

Focus: Students use random number tables and an Internetbased simulation to test several hypotheses about the development of cancer.
Major Concepts: No single event is enough to turn a cell into a cancerous cell. Instead, it seems that the accumulation of damage to a number of genes ("multiple hits") across time leads to cancer.
Objectives: After completing this activity, students will
Prerequisite Knowledge: Students should be familiar with the concepts taught in Activities 1 and 2. Students also should have a basic knowledge of probability. The annotation to Step 6 describes a short exercise you can do with students to remind them of the laws of probability.
Basic SciencePublic Health Connection: This activity highlights the contribution epidemiology has made to our understanding of cancer. Students discover how determining and analyzing the frequencies with which cancer occurs in large populations has provided compelling though indirect evidence that human cancer is a multistep process. Students then consider the implications of this understanding of cancer for personal and public health.
The process by which a normal cell is transformed into a malignant cell involves many changes. Cancer cells display a host of striking differences from their normal counterparts, such as shape changes, changes in their dependence on growth factors, and a multitude of biochemical differences.
One of the earliest questions scientists asked about these phenotypic differences was how they are generated. Another question was whether these differences arise all at once, at a moment when the cell experiences a sudden, catastrophic shift from "normal" to "malignant," or gradually, across time, as a result of many small events, each contributing yet another characteristic to a set that in sum gives the cell a malignant phenotype.
In this activity, students examine some of the epidemiologic data that suggest that the development of cancer is a multistep process. Students study a graph of colon cancer incidence by age, answer an initial set of questions about the relative risk of developing colon cancer at various ages, and propose answers to the question of why this risk increases with age. Students then use random number tables and a Internetbased simulation to test several hypotheses about the development of colon cancer (for example, colon cancer develops as a result of a single event within a cell, colon cancer develops as a result of two independent events within a cell, and so on). Finally, students use their understanding of the development of cancer as a multistep process to explain (1) the increased incidence of cancer with age, (2) the development of cancer decades after exposure to known carcinogens, and (3) the increased incidence of cancer among people with inherited predispositions.
You will need to prepare the following materials before conducting this activity:
Copy the master and cut out one data set for each student in your class.
1. Open the activity by reminding students of the increase in cancer incidence with age that they observed in Activity 1. Explain that in this activity, they will investigate the biological basis for this increase.
It is very important to set this activity in the context of Activities 1 and 2.
Without this context, students may complete this activity "by rote" and never see how it relates to our growing understanding of the biological basis of cancer.
2. Distribute one copy of Master 3.1, Colon Cancer Incidence by Age, to each student and ask the students to work in pairs to answer the questions below the graph.
Give students about 5 minutes to complete this task.
3. Display a transparency made from Colon Cancer Incidence and invite the students to share their answers to the questions.
Question 1 How likely is it that you will develop colon cancer this year?
Students should answer that the risk is so low that they cannot read it from the graph. You may wish to ask whether children under 15 ever develop colon cancer. In fact, those few children who do have genetic conditions that predispose them to the development of cancer.
Question 2 How likely is it that someone who is 60 years old will develop colon cancer this year?
The risk is significantly higher (approximately 70 per 100,000 persons).
Question 3 How likely is it that someone who is 80 years old will develop colon cancer this year?
This risk is even higher (about 350 per 100,000 persons).
Question 4 How can we explain this change in the risk of a person developing colon cancer?
Answers will vary. Students may suggest that as people age, they become more susceptible to cancer. Some may also suggest that it takes time for the mutations involved in the development of cancer to accumulate. Accept all reasonable answers, explaining that in this activity, students will have a chance to test a possible answer to this question.
4. Circle the last question on the transparency or write it on the board and point out that this question is the central issue in this activity. Explain that many years ago epidemiologists recognized that this change in cancer risk provided an important clue about the cause of cancer. This activity challenges students to retrace the thinking of these scientists and discover this clue for themselves.
If students are unfamiliar with the term "epidemiology," explain that it is the study of the incidence of disease in a population.
5. Remind students that one way scientists answer questions is by developing and testing hypotheses, or tentative explanations. For example, one explanation that might be offered for the development of cancer might be summarized as, "One mutation in a certain gene in a cell causes that cell to become cancerous" (the onehit hypothesis). Another explanation might be summarized as, "Two mutations in separate genes of a cell are required before the cell becomes cancerous" (the twohit hypothesis), and so on. Ask students if they can tell by looking at the colon cancer graph which of these two explanations for the development of cancer best explains the data.
Students likely will answer that they cannot tell just by looking at the graph.
6. Explain further that scientists often use models to test their explanations.
In this activity, students will use two simple models, one involving random number tables and the other using a simulation on the Cell Biology and Cancer Web site, to test several alternate explanations for the development of cancer.
If your students are not familiar with some of the basic concepts of probability, you may wish to conduct the following short exercise:
Give each student a penny, a nickel, and a dime, and ask students to toss each coin one time and leave the coins lying on their desks where they landed. Ask the students to raise their hands if they got a "heads" on their penny. Count the number of students who raise their hands and point out that this represents about 50 percent of the class. Then, ask students to indicate how many got heads on both their penny and their nickel. Again, count the number of students who raise their hands and point out that this value is close to 25 percent of the class. Finally, ask students to raise their hands only if they got a heads on all three of their coins (the penny, the nickel, and the dime). This number should be about oneeighth of the class. Ask students what pattern they see in these data. Students should see that the probability of independent events happening together is lower than each event's individual probability. Use your judgment to decide whether to explain to students how to calculate the probability of such occurrences (for example, the probability of getting heads on three coins tossed individually is 1/2 . 1/2 . 1/2 = 1/8).
7. Distribute one data set from Master 3.2, Random Number Tables, to each student and explain that students will use these data to understand the implications of the following two hypotheses for the incidence of cancer in a population (the class):
8. Explain that the data sets the students hold are called random number tables and were made as a computer randomly chose numbers between 1 and 25 to correspond with the students' imagined life spans. Explain that the first column on the table represents the students' ages, and that the second and third columns on the table represent the numbers the computer chose.
9. Conduct the following exercise:
. Ask a student to draw a number out of the hat and announce the number to the class. Write the number on the board.
For example, imagine that the student drew the number 10.
. Explain that this number represents a mutation in gene 1. Ask students to examine the column labeled "Gene 1" on their random number table to determine whether they have the number chosen. If they do, they should circle it and note the age at which it occurred.
Students should look down the column labeled "Gene 1" for the first occurrence of the "unlucky" number (in this example, 10). If the number occurs more than once, they should ignore the second (and any subsequent) occurrence.
. Ask another student to draw a number out of the hat and announce it to the class. Write the number on the board.
For example, imagine that the student drew the number 4.
. Explain that this second number represents a mutation in gene 2.
Ask students to examine the column labeled "Gene 2" on their random number table to determine whether they have the second number chosen. If they do, they should circle it and note the age at which it occurred.
Students should look down the column labeled "Gene 2" for the first occurrence of the "unlucky" number (in this example, 4). If the number occurs more than once, they should ignore the second (and any subsequent) occurrence.
