MTH 930 Discrete Math Summer II 2002

NCTM Illuminations http://illuminations.nctm.org/pages/across.aspI found this site to be very useful. It is well organized and I feel that it would be an excellent resource. There are lesson plans given that are easy to follow and provide plenty of instructions to help the teacher implement the lesson.   This web site site was very informative as it contained activities and resources that were available to both teachers and students across grades pre-k to 12.   The site is beneficial to teachers as it encompasses lesson planning, lesson assessment, is standards based, and allows for teacher reflection. Problem solving is addressed through the use of video clips and i-maths. nice, informative site.

NCTM standards http://standards.nctm.org/previous/currevstds/This site is a good reference to quickly view the NCTM standards.You can choose the standard you wish to inquire about and click on it to find detailed description on what the standard means and some suggestions on how one might implement it.    This web site is very useful to teachers who have novice, minimal, moderate, or maximum knowledge of the math standards across curricula and grade level. I find myself always visiting this site for curriculum and development of standards based lessons.

Rhode Island department of Ed http://www.ridoe.netAt this site you may view different reports put out by the state such as RIDE Reports, Perkins Data Collection Information and Educational Jobs in RI. This can be a good place to go if you need to quickly view the requirements for teacher certification. This site is a necessity for any teacher who is certified in the State of Rhode Island, whether actively teaching or retired. Since it is almost impossible to speak to anyone directly at the Board of Education anymore, this is a great site to research teacher certification procedures/requirements, adult education curricula/ged requirements, state assessment testing, current educational research and headlines(Hope High School recently), standards and assessment topics, professional development opportunities, retirement procedures, and even the school calendar. Very nice site.

Discrete Math games http://www.ship.edu/~deensl/pgss/games.htmlA: This site has a variety of different games that may be good leads into discrete math topics. The Josephus “Game” looks interesting. I could not find exact answers, but there are hints on where to begin. This is a great site to get students actively engaged in their own learning. It has many hands-on applications such as the Simple Dice Game, and kids would love the "time away from math" with the Brain Teasers and Problem-Puzzlers. B: I like this site because it is interactive. Students will enjoy the challenge the puzzles offer and can be used when there is a bit of free time. We have block scheduling and at times, I am tied up with students who learn at different rates. This site would be good for the students who are ready to move on.

About Homework help, Discrete Math http://math.about.com/cs/discretemath/index.htmlA: This site I found to be very useful. There is help for many math topics as well as software demos and many other topics. This site is set up for reviewing many topics at different ability levels.Excellent site!!! This site has it all!!! It is interactive, visually appealing, mathematically/linguistically simplistic, and comprehensive. It is standards based and takes on a problem solving real world applications approach. It has many different types of    problems and encourages use of calculators; it walks the student through difficult portions of the problem. It incorporates definitions, pictorials, and and explanations to problems. B: Math about is a very interesting web site because presents discrete math/graph theory clearly and simply by using examples. I am planning to use it in my classroom. C: Link regarding what Discrete Math is. It shows how if fits into curriculum, why we should teach it, it also includes 7 & 8th grade applications.

Drexel Math Forum http://mathforum.org/students/high/Good site to get “problems of the week” or to send your students to. This site is the most bountiful of all. Not only is Dr. Math there to help you with your homework, the problem of the week is also available. Top that off with the link to: http://mathforum.org/students/high/ml_browse.html and you have over 8000 sites at your fingertips ... information overload!!!

Group 2

Data Analysis and discrete math http://www.ucs.mun.ca/~mathed/Stats/introd1.htm I found a great resource for when I teach variables and patterns next year. It has a bunch of different exercises showing the correlation of data and to work on scatter plots. Not bad. Had some activities along with student worksheets to help students recognize patterns, think about using scatter plots to represent the data and find equations to represent it as well. This is an excellent site!! This is a standards based site with realize applications and stresses a problem solving approach. Students get actively engaged in learning (Height and shoe size project) and then must justify their findings with time for reflection. It also contains interactive math puzzles and mind bogglers.

Ask Dr Math http://mathforum.org/dr.math/This is a site I have used before and found to be helpful to a certain degree (depending on the difficulty of the problem) when I was stuck on a problem. I have also sent students there.

Math contest web sites http://www.nctm.org/site is composed of News, Hot Topics, statements on learning and principles and standards.

Connect http://www.co-nect.net/index.htmSite to check out for professional development.

Interactive mathematics http://www.cut-the-knot.com/games.shtmlA: A site that I have reproduced some very challenging games! puzzles from for all areas of middle school math. This site seems to have something that was relevant to topics I cover in 71~ and 8th grade math class. There's always something here if a worksheet was needed asap. B: There are 57 puzzles to choose from. One needs to have Java script to use these. Some examples include the Gordian Knot, Latin Squares, Lewis Carroll, Famer and Wife to Catch Rooster and Hen, Euclid’s Game.

