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.
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.)
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.)
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
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.
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.
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
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
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.)
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.
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.)
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.)
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.)
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).
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.)
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.)
Students are now ready to apply an understanding of shadows and their
application to the real world. This activity assumes that students know:
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).
- How to measure angles
- That a right angle is 90 degrees
- That the sides of a triangle are called the base, the height, and
- How to read a table of trigonometry functions
- How to do division by decimals
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
Adjacent = Shadow's Length
Tan of 50° = 16 feet
- 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)
1.192X = 16 feet
Now divide both sides of the equation by 1.192:
1.192X = 16 feet
X = 13.4 feet
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
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..
- Set up a proportion or ratio using the tangent ratio.
Tan of 28° = Side Opposite = Height of Tree
Adjacent = Shadow's Length
Tan of 28° = X
- 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)
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
Then 7.980 inches = X (height of tree)
Research the role that shadows and the sun play in mythology.
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.
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.
Who was the French artist August Edouart and what were his famous art
Teachers may create a silhouette art gallery of their class, then have
students not only find their silhouette, but identify other class members.
How did the people of ancient civilizations tell time using shadows?
Have your students construct sundials.
Students may design shadow puppets, write dialogue and put on a shadow
theatre puppet show for their class or for the school.
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.