Math Problems for Open House
1. The Mathletes is a very active club! The members of the Mathletes want to raise
money so they can take a trip. They decide to sell t-shirts with a logo. The president of
the club calls two t-shirt vendors to find out how much it will cost to make the shirts.
Screeners charges a setup fee of $50 to prepare the silk-screen for the logo. In addition,
Screeners charges $7 for each shirt imprinted with the logo. The second vendor,
Teesers, charges $78 for the setup fee and $5 for each t-shirt. The president’s cousin
told her about a third place called Tanks-A-Lot, which charges a set up fee of $120 and
an additional cost of $3 per shirt. Compare prices from the three different t-shirt
venders: Tanks-A-Lot, Teesers, and Screeners.
The club does not know how many shirts they will need to order. Use a graph to help
them decide which company should be selected, depending on the size of the order.
2. Six members of a Sumo wrestling team weighed themselves and discovered that the
sum of their combined weights totaled 30 pounds less than one tone (2000 pounds).
Boyd weighed 20 pounds more than twice Trede’s weight. Kerber weighed 40 pounds
less than Adam. Smith and Craig each weighed five pounds more than Kerber. Adam
weighed 35 pounds less than twice Trede. Trede is the smallest of the six guys. How
much did each player weigh?
3. You’ve been hired to furnish the rooms of a local hotel. This hotel has both suites and
standard rooms. After deciding on furnishing for one of each room, you must
determine the total cost. Hotel Patterson has 110 suites and 330 standard rooms. You
have $100,000 in cash to furnish the hotel. If you go over this, you must use the Hotel's
credit. Anything over $100,000 will have a 15% simple interest rate applied. The loan
is to be paid back in one year.
Explain how much it will cost to furnish 1 room and 1 suite. Use this information to
explain how much money the hotel will make on a daily basis if it is 100% occupied,
75% occupied, and 60% occupied. Explain how long it will take to pay off the loan at
each level of occupancy. Also, explain how this situation is a rough model of reality.
Hint: In real life there are other factors that would need to be considered when running
a hotel. What might those factors be?
4. (Extra Credit) The PTSA is going to make and sell pizza to raise money for this year’s
trip to Stinson Beach. Based on prior lunch sales, you expect to sell 1,400 slices of
pizza during lunch on Thursday. You can buy large cheese pizzas (10 slices) for $17,
medium veggie (7 slices) for $13, and medium pepperoni (7 slices) for $15. You also
need to purchase compostable plates and napkins- bundled 250 for $175. You plan to
sell the pizza at $3.50 (for 1 slice) or $6 (for 2 slices).
How many slices, of each type, you will need to order? How much profit do you expect
to make?
5. Our goal is to create a bungee line for Barbie that will give her the most thrilling, yet
safe, fall from the top of the doorframe.
Barbie is an adventure seeker to the max. She loves the thrill of death defying activities.
She believes the adrenaline rush makes her hair more lustrous and her waistline
thinner; so she is willing to pay big bucks to the company that can give her the most
thrilling ride. In the back of her mind though, she wants to be sure that she is really
safe.
Number of Rubber Bands
Height (cm)
1
12
2
15
3
18
4
24
5
29
6
32
7
38
6. Candy Callipso, the CEO of the Moon & Mercury Candy Company, has a crisis! She
has hired your team to help her solve a problem. A customer ordered a thousand
bubblegum machines and specified that each one should have a probability of exactly
1/3 for getting a blue gumball. The bubblegum machines were created and sent out,
but the customer has called, claiming that the machines were filled incorrectly. Candy’s
records show that each machine was filled with 4 yellow gumballs, 8 red gumballs, 16
green gumballs, and 20 blue gumballs.
Do the machines meet the customer’s requirements? If they do, find at least two other
combinations of gumballs that would satisfy the picky customer. If they do not, find at
least two ways to adjust the contents of the machines so that the probability of getting
a blue gumball is exactly 1/3.
7. Winter Hat- you must actually make a model hat
8. (Double Extra Credit) Ice Sheets & Sea Level Rise
The ice sheets of Greenland and Antarctica contain massive amounts of frozen water
(i.e., ice) that, if broken off or melted (from extended global warming) would go largely
into the oceans. Would the addition of ice or melted ice from the ice sheets have an
impact on global sea level? If so, how much?
