CECmath.51 TITLE: WORLD POPULATION STUDY AUTHOR: Margaret V. Smith, Reg. II Observation & Assessment Center; Salt Lake City, UT GRADE LEVEL: 7-12 This lesson is designed for students in grade levels 7 to 12 who have mastered basic math concepts or can use a calculator to solve basic operations. This lesson is relevant in math, biological and physical sciences, global studies, and current events subject areas. OVERVIEW: The concept of exponential (vs. linear) relationships is a difficult concept for many students to understand. This lesson helps students understand the difference between the two and relates this knowledge to human population growth over time. PURPOSE: The purpose of this lesson is to help students learn about an exponential relationship and how it relates to human population growth and the current global population crisis. Students will learn how to graph both exponential and linear information. MATERIALS: Graph paper, pencils, rulers, calculators, blackboard & chalk. OBJECTIVE(s): Students will learn how to: 1. Solve a real life math problem involving multiple and sequential steps in order to answer a question. 2. Graph the results of their problem solving to give a visual representation of the results. 3. Explain the difference between a linear and an exponential relationship. 4. Apply this knowledge to a study of world population growth by making a graph of world population data from 1650 to 2000 (projected). 5. Explain some of the reasons for the growth in the world's population. ACTIVITIES AND PROCEDURES: 1. Present the following problem to your students: Imagine you are four years old. A rich aunt wants to provide for your future. She has offered to do one of two things. Option 1: she would give you $1000 a year until you are twenty- one (seventeen years from now); or Option 2: she would give you $1 this year, $2 next year, and so on, doubling the amount each year until you were 21. Which would you choose? Why? Which way would you have the most money when you were twenty-one? 2. After checking your results with your teacher, get some graph paper and a ruler. Put money on the left, vertical margin, using units of $5,000. Put years on the horizontal margin, starting with year one to seventeen years. Your teacher will demonstrate on the board where to put the information on the graph and how connect the lines, and you will do this as a class. Find the year along the line at the bottom of the graph, then find the amount of money for that year along the left side of the page. Match up these two amounts and place a dot. When you have placed all your dots, draw a straight, solid line to represent option 1, $1000 per year, and a curved, dotted line to represent option 2, $1 the first year and double that amount every year. (If you suspect that the computations part of this problem and the graphing aspects might be too difficult for some of your students, you could pair strong with weaker students or do the entire problem on the board as a class, and allow the use of calculators. You could give students an empty, labelled graph if this is new and difficult for them. If some students cannot complete the graph, allow them access to a completed graph to study.) 3. Study the graph and answer the following questions: A. How much money would you have when you were 21 if you chose option 1? How much would you have if you chose option 2? B. If you only received money for ten years, which option would give you the most money? C. How many years would it be before you had the same amount of money with both options? D. Why did the money in option 2 increase so rapidly after the fourteenth year? E. Which line do you think would look most like the world's population growth from 1650 to 2000? Why? F. Look at the graph. Option 1 represents a simple, direct relationship and is called a linear relationship. Option 2 shows an exponential relationship in which for every year the amount doubles. Some exponential relationships increase even more than this. Which option is linear? Which option is exponential? 4. The estimated world population from 1650 to 2000 is listed in the chart below. Make your own graph of this information, putting population figures (in millions) on the left vertical margin, and years on the horizontal margin. Your teacher will show you an example and help you do this. This line graph will show how fast the world's population is growing. Do you think that a line showing this population growth would look more like the linear or the exponential line from the last exercise? Why? Find the year along the line at the bottom of the graph, then find the correct population for that year along the left side of the page. With your pencil and ruler, draw one dot for each pair of information. When you have placed all of the dots on the graph, connect them with one curved line. YEAR WORLD POPULATION (in millions, estimated) 1650 500 1700 600 1750 700 1800 900 1850 1300 1900 1700 1950 2500 1976 4000 2000 7000 Which type of relationship does your graph represent-- linear or exponential? 5. To understand why world population is now growing so fast, we will discuss some issues. This activity will help you understand one of them. Read the four "family histories" below and answer the questions. It might be useful to draw a "family tree" for each one to help you with the math. Family A: A has one child. If that child has one child, how many grandchildren does A have? If the grandchild has one child, how many great grand-children does A have? Family B: B has two children and each of them has two children. How many grandchildren does B have? If each grandchild has two children, how many great- grandchildren does B have? Family C: C has three children and each of them has three children. How many grandchildren does C have? If each grandchild has three children, how many great- grandchildren does C have? Family D: D has four children and each of them has four children. How many grandchildren does D have? If each grandchild has four children, how many great- grandchildren does D have? TYING IT ALL TOGETHER: The number of children "multiply" each generation. For family B there are twice as many children each generation and for family D there are four times as many. Few families really have the same number of children each generation. But these examples help explain one reason why the world's population has grown rapidly in the last 100 years. Another reason is that in most areas of the world, people are living longer. Up until 125 years ago, the world's population was increasing slowly. Although the number of births multiplied, many babies did not live and large numbers of children and adults died from diseases. Over the past 150 years diet, nutrition, and health care have improved. Scientists have discovered cures for many diseases. As a result, the death rate has been declining rapidly. With more people being born and living longer, the result has been a big jump in the world's population. There are concerns that as world population increases there will be shortages of food, water, and the quality of life will be threatened worldwide. What do you think? Discuss &/or debate.