Illuminations: The Next Billion

# The Next Billion

 In 1999, the world population reached 6 billion, and in 2011, the world population reached 7 billion. In this lesson, students predict when it will reach 8 billion. Students discuss the reliability of their predictions, compare them to past trends, and discuss social factors that can affect population growth.

### Learning Objectives

 Students will: apply proportional reasoning look for patterns and draw conclusions about world population growth

### Materials

 Clock with a second hand or a stopwatch Calculator Comparing Predictions to Past Trends Activity Sheet

### Instructional Plan

Prior to the lesson, find several web sites that contain world population projections. A few sites are listed below, but you may find others that will be more suitable for your students.

To begin the lesson, have students identify things that continually change; for example, their age and height, the date, the temperature outside, or the position of the sun in the sky. Make a list of student responses.

Pose questions such as the following:

• Do any of the items on the list ever stop changing? [For example, their height increases as they get older, but at some point the growth stops.]
• If an amount continually changes, does that mean it is always getting larger? Why or why not? [No, because it could be decreasing all or some of the time.]
• Can you name something that continually changes, but never decreases? [For example, the age of the earth.]

Predicting the Next Billion

Organize the class into groups of 2-3 students and share the following information with them:

According to the United Nations, the world population reached 7 billion on October 31, 2011.

Explain to students that their job is to predict, as best they can, when the world population will reach 8 billion. At this point, ask students to guess when they think that will happen. Tell students to record this information, because they will use a mathematical method for making a more precise prediction later in this lesson.

Allow students to reserach the current change in population, using a world population web site (such as one of the three listed at the top of this lesson). Because predicting world population is imprecise, these sites often do not agree. However, most sites seem to indicate that the population is increasing by approximately 6.5 million people per month (as of November 2011), which is roughly 2.5 people per second. A more precise estimate has been used for the calculations below.

Students might begin by measuring the time for the population to change by 50. Then they might make a chart to keep track of each interval, converting seconds to minutes, minutes to hours, and so on, as shown in this example:

 Increase in Population Time 50 19 sec 100 19 sec • 2 = 38 sec 1000 38 sec • 10 = 380 sec = 6.3 min 10,000 6.3 min • 10 = 63 min = 1.05 hr 1,000,000 1.05 hr • 100 = 105 hr = 4.4 days 1,000,000,000 4.4 days • 1000 = 4400 days = 12 yrs

Or they might first find the total number of seconds:

 Increase in Population Time 50 19 sec 100 38 sec 1,000,000,000 38 sec • 10,000,000 = 380,000,000 sec

And then divide to find the number of years:

380,000,000 sec × 1 min/60 sec × 1 hr/60 min × 1 day/24 hr × 1 yr/365 days = 12 yrs

The results above are samples. Students' results may vary depending on how the students measure and round. If an estimated increase of 2.5 people per second is used, the amount of time to increase by 1 billion is found to be closer to 12.7 years.

As students work on their predictions, observe and ask questions such as the following to give help as needed and to assess students' progress.

• How much change in population do you want to time? [Use amounts that will be easy to work with, such as 25, 50, or 100.]

• How will you keep track of time as you watch the population grow? [If a stopwatch isn't available, one person can watch the population numbers while the other looks at a watch or clock.]
• How can you use your measurement to estimate the time for a change of 100? …1000? …100,000? [Apply proportional reasoning. For example, if it takes 21 seconds for the population to increase by 100 people, it will take 210 seconds for the population to increase by 1000 people, because 1000 is 10 times 100. Or students may divide and multiply. For example, since 21/100 = 2.1, it would take 2.1 seconds for the population to increase by 1 and 2.1&bsp;• 1000, or 210 seconds, to increase by 1000.]

Summarizing the Activity

Use questions to lead a class discussion which brings the various components of the lesson together.

• How will you record and calculate with numbers in the billions? [Use scientific notation. Use a scientific calculator.]
• How will you convert seconds (or minutes) to years? [Use division for these conversions. See sample charts above.]
• Do you need to include leap years? [Leap years can be ignored because the population counter and the students' time measurements are not completely precise.]
• If it will take about 12 years for the eighth billion, in what year will the 8 billion mark be reached? [2011]

Distribute the Comparing Predictions to Past Trends activity sheet to the students. They should work individually to answer the questions.

Possible responses to the questions on the activity sheet are shown below:

1. The time needed to add a billion to the population has decreased and then leveled off at about 12 years.
2. Student responses will depend upon their predictions.
3. Policies in large countries could affect the birth rate. Medical advances could help people live longer.
4. The 3-billion benchmark could have been reached near the end of 1960 and the 4-billion benchmark near the beginning of 1974.
5. If the 4-billion benchmark was reached near the beginning of 1974, then it would be 13 or 14 years to any part of 1987.

### Extensions

 Have students make a line graph of world population from 1927 to 1999, using the data obtained from any world population web site: 1927: 2 billion 1960: 3 billion 1974: 4 billion 1987: 5 billion 1999: 6 billion Then ask the students to show three extensions for the graph, with a separate line for each of the following conditions: The birth rate stays about the same. The birth rate increases. The birth rate decreases. Students can compare their graph to the one below. World population (billions) 1950-2050 Students can compare their tables and data to the information found on the World POPClock Projection site.

### Teacher Reflection

 Did students achieve the objectives for this lesson? What additional experiences do students need to be successful with this lesson? Are students able to give and explain their reasoning? Are their reasons logical?

### NCTM Standards and Expectations

 Algebra 6-8Relate and compare different forms of representation for a relationship. Use graphs to analyze the nature of changes in quantities in linear relationships. Data Analysis & Probability 6-8Find, use, and interpret measures of center and spread, including mean and interquartile range. Use observations about differences between two or more samples to make conjectures about the populations from which the samples were taken. Use conjectures to formulate new questions and plan new studies to answer them.

2 periods

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