Lesson Plans

Only the Shadow Knows

Prep for Teachers

Prior to teaching this lesson, bookmark the Web sites used in the lesson on each computer in your classroom. Materials distributed for Introductory Activity #1 should not all be opaque. Materials should be organized and available in students' material baskets.

Prepare the hands-on element of the lesson by making copies of the following worksheets for each student:

Data Sheet #1: Assessment Worksheet
Data Sheet #2: Measuring Shadows
Data Sheet #3: Measuring Shadows
Data Sheet #4: The Geometry of a Right Triangle
Data Sheet #5: Practice Tangent Table
Data Sheet #6: Trigonometric Function Table

When using media, provide students with a FOCUS FOR MEDIA INTERACTION, a specific task to complete and/or information to identify during or after viewing of video segments, Web sites, or other multimedia elements.

Step 1:

Ask students what they think would happen if you place a basketball over a lighted opaque projector. (Shadows happen when light cannot pass through an object or material. Light cannot shine through the basketball. This makes a shadow on the opposite side of the ball to where the light is coming from.) Ask them what type of material or object they consider the basketball to be. (Anything that light cannot shine through is said to be opaque.) Give students the opportunity to look into their organizing baskets and find objects they think are opaque, then try them out on the lighted overhead projector. Review the concept of "what is or what forms a shadow" with students. Ask students to name the parts of a shadow. (Umbra: the darkest part of the shadow. Penumbra: the lighter part found at the edges of the shadow.)

Step 2:

Tell your students to look in their baskets, where they will find a flashlight and a large Ziploc bag with several objects. Students should take these items out of the bag and place them on the table. Ask them to manipulate the angles at which they hold their flashlight over the objects taken from the bags and infer what happens to the shadows their objects cast. Have students draw their shadow observations into their journals. (Students should observe that long and short shadows can be made by manipulating the angle at which the flashlight is held. Students should infer that the length of a shadow depends on the position or angle of their flashlight.)

Step 3:

Give students “Data Sheet #1: Assessment Worksheet” (see end of lesson) in order to CHECK and reinforce their understanding of the concept of the manipulation of angles of light source and shadow length.
The “Assessment Worksheet” suggests that the sun is shining on four objects. The angular position of the sun's rays varies. Students are required to draw the direction of the shadow the objects cast based on the angular position of the sun. Teachers should ask students to give a rationale for the direction of their shadow. The understanding for this Assessment is directly related to Introductory Activity Step 2. The teacher should prepare an overhead transparency with correct shadow directions for class viewing.

Step 1:

Tell students that in order to jog their minds a bit more into thinking about shadows and their formation, you are going to read a poem entitled "My Shadow" by Robert Louis Stevenson from a prepared overhead transparency. The poem "My Shadow" can be found at http://www.poetryloverspage.com/poets/stevenson/my_shadow.html.

Step 2:

Ask students what other images are conjured up in their minds when they hear the word "shadows." (Based on the Introductory Activity and the poem, students may say light, opaque objects, silhouettes, sun play, etc.)

Step 3:

Explain to your students that they are now going to view segments of the video Reading Rainbow: My Shadow in order to enhance their understanding of shadows.

Step 4:

Insert Reading Rainbow #109: My Shadow into your VCR. Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them, "Does light have anything to do with the formation of shadows?" START the video as the Reading Rainbow title comes on the screen, the introductory song ends, and a silhouetted rocking horse appears. STOP the video when LeVar states, "If light travels in straight lines, what happens if something gets in the way?" (Light has a lot to do with the formation of shadows. Shadows are formed since light travels in a straight line from its source.)

Step 5:

Tell students that they are going to do an activity to demonstrate that light really travels in straight lines. Students should look in their baskets, take out four index cards, and find the center by drawing diagonals on each card. Students should then make a good-sized hole at the center of each card and attach each card with thumbtacks to a small block of wood from their baskets. Place index cards one in front of the other, some distance apart, making sure that the holes are in a straight line with each other. Students should hold the flashlight at the opposite end of the lined up index cards, making sure that the height is just right for the flashlight to shine directly through the holes.

Darken the room and turn on the flashlights. Students can look through the holes in the cards and see the light of the flashlight. Students can infer that the light can be seen only because it is passing through each hole in a straight line. Tell students to move one card so it is out of line. They will be unable to see the light because it travels in a straight line and is stopped by the card.

