Algebra

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Algebra

Extra Credit

1. Population Densities

A population density is a rate, defined as the number of people living in a region divided by the area of that region.

a)Find the population and area of your town or city, your state, the United States, and the world. Calculate the population densities in people per square mile. On the basis of population density, rank these four places from least crowded to most crowded.

b)Which five states in the United States have the highest population densities? Which five have the lowest?

c)Name three countries that have much high population densities then the United States; name three countries that have much lower population densities.

2. Area, Perimeter, and Size Changes

a) Draw an interesting figure on a coordinate grid. Find its perimeter and area.

b) Draw its image under size changes of magnitude 2, 3, 4, and .5. Find the perimeter and area of each image.

c) Describe the patterns you find in you data. How are teh perimeter and the area of the images related to teh perimeter and the area of its preimage?

3. Density and Floating

In science the density of an object is determined by dividing the mass (weight in grams) of the object by its volume (in cubic centimeters). For instance, the density of cool tap water is one gram per cubic centimeter.

a) Find some blocks of different types of wood, such as pine, oak, maple, and cedar. Calculate the densities of each block.

b) Fill a tub with enough tap water to see if the blocks of wood will float. Which blocks of wood float?

c) Write up you methods and conclusions. How does density appear to be related to an objects ability to float?

Course Syllabus

Algebra syllabus.doc