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.
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John Kurilecjmk@ofcn.org