Mathematics

INDIANA STATE PROFICIENCIES:

Mathematics #8: Develop An Understanding Of Geometric Terms And Concepts And Apply Those Concepts In Problem-Solving Activities.

This proficiency provides students with experiences in geometry that will develop their intuitive sense of the concepts of shape, size, symmetry, congruence, and similarity in both two- and three- dimensional space. These experiences include a wide variety of concrete materials that will develop appropriate vocabulary and provide for intuitive learning of geometric properties and relationships. The activities provide problem-solving experiences in geometry appropriate for the application of the intuitive sense of concepts being developed.

There are many realistic problem-solving activities which, with an understanding of basic geometry, can be implemented into the mathematics classroom. Application of geometric concepts to real world problems can take students beyond the classroom to see the importance mathematics plays in their lives.

MATERIALS and RESOURCES:

• Meter sticks

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• Coca-Cola Website
• PepsiCo Website

PREPARATION:

1. The teacher will ask the students in advance to bring in empty 24-can cases of Coca-Cola and PepsiCo products.
2. The teacher will provide instruction on the calculation of surface area. Rectangular prisms are good examples to use to teach the concepts of calculating surface area and volume.

STUDENT INSTRUCTIONS:

1. The teacher will divide students into small groups, and will provide each group with a meter stick or a yard stick and an empty case from each of the soft drink companies.
2. Compare the volumes of the two boxes without measuring. (How many 12-ounce cans will each box hold?)
3. In small groups, use a meter stick or a yard stick to measure the length, width, and height of each box.
4. Calculate the surface area of each box.
5. Compare the surface areas of the Pepsi box to that of the Coca-Cola box. (Which one uses more cardboard?)
6. Discuss in class the environmental impact of the two different types of cardboard boxes. (Which one is better for the environment?)
7. Use their websites to find out more information about the companies, such as their mailing and e-mail addresses.
8. Using a proper business letter format, e-mail or write a letter to one of the companies, describing the classroom activities, the surface areas of the two boxes, the environmental impact of different kinds of packaging, and suggestions for the future.

STUDENT ASSESSMENT:

1. Each student will be responsible for participation in the small group activity (measuring).
2. Each student will be responsible for the computations used to find the surface areas of the boxes.
3. Each student will be responsible for participation in the whole class activity (discussion).
4. Each student will be responsible for a letter written to one of the soft drink companies.

EXTENSIONS:

This lesson may by extended by:
• Having students use their measurements to calculate the volumes of the boxes.
• Taking a class survey of soft drink preferences, converting the findings into percents, and graphing the results.

TEACHER NOTES:

• Assign a role to each student in the small groups. One student may be the measurer, one the calculator, and one the recorder.
• Be aware that the measurement of the surface area of the two boxes does not include overlapping of flaps and any extra inserts inside the boxes.
• Students are likely to be more concerned with the wide difference between the surface areas. (PepsiCo products have less.)

• Having each student write to the soft drink company that makes his or her favorite product will help to eliminate most derogatory comments. Students may wish to congratulate the company that uses less surface area or encourage the company that uses more to change its packaging. Proofread all letters before mailing.
• A drawback to using e-mail is that the companies may feel they are being bombarded by a class project. The preferred method is to write a cover letter to each company, and mail the printed student letters to each company together in a single envelope.

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