Step 6:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them to think back to the activity with the opaque projector and basketball and to infer from that what LeVar would answer to the question, "What would happen if some object gets in the path of light?" RESUME the video from the previous point. PAUSE the video when you hear LeVar say, "When I place my hand in front of the lamp, light cannot get through. It gets blocked, so my hand casts a shadow on the wall." The concept of shadow formation is so important that student understanding must be reinforced. Ask students to explain what LeVar proved by the demonstration they just viewed. (Whenever opaque material is placed in the path of light, shadows are formed.)

Step 7:

Provide students with a FOCUS FOR MEDIA INTERACTION, asking them the question, "Does the size of shadow have any relationship to the distance an object is from the light source? PLAY the video from the previous pause point. STOP the video when LeVar confirms the relationship between size and distance from the light source. LeVar holds a model of a butterfly in front of a light source. A shadow is cast on the wall. LeVar then begins to move the model butterfly forward. Ask students to explain what changes can be observed in the shadow formation. LeVar states, "When I place the model butterfly close to the lamp, it's a huge shadow. But watch this... It is the incredible shrinking butterfly." Ask students if size makes a difference? (Yes. Students should infer that the closer an object is to the light source, the larger the shadow. Conversely, the farther an object is from the light source, the smaller the shadow.)

Step 8:

Tell students that it is important for them to see the mathematical relationship in the segment they just viewed. They are now going to measure shadows. Have students place their flashlight on the 8" blocks of wood provided. This will become the fixed point for their source of light. Place an object between the light source and a screen, move the object after each measure, and do the following as outlined on “Data Sheet #2: Measuring Shadows” (see end of lesson).

Pose the following questions to students: Do you see any kind of pattern developing in relation to the size of the shadow? Can this relationship also be stated in mathematical terms? (Yes. While answers may vary, students should see that the shadow gets smaller as the objects is moved away from the light source. When the screen is four times farther from the light than the object is, the shadow is also four times larger than the object.)

Step 9:

Ask students to investigate and draw inferences based upon their findings from the following problem. What should happen if the light source is moved to varying distances from the screen, but the object is held at a constant distance from the screen? Students should record their findings on “Data Sheet #3: Measuring Shadows” (see end of lesson).

Step 10:

Have students log on to the LEARNING MEDIA Online Classroom Resources Web site at http://www.learningmedia.co.nz/onlineclassres.htm. Explain that they are going to an interactive site to see another relationship between light and shadow. Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them to determine the position of a shadow based on the time of day.

As this activity comes up on the screen, users are given the instruction: "Look at How the Shadow Changes." There is a clock in the upper left corner. In the bottom right corner, there are two symbols: LOOK and DO. At the bottom center of the screen there is a bar with a bold blue dot in the middle. Moving this dot to the left stops the activity; to the right speeds up the activity. Have students click the mouse on DO. A question is given: "Where will the shadow be at ___ o'clock?" Students may select a time by clicking on the UP or DOWN arrow. Once that is done, another direction is given: "Put your towel on the area you think the shadow will be for the selected time." The towel is moved by clicking the mouse on the towel and dragging the mouse to the chosen area. Users are then directed to click on the symbol "the sun." If the position is correct, an image of a person sitting on the towel appears. Users click on the "time arrow" to restart the process. Ask each group of students to select a time of day and to predict where the shadow will be placed at that time by moving a beach towel to that place. Teachers should CHECK for comprehension and observations of shadow movement. (Students should notice that early in the morning, shadows are long and off to the left side of the beach towel. As time progresses, shadows begin to become shortened. At midday, the shadow is directly under the umbrella. After midday, the shadows are short and begin to move to the right of the umbrella. By mid afternoon, shadows begin to lengthen.)

Step 1:

Show students Plate #1 from the book Shadows and Reflections by Tana Hoban, published by Greenwillow Books. The book has no words, only photographs of shadows and reflections that often allow us to guess what object creates the given shadow. Ask students if Plate #1 is a shadow or a reflection? (Clouds are reflected in the shiny surfaces of the building's glass windows.) In Plate #2 ask, "Who is sweeping the pavement?" (A man, as we are able to see his reflection in the mirrored surface of the water in the gutter.) Go to Plate #5 and ask, "shadow or reflection?" (Shadow: light rays of the sun are blocked by the human figures standing at the street rail.) Ask students if they can determine where the sun would be in relation to the direction of the shadows. (High in the sky and behind the human figures.) Go to Plate #16. Ask students, "Could you describe what you observe? What do you think creates the shadows on the car?" (The shadows on the car have been caused by a picket fence.)

