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 23 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  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.
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?
[2011]
 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.
Possible responses to the questions on the activity sheet are shown below:
 The time needed to add a billion to the population has
decreased and then leveled off at about 12 years.
 Student responses will depend upon their predictions.
 Policies in large countries could affect the birth rate. Medical advances could help people live longer.
 The 3billion benchmark could have been reached near the end of 1960 and
the 4billion benchmark near the beginning of 1974.
 If the 4billion benchmark was reached near the beginning of 1974, then
it would be 13 or 14 years to any part of 1987.