THE SIX FACES OF GARBAGE
Grades 6 - 8
This lesson will provide students with the opportunity to use
the mathematics of surface area to approach the problem of garbage pollution
from the classroom.
As an introduction to surface area, before viewing the videos, students
will construct small replicas of cereal boxes, and compute their surface
areas by measuring each side and calculating the areas of each face.
During the first video, Futures II, students will be introduced to the problems
created by the amount of garbage that is produced in this country daily.
They will estimate how much garbage is being produced by each of us, and
recognize the occupations and genders of scientists and engineers who are
trying to solve the problems this form of pollution is creating. They will
be introduced to the three R's of recycling.
While viewing the Bill Nye video, they will calculate the amount of cardboard
needed to make a large box of cereal and compare that to the amount needed
to make enough small boxes to hold the same amount of cereal, by finding
the respective surface areas. This gives students a concrete example of
how much waste is produced by convenience packaging.
They will lastly address the problem of garbage pollution in a personal
way, by writing an essay. In this essay they will explain their findings
from the experiment, and using this situation as an example formulate a
plan by which they can help reduce waste in their homes or communities.
FUTURES II: Environmental Science and Technology
BILL NYE THE SCIENCE GUY: # 122 Garbage
The students should be able to
- recognize the problems created by garbage and the types of garbage
that are biodegradable and non-biodegradable estimate how much garbage they
will personally produce in their lifetimes
- list 4 specific occupations of people who deal with the problem of
- compare the cardboard amounts needed to make a large box of cereal,
as opposed to many small boxes that would hold an equal weight, by finding
the respective surface areas
- formulate a plan to find ways, on a personal level, to help alleviate
the problem of garbage pollution
- scissors-one pair per student or pair of students
- rulers - one per student or pair of students
- tape or glue
- a large box of cereal-one for teacher demonstration, or one per group
- a single-serving size box of the same cereal - one for teacher demonstration
or one per group pattern for a cereal box - one per student
- calculators - one per student
- activity worksheets
Face - the surface of one side of a prism or polyhedron
Edge - the line where two faces of a prism meet
Vertex - the corner of a prism
Area - the number of squares needed to cover a two-dimensional surface
Prism - a three dimensional figure which contains parallel bases
Surface area - like wrapping paper, the total area of all
faces of a prism
It is beneficial if students have had some experience with three
dimensional figures before beginning this lesson. This activity can be completed
in part of a class period any time before this lesson. It is well-suited
for a partial schedule day. It will provide them with the experience of
building 3-dimensional objects and introducing the requisite vocabulary.
Obtain 2-3 sets of polydron shapes. Divide the pieces into plastic bags
so that each set will create a unique convex polyhedron. Include both regular
and non-regular polyhedra in the bags. Have students identify the faces,
edges, and vertices of the polyhedron, and share this information with the
class. Have them devise a name for their figure. The teacher could then
provide the correct geometric name for each polyhedron.
On the day of the lesson, begin the class by passing out the outline of
a small cereal box, scissors, rulers, and tape or glue. Instruct the students
to cut out the shape, fold on the dotted lines, and determine what shape
is produced by the folding. Before taping or gluing, identify and count
the faces, vertices, and edges of the box, and label the front, back, top,
bottom, and both sides of the box. Define this polyhedron as a rectangular
prism. Have students then measure, to the nearest tenth of a centimeter,
the edges of all rectangles in the prism, and find the area of each face.
Have them write the area of each individual face on the correct rectangle,
and find the sum of the areas of all of the faces. Define this calculation
as the surface area of the prism. Have them then tape or glue the prism
together, or leave flat as a reference.
To give students a specific responsibility while viewing, tell
them that they are going to watch clips from two videos dealing with garbage.
During the first video, they will have the task of finding four different
occupations of people involved in the pollution industry. The first clip
shows Jaime Escalante and Olivia Newton John. Have them listen for and determine
the job that Olivia Newton John has at the United Nations.
Begin with the Futures II video.
START the video as Olivia Newton John enters the classroom. PAUSE
after the video shows her as the UN Environmental Ambassador where she states
that if we all accept responsibility for pollution, we can begin to solve
it's problems. Ask "What is Olivia Newton John's job at the UN?"
Instruct students to find the occupations of four different people, as they
watch the remainder of this video. RESUME the video as it shows a
landfill. The recycling engineer in Seattle is being interviewed.
PAUSE the video after he defines a landfill and ask students to give
you a definition for a landfill. Ask them to raise their hands if they have
been to a landfill. Ask them why they were there. Ask them where they think
this particular landfill is located, (the engineer is from Seattle), and
ask them why they think Seattle was selected to be used in this video. (Because
of the strong recycling program there.) Tell them to listen and find out
how much garbage each of them will produce in a lifetime. RESUME
PAUSE when he states that '650 times our adult weight', and have
them estimate how much garbage they personally will produce in their lifetimes.
They might want to estimate their adult weight by using their parents weight
as an approximation number. RESUME the video.
