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Volume 1
Mathematics
Portfolio
Algebra Problem
Air Conditioner Problem
Type A
Suppose that your family is going to buy a new air conditioner. The GE brand costs $750 to buy and $30 a month to operate. A more expensive brand, Westinghouse, costs $925 to buy. However, it is more efficient and costs only $25 a month to operate.
1. Write equations in slope-intercept form to describe the cost of owning and operating each air conditioner based on the number of months owned.
2.Graph each equation to find the break-even point. Label your graph.
3.Find the break-even point using your system of two equations.
4.In how many years will the cost of the more expensive air conditioner save you money?
5.The average air conditioner lasts 12 years. Find the total cost of each air conditioner over a 12-year period and over a 20-year period.
6.Write a recommendation speech convincing the rest of your family members that one air conditioner is better than the other. How much could the family save if the air conditioner lasted 12 years? 20 years?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Bacteria Cultures
Type A
A biologist had two separate bacteria cultures. The biologist had just started Culture A with 15 bacteria. She determined that this bacteria increased by 55% each hour. Culture B bad been around for a day and contained approximately 225 bacteria. The biologist introduced a virus into Culture B which killed the bacteria. After observing for the day, she determined the virus was killing the bacteria at a rate of 35% per hour.
1. .Write an exponential growth (or decay) equation for each culture.
Culture A: ______Culture B: ______
2.Complete the T-tables for each culture.
3.Complete a graph with the data for both cultures on one graph. Label the graph completely.
4.After 5 hours, which culture has the greater population? Approximately how many more bacteria does it contain?
5.When do the two cultures have approximately the same population? Circle when this occurs on both the tables and the graph.
6.After how many hours do you estimate Culture B will cease to exist? How did you determine this?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Basic Skills Tests
Type B
According to the Coalition for Literacy, many companies give basic skills tests to those applying for jobs. The following are the percentages of companies that have given basic skills tests to their job applicants from 1993 through 2002:
Year Percentage
1993 33
1994 38
1995 43
1996 45
1997 49
1999 59
2000 61
2002 65
1.. Draw a scatter plot for the data. Label the graph appropriately.
2. Draw a “best-fit” line for your graphed data. Choose and name two coordinates
from this line.
3.A. Describe any pattern(s) that you may see on the graph.
B. Why do you think the pattern(s) occur(s)?
4.A. Calculate the slope of your graphed line.
B. Explain what the slope means in relationship to your data.
5.State the equation of your graphed line.
6.Using your equation and graph, make a reasonable prediction about what percent of companies will be giving basic skills tests four years from now.
7.How does the information in this prompt affect you now or how can it affect you in the future?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Car Rentals
Type A
Avis Rent-A-Car charges a daily rate of $29.00 plus $0.15 a mile.
Dropp’s Rent-A-Car charges a daily rate of $38.00 plus $0.10 a mile.
1..Make a table comparing the costs of the two companies for one day based on the number of miles driven (use values from 0 to 300 miles).
2.Graph the data for the two companies on the same graph. Label each axis clearly and name the lines by company names.
3.Write the cost expression for each company.
4.For $40, how far could you drive with each company?
5.Using your equations, solve for the break-even point.
6.Use your break-even point to determine:
•under what condition(s) you would rent from Avis.
•under what condition(s) you would rent from Dropp’s.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Cellular Telephone Company
Type A
The Cellular Telephone Company offers two plans:
Plan A: $0.35 per minute plus a $29 monthly service fee
Plan B: $0.27 per minute plus a $55 monthly service fee
1.Make a table comparing the costs of the two companies for one month based on
the number of minutes used (use values from 0 to 500 minutes).
2.Graph the data for the two companies on the same graph. Label each axis clearly and name the lines by company names.
3.Write a cost expression for each company.
4.You talked for a half-hour every day during the month of October. Determine which plan would have been better. Explain your answer,
5.Using your equations, solve for the break-even point.
6.You have used 3 different methods of representing the plans (table of values, equations and graphs). Look at each of these methods and decide which way of representing the data for Plan A and Plan B would be most useful for each of the following people. Explain your reasoning.
Karla:I am the marketing manager. I want to show potential customers that the plan that is best for them depends on the number of minutes of air time they expect to use.
Wilfred:I work in the business office. My job is to calculate the exact charge for a customer’s bill.