Determine the amount that sea level would rise, averaged around the globe, in
response to the complete melting of (a) the Greenland ice sheet, (b) the Antarctic ice
sheet, and (c) both the Greenland and Antarctic ice sheets.
Use a map with contour lines to explain the ramifications of your calculations.
Needed information: The calculations require the area of the Earth’s oceans and major
seas (either as a total or as individual areas to be added), the volume of the ice sheets
overlying land, the densities of ice and water, and knowledge that glacier ice is freshwater ice rather than sea-water ice. This information can be obtained by the students
from a world atlas or various other sources, or it can be handed to them in the form of
tabulated information, as in Tables 1-3.
Table 1. Water Areas of the Earth.
Ocean or Sea
Area (in square kilometers)
Pacific Ocean
166,241,700
Atlantic Ocean
82,522,600
Indian Ocean
73,426,500
Arctic Ocean
14,056,000
Caribbean Sea
2,512,300
Mediterranean Sea
2,509,700
Bering Sea
2,266,250
Gulf of Mexico
1,554,000
Sea of Okhotsk
1,528,100
East China Sea
1,248,400
Sea of Japan
1,007,500
Hudson Bay
822,300
North Sea
575,000
Black Sea
479,150
Red Sea
437,700
Baltic Sea
422,170
Remaining surface water area
9,522,630
Source: Hammond Citation World Atlas, Hammond, Maplewood, New Jersey, 1992, p.352.
Table 2. Ice Sheet Areas and Thicknesses.
Ice Sheet
Greenland
Antarctica
Area (in square kilometers)
1,736,095
11,965,700
Average Thickness (in kilometers)
1.50
2.45
Source for the Greenland data: Williams, R. S., Jr., and J. G. Ferrigno, editors, Preface,
Satellite Image Atlas of Glaciers of the World: Greenland, USGS Professional Paper
1386-C, United States Geological Survey, Washington, DC, 1995, p.v.
Source for the Antarctic data: Swithinbank, C., Antarctica, Satellite Image Atlas of
Glaciers of the World: Antarctica (Richard S. Williams, Jr., and Jane Ferrigno, editors),
USGS Professional Paper 1386-B, United States Geological Survey, Washington, DC,
1988, p.B12.
Table 3. Densities.
Substance
Fresh water
Glacier ice
Density (in kilograms per cubic meter)
Approximately 1000
Approximately 900 (generally between 830 and 917)
For each problem you must use a modified version of the 5-D method.
 Describe/Draw the problem you are trying to solve.
 Define: What is it that you know? What do you still need to figure out and how
are you going to go about doing that? Are you going to use variables to represent
certain quantities? What are those variables?
 Do & Decide: CLEARLY show your work (explain each major step). You will not
be using a “guess and check” method. So the “decision” will mostly take place in
your head. Only your “final trial” should be shown on your poster.
 Declare: Explain what it all means. Explain the solution to your problem.
Name ________________________
Open House
Poster Project Rubric
Partner’s name ________________________
Date__________________________
Your poster project will count as an exam. You will receive a group score as well as an individual
score. Some posters will be displayed “live”, others will be displayed “electronically”. All posters
must be completed by May 24th as they will be displayed at Open House on May 29th.
Criteria
Score & Comments
(5 points)
Describe/Draw
--Description completely describes the problem
--Picture drawn helps the reader to understand what is known
and what still needs to be determined
Define
(5 points)
--Poster states what is given in the problem.
-- You have clearly stated still needs to be figured out and how
are you going to go about doing that.
--Are necessary variables are clearly defined.
Do & Decide
(5 points)
--Work is clear and logical, such that another person could
follow what you are doing. You explain each major step.
Declare
(5 points)
--You have clearly explained how you are going to resolve your
question/problem. You use math to support your statements.
Overall poster
(5 points)
-Poster is neat and well organized.
-Font/writing is large and clear.
-Poster has a polished look.
-Rough and final drafts were completed on-time.
Partner Feedback
-How well did you and your partner work together? If you
could give your partner a grade for how well they collaborated,
what would you give them? Take the following questions into
consideration: Did they do what they said they were going to
do? Was everything on time? Did they complete their fair
share? Was the work high quality?
(A=5 points; B=4 points; C=3
points; D=2 points; F=0 points)
TOTAL _____________________/ 30 points