As an extension, have students research other types of pets in various
countries around the world. Have them make appropriate graphs to display
the data. Ask them to write statements about the data that may or may
not have counterexamples.
Proceedure for the Activity
Answers:
Procedure for the Activity
Step 1
Step 2
Step 3
Yes; sample answer:
Japan has a greater human population that Germany, but Germany has
a greater fish population than Japan.
Step 4
Country
People:
Fish
China
11.32
United
States
2.67
Germany
1.66
Japan
3.60
Italy
1.99
France
2.20
United
Kingdom
2.24
Russia
7.12
Australia
1.55
Sweden
0.94
Step 5
Yes; sample answer:
The population of Russia is less than the population of the U.S.,
but the ratio of people to fish is greater for Russia than for the
U.S.
Step 6
Country
Fish:
People
China
0.09
United
States
0.38
Germany
0.60
Japan
0.28
Italy
0.50
France
0.46
United
Kingdom
0.45
Russia
0.14
Australia
0.65
Sweden
1.06
Step 7
Yes; sample answer: The population
of Germany is greater than the population of the United Kingdom,
but the ratio of fish to people increases from United Kingdom to
Germany.
Wrapping Up the Activity
See students’ work. Some students may prefer
finding counterexamples by just looking at the tables of data, while
others may choose to use the graphs. A scatter plot may be helpful in
looking at the relationships between two data sets in order to determine
whether counterexamples exist.