Juline:I am the sales manager. Most customers want an idea of how much their monthly bill will be using the cellular phone. I like to show them, at a glance, some typical charges.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Life Expectancy
Type B
Life expectancy is the average number of years that a group of people born in a particular year may expect to live.
The table below gives the life expectancy of males and females at birth in the United States from 1970 - - 2000:
Year Male Life Expectancy Female Life Expectancy
1970 67.1 74.7
1975 66.8 76.6
1980 70.0 77.4
1965 71.1 78.2
1990 71.6 78.8
1995 72.5 78.9
2000 73.6 81.2
1..Just by looking at the table above, who generally lives longer, males or females?
2.Draw a scatter plot for one set of data (male or female). Label the graph appropriately.
3.Draw a “best-fit” line for your graphed data. Choose and name two coordinates from this line.
4.A. Describe any pattern(s) that you see on the graph.
B. Why do you think the pattern(s) occur(s)?
5.A. Calculate the slope of your graphed line.
B. Explain what the slope means in relationship to your data.
6.State the equation of your graphed line.
7.Use your graph and your equation to predict the life expectancy of a person born in the year 2005.
8.How does the information in this prompt affect you now or how will it affect you in the future?
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Algebra Problem
Oil Changes and Engine Repair
Type B
Joe is the owner of Joe’s New Cars and has collected the following data about cars he sold last year as to the number of oil changes and cost of engine repairs needed in that year.
Joe’s Data:
Oil Changes / 3 / 5 / 2 / 3 / 1 / 4 / 6 / 4 / 3 / 2 / 0 / 10 / 7 / 8Repair Cost $ / 300 / 300 / 500 / 400 / 700 / 400 / 100 / 250 / 450 / 650 / 600 / 0 / 150 / 100
1. . Draw a scatter plot for the data. Label the graph appropriately.
2.Draw a “best-fit” line for your graphed data. Choose and name two coordinates from your line.
3.A. Describe any pattern(s) that you may see on the graph.
B. Why do you think the pattern(s) occur(s)?
4.A. Calculate the slope of your graphed line.
B. Explain what the slope means in relationship to your data.
5.State the equation of your graphed line.
6.Using your equation, predict the cost of engine repair if the car had four oil changes.
7.How does the information in this prompt affect you now or how can it affect
you in the future?
Geometry Problem
Badgers Win
Type D
After the University of Wisconsin-Madison Badgers won the title game, the police estimated that 40,000 people flooded State Street in downtown Madison. Barricades were placed along a 6-block section of State Street and no traffic was allowed on or across this section while the jam-packed crowd celebrated for 6 hours.
Using the data supplied below,
1. Make a scale drawing of one block of State Street with one
intersection.
2. Label your scale drawing with all dimensions. Be sure to include your
scale.
- Explain how the police may have made their estimation of the crowd
size. Show all your calculations.
Madison Police DataLength of a city block on State Street: 290 feet
Width of State Street and all crosswalks: 30 feet
Width of the sidewalks on State Street: 6 feet
At 9 P.M., a police officer estimated that there
were about 54 people packed into a section of
State Street measuring 10 feet by 10 feet.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Geometry Problem
Building a Garden for the Boss
Type D
Your boss wants you to supervise the building of a decorative floral garden. He wants the entire construction to be in the form of a capital T. The dimensions of the top rectangle of the T are 14 yards by 6 yards. The dimensions of the rectangle forming the stem of the T are 6 yards by 10 yards. Around the outside of the garden he wants a fence. Outside the fence he wants a 6-foot wide concrete sidewalk. For each task below, be sure to justify your decisions mathematically. Clearly show your processes and organize your work.
1 -Make a scale drawing of the garden and the sidewalk. Be sure to include your scale. Label your scale drawing with all dimensions.
2.The gardener has informed you that he charges $14.95 per square foot for planting and maintaining a garden for one year. Find the cost of
hiring this gardener for one year.
3.For the fence, posts need to be placed 2 yards apart on all sides of the garden and a post is needed at each corner. On your scale diagram, show the placement of all the posts you will need.
4.Fencing costs $8.29 per linear foot and posts cost $3.49 each. Calculate the total cost for building the fence, including the fencing and the
posts.
- The depth of the concrete for the sidewalk will be 4 inches. The cost of concrete, including delivery and labor, is $29.95 per cubic yard. Find the
total cost to build the sidewalk.
