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DECOMPOSITION METHOD OF SOLVING SIMPLE TRINOMIALS
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Teaching Middle and Secondary School Mathematicswith Technology
Annotated Website Resources
compiled by Spring 2002 Class Members

EMS480 students found many websites that would be valuable resourcesin the teaching and learning of a particular mathematics topic. This listis organized around several Topics in Mathematics.

FactoringPolynomials  and Quadratics (Wendy Nuzzo and Kim Brown)

The VirtualTileslink is the demo download.It isan interactive version of the algebra tiles manipulative.Thesoftware is capable of modeling adding, multiplying, dividing, factoringpolynomials.Cost for 1 is \$69, anda school site license is \$349.The MathTrek 10,11,12 Factoring Demo has an interactive quiz where you canselect type of factoring and degree of difficulty.

Adiscovery lesson on graphing a quadratic function and its factors.Itincludes great thought questions for students to see the patterns, andmake their own conjectures.

Hasa variety of interactive and animated links.Itincludes common factors and factoring trinomials.

Factorstrinomials, difference of squares, and common factors.Enterin the polynomial, and it factors expression.Noexplanations are given.

Isa non-interactive, written tutorial with links to information and examples.Itcovers common factors, decomposition method (Dr. Waters magic method),perfect squares, difference of squares, difference of cubes, and sum ofcubes.There are links to introductory,moderate, and advanced exercises.Hintsand solutions are provided for the exercises.

Alesson plan for teaching multiplying and factoring polynomials with algebratiles.It includes worksheet andspace to make notes.

Awalk-through guide for factoring common factors, difference of squares,trinomials, sum of cubes, and difference of cubes.Thequiz is not recommended.It has noproblems to solve and does not accept correct answers that are in a differentform.

Factorsan entered polynomial either over real integers or Gaussian integers.Thefactors are given in the form (a+bx) (c+dx).

Containsa brief lesson plan for using Algebra Tiles manipulative.Suggestssetting up the activity as The Rectangle Game to make it more of a puzzleto solve.

Aguide to factoring a variety of polynomials.Itgoes into extreme detail of the thought process required when factoring.

Quadratic Equations
1.SolvingQuadratic Equations
Thisis quadratic equation calculator.Itasks the user to input the coefficients of the ,and constant terms and then gives the real or complex solutions.

2.MultimediaActivities:Quadratics/Polynomials

This site includes activities and lesson plansfor the investigation of quadratic functions.Thesite does not focus on the method of solving quadratic equations, but itdoes allow students to manipulate graphs and equations and relates thex-intercepts to the solutions of the equations.

3.Quadratic,Cubic and Quartic Equations

Thissite focuses describes a brief history of Quadratic, cubic, and quarticequations and contains links to pages about the mathematicians that influencedtheir evolution.

4.AddisonWesley Longman- Practice Test

Thissite consists of a practice test in solving quadratic equations by factoring.Thequestions are multiple choice, and the student is told whether they arecorrect or not immediately after choosing their answer.

5.AnIntroduction to Complex Numbers

Thissite contains a detailed and well-illustrated introduction to the complexnumbers.It includes many topicsfrom why they are necessary to the their role in the roots of polynomialequations.

6.Fashion Design: Patterns and Weaving Application (Grade Level 8-11)

Awonderful application to the solving quadratic equations can be found atthis

site.Theweaving of multiple colors is developed into a quadratic function, whichis then solved using the quadratic equation.

7.Createyour own quadratic practice worksheets online

Thissite allows you to create your own worksheets with quadratic functionsthat are actually solvable.The sitealso allows you to specify if any of the coefficients can be fractions,and, in fact, allows for the specification of how many of each type ofproblem is included in the worksheet.

8.SolvingQuadratic equations algebraically

Thisis a concise tutorial on solving quadratic equations and would be a goodsite to refer students with difficulties or for a subject review.Itis one of the few sites that shows solving by factoring, completing thesquare and the quadratic equation.

9.Ideas for an interactive lesson

Thisis a tutorial on solving quadratic equations that involves tables and graphs.Whilethis site is not the most interactive, the multidisciplinary teaching ideaspresented there (spreadsheets, etc.) might benefit a teacher looking forideas. (Development of your own spreadsheet is required).