Group 3

Discrete math problem of the week http://mathforum.org/dmpow/This web site looks good for a beginner problem. It may be a little too babyish for 8th graders but it would be appropriate for 6th or even 7~graders. Color coding would work out nice for students since many of them like to work with their hands and doodle on paper. Some even would like to show off their artistic ability with this problem. Like another web site, this may be a problem that I can open the class with and see what they can do on their won.

Franklin Institute http://www.fi.edu/school/math2/index.html A: Offers a lot of open-ended problems designed to make students think. B: This site is superb as it prepares students for the state assessment tests. It is characterized by real world open-ended math problems for junior high school students organized by months of the year. This is an asset for teacher planning. C:This web site looks awesome and can offer a plethora of material. It is categorized by months and topics. It is divided into the 5 strands of the Philadelphia math standards but can be used in anywhere. This, to me, is the best web site yet. It even offers rubrics for the teachers. Like can't get much better than this.

Mathematics contest web sites http://www.olemiss.edu/mathed/contests.htm A: Offers a lot of problem solving contests. B: Categorized into all levels. Many links are no longer available. Check out Go figure - with a math mountain. The higher you go up the mountain the more difficult the question. You’re given an opportunity to answer the question and get immediate response. It gives the correct answer.

Solving traveling salesman problems http://www.math.princeton.edu/tsp/

Operations Research Analysts http://stats.bls.gov/oco/ocos044.htmIt has an occupational Outlook Handbook where you pick a letter and out comes an extensive list of occupations requiring the use of math.

Group 4

Eulerian and Hamiltonian graphs http://www.cs.columbia.edu/~sanders/graphtheory/research/05C45.html I found the difference between an Euler circuit which must touch every edge of a graph once and a Hamilton circuit which must touch every vertex of a graph once but is not concerned about the edges.

Chaos theory and fractal geometry http://home.inreach.com/kfarrell/course.outline.html

Sierpinskis Carpet http://www.math.umass.edu/~mconnors/fractal/generate/carpet.htmlYou can actually make great designs by using various colors as you meander from one iteration to another, trying different combinations. For example, ). The area of the triangle that gets inserted is one fourth the area of the original triangle and it gets inserted right in the center. To go to the next iteration, the exact same process is done recursively to each of the resulting triangles that are pointing up. You can fill in table and watch triangle grow before your very eyes! They claim it is quite simple!

Fractals, an introductory lesson http://arcytech.org/java/fractals/Gives some probing questions for students to contemplate. One begins by finding a simple sequence and the number of line ends for each iteration. You see how the transformation from one iteration goes to the next.

What is a tiling http://mathforum.org/sum95/suzanne/whattile.html

Group 5

http://archivesmath.utkedu/topics/discretemath.htmlThis site starts out with questions that are intriguing. It introduces students to new vocabulary. It offers instruction on how to answer the questions for graphs, etc. And it shows how to represent graphs on the computer.

http://lennes.math.umt.edu/~mcnulty/325/links.html You can download Algorithms etc. and this site has a huge collection of math applets,math resources etc.

http://www-math.cucenver.edu/~wcherowi/courses/m44081/glossary.htm This has great Vocabulary. It is broken down to more simpler terms and it gives diagrams. etc.

DICE GAME. http://www.maa.org/mathland/mathtrek_5_17_99.html Good site for elementary or middle school students, whereby 2 players roll rice and percentages of wins per child.

WATER PUZZLE http://www.ship.edu/~deensl/pgss/water/ Good for middle school students. Students need to carefully read instructions and follow the rules. Students could devise their own water capacity puzzle using different numbers. It works well.

GAME OF NIM http://www.ship.edu/~deensl/pgss/nim/ Based on the binary operations this game is great for students and could employ probability probes.

TESSELLATION http://mathforum.org/sum95/suzanne/whattile.html Colorful photos show how tessellation's are constructed using rectangles, triangles or pentoninoes and there are links to explain just what a tessellation is,

GEOMETRY http://www.scienceu.com/geometry/articles/tiling/index.html This site has various links to such things as an explanation of tilings, interactive geometry center, articles, facts and figures, and activities. It explains the different types of tilings with colorful illustrations. You are given step-by-step instructions on how to build an icosahedron of any size as a class or at-home project or how to make a tetrapuzzle in a least 2 different ways using cut out pieces of paper.

