Superlesson
Project 2-1
Algebra
Chapter 2
Patterns, Change, and Expressions
Changes in one quantity can produce changes in related quantities. In the following activities, you'll investigate how changes in a quantity can affect the density of matter, the characteristics of human populations, and the physical properties of water.
Part A, Quantities and Change
1. Density is a measure of the weight of a substance per unit of volume.
The density of sea water is 64 pounds per cubic foot. This means that the
sea water in an aquarium with a volume of 1 cubic foot weighs 64 pounds.
a. Click on the element manganese (Mn) in the Periodic table of the elements Web site. The number 25 represents the number of protons in the nucleus of an atom of manganese. Choose "Bulk properties" in the list Manganese: the element. What is the density of manganese? Hint: kg m3 means "kilograms per cubic meter."
b. Is the density of manganese, as given in the table, constant or variable?
c. Find the densities of iron (Fe, atomic number 26) and cobalt (Co, atomic number 27).
d. Is the property of matter known as density variable or constant? Explain.
e. The cubes are made of iron. What is the weight of each?
f. Is weight a constant or a variable? Explain.
g. Name a property of the cube on the left, above, that is constant. Then name a property that may vary. (Choose properties other than weight or density.)
Part B, Describing Change
2. Massive amounts of data on the geography, people, governments, and economies of the world have been collected for the World Factbook Web site.
a. Click on "Countries" and complete the table.
| People | Economy | |||||
1 |
2 |
3 |
4 |
5 |
6 | |
| Argentina | ||||||
| Belgium | ||||||
| Malawi | ||||||
| Vietnam | ||||||
b. Are the quantities in Column 1 and Column 2 directly or inversely related? How can you tell?
c. What reasons might explain the relationship you observed in b?
d. GDP stands for "gross domestic product," a measure of a country's annual economic growth. Are the quantities in Column 4 and Column 6 directly or inversely related? How can you tell?
e. What reasons might explain the relationship you observed in d?
f. Column 5 gives the portion of a country's growth earned through agriculture. Are the quantities in Column 3 and Column 5 directly or inversely related?
g. What reasons might explain the relationship you observed in f?
Part C, Graphing Change
3. Find the table Boiling Point of Water vs. Altitude on the Web.
a. If you traveled gradually from sea level (0 ft altitude) to 10,000 ft. altitude, how would air pressure change during your journey? How would the boiling point of water change?
b. State whether the following quantities are directly or inversely related:
- · altitude and air pressure
· altitude and boiling point of water
· air pressure and boiling point of waterc. Graph altitude versus boiling point of water. Place altitude (ft.) on the horizontal axis and boiling point (° F) on the vertical axis. Use altitude values from 0 ft. to 10,000 ft. in intervals of 1,000 ft..
d. Contaminated water can be purified (sterilized) by boiling. To see how sterilization time changes with altitude, see Paragraph 4 under Dehydration at the Military Field Operations Web site. Graph altitude versus sterilization time. Place altitude (ft.) on the horizontal axis and sterilization time on the vertical axis. Use altitude values from 0 ft. to 20,000 ft. in intervals of 2,000 ft..
e. Are altitude and water sterilization time directly or inversely related?
Part D, Making Connections
4. Refer again to the table Boiling Point of Water vs. Altitude to answer the following questions.
a. When you examine a table of values, how can you determine whether two quantities are directly or inversely related?
b. Look again at the graphs you drew for 3c and 3d. When you examine a graph, how can you determine whether two quantities are directly or inversely related?