CTL Resources for Geometry

FACULTY DESIGNED I STUDENT DESIGNED I WEB

FACULTY DESIGNED UNITS & ACTIVITIES

» The Three Point Problem From Geology [HTML]

Description: 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 slope.

» Volume of An Irregular Solid Problem [HTML]

Description: Estimate the number of cubic yards of material in a waste stockpile

» Area of Golfing Greens Problem [HTML]

Description: 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]

Description: 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 §.

»» STUDENTS' SOLUTIONS [HTML]

» Cutting the Cake Problem [HTML]

Description: 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]

Description: 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]

Descriptiopn: 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]

Description: 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 [HTML]

Description: 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?

» Minimum Surface Area of a Can [HTML]

Description: 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.

»» STUDENTS' SOLUTIONS [HTML]

» Distance to the Nearest Road [HTML]

Description: 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 Problems [HTML]

Description:In 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 speed.

» Texas Area Estimate [HTML]

Description: Estimate the 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 problems.

» Ladder and Box [HTML]

Description: 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?

»» STUDENTS' SOLUTIONS [HTML]

» Mirror Image [HTML]

Description: 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 mirror.

» Where is the Store? [HTML]

Description: 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?

»» STUDENTS' SOLUTIONS [HTML]

» The Salesperson's Journey [HTML]

Description: The following 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...

STUDENTS DESIGNED UNITS & ACTIVITIES

» Geometric Aspects of the Structure and Design of Commercial and Residential Field Irrigation [HTML]

Description: 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 irrigation system.

» Combinatorics [HTML] [PDF]

Description: A lesson plan investigating combinatorics in a restaurant environment.

» Public Transportation and Mathematics [HTML]

Description: A class activity involving experimentation, statistics, and network optimization.

» Networking in a Grocery Store [HTML]

Description: The object of the study is to understand how networking is part of our everyday routine.

» Taxicab Geometry [HTML]

Description:We've 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.

» Modeling Linear and Non-linear Motion [ HTML]

Description: 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.

WEB RESOURCES

» http://www.micron.com/education/math/intro.html

Description: MATH IN THE WORKPLACE: Lot's of examples of how math is used in real workplaces

» http://www.learner.org/exhibits/dailymath/

Description: Math in Daily Life

» http://www.scas.bcit.bc.ca/scas/math/examples/table.htm

Description: 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.

» » http://www.readiowa.org/workplacemath/contents.html

Description: 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.

» http://www.bced.gov.bc.ca/careers/aa/lessons/math.htm

Description: Lesson plans 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)

» http://www.enc.org/topics/realworld/handson/documents/0,1946,FOC-000892-index,00.shtm

Description: Math from the Toy Store: Use of scaled replicas makes learning about ratio and proportion fun in this teacher's middle school math classes.

» http://www.c3.lanl.gov/mega-math/workbk/dom/dobkgd.html

http://www.c3.lanl.gov/mega-math/workbk/map/mpbkgd.html

Description: Mathematics in Maps and Planning

» http://octopus.gma.org/surfing/imaging/mapproj.html

Description: Make a map of the Earth

» » http://math.rice.edu/~lanius/pres/map/mapque.html

Description: Investigate four math problems related to the use of maps. Math content: Aalgebra (coordinates and linear equations), scale, etc.

» http://www.paperfolding.com/math/

Description: Origami and Math

» » http://www.nap.edu/html/hs_math/ch5.html

Description: Working with Algebra: Algebra at workplace including an example (cost of cerpet) activity with spreadsheets.

» http://www.nap.edu/html/hs_math/hq.html

Description: 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.

» http://www.nap.edu/html/hs_math/ro.html

Description: 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.

» http://riceinfo.rice.edu/armadillo/Vanishing/Corn/natrpat1.html

Description: Outdoor Math/Art: Nature's Patterns, Fibonacci Sequence, Golden Ratio

» http://library.thinkquest.org/12006/resources.shtml

Description: Math & Basketball

» http://www.ebmic.com/text/bike.htm

Description: Bike Sizes

» http://www.showmecenter.missouri.edu/showme/mic.shtml

Description: Mathematics in Context Project sample lessons and teacher pages

» Art & Mathematics

http://archives.math.utk.edu/topics/artMusic.html (A Great Site for Math in Art&Music. Lot’s of examples.)

http://www.pd.astro.it/ars/arshtml/arstoc.html (The Art of Renaissance Science: Galileo and Perspective)

http://tlc.ai.org/fibonacc.htm#MUSIC (Fibonacci Numbers, Golden Ratio and Music)

http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html (The Golden Section in Art, Architecture and Music)

http://library.thinkquest.org/3044/index.html (Works of Leonardo da Vinci)

http://archives.math.utk.edu/images.html (Images and Mathematics)

http://www.mathacademy.com/platonic_realms/minitext/escher.html#intro (Escher’s Art)

http://library.thinkquest.org/16661/history.html (History, instructions, and examples of tessellations)

http://www.dartmouth.edu/~matc/math5.pattern/pattern.html (Mathematical Patterns)

http://members.nbci.com/bsms/perspect.html (Mathematics in Art: Drawing in Perspective)

http://www.newyorkcarver.com/geometry/geometry.htm (Tips and Tricks to Gothic Geometry)

http://forum.swarthmore.edu/geometry/rugs/

Description: 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.

http://www.bmalearningcenter.org/links.html

Description: Links to different cultural arts (African, American Painting & Sculpture, Asia, Ancient Egypt, European, Islamic)

http://forum.swarthmore.edu/sum95/suzanne/historytess.html

Description: Historical and Geographical Connections: Tessellations and Tilings (Egyptian, Persian, Byzantine, Arabian, Moresque, Indian, Hindoo, Chinese, Japan, Middle East, Spain, etc.)

http://library.thinkquest.org/16661/gallery/index.culture.html

Description: Real examples of tessellations and related designs in different cultures.

http://www.ee.bilkent.edu.tr/~history/geometry.html

Description: The Topkapi Scroll: geometry and ornament in Islamic architecture.

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