The Math Page 

Table of Contents

Web Sites
 Featured Math Lessons
Featured Mathematician - Escher
 Where and How Mathematicians Work
  Back to My Home Page
  Link to My Science Page

            These math topics and links are designed for grades 6 through 8.
 Susan Grubbs

 Please E-Mail Me!

 

WEB SITES                                                            RETURN TO TOP

I hope you enjoy the sites!
 

Math WEB SITES w/site information
World of Escher
World of Escher [web site]. (1995-2001). Retrieved July 10, 2001, from World Wide
Web: http://www.worldofescher.com

“M.C. Escher was a Dutch graphic artist, most recognized for spatial illusions, impossible buildings, repeating geometric patterns (tessellations), and him incredible techniques in woodcutting and lithography.  M.C. Escher was born June 1898 and died March 1972. His work continues to fascinate both young and old across a broad spectrum of interests. M.C. Escher was a man studied and greatly appreciated by respected mathematicians, scientists and crystallographers yet he had no formal training in math or science. He was a humble man who considered himself neither an artist or mathematician.  Intricate repeating patterns, mathematically complex structures, spatial perspectives all require a “second look”.

“In Escher’s work what you see the first time is most certainly not all there is to see. We at the World of Escher are proud to be here to tell you stories, discuss M.C. Escher’s works, provide insight, and offer our high quality products promoting the intriguing work of Escher. If you already know of Escher and his work you'll have a great time just looking around, otherwise its time to get ready to explore a world as fascinating as the Internet; The World of Escher! Along with discussions on Escher we have also included ideas and readings regarding Professor Roger Penrose and his mathematically based puzzles.”
 

Escher's Page
Escher's page [web site]. Retrieved November 21, 2001 from World Wide Web: http://www.etropolis.com/escher/

This is a site with information about the artist and his art.
 

M. C. Escher
Optical Illusions

M. C. Escher Optical Illusions [web site]. Retrieved November 21, 2001 from World Wide Web: http://www.geocities.com/SoHo/Museum/3828/

M. C. Escher Optical Illusions is a site for information on the artist, illusions, tesselations, books, and other links dealing with Escher.
 

Escher Type Tessellations
Tessellations [web site]. Retrieved October 10, 200, from World Wide Web: http://library.thinkquest.org/16661/essentials.html

A ThinkQuest site for information about tessellations. What is a tessellation? A tessellation is any repeating pattern of interlocking shapes. M.C. Escher made this art form famous. This site gives students a comprehensive introduction to tessellations and explains the basic math that is used in creating them. So enter Totally Tessellated to learn, create, explore, and have fun!
 

E-Tutor
E-Tutor [web site]. (2000). Retrieved July 5, 2001, from World Wide Web: http://www.e-tutor.com
“e-Tutor is the premier K-12 Internet education program for students, educators and parents, providing empowering tools and quality educational content, to create a customized learning community.”
Automatic Math Solutions http://www.quickmath.com/
Quick Math supplies automatic math solutions to many problems.
Glencoe Online Tutor
Glencoe Online Study Tools [web site]. Retrieved October 17, 2001, from World Wide Web: http://www.glencoe.com/sec/math/studytools/index.html

Students can choice their textbook and lesson and get online study help.
 

America OnLine At School
America OnLine At School [web site]. (2001). Retrieved July 17, 2001, from World
Wide Web: http://school.aol.com/elementary/research.adp

“This website is designed for students, teachers, and administrators. It has a
selection of information for each audience. It is divided into appropriate grade
levels: Primary (K-2); Elementary (3-5); Middle (6-8);
High School (9-12); Teachers; and Administrators. This site includes lesson plans, activities, teaching tools, research aids, current events and a school store. It has links that are appropriate for classroom work, professional development, and for students online. It also has a link to education updates from your state. Students and teachers would use the site. The teacher page has classroom items, resource items and a toolbox, which includes a calendar and online grade book.  This would be useful both in the classroom for students and in planning and development for teachers.”
 

The Global Schoolhouse
The Global Schoolhouse [website]. (2000). Retrieved July 18, 2001, from World Wide Web: http://www.gsn.org

“Global Schoolhouse has joined forces with Lightspan.com to bring you the best online collaborative learning. Please use the links on this page to find Global Schoolhouse content and tools plus easy access to the wealth of material on Lightspan.com.”
 

