Pin it!
Google Plus

The Next Billion

  • Lesson
AlgebraData Analysis and Probability
Location: Unknown

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

Introducing The Activity: Continual Change

Have students identify things that continually change, for example, their age and height, the date, the temperature outside, 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?

    [As an example tell students that 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?

    [Sample response: 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:

The world population reached 6 billion on October 12, 1999.

Explain to students that their job is to predict, as best they can, when the world population will reach 7 billion. At this point, ask students to make a prediction of when they think that will happen. Tell students to record this information, because they will use a mathematical method for making a more precise predication in this lesson.

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 sample:

Increase in Population 



19 sec


19 sec • 2 = 38 sec


38 sec • 10 = 380 sec = 6.3 min


6.3 min • 10 = 63 min = 1.05 hr


1.05 hr • 100 = 105 hr = 4.4 days


4.4 days • 1000 = 4400 days = 12 yrs

Or they might first find the total number of seconds:

Increase in Population 



19 sec


38 sec


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.

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

  • How much change in population do you want to time?

    [Guide students to time amounts that will be easy to work with, such as 25, 50, 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?

    [Help students 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 millions?

    [Sample responses: Use scientific notation. Use a scientific calculator.] 

  • How will you convert seconds (or minutes) to years?

    [Help children see how they can use division for this. See sample charts above.] 

  • Do you need to include leap years?

    [Help students see that leap years can be ignored because the population counter and the students' time measurements are not that precise.] 

  • If it will take about 12 years for the seventh billion, in what year will the 7 billion mark be reached?


  • If it will take about 12 1/2 years for the seventh billion, in what year will the 7 billion mark be reached?

    [2012, if you use the October date for when 6 billion was reached.] 

Distribute the Comparing Predictions to Past Trends Activity Sheet to the students. They should work individually to answer the questions.

pdficon Comparing Predictions to Past Trends

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.

Assessment Options

  1.  Have students make a line graph of world population from 1927 to 1999, using the data obtained from the Web site:

    1927: 2 billion

    1960: 3 billion

    1974: 4 billion

    1987: 5 billion

    1999: 6 billion

  2. Then ask the students to show 3 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.

  3. Students can compare their graph to the one below.

    World population (billions) 1950-2050

    2514 p982 

  4. Students can compare their tables and data to the information found on the World POPClock Projection site. This site can be found on the US Census Bureau website.

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?

Learning Objectives

Students will:

  • Apply proportional reasoning.
  • Look for patterns and draw conclusions about world population growth.

NCTM Standards and Expectations

  • Relate and compare different forms of representation for a relationship.
  • Use graphs to analyze the nature of changes in quantities in linear relationships.
  • Find, 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.