Lesson Plan 1: Overrun by Skeeters - Exponential Growth
Teachers will need the following:
Students will need the following:
- Graphing calculator
- Skeeters (tokens or candies with a marking on one side)
- A large, flat box (one for each group of four students)
1. Divide students into groups of four. In each group, assign the roles of captain, recorder, reporter, and timekeeper.
2. Explain that the class will examine population growth.
3. Distribute the handout.
4. Have students read aloud the introductory paragraphs for the lesson.
5. Ask students to consider what things they can do mathematically to make predictions about the future. Students should suggest that collecting data, making graphs, and looking for patterns would be useful in making predictions.
6. Show PowerPoint data regarding the world population from 1650 to 1850. (The PowerPoint slide show uses animation to proceed through a series of questions for students, which correspond to steps 7-14 below. If PowerPoint is not available, these images can be used to present similar material on an overhead projector.)
7. In groups of four, have students describe any patterns they notice in the changes in world population from 1650 to 1850.
8. Have student groups predict the world population in 1950.
9. Have reporters state their team's prediction for 1950. Record the various predictions on the chalkboard or overhead projector. Be sure that students explain how they made the prediction, and have students discuss the various predictions. (Once students agree on which predictions are reasonable, you may wish to have them take the average of these predictions to come up with a whole class prediction.)
10. Have student teams plot their 1950 point on the graph containing the points for 1650, 1750, and 1850. Because the three points for 1650, 1750, and 1850 lie somewhat along a straight line, have students check the reasonableness of their prediction by noticing if it lies along the same line.
11. Reveal the actual population in 1950. (The student predictions will likely have been much lower.) Then, ask them to use this new information to predict the world population in 2000. Again, have students discuss this problem in their groups.
12. Record the groups' predictions for 2000 on the chalkboard or overhead projector. Be sure to have students state how they arrived at their predictions, and allow them to discuss the reasonableness of these predictions.
13. Reveal the actual population in 2000.
14. Explain that things can grow in different ways, following different patterns and in ways we might not expect. Consequently, we adjust our predictions based on new information. Explain that students will conduct an exploration.
1. Have a student read the directions for the exploration:
To help make predictions in real-world situations, researchers often use experiments known as simulations. The results of the simulations are gathered and analyzed. This data is then compared with known information about the actual population. If the result seems questionable, the simulation may be revised.
2. Have students explain what a simulation is in their own words. Elicit from students that a simulation is a model of a real-world situation.
3. Have several students give examples of simulations.
4. Have a student continue reading under the Exploration section:
This modeling process can be summarized by the following five steps:
In the following exploration, you investigate this modeling process using a population of Skeeters.
5. Have students read the directions for the exploration. Then, give them 30 minutes to run the simulation and complete the portion of the handout under the heading Discussion 1.
- creating a model
- translating the model into mathematics
- using the mathematics
- relating the results to the real-world situation
- revising the model
6. Record the teams' predictions for "Shake 20." (Students make this prediction in Discussion 1, Part c.1 of the handout.)
7. Lead a class discussion about the predictions. Have students explain the patterns they noticed as they ran the simulation, and how they used those patterns to make their prediction.
8. Give students 10 minutes to complete Discussion 2. (In Discussion 2, student teams decide the best way to describe the shape of the graph.)
9. Ask the reporter from each team to share the team's description of the shape of the graph. Record their descriptions on the chalkboard or overhead projector. Discuss the descriptions and elicit from students that the graph is a curve.
10. Give students the remainder of the class period to record what they learned in their journals.
You may wish to follow this lesson with an activity that allows students to compare linear growth with exponential growth. A lesson plan for such an activity is provided in Workshop 8 Part II.