Lightspan.com – Online Learning for School and Home
Lightspan.com – Online Learning for School and Home [web site]. (2000). Retrieved
July 17, 2001, from World Wide Web: http://www.lightspan.com
“Lightspan.com is a FREE education portal for educators, parents, and students, providing resources, research tools, and grade-specific activities.”
NASA Kids
NASA Kids [web site]. (2001). Retrieved July 5, 2001, from World Wide Web:
http://kids.msfc.nasa.gov

“Science @ NASA's motto is to Inform, Inspire, and Involve.  To achieve our
goal, we produce materials at multiple reading levels, language and for multiple purposes.  We hope that once informed, you will be inspired to get involved! NASA KIDS, is the place for kids grades 5-8 and younger. It has puzzles, games, and science stories just for kids. Kids can join the NASA KIDS Club with activities to learn to earn NASA certificates. They can even have a NASA KIDS e-mail address.”
 

Ask Dr. Math
Ask Dr. Math [web site]. (1994-2001). Retrieved July 17, 2001, from World Wide
Web: http://mathforum.com/dr.math
“Students submit questions to Dr. Math by filling out our Web form. Answers are sent back by e-mail, and we then gather the best questions and answers into a searchable archive organized by grade level (elementary, middle school, high school) and topic (exponents, infinity, polynomials, etc.). We recommend using the Dr. Math searcher to find what you want (try keywords like fibonacci, fractal, or proof), and investigating the Dr. Math FAQ (topics include prime numbers, pi, the golden ratio, Pascal's triangle).”

Links Include: Math Forum Problems of the Week: Elementary, Middle School, Algebra,
Geometry Problem of the Week, Geometry Project of the Month, Discrete Math, Trigonometry & Calculus. More problems and puzzles: Macalester College Problem of the Week, Problems
of the week administered by others, K12 Math Problem & Puzzle Sites - Internet Mathematics Library, Math Forum, The rec.puzzles newsgroup archive, Interactive Mathematics Miscellany and Puzzles - Alexander Bogomolny.
 

ThinkQuest 
ThinkQuest [web site]. Retrieved November 21, 2001, from World Wide Web: 
http://www.thinkquest.org

"ThinkQuest is a global network of students, teachers, parents and technologists dedicated to exploring youth-centered learning on the Net. ThinkQuest is an online community where young people learn, teach, mentor, discover, research and grow through ThinkQuest programs. 

The ThinkQuest World encompasses young people, educators and technologists in more than 100 nations who come together as digital learners, web creators, and Net entrepreneurs."
 

Dave's Math Tables
Math2.Org  (Formerly "Dave's Math Tables). [web site]. Retrieved November 21, 2001, from World Wide Web: http://www.math2.org/index.xml

This is the same resource for math information and link as was at Dave's Math Tables. David Manura's new site. Great source of information and help.
 

Bamdad's Math Comics Page
Bamdad’s Math Comics Page [web site]. (1998-2001). Retrieved July 18, 2001, from
World Wide Web: http://www.csun.edu/~hcmth014/Comics.html
This site hosts a collection of math related cartoons.
Olson’s Math Cartoon Page
Olson's Math Cartoon Page [web site]. (1998-2001). Retrieved July 18, 2001, from
World Wide Web:http://www.hoxie.org/jo/cartoon.htm

This site hosts a collection of math related cartoons.
 

The Dance of Chance
The Dance of Chance [web site]. Retrieved July 18, 2001, from World Wide Web:
http://polymer.bu.edu/museum

The focus of this web site is to exhibit patterns in nature. Patterns listed are:
Music of the Heart, Bacteria, Frozen Lightning, Metal Deposition, Erosion,
Termites, and Viscous Fingering.
 

Cool Math
Coolmath [web site]. (2001). Retrieved October 27, 2001 from World Wide Web:http://www.coolmath.com/home.htm

An amusement park of math for children of all ages.
 

The Math Forum
The Math Forum [web site]. (1994-2001). Retrieved July 17, 2001, from World Wide
Web: http:// forum.swarthmore.edu

This web site has forum features: Ask Dr. Math, Discussion Groups, Forum
Showcase, Internet Newspaper, Problems of the Week, Teacher2Teacher, and
Web Units and Lessons.

The Math Forum [web site]. (1994-2001). Retrieved July 17, 2001, from World Wide
Web: http:// forum.swarthmore.edu

This web site has forum features: Ask Dr. Math, Discussion Groups, Forum
Showcase, Internet Newspaper, Problems of the Week, Teacher2Teacher, and
Web Units and Lessons.
 