6.Prepare a statement for your boss itemizing the costs for building thesidewalk and fence, and for planting and maintaining the garden. Be sure to include the total cost of the garden.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Geometry Problem
Marco Roni
Type C
Marco Roni is making meatballs to add to his sauce. Each meatball has a 2-inch
diameter. He needs to cook them in the sauce for a while. Right now, before
the meatballs are added, the sauce is 4 inches from the top of the 15-inch
diameter pot. The total height of the pot is 10 inches. He must have a minimum
of 1 inch of free space at the top of the pot to eliminate “boil over”.
1.Draw a scale drawing of this situation. Be sure to include your scale. Label your scale drawing with all dimensions.
2.Determine how many meatballs can be added before reaching the 1 inch of free space at the top of the pot. Show all work.
3.What would the height of the pot have to be in order to cook 200 meatballs with the same amount of sauce? Show all work.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Geometry Problem
New Cans
Type C
You work in the marketing department of a vegetable cannery. You are testing
customer reaction to the new sizes of cans. The regular size can for your
vegetables is 12 cm high and has a radius of 4 cm.
- Make a scale drawing of the following four cans. Use the same scale for all
four drawings. Be sure to include your scale. Label your scale drawings with
alldimensions:
• the regular size can
• new can #1 which is half the radius and twice the height of the regular can
• new can #2 which is twice the radius and half the height of the regular can
• a jumbo can which is twice the radius and twice the height of the regular
can
2. The regular size can sells for $0.75. Determine a price for each of the other
three cans based on each one’s volume and the price of the regular can.
Show your work.
- Write a memo to the company president explaining the advantages and
disadvantages of each can.
Geometry Problem
On Target
Type D
The Semi-Divers, a sky-diving club, sponsored a contest to create a pattern for a new landing target to be painted on the ground. The winning pattern, shown below, was created using several semi-circles placed on the large circular target. The club must now decide how much paint of each color to purchase in order to paint the target. Use the following information to determine the amount of paint:
• the diameter of the target is 36 feet
• a gallon of ground paint covers 325 square feet
• two coats of paint are needed
• paint is sold only in gallon-sized cans
Winning Target Design
How many gallon cans of paint of each color (red, white and blue) will the club need to buy? Show all your work.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Geometry Problem
Radio Antenna
Type E
A radio antenna is to be kept perpendicular to the ground by three guide-wires. The guide-wires are to be staked at three points equally spaced around a circle with a diameter of 100 feet. The antenna base is the center point of the circle. The antenna is 130 feet tall and the guide-wires are to be located 10 feet from the top of the antenna.
- Make a top view scale drawing showing the circle, the antenna base,
and the placement of the stakes. Remember to state the scale you use on the
drawing and to measure your angles accurately.
2. A safety fence is to be installed to surround the staked area. It must be 5 feet away
from each of the stakes. Add this fence to your scaled drawing.
3. If fencing costs $19.95 a yard, how much will the safety fence cost?
4. Find the length of each guide-wire. Show any formulas used and all
work should be labeled.
5. Write a paragraph explaining why you need three guide-wires instead of
only two.
Developed by the Milwaukee Mathematics Partnership (MMP) with support by the National Science Foundation under Grant No. 0314898.
Geometry Problem
Rap Singer
Type E
Oni Meter is a rap singer who lives in Miami, Florida. She is starting a fall concert tour and is planning to fly her own plane to every concert. Here is her tour schedule:
Dallas, Texas September14-16
Boston, MassachusettsSeptember18-20
San Diego, California September 22-25
Detroit, Michigan September 27-30
Miami, Florida October 2-8
To fly from one city to the next, Oni needs a flight angle and compass direction to direct her plane. A flight angle is formed by two lines that start in the city from which the flight takes off. One line points north and the other points to the flight’s destination. The flight angles are labeled with degree measures and a direction (east or west).
For example, to fly from Miami to Dallas for the first concert, Oni flies along a 77° West (77°W) flight angle.
1. Find the flight angles for the rest of Oni’s concert tour. Be sure to mark the angles on
the map(s) provided.
2.It is a known fact that the straight line distance from Detroit to Miami is 1300 miles.
Use this distance to help determine the distance from each city to the next one on the
tour.
3.Assume that all flights take place with no wind factors and the average plane
speed is 350 miles per hour. How long will each flight take?
4.Organize the above information into table format.
5.The kind of plane that Oni flies averages 7 gallons of flight fuel per hour. The fuel
costs $2.50 per gallon. How much will the entire tour cost?