun, Moon or Stars.
• Can your students find the four directions with a magnetic compass? How will magnetic north differ from astronomical north, i.e. north defined by the North star, Polaris?
• What evidence is there that the Earth is spinning or rotating on its axis everyday? How does the Sun's position change throughout the day?

The more time students are allowed to develop their own ideas into actual experiments and collect and analyze data, the more you will learn about their current knowledge in the topic as well as some important insights into their misconceptions.

 

D. Procedures:

1.) The Set-Up: A Gnomon Within a Circle

In this lesson students will use the shadow cast by a gnomon to identify the four directions. A gnomon is a freestanding, vertical object, which casts a shadow on the ground. Some examples of gnomons include a pencil stuck into the ground, tinker toys, tetherball pole, or even an golf tee glued upside down onto a piece paper. The type of gnomon is not as important as having a flat surface from which you can draw or trace the length of the shadow as it changes throughout the day and having the gnomon be absolutely perpendicular to the flat surface. Never move a gnomon once you begin an experiment. If a gnomon is glued onto paper, then anchor the paper down with tape or rocks. It is also important to choose a location with full sun throughout the day. Be careful not to use an area that gets shade in the afternoon. A classroom with south-facing exposures can work during certain times of years, but they may not work year-round if you plan on repeating the experiment.

The gnomon should be placed in the center of a circle with a radius specified in column 4 of the following table. Ideally, the morning shadow should extend beyond the outside of the circle, the noontime shadow should be within the circle, and the shadow should lie exactly on the circle about 10a.m. and 2-3 p.m. If the morning shadow is within the circle, then the circle is either too large or the gnomon is too small. Let the students hypothesize how big they think their circle needs to be in order for the longest shadow to extend beyond the edge. You might be surprised to see how few students can actually predict how an object's shadow will change in a day or throughout the year. Depending upon your time restraints and space available, you can either let students create their own gnomon and then determine the appropriate size circle or you can photocopy a circle on paper and have everyone use the same size gnomon, such a golf tee glued upside down. Always make sure the gnomon is located exactly in the center of the circle.

2.) Recording Data: Measuring the Gnomon's Shadow Lengths

If you are teaching several classes in the same day, then each class can take measurements during their class period. The measurements themselves only take a few minutes. You could try assigning this activity as weekend homework project if you wanted students to collect their own data throughout the day.

In order to find the four directions, the students will have to trace over the entire shadow roughly every hour. The students can record the time of day next to each drawing. In the morning when the Sun is low on the horizon the shadow extends westward beyond the outside of the circle. In an hour or so, as the Sun appears to move higher in the sky the shadow's length shortens. The first important data point is when the shadow falls exactly on the edge of the circle. In another hour or two, as the Sun is due south and is highest above the horizon, the shadow will reach its smallest size. In the afternoon, the shadows will begin to lengthen again and fall eastward. The second important data point is when the shadow once again lands precisely on the circle. At the end of the afternoon, the students should have a recording sheet that looks like Figure l.

 

Figure 1. Student Recording Sheet.

Example of how shadows will appear in February or October



Teacher Note:

At noontime, you can have the students estimate how high the Sun is above the horizon, where zero is the horizon and 90° is overhead. Again, many students assume the Sun is directly over their head at noon. You might discuss later that the Sun is never overhead at this latitude (42°). One has to stand on the Tropic of Cancer at latitude 23 1/2° on the summer solstice in order for the Sun to be at zenith or overhead at noon.

3.) Data Analysis: Establishing the Four Directions

a. Ask the students to make X's at the ends of these shadows that landed on the circle.

b. Connect the X's using a meter stick or ruler as shown in Figure 2. The line connecting these two points identifies the East-West directions.

c. Indicate the East end and West end of this line. (East being the direction to the morning Sun when the shadow pointed westward).

d. Ask the students to find the midpoint of the East-West line.

e. At the midpoint of the East-West line, create a perpendicular line (which also goes through the gnomon and the center of the circle).

f. The students should mark this line with the North and South directions. (All noon-time shadows will appear on the North side of the gnomon).

 

Figure 2: Calculating the East-West direction.



 

Table 1: Shadows to Expect for a 12" Gnomon

Month	Noontime Angle to the Sun (Amherst)	Noontime Shadow	Optimal Circle Radius
December 21	24°	26.3"	32"
Jan, Nov. 21	24°	22.6"	30"
Feb, Oct. 21	36°	16.5"	24"
March, Sept. 21	48°	10.8"	16"
April, August 21	59°	7.2"	10"
May, July 21	68°	4.8"	7"
June 21	71°	4.0"	7"

 

Things to remember for this activity to be successful:

Direct Sunlight is essential.

Choose a site with direct sunlight for most of the day. Is important that the gnomon be in direct sunlight in order to get accurate data. This is not always possible indoors. This may work in a south-facing window -- but there may not be enough light in the winter if you want to repeat the experiment.

The gnomons and shadow records must be stationary all day long.

The gnomon and shadow recording sheet should be in the same place for every measurement. These objects should be secured to the ground or made immovable -- and left where they will not be disturbed. Some teachers may choose a large fixed gnomon outdoors like a pole, post, etc. Data can be recorded in chalk on the sidewalk, with shadow measurements and times written down on the data sheet.

The activity is flexible for an individual, group or whole-class exercise.

This is a matter of personal preference and should be based on the teaching and learning styles of both the teacher and the students. This choice may also be based on the duration of the activity. If you plan to continue recording shadows throughout the year -- it might be best to have just one permanent gnomon for the whole class. While it might be good for the students to have their own at first. If you teach multiple classes in a day and you feel it important for students to see the continuous motions of the Sun's shadow, then try assigning the activity as homework.

 

Extensions and Related Lessons:

Allow your students to compare the four directions they determined with those shown by a magnetic compass. This discrepancy can lead students towards investigating true or astronomical north versus magnetic north in their particular geographic area.