This page is intended to be used with the Systemic Initiative for Montana Mathematics and Science  
Integrated Math (SIMMS IM) curriculum Level I. Eight of the fifteen modules contain research projects. Click at the right to view  the research project description for that module and to find links to sites that will help you complete the project. For general math questions try:  
 

OR   
 

Suggest additional sites and/or provide feedback 
 

 

Reflect on This

So You Want to Buy a Car

A New Look at Boxing

What Will We Do When

the Well Runs Dry?

Skeeters Are Overrunning

the World

I'm Not So Sure Anymore

AIDS: The Preventable

Epidemic

Digging into 3-D

Research Project 

1. Describe how to determine the length of the smallest mirror that would 
allow every member of your family to see a complete reflection from head  
to toe. Include a diagram with your report. 

2. Write a report about periscopes that answers the following questions. 

a. What is a periscope? 
b. In what types of situations are periscopes useful? 
c. How does a periscope work? (Include a diagram in your report.) 
d. How can you make a simple periscope using a tube and  
two mirrors? (Include a model with your report.) 

Encarta Definition 

of a Periscope

How to build a

Periscope out of 

Milk Cartons

Interactive Simulation

of Light Reflection

with Definitions

Research Project  

1. The cost of owning a vehicle involves more than just the sticker price. If  
you finance your purchase, for example, your interest payments increase  
the cost of the car. Additional costs result from operating and maintaining  
the vehicle. 

2. In this project, you must determine the cost per mile to operate a vehicle  
of your choice for the first five years of ownership. Your report should  
include the purchase price and the criteria you used to choose the vehicle.  
If applicable, your report also should describe the down payment, the  
annual interest rate, the number and size of the monthly payments, the  
total amount of interest paid, and the total cost of the vehicle (including  
interest). 

3. When determining operating and maintenance expenses, consider each  
of the following items: 

• The number of miles the vehicle is driven annually
• The cost to insure the vehicle
• The cost to license the vehicle 
• The cost of replacement tires
• The cost of regular oil changes, tune-ups, and other scheduled repairs
• The cost of unscheduled repairs
• The vehicle's loss in value over the five-year period

Kelly's Blue Book

Edmund's Consumer Information

Consumer Reports - Online

NHTSA - Buying a Safer Car

Electric Insurance Company -get an  insurance quote without giving out too much information. You may need to claim that you have 9 years of driving experience. Do NOT have an agent contact you.

Research Project 

Regular polygons can be arranged in many interesting patterns. 

a. Find at least six ways in which a combination of regular  
polygons will tessellate a plane. In each tiling, use at least  
two different regular polygons. 
b. Make a careful drawing of each of your patterns. 
c. Describe each pattern in a few sentences. 
d. Find at least two examples of tilings that use polygons  
other than squares and rectangles in your home or community. 

Here are some samples

and ideas for tessellating:

The Access Indiana

Teaching and Learning

Center Guide to

Tessellation

Escher-like

Tessellations

Elk Grove, CA

HS Student Tessellations

Totally Tessellated

 Links to 15-20 MORE

Tessellation Sites

Research Project  

1. On average, each resident of the United States uses about 420 L of  
water per day. How does your daily water use compare to this value?  
In the following research project, you analyze your own personal  
water use. 

2. Create a table with headings like the one shown below. To  
complete the table, you will need to develop some innovative ways to  
measure water use. For example, how can you determine the volume  
of water used in a shower or bath? And how much water does it take  
to flush a toilet?  

3. Your report should include a description of the methods you used  
to determine each measurement, a comparison of your daily water  
usage to the national average, and a discussion of any difference  
you observe. 

Table of Areas

and Volumes

CNN Report -- U.N.

Announcement of

Water Shortage

The Montana Water

Resource Page

Friends of the Earth

Report leaked

government plan

concerning water

shortage (Be sure to

consider the source

of information)

U.S. Water News

A whole online paper

dedicated to water

U.N. Fact Sheet  

Research Project  

1.  Imagine your own population of creatures with a growth rate and  
initial population different from those used in the explorations.  
 

a. Use a spreadsheet to simulate the growth in this population  
for at least 10 time periods. Display your simulated data in both  
a table and a graph.  
b. Find an equation that models the growth in the population  
over time.  
c. Write a story about your population. Include a description of  
the growth rate and explain the consequences this rate will have  on the population over time.  

U.S. Census Bureau

Negative Growth

Population - Facts and

Figures: A group in

Washington D.C. whose

goal is to educate people

about the detrimental

effects of over population

 Exponential Growth-

Paper Folding Activity

Table of Exponential

Identities

Research Project  

1. A new game called the Match Lottery has the same rules as the  
Apple Lottery, except that the second number drawn need not be  
different from the first. In the Match Lottery, for example, players  
may select the numbers 3, 3. 

2. Write a report on the Match Lottery that includes the following: 

a. a description of the sample space 
b. an explanation of how the difference in rules affects its simulation 
c. the results of at least 100 trials in which the lottery ticket chosen has two different numbers 
d. the results of at least 100 trials in which the lottery ticket chosen has two identical numbers 
e. the experimental probabilities of winning each prize 
f. the theoretical probabilities of winning each prize 
g. an explanation of whether or not the results of the simulations support the theoretical probabilities 
h. An explanation of whether or not any tickets have a better chance of winning a yellow apple than other tickets. 

Joke

The definition of Lottery:

A tax for the mathematically 

incompetent

The Math League--

Explanation of Chances

and Probability

Lottery Simulation

Game

Southwest Research

Institute--The Lighter

Side: Are the odds

better when more 

tickets are sold?

Research Project  

1. Obtain the most recent data for U.S. AIDS cases and exposure  
categories. You may use the National AIDS Hotline (1-800-342-AIDS),  
a physician, medical clinic, or local health department as sources.  
You may also obtain information from the Centers for Disease Control's  
(CDC) National Aids Clearinghouse at the following electronic address: 

>http://cdcnac.aspensys.com:86/aidsinfo.html  
(Note: This address did not work for me)

a. Compare the most recent data with the data presented in  
this module. 

1. What changes do you notice? 
2. Which category seems to be growing the fastest?

b. Write at least two problems involving this data that can be  
solved with the help of a Venn diagram. 

CDC Basic Statistics

CDC Exposure Category

Statistics

Graph of Exposure

Category Statistics

CDC Complete HIV/AIDS

Surveillance Report

You will need adobe

acrobat to read--takes

about 8 min to download

Research Project  

On a typical two-dimensional map, differences in elevation can be hard  
to visualize. For this reason, hikers and others often use topographic maps,  
which show elevation on contour lines. Although this feature makes it easier  
to identify the elevation of a specific location, forming a mental picture of  
the terrain can still be difficult. 

When a clear representation of the landscape is needed, mapmakers create  
relief maps. Relief maps show the features of the terrain in three dimensions.  
In this research project, you make a relief map of a region of your choice.  
(The area you select should have identifiable difference in elevations.) 

a. Create a two-dimensional map of your area on graph paper. For  example, Figure 7, shows a map of Montana on graph paper. 

MIT Geography-Elevations

Find the elevation of any

town or city, as well as

other information

Maps of Montana

  MORE Links to Maps