DESIGNED I STUDENT
DESIGNED I WEB
DESIGNED UNITS & ACTIVITIES
The Three Point Problem From
Given the elevation of three points, determine the orientation
of the plane containing the three points. That is, determine a level
line in the plane, the direction of its slope, and the amount of the
Volume of An Irregular Solid
Estimate the number of cubic yards of material
in a waste stockpile
Area of Golfing Greens Problem
You are a greenskeeper at a golf course. In order to know how much
fertilizer to apply to the greens, you need an estimate of their areas.
How would you estimate the area of a golf green?
The Best Angle of View [HTML]
You are standing on level ground in front of a billboard. When
you look up at it, the top of the billboard measures a feet up the
support from eye level and the bottom of the billboard measures b
feet up the support from eye level. You wish to position yourself
in order to maximize your "viewing angle" (the angle between the lines
of sight of the top and the bottom of the billboard). However, a storm
has tilted the billboard, as shown in the accompanying figure. Find
the distance x that maximizes §.
Cutting the Cake Problem [HTML]
We have a square cake (that is, its horizontal cross-sections are
congruent squares). It is frosted evenly on the four sides and the
top. How can we cut the cake into n pieces so that all the pieces
have equal amounts of cake and equal amounts of frosting?
Flowing Stream Problem [HTML]
A rural village has no electricity other than a diesel generator for
about 2 hours a day. A stream runs nearby, so you (the consulting
engineer) are considering the possibility of building a small hydroelectric
station on the stream. One piece of information you want is the amount
of water flowing in the stream. This is the flow rate of the stream
which is given in cubic feet per second. How can you obtain an estimate
of the flow rate?
Island Treasure [HTML]
A young man was
going through the attic of his grandfather's house and found a paper
describing the location of a buried treasure on an particular Island.
Height of a Kite [HTML]
A kite is being flown with a lightweight, 100 ft. length of string.
What other measurements might you use to compute an estimate of the
height of the kite? Find four different methods that might be used
with students at different grade levels.
The Notch for Felling a Tree
In its September/October 1998 issue, Workbench, had an article on
"Felling a Tree Safely." Part of the process of felling a tree is
to cut a notch on the side of the tree toward the direction you want
it to fall. This notch is opposite the cut line to be made in felling
the tree and its crease is an inch or two below the cut line. Can
the crease length be 80 % of the tree's diameter and the depth of
the cut be one-third of the tree's diameter?
Surface Area of a Can [HTML]
In packaging a product in a can the shape of right circular cylinder,
various factors such as tradition and supposed customer preferences
may enter into decisions about what shape (e.g. short and fat vs.
tall and skinny) can might be used for a fixed volume.
to the Nearest Road [HTML]
Four roads form
a square ACDE with side length s. A barn B is 5 miles from A, 8 miles
from C, and 13 miles from D. What is the shortest distance from the
barn to the nearest road?
navigation, the usual designation of a bearing is the direction measured
from the south to north line. A bearing of 0 degrees is due North.
Find the bearing the pilot should fly, and find the plane's ground
Area Estimate [HTML]
area of Texas, in square miles, given the following map and the indicated
scale. We will use the same map and scale in miles on the subsequent
Ladder and Box [HTML]
A ladder 5 meters long leans against a wall, reaching over the top
of a box that is 1 meter on each side. The box is against the wall.
What is the maximum height on the wall that the ladder can reach?
Suppose a mirror was to be placed flat on a wall that is perpendicular
to the floor. What is the shortest mirror a 6 foot tall person could
use so as to be able to see an image in the mirror from the top of
the head to the toes? Assume the person is standing 5 feet from the
is the Store? [HTML]
Three towns in
Ireland, Poole, Bray, and Alton, are located 8, 3, and 5 miles, respectively,
from a store. How far apart are the towns from one another if they
are located at the vertices of an equilateral triangle?
Salesperson's Journey [HTML]
table presents the airplane fares (in dollars) among pairs of seven
cities. A salesperson needs to visit each of the cities at least once.
Find the minimum fare for...
DESIGNED UNITS & ACTIVITIES
Aspects of the Structure and Design of Commercial and Residential Field
T here are designs
specific to commercial crop farm irrigation and to residential (lawn
and garden) irrigation. In each case several geological, economical
and topographical factors came into play when deciding the proper
plan investigating combinatorics in a restaurant environment.