FOUR COLOR THEOREM PROVED http://www.maa.org/mathland/mathtrek_5_17_99.html Complete with explanation and colored figures to prove the four color theorem.

http://www.middletownri.com/mhs/math/fagan/Geometry%20Web%20page%201.htm You missed this site. It's my web page with online projects that are available for my students. Read Flatland online, discover SherlockHolmes' logical deductive reasoning ability, create non-Euclidean Triangles, adventure into the fourth dimension or be stunned by the awesome beauty of Fractal Geometry and Chaos Theory. It's all at your fingertips!

Here are some more favorites:

http://www.lboro.ac.uk/departments/ma/gallery/hyper/index.html This site gives some fundamental information on hypercubes and the hyper-torus. The movies that are contained on links 1, 2 and 3 are quite good as well.

http://www.lboro.ac.uk/departments/ma/gallery/index.html This contains a plethora of interesting Mathematical sites. You may want to share some of these with your colleagues.

http://www.rose-hulman.edu/~berglunb/Rubik/ This site contains Rubik’s hypercube for your downloading pleasure. This answers the question “When am I ever going to use this stuff?” ;^)

Internet Sites for Mathematics Lessons, http://math.smsu.edu/~lynda/lesson.html Here, there are sites on Combinations: http://team.liunet.edu/studprojects/pvs/sal/Combinations.htm , Golden Rectangles http://wony.ai/KW/goldengeom.html , The Golden Ratio http://www.geom.umn.edu/~demo5337/s97b/discover.htm and
http://math.rice.edu/~lanius/Geom/golden.html . There are discrete math puzzles like "Hooking Up Houses" http://www.aimsedu.org/Puzzles/hookHouses/houses.html , and others: Ken’s Puzzle of the Week http://www.ecst.csechico.edu/~kend/potw/current.html Middle School Madness http://www.olemiss.edu/mathed/middle Ups and Downs http://www.aimsedu.org/puzzles/upsNDowns/cups.html .

On this page you will fun lessons by Cynthia Lewis, including one on the four-color problem (or go to http://math.rice.edu/~lanius/Lessons/ ).

http://www-leibniz.imag.fr/GRAPH/english/overview.html This site has a lot to do with graph theory. The concepts shown are defined and explained before any problems are fully
discussed. The site gives proofs and diagrams that pertain to the examples given and this allows for easier analyzing of the problems. The web site is colorful and interesting and does not bore people browsing it. I will definitely use this web site this following school year with my students.

http://students.ceid.upatras.gr/~papagel/minKrusk.htm Minimize a weighted tree at this interactive site

http://students.ceid.upatras.gr/~papagel/project/contents.htm This site has various tutorials
-Choosing from a forbiddingly big number of solutions. Greed (and hill elevation). Order Projects by Deadlines. Minimum Genetic Tree. Prim Algorithm. Kruskal Algorithm. Heuristic Algorithms. Dynamic Programming. Minimum Routes Dijkstra Algorithm. Backtracking.

Prim's Algorithm website gives you a blank slate and allows you to add
vertices, edges, and weighted edges. www.cs.usask.ca/resources/tutorials/csconcepts/graphs/tutorial/advanced/prim/prim_kruskal.html

http://www.csun.edu/~hcmth014/comics.html This site is just for fun. It offers all kinds of comic strips that relate to math. They could be useful as class openers on transparencies or for decorations in the classroom. All of the comics are printable. I hope you enjoy it.

All Branches of mathematics: Sparknotes http://www.sparknotes.com This site offers the students a review of whatever lesson the teacher addresses in class. It provides definitions, illustrations, and practice problems. great for the low-level to advanced classes.

Eisenhower Clearing Project: http://www.enc.org This site is useful for all subjects as well. Under math topics, it will direct you to various sites based on branch of math required. problem-solving standards-driven approach.

AP College Board: www.collegeboard.com great site to provide instructors of Advanced Placement Courses with questions from previous tests of Calculus, statistics, and probability.

http://www.ship.edu/~deensl/pgss/Joseph/ This website can be used to grab kids attetnion. It
does involving men dying so please make sure that the students you teach will understand the signfiance behind it. It is a game based on having n amount of people and killing off every knth one.

http://www.ship.edu/~deensl/pgss/hank-and-ted/ The Hank and Ted Game This is a very basic game but offers some good insight into probability and chance. It involves tossing a coin and the use of "markers" to win. This can only be done with one person at a time and online.

http://www.ctl.ua.edu/math103/euler/euler.htm This is a wonderful website for teachers and students alike who are looking for resource on the topics of Euler circuits. It provides drawings, history, and problems.

pbsmathline.org-this site provides labs with background information, standards, step-by-step procedures, data sheets, worksheets, quizzes and solutions with graphs. It is wonderful to use after teaching a unit to reinforce a concept. Answers the question "When will we ever use this?" nicely. Site provides labs from middle school through high school.