Mega Math
Mega Math [web site]. Retrieved July 17, 2001, from World Wide Web: http://www.c3.lanl.gov/mega-math/

“Mathematics is a live science with new discoveries being made every day. The frontier of mathematics is an exciting place, where mathematicians experiment and play with creative and imaginative ideas. Many of these ideas are accessible to young children. Others (infinity is a good example) are ideas that have already piqued many children's curiosity, but their profound mathematical importance is not widely known or understood. The MegaMath project is intended to bring unusual and important mathematical ideas to elementary school classrooms so that young people and their teachers can think about them together.”

Links and Resources include:

Mathematical Topics:  The Most Colorful Math of All, Games on Graphs,
Untangling the Mathematics of Knots, Algorithms and Ice Cream for All,
Machines that Eat Your Words, Welcome to the Hotel Infinity, A Usual
Day at Unusual School

Other Things to Look At: Hints for Navigating MegaMath, Stories, Writings from
the MegaMath Project, The MegaMath Glossary and Reference Section,  The MegaMath Mailbox, Some Interesting Links.
 

AIMS 
Activities Integrating Math and Science

AIMS Activities Integrating Math and Science [web site]. Retrieved September 23, 2000, from World Wide Web: http://www.aimsedu.org/ 

AIMS began in 1981 as a project funded by the National Science Foundation at Fresno Pacific College. Eighty classroom teachers and the faculty explored the
effectiveness of integrating mathematics and science in grades 5-8. Even though long recommended by thoughtful educators, very few meaningfully integrated
materials existed at the time. The initial AIMS materials produced such positive results that a major curriculum research and development effort was launched to fill
this void. 
 

Fibonacci Numbers and the 
Golden Section
Fibonacci Numbers and the Golden Section [web site]. (2001). Retrieved July 18, 2001, From World Wide Web:
http://www.ee.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html 

This web site is the Home Page for Fibonacci Numbers and the Golden Section. There is a large amount of information at this
site about Fibonacci Numbers, the Golden Section, and Golden String. There is information about their applications. 
 

The MacTutor History of Mathematics
The MacTutor History of Mathematics [web site]. (2001). Retrieved July 18, 2001,
from World Wide Web:  http://www.asap.unimelb.edu.au/hstm/data/276.htm

“The MacTutor History of Mathematics archive was created and is maintained by John O'Connor  and Edmund F Robertson. It was developed initially as part of the Mathematical MacTutor system for learning and experimenting with mathematics.
 

The archive contains the biographies of more than 1300 mathematicians. You can access them from a selection of Alphabetical or Chronological Biographical indexes. We have written some articles on the development of mathematical ideas cross-referenced to the biographies. You can access these using the History Topics Index. There is a collection of more than 60 articles on Famous Curves mathematicians, giving their history as well as pictures of the curves and various curves (evolutes, inverses, caustics etc.) which are associated with them. If your browser is capable of handling JAVA, you have the option of experimenting with these curves in an interactive way.


There are Chronologies showing the overlapping lives of the mathematicians in our archive. We have a Mathematicians of the day page which contains details of the mathematicians who were born or died on today's date and another file: Anniversaries for the year containing details  for all dates. You may like to try our Birthplace Maps. These are maps showing the birthplaces of those Western European or North American mathematicians in our list of biographies. One can click on them to locate a birthplace. The maps are reachable from the biography of any mathematician whose birthplace is marked.

There is a Search Form (or a Simple Search Form for browsers without forms) which allows you to find references to keywords throughout the archive. You may like to try some of our Search Suggestions. More details of the Mathematical MacTutor system are available. There are other good sources of information concerning the history of mathematics available on the web.

The On-Line Encyclopedia of Integer Sequences The On-Line Encyclopedia of Integer Sequences [web site]. Retrieved July 18, 2001, from World Wide Web: http://www.research.att.com/~njas/sequences/

Most people use this web site to get information about a particular number sequence.
 

Math Art Gallery
Math Art Gallery [web site]. Retrieved July 17, 2001, from World Wide Web:
http://www-math.sci.kun.nl/math/knopen/art_gallery.html

This web site host an interactive art gallery which includes 3D fractals, knots, and
other pictures generated involving the art of math.
 

Mersenne Primes:  History, Theorems and Lists 
Mersenne Primes:  History, Theorems and Lists [website]. (2001). Retrieved
July 18, 2001, from World Wide Web: http://www.utm.edu/research/primes/mersenne.shtml

This is a web site that is the Research Page for GIMPS and is dedicated to finding the largest prime. To keep up to date on the hunt access this page.
 