10.Etap

hfiles/english/grade7/hspm16/hspm16ins.html

Thissite gives many sample problems and even includes sample quadratic wordproblems. It also contains information on perfect square trinomials thatstudents often overlook.I woulduse this as a place to find examples to use for class or as a resourcefor students.

Slopeand Rate of Change (Devon Smith and Denise Williams)

Slope (Devon Smith)
nius/Algebra/stress.html
Thiswebsite provides a math lesson on slope as rate of change.Itgives three different graphical situations (parabola, piecewise function,diagram displaying lines with various slopes) and asks analytical questionsabout the graphs and how slope is related to each.

edu/REU/reu94/williams/ch1/section3_2.html

Thiswebsite describes slope, how it is calculated, and what it is used for,including parallel and perpendicular lines, and equations of lines of specialcases (vertical/horizontal lines), point-slope form, and slope-interceptform.It also has a good descriptionof change, which precedes the description of slope.

nstitute/linearFunctions/lsif.html

Thiswebsite is a neat applet that shows what happens to the graph of a linewhen you change the slope and y-intercept.First,it simulates it for you, but you can click on you control and use slidersto change the slope or y-intercept.Italso provides a summary of how these parameters affect the graph of a line.

graph/cslope/

Thiswebsite is a collection of links that takes you to an introduction to slope,how to calculate and use slope, and what slope-intercept form is.Ituses a chameleon as a fun way of introducing lines with different slopes.

document/chapter7/alg.htm

Thisis the e-standards website for the Principles and Standards for SchoolMathematics.In particular, thiswebsite contains the Algebra Standard for grades 9-12, which include manydiscussions about slope.

12.il.us/gbssci/phys/Class/1DKin/U1L3a.html

This websitepresents a physics lesson about describing motion with position versustime graphs.It discusses the meaningof the shape of position-time graphs as well as their accompanying velocity-timegraphs.It also talks about the relationshipbetween slope and velocity.Thereis a link to see animations of various motions with accompanying graphsthat is neat as well.

tion-graphs/graphs-motion-compared.pdf

Thistakes you to a PDF file that has a worksheet and answers dealing with comparinggraphs of motion.It has spaces tofill in the blanks for areas of interest when dealing with position-time,velocity-time, and acceleration-time graphs (such as what the y-interceptmeans, what a positive/negative/zero slope means, etc.)

This websitegives a lesson dealing with slope as a rate of change.Init, students relate the concept of slope to velocity, analyze and interpretgraphs to find slopes, and discover why rates of change vary in parabolas.Studentsuse the CBL and graphing calculator in the lesson.

Thiswebsite provides a neat kid-friendly lesson on studying slope in distance-timegraphs.It discusses average speedand instantaneous speed and how to calculate and interpret each.

Thiswebsite has a lesson on distance-time grahps and slope.Ithas a NEAT demonstration of a car traveling certain speeds and its correspondinggraph!It also has a neat activitycalled Alphabet walk where a students tries to produce some of the lettersof the alphabet by walking a certain distance-time graph.

Rate of Change (Denise Williams)

This is an example of a lesson plan a teacher coulduse in discussing rate of change. It allows students to see the relationshipbetween stress and performance.

This website can be helpful in teaching rate of change.It includes a technology tool a teacher might consider using to teach thisparticular topic and suggest ways you can go about teaching it (questionsto ask, etc.)

With this lesson, students calculate the rate of changebetween two points on a curve by determining the slope of the line joiningthose two points. They then extend this method to estimate the instantaneousrate of change at a given point by taking two points very close to andon either side of the given point.

This is a classroom project a teacher could use afterdiscussing rate of change. It takes something that is real world (UnitedStates population) and uses it to talk about rate of change.

This is an Algebra I lesson plan used to help studentsinvestigate the meaning of slope as a rate of change.

This is a lesson that a teacher could use to teachtransformations of quadratic functions.

This website shows how you can use a Java applet toexplore graphically the effect of transforming a given graph with translations,vertical and horizontal

stretchings and reflections.

This website includes a game that your students canplay when learning about transformations of functions.

This website includes several programs that your studentscan play with to help them better understand the transformations of functions.

