Teaching Mathematics with the Internet Workshop 1999

Ratios Through Social Studies

by

Aniekan Ebiefung, Ph.D.

Goals

To create an integrated lesson plan so that mathematical concepts are studied in the context of social studies.

Rationale

If students are actively involved in gathering, presenting, and interpreting information, then they are the creators and discoverers of their own knowledge. Studies have shown that active learning encourages and motivates students to seek and learn more. In the process of exchanging information, students will improve their thinking and communication skills. They will also learn about the history, culture, and the way of life of their city and of their pals in a way not possible in a passive learning environment.

Objectives

  1. To gather, present and analyze information on a bar chart, pie chart, and so on.
  2. To compute ratios.
  3. To demonstrate that ratios have real-world applications.
  4. To summarize the history, culture, geography, et cetera, of their cities while studying ratios and descriptive statistics.
  5. To see the connection between mathematics and every day life activities.

Methodology

  1. Teachers from different schools make arrangements for the project. When and how the different classes communicate are decided by the teachers in advanced.
  2. Students from one class take a virtual trip to the city, state or country of the other class using the Internet. The purpose of this virtual trip is to learn more about the other students with which they will be working with during the semester.
  3. Students start collecting data about their cities. The information includes population, number of public and private schools, churches, hotels, recreational facilities, violent crimes, the average rainfall, the average summer temperature, and so forth.
  4. All collected information is properly grouped into categories. Information in each category is properly presented by means of bar graphs, pie charts, and so on.
  5. Students exchange information.
  6. After receiving data, students compare the information with what they have on their city. The teacher helps the students devise different means of comparing the data.
  7. Through discussions, students come to realize that the numbers themselves do not convey much information. For example, if city A has 10 cemeteries and city B has 8, what does that tell us about 'deaths' in the different cities? This is a very important stage in the project. To help students to reason, the teacher should give some examples. One such example is the following. Suppose student A has $10 for his school lunch for the week and student B has $5. If student A lost $1 to the old vending machine and student B lost $1, who suffers most as a result of the lost? To answer the question we reason that student A lost $1 out of $10 or 1/10 or 10% of his money; and student B lost $1 out of $5 or 1/5 or 20% of his money. Thus although each lost $1 each, the relative loss is different for each student. Student B suffers most. Through examples like the above, students come to realize that they can get more useful information from data by relating them to other available information. What does the number of churches divided by the population mean? What does number of churches divided by the number of restaurants mean? And so on. Students compute the ratios, give their meanings and send via e-mail to the other class and vice versa.
  8. More meaningful ratios can be computed. For example, students collect information on the number of square feet of available cemetery space. This information is compared with the city population to determine the amount of land available for the burial of each person in the city (with some assumptions). Many such ratios can be computed as the teacher deems fit or as time permits. In each case, information is exchanged with the other class through e-mail.

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