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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.
ITV Series
FUTURES II: Environmental Science and Technology
The students should be able to
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
Pre-Viewing Activities
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.
Focus Viewing
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.

Viewing Activities
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 the video.

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 time.

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 problem.

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 problem.
Post-Viewing Activities
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.
Action Plan
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.


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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