Illuminations: Mathematics and Environmental Concerns

# Mathematics and Environmental Concerns

## Aluminum Cans

 Students participate in an activity in which they investigate data in connection with recyclable materials and develop plans to help the environment. Students collect data about aluminum can usage and graph that data in a line plot.

### Learning Objectives

 Students will: gather and graph data about aluminum can use interpret data, including figuring and displaying the mean of a set of data develop a plan for future actions

### Instructional Plan

 Show an aluminum can. Discuss what students know about such cans. Of what are they made? [Aluminum.] What products are sold in similar cans? [Soda, other soft drinks, juice, motor oil.] What other products are made of aluminum? [Siding for houses, rain gutters, silver paint, mirrors, packaging (i.e., aluminum foil), CD's, and the hood of a Model T Ford.] Why is aluminum an important metal? [It's relatively inexpensive, malleable, and lightweight.]

Distribute the Aluminum Cans activity sheet.

Allow time for students to record their own numbers, and poll eight classmates. The data should be recorded in the chart on the activity sheet. A sample chart is shown below.

 Name Number of Aluminum CansUsed Yesterday Me 1 Sarah 2 Jose 0 Wally 3 Helene 2 Sachin 1 Grace 3 Billy 2 Noel 2

Next, each student should create a line plot or bar graph of his or her data. (Or, you may ask half the class to create each type of graph. Then, a rich discussion can occur about the differences between the graphs and the types of information that each shows.) A sample of each type is shown below; the line plot is on the left, and the bar graph is on the right:

Have each student look at the line plot and write several things that the graph shows. Students should note the range of numbers on their graphs. Review, as needed, how to figure the mean (average). Have students compute the mean of their sets of data. They may check their calculations by using the calculator.

Discuss ways to compare an individual's can use in a day with the typical American's use of 1500 cans per year (Javna, 1990). Have students compute per-year use and compare it with 1500. They should also work with the group mean, figure the number of can used per year on the basis of this number, and compare the number per year with 1500. Students should use calculators and may check each other's work.

Students should discuss some things they learned from the activity. Discussion questions could include:

• Were they surprised at their own or the mean for the people they polled?
• What did they learn about the mean as compared with individual numbers in their data sets?

Have students work individually or in small groups to discuss and write plans for conserving aluminum. A committee should post examples of the plans; alternatively, have students report the plans to the class.

### Extensions

 Have students gather data for the number of aluminum cans they use each day for a week. They can find a mean number for these data and compare it with the "yesterday's number" used for the graph and with the group mean found on the graph. Have students discuss whether "yesterday's number" or their weekly mean was more typical of the number of can they use. Let students compile similar data for their family's use of aluminum cans. Start or expand a school project for recycling cans.

### NCTM Standards and Expectations

 Data Analysis & Probability 3-5Collect data using observations, surveys, and experiments. Represent data using tables and graphs such as line plots, bar graphs, and line graphs. Compare different representations of the same data and evaluate how well each representation shows important aspects of the data.

### References

 Shaw, Jean M. and Firkins, John. September, 1993. The Arithmetic Teacher. p 27-40. Javna, John. 1990. Fifty Simple Things Kids Can Do to Save the Earth. Kansas City, Mo.; Andrews & McMeel.

1 period

### NCTM Resources

Principles and Standards for School Mathematics

 More and Better Mathematics for All Students
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