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Chapter 5 Project

The Chapter 5 Project is due MONDAY, NOVEMBER 29. Please choose from the following options. Let Mrs. Shutters know which project you will be completing by Wednesday, November 17. If you have another idea that will showcase what you have learned in Chapter 5, please speak to Mrs. Shutters by this Wednesday.

IMPORTANT DATES:

  • Wednesday 11/17: Tell Mrs. Shutters your project choice.
  • Friday 11/19: Show Mrs. Shutters your initial research for the project.
  • Tuesday 11/23: Show Mrs. Shutters a “rough draft” of your project.
  • Monday 11/29: Final projects due in class.

1. Population Densities
This project can also be found on page 315 in your textbook.
A population density is a type of rate, defined as the number of people living in a region divided by the area of that region.

  • a. Find the most dense and least dense countries in the world. Note: One source that may be helpful is the CIA Factbook: https://www.cia.gov/library/publications/the-world-factbook.
  • b. The area of the United States is 5,984,685 square miles. What would the population of the United States be if it had the same population density as the most dense country in the world? What would the population of the United States be if it had the same population density as the least dense country in the world?
  • c. Which would you expect to have a higher population density: the United States or Singapore? Explain your answer. Give some examples of geographic and cultural features that affect a country’s population density.
  • d. Suppose a country has population density d. What is the meaning of the number 1/d (the reciprocal of d)?

 

2. Copy Machine Puzzle
This project can also be found on page 316 in your textbook.
Most copy machines have an enlargement feature that creates a figure similar to the one being copied.

  • a. Use the enlarge feature on a copy machine to enlarge the figure on the left on page 316 in your textbook so that the copy is exactly the same size as the figure on the right. You may have to enlarge more than once. Record how much you enlarged the figure each time.
  • b. Many copiers can copy in a range of sizes that goes from 100% to 141%. Why is 141% used in this case?

 

3. Calculating Density
This project can also be found on page 316 in your textbook.
In science, the density of an object is determined by dividing the mass of the object (weight in grams) by its volume (in cubic centimeters). For example, the density of cool tap water is one gram per cubic centimeter. You already know how to measure the weight of an object. But how do you measure its volume? The Greek mathematician Archimedes (287 BCE–212 BCE) discovered that when an object is placed in a FULL container of water, the volume of the water that spills out is equal to the volume of the object that was placed in the water.

a. Use Archimedes’ discovery and the density of water to explain how you could calculate the volume of an object. Note: To calculate the amount of water spilled, you can simply subtract how much water is left in a container from the original amount of water.

b. Explain how you could use the result from Part a to calculate the density of an object.

c. Look up the story of Archimedes’ discovery. How was density used in this story? Note: You can start here: http://library.thinkquest.org/25672/archimed.htm.

 

4. Money Makes the World Go Around
Visit http://realworldmath.org/Real_World_Math/Exchange_Rate.html. Download the Kmz and Word files (or access them from the Algebra 1, Chapter 5 Project folder here at school). The Kmz should open with Google Earth. Follow the instructions there and complete the Word document worksheet. Be sure to show ALL your work and give explanations. You can print the finished worksheet or email it to Mrs. Shutters.

 

5. Spinners and Boards
You may want to refer to Lessons 5-7 and 5-8 for this project. Also, take a look at: http://www.shodor.org/interactivate/activities/AdjustableSpinner.

a. Design a spinner with at least five different colored sections. Each section should be a different size (do not just divide a circle evenly into five sections!). Determine the probability of landing in each section. Show all work.

b. Design a game board with five different colored sections, using the same colors as your spinner from Part a. The board should be rectangular in shape, but may be any size. Configure the board so that the probability of randomly landing in any of the five sections is the same as landing in the same colored section of your spinner.

c. Spin the spinner at least 20 times and record your results. Drop a small object (such as a penny) onto your board at least 20 times and record your results. Do your results coincide with the probabilities you calculated in Parts a and b? Why or why not? How could you make your results closer to the calculated probabilities?

 

6. Videotape Store Design
See the last page of this document (PDF) for the description of this project choice.