Public Transportation and Mathematics [HTML]
class activity involving experimentation, statistics, and network
Networking in a Grocery Store [HTML]
The object of the study is to understand
how networking is part of our everyday routine.
always heard that the shortest distance between two points is a straight
line, right? Wrong - not always so in Taxicab geometry, here, things
work a bit differently.
Linear and Non-linear Motion [
This is a unit on modeling linear and non-linear motion. It includes
the fallowing concepts; vector, magnitude, direction, navigation,
linear motion, non-linear motion, circular motion.
MATH IN THE WORKPLACE: Lot's of examples of how math is used in real
Math in Daily Life
Exactly How Math Used In Technology?
Lots of examples on the use of basic mathematical principles ( in
algebra & geometry, linear algebra & matrices, statistics,
trig, log, etc) in Biomedical Eng., Food Tech., Building Tech., Robotics,
Surveying, Environmental Health, etc.
Workplace Math Skills: Addition and Subtraction of Whole Numbers;
Addition and Subtraction of Shop Decimals; Addition and Subtraction
of Shop Fractions; Scale Drawing; Metric Conversion; Ranking Decimals
and Fractions; Measurement.
for applications of Mathematics: All Fired Up (Firefighter) Life Saver
Anyone? (Lifeguard) Circuit Challenges (Electrical Engineer) Making
Plans (Event Planner) Daunting Peaks (Vulcanologist) On a Roll (Roller
Coaster Designer) Fit by Design or Design to Fit (Mechanical Drafter
Designer) Paint by Numbers (House Painter) Formula for Success (Market
Analyst) Pixelmaniacs (Computer Game Designer) Hearing is Believing
(Audiologist) Record Breaking News (Sportscaster) In Dog Pounds (Animal
Health Technologist) Teeing Off (Golf Pro) Let it Fly! (Aerospace
Engineer) Tuning In (Piano Repair Technician)
Math from the Toy Store: Use of
scaled replicas makes learning about ratio and proportion fun in this
teacher's middle school math classes.
Mathematics in Maps and Planning
Make a map of the Earth
Investigate four math problems related
to the use of maps. Math content: Aalgebra (coordinates and linear
equations), scale, etc.
Origami and Math
Working with Algebra: Algebra at workplace
including an example (cost of cerpet) activity with spreadsheets.
Hospital Quality: As health care director
for your company, your job is to select which of two local hospitals
you will send your employees to in case of emergency.
Rounding Off: In a certain multi-million
dollar company, Division Managers are required to submit monthly detail
and summary expense reports on which the amounts are rounded, for
ease of reading, to the closest $1,000. One month, a Division Manager's
detail report shows $1,000 for printing and $1,000 for copying. In
the summary report, the total for "printing and copying" is listed
as $3,000. When questioned about it by the Vice President, he claims
that the discrepancy is merely round-off error. In subsequent months,
the Vice President notices that such round-off errors seem to happen
often on this Division Manager's reports. Before the Vice President
asks that the Division Manager re-create the reports without rounding,
she wants to know how often this should happen.
Outdoor Math/Art: Nature's Patterns,
Fibonacci Sequence, Golden Ratio
Math & Basketball
Mathematics in Context Project sample
lessons and teacher pages
Art & Mathematics
(A Great Site for Math in Art&Music. Lots of examples.)
(The Art of Renaissance Science: Galileo and Perspective)
(Fibonacci Numbers, Golden Ratio and Music)
(The Golden Section in Art, Architecture and Music)
(Works of Leonardo da Vinci)
(Images and Mathematics)
(History, instructions, and examples of tessellations)
(Mathematics in Art: Drawing in Perspective)
(Tips and Tricks to Gothic Geometry)
Symmetry and Pattern: The Art of Oriental Carpets. This site offers
information on symmetry, pattern, carpets, and carpet-making. There
are clear, concise definitions of terms and an extensive glossary.
The site provides images of carpets and pictures and explanations
of how they are made. There are also several activities for classroom
use, a bibliography, and links to related Web sites.
Links to different
cultural arts (African, American Painting & Sculpture, Asia,
Ancient Egypt, European, Islamic)
Geographical Connections: Tessellations and Tilings (Egyptian, Persian,
Byzantine, Arabian, Moresque, Indian, Hindoo, Chinese, Japan, Middle
East, Spain, etc.)
of tessellations and related designs in different cultures.
Scroll: geometry and ornament in Islamic architecture.