PAUSE when the project manager (female) is interviewed. Note her
gender and occupation. Tell students to watch and find out how much of a
landfill is paper. Tell them to say 'PAUSE IT' when they hear
the answer. Do so when they say to. Tell them now to listen for how long
paper stays in the landfills. RESUME the video reminding them to
watch for occupations, and have them find two types of garbage that are
successfully recycled at this time.
The video returns to the classroom, and when Olivia Newton John says "there
are so many different ways that you can help," STOP the video,
and discuss the occupations, the genders, and the educational requirements
of these careers. Also discuss the longevity of paper in landfills, and
the types of materials that are being successfully being recycled at this
EJECT this video, and INSERT the Bill Nye video. This should
be set to start in the last 3/4 of the video, where garbage is being thrown
into various containers, all set to music.
FOCUS the students on this video, by telling them that they will
see a problem that they can help solve by using mathematics. PLAY
the video until the girl is pouring the small boxes of cereal into the bowl.
PAUSE the video and distribute the worksheets. Ask students to estimate
how many small boxes it will take to fill the large box. Have them write
this down on the place provided on the worksheet. RESUME to see if
their guesses were correct.
STOP the video after they see the answer (1 large box = 24 small
boxes). Have them follow the steps in Part I of the worksheet to calculate
how many small boxes of cereal they would need to purchase in order to have
the same amount of cereal as in the large box. Use the specific boxes you
have for demonstration purposes. RESUME the video after asking them
to identify how the girl next compares the two different sized boxes.
STOP the video after the girl states that "a large box uses
less cardboard, a lot less," and follow the steps in Part II of the
worksheet which calculates and compares the surface areas of both sized
boxes. This activity can be completed as a whole class activity with the
teacher making the measurements of the box faces, or in groups with each
group completing these tasks. The level of math ability should determine
how it is to be completed. Time may also be a factor in determining if the
students or the teacher will make the measurements. The demonstration boxes
could even be pre-measured and marked.
Discuss the findings of the students. START the video after telling
them to listen to find three ways that they can help solve the garbage problem.
PLAY until the reduce, reuse, recycle segment is finished.
PAUSE and ask them what the three R's were in their parents' and
grandparents' day. RESUME the video, after instructing students to
listen for the focus of the writing assignment that they will have. PLAY
until Bill Nye states a possible solution for this part of the pollution
STOP as garbage begins to fall on Bill Nye and cover him up. Ask
the students what Bill Nye suggests they do to help the garbage pollution
To allow the students to review the concepts from the videos,
the findings of their calculations, and in order to begin to form a personal
plan for garbage, have a class discussion. Review the points made in the
videos, and their findings from their surface area work. Focus on the garbage
pollution problem, the occupations of the people trying to solve it, and
begin to discuss how they can help solve the problem. Discuss the efforts
of your community to recycle, and determine if students know what happens
to their garbage after it leaves the can at home. Assign them the essay
as described at the end of the worksheet.
Another hands-on lesson involving surface area uses cubes and graph paper.
Give each student a 1 inch cube, scissors, and graph paper with 1 inch squares.
Instruct them to cut out enough squares to make a coat for their cube. There
can be no overlapping of squares or gaps when the pattern is folded around
the cube. The pattern must be in one piece, no taping allowed. Once they
have discovered one pattern, instruct them to find as many different patterns
as possible. Display these on the overhead as new patterns are found, and
continuing until most students have a set of possible coat patterns. Next
pass out another cube to each student, and have them create coats for 2
cubes together. This could be extended to 3 or 4 cubes. The patterns make
good posters for the classroom, when mounted on construction paper. This
could also be completed as a pre-viewing activity for this lesson.
Invite a person from the local landfill, recycling center, or
waste disposal center, into the classroom and have them discuss their occupations.
They could also focus on what their particular entity is doing in the community
to help the pollution problem.
Students could go on-line to find classrooms of students in different parts
of the state and compare the efforts of these communities in solving the
pollution problems of garbage.
Students could start a paper recycling effort at school, if one is not in
place. Schools use large amounts of paper each day, and students can feel
an immediate sense of worth in helping lessen the problem in their community.
Take a field trip to the local recycling center.
Have students calculate the volumes of both the large and small
boxes of cereal. Ask them to compare the number of small of boxes needed
to fill a large box, by volume alone. There will be a difference, as cereal
is sold by weight. Discuss why this is the case.
Have the students calculate the unit cost of the cereal in both the large
and small boxes. Have them determine how much more it costs to purchase
small boxes as opposed to the large box. Have them find the cost for cereal
in bags, and compare these costs to the cardboard. An analysis of their
findings could include advice to give their mothers as they go to buy groceries.
Mobius is the mascot for recycling. Do a demonstration/activity with mobius
strips, and help students discover why this was chosen as a symbol for recycling.
Obtain a class set of bookmarks from BFI, Inc., to give to the students
as reminders to recycle.
VIDEO AVAILABLE FROM
Can be taped off-air. Consult your local PBS station for broadcast schedule.
Lesson plan developed by Master Teacher Kit Parker, South
Junior High School, Boise, Idaho
Click here to view the
worksheet associated with this lesson.
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