Picking up on the idea from the book Shadows and Reflections, have students log on to the Geometry Shadows site at http://www.learner.org/teacherslab/math/geometry/space/shadows/index.html.

Provide your students with a FOCUS FOR MEDIA INTERACTION, asking them to determine if shadows are always the same shape as the opaque object. Reflect on the activity you did with the objects from the Ziploc bag. Consider having students revisit some aspects of that activity before you begin the interactive activity. (Shadows do not always look like the objects that cast the shadow. The shape of the shadow is often dependent on the direction of the light source.) Ask students, "Is it possible for a square object to produce a cubed shadow?" (Yes. Again remember, the shape is dependent upon the direction of the light source.)

Step 2:

Students are now ready to apply an understanding of shadows and their application to the real world. This activity assumes that students know:

How to measure angles
That a right angle is 90 degrees
That the sides of a triangle are called the base, the height, and the hypotenuse
How to read a table of trigonometry functions
How to do division by decimals

Review with students “Data Sheet #4: Geometry of a Right Triangle” (see end of lesson). Practice with your students how to read the trigonometric table for given tangent angles. Ask your students to complete “Data Sheet #4: Geometry of a Right Triangle” by reading the Data Sheet #5: Practice Tangent Table” (see end of lesson).

Application A
A flagpole is 16 feet tall. A child standing at the farthest length of the pole's shadow makes an angle of 50° with the top of the flagpole. What is the length of the flagpole's shadow?

Ask students to draw the problem.
Set up a proportion or ratio using the tangent ratio outlined.

Tan of 50° = Side Opposite = Height of Flagpole
Side Adjacent = Shadow's Length

Tan of 50° = 16 feet
?? Shadow's Length
Look on the Trigonometric Function Table for Tangent of 50°.
Tan 50° = 1.192
Fit this into the proportion/ratio.
Tan 50° = 1.192 = 16 feet
?? Shadow's Length (let's call this X)
Multiply both sides of the proportion by X, and you get
(1.192) (X) = 16 feet (X) (X's cancel each other out)
X

Then
1.192X = 16 feet

Now divide both sides of the equation by 1.192:
1.192X = 16 feet
1.192 1.192

X = 13.4 feet

Application B
A small tree casts a shadow of 15 inches. The top of the tree forms an angle of 28° with the ground at the far end of the shadow. How tall is tree?

Set up a proportion or ratio using the tangent ratio.
Tan of 28° = Side Opposite = Height of Tree
Side Adjacent = Shadow's Length

Tan of 28° = X
15 inches
Look on the Trigonometric Function Table for Tangent 28°
Tan 28° = 0.532
Fit this into the ratio
Tan 28° = 0.532 = X (height of tree)
15 inches (length of shadow)
Multiply both sides of the equation by 15 inches, you get
(0.532) (15 inches) = (X) 15 inches (15's cancel each other out)
15 inches

Then 7.980 inches = X (height of tree)

You may want to design a series of problems/work cards for the students to try. The work cards can be set up with the problem on one side with its solution on the opposite side..

LANGUAGE ARTS
Research the role that shadows and the sun play in mythology.

SOCIAL STUDIES
Have students research the origin of Groundhog Day in the United States. Have them find out if any other country has a similar type event.

SCIENCE/ART
A silhouette is a shadow portrait, a paper cutout of someone's shadow profile. Have students select a friend, parent or sibling and create a silhouette of that person.

RESEARCH
Who was the French artist August Edouart and what were his famous art creations?
Teachers may create a silhouette art gallery of their class, then have students not only find their silhouette, but identify other class members.

SOCIAL STUDIES/TECHNOLOGY
How did the people of ancient civilizations tell time using shadows?
Have your students construct sundials.

DRAMA/ART/LANGUAGE ARTS
Students may design shadow puppets, write dialogue and put on a shadow theatre puppet show for their class or for the school.

SCIENCE/MATHEMATICS
A fantastic investigation carried out over an entire school year could be Shadows and Changes: A Study of Solar Position. This activity could involve time and time zones, learning compass directions, and learning how to observe, measure, graph, compare, and predict shadow lengths.

Make an arrangement with a local professional photographer to visit his/her workshop to view the taking of pictures and the development of these photos in a darkroom setting. Students can be encouraged to learn how to develop their own black and white negatives.
Visit a local theatre and talk to the lighting specialist to see how light and shadow play an important role in the theatre, especially the use of rear-screen projections.