GIMPS, the Great Internet Mersenne Prime Search 
GIMPS, the Great Internet Mersenne Prime Search [web site]. Retrieved July 18, 2001, from the World Wide Web: http://www.mersenne.org/prime.htm

"GIMPS, the Great Internet Mersenne Prime Search, was formed in January 1996 to discover new world-record-size Mersenne primes. GIMPS harnesses the
power of thousands of small computers like yours to search for these "needles in a haystack".
 


 
 
 
 
                                                      RETURN TO TOP

Featured Mathematician and Related Math Lesson

M. C. Escher

“M.C. Escher was a Dutch graphic artist, most recognized for spatial illusions, impossible buildings, repeating geometric patterns (tessellations), and him incredible techniques in woodcutting and lithography.  M.C. Escher was born June 1898 and died March 1972. His work continues to fascinate both young and old across a broad spectrum of interests. M.C. Escher was a man studied and greatly appreciated by respected mathematicians, scientists and crystallographers yet he had no formal training in math or science. He was a humble man who considered himself neither an artist or mathematician.  Intricate repeating patterns, mathematically complex structures, spatial perspectives all require a “second look”.
From: World of Escher [web site]. (1995-2001). Retrieved July 10, 2001, from World Wide
Web: http://www.worldofescher.com


 

Sites for Escher:
The Official M.C. Escher Website
M. C. Escher - Optical Illusions and Tessellations
M.C. Escher Centennial Celebration Page
Teaching Escher: Using Escher in Classrooms
The World of Escher
 
 

Related Math Lessons           RETURN TO TOP
 
 

Tessellations:
The Geometry of Patterns
 
 
 
 



 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

QCC 8:25

(Georgia QCC 8th Grade - Strand: Geometry & Spatial Sense; Measurement  - Objective 25)
 

               Topic: Reflection, Rotation, Translation

               Standard:  Analyzes effects of basic transformations on geometric shapes.
 


 

Background Information:

Generally by fifth grade, students have received some geometry lessons in an informal setting. They know about points, lines, triangles, squares, and such. Before moving into the formal study of geometry, it is recommended that students be allowed the opportunity to play with and enjoy geometry.  Many students become bored of the formal geometry or it is too difficult for them. The tessellation unit provides the chance to play and enjoy the patterns. The lesson is best suited for the end of a basic study of geometry and before formal proofs.
 

In mathematics, the word tessellation (or tiling) has come to mean the repeated use of polygons and other curved figures to completely fill a region (or space) without gaps or overlapping. The patterns in tessellations can be described in terms of  transformation (movement geometric figures) in the following ways:
Reflections - a type of transformation where a figure is flipped over a line of symmetry (mirror image).
Translations - a type of transformation where a figure is slid horizontally, vertically, or both (slide).
Rotations - a type of transformation where a figure is turned around a central point (turn).
 

Web site for introduction lesson and extensions:

Make Your Own Tessellations

Symmetry and Tessellations

Totally Tessellated: An Introduction to Tessellations [web site].
Retrieved October 10, 200, from World Wide Web:
http://library.thinkquest.org/16661/essentials.html
 

A ThinkQuest site for information about tessellations. What is a tessellation? A tessellation is any repeating pattern of interlocking shapes. M.C. Escher made this art form famous. This site gives students a comprehensive introduction to tessellations and explains the basic math that is used in creating them. So enter Totally Tessellated to learn, create, explore, and have fun!
 
 

Where and How MathematiciansWork     RETURN TO TOP

NCTM - National Council of Teachers of Mathematics - Online jobs - career opportunities

Employment Opportunities in the Mathematical Sciences

Society for Industrial and Applied Mathematics (SIAM)

Careers in Applied Mathematics

American Mathematical Society

Mathematical Association of America

Opportunities in the Mathematical Sciences - Careers that Count

Math Career Profiles

Math Careers - A whole web site

Mathematics Job Listing w/salaries

Math Careers with mathematics occupation links. Math Careers

Karen's Careers in Math Page

Careers in Mathematics as listed Career Education Project in Mathematic at COOL MATH Career Ed.
  Career Names:
   Veterinary Medicine
   Agricultural Management
   Biomedical Research
   Petroleum Engineering
   Construction Engineering/Management
   Independent Music Production
   Cartography
   Aerospace Medicine
   Astronomical Research
   Meteorology
   Food Management
   Operations Research
   Government Finance
   Special Education
   Public Accounting
   Computer Consulting
   Manufacturing Engineering
   Architect
   Structural Engineer
   Navigator
   Physicist
   Seismologist
   Surveyor
   Product Manager
   Statistician
   Math Textbook Editor
   Opinion Researcher
   Actuary
   Math TV Content Director
   U.S. Navy Officer
   Casino Manager