This is a website in which ajava applet draws graphs of functions that contain constants a and b fordifferent values of those constants. It illustrates how changing constantscauses vertical and horizontal shifts, and vertical stretches, a very helpfultool when teaching transformations.

LeastSquares Regression (Cheri Stotesbury)

This is a very basic site that includes links to thedefinition of linear regression.Itgives examples of each topic, and there is a quiz at the end.

This site links many different and interesting datasets, which is something every math teacher needs to have readily available.

The people who worked on this site assume the readerknows nothing.It goes step by stepand troubleshoots in each step.

This page gives a very detailed introduction to linearregression.There is an explanationof how linear regression works as minimizing the sum-of-squares and howthis relates to the slope and intercept.Thissite also includes a checklist to figure out if linear regression is theright analysis for the data at hand.Onthe left hand of the page is a list of links that deal with linear andnonlinear data.

This is an extremelyinvolved (12 day) lesson plan designed for an Algebra II class.Ituses election 2000 data in order to teach line fitting linear regressionthe correlation coefficient and probabilistic models.

The teacher of an integrated algebra class used theactivities at this site.The teacherwanted her students to use what they learned about their slope-intercept,point-slope, and point-point exam, so she spent a week working on statisticsproblems.

This applet allows you to place points in the firstquadrant, and it determines the equation of the regression line and graphsit.It also shows the residual asa variable and how it fits in graphically.

This is a detailed lesson plan that includes manylinked lessons and problems.Eventhough the links quit working at one point, there is still a great wealthof information here on Linear Regression and related topics.

This site focuses on complex models, which are modelswhere there is more than one independent variable.Thisis a higher level topic, I think, and it focuses on considering the dataand figuring out what is going on before doing any statistical modeling.

This page has some ideas for using the ti-83 for linearregression.The lesson plan is notone I would use, but the keystrokes are helpful, and it provides a startingpoint for a lesson in linear regression.

Similarityand Isoceles Triangles (Kate Mansi and Dail Nixon)

Similarity(Kate Mansi)

NCTMIlluminations

NCTM has compiled a listof Internet-based Websites for all grade levels.Thisparticular site features lesson plans for grades 9-12 in a variety of topicsranging from functions and variables to similarity and congruence.

ExploringSimilarity Using Scale Drawings

Students use scale drawingsto create three dimensional models.Surfaceareas and volumes of similar solids are calculated and compared.

Scalesare Not Just for Fish

In this lesson plan, studentsuse blueprints to determine dimensions of objects represented in the prints.Studentsthen create a blueprint of the classroom, drawing upon knowledge of similarityand scale factors.

ParallelLines in Triangles

This lesson plan requiresthe use of Geometers Sketchpad to discover the Similarity Theorems ofSide-Side-Side, Side-Angle-Side, and Angle-Angle.Studentsdraw upon knowledge of ratio and proportion and triangle congruence.

# GeometricConstructions: Similarity

This website is maintainedby the Oswego City School District.Ithas sample lesson plans for teaching similarity as well as interactiveactivities.Application and extensionproblems are provided.

# SimilarTriangles and Measuring Distance

This lesson plan showsreductions and enlargements (dilations) in terms of photographs and scalefactors.The example is given ofa picture taken from space.Studentsuse properties of dilations to determine the actual size of an object ifits picture is taken from space.

# GeometryJava Applets: Similar Triangles

This applet allows students to explore propertiesof a segment drawn inside a triangle parallel to the opposite side, thuscreating similar triangles.Studentswill notice how the triangles are similar by AA Similarity Postulate.

PtolemysPtools

This is a student-created site that contains activitieswhich explore properties of similar triangles in real-world settings.Interactivecomputer games are included.

VirtualManipulative: Similar Triangles

Interactive applet that allows students to createsimilar and congruent triangles by manipulating segments and angles.Theprogram allows students to check if their triangles are similar by liningup angles.

GeometryGallery

This is an index of java applets for a variety ofgeometry topics, including similarity, ratio and proportion, and congruenttriangles, as well as some more advanced geometry topics.

Isosceles Triangles (DailNixon)

1.www.geom.umn.edu/~dwiggins/conj13.html

# Isosceles Triangle Conjectures

Thepurpose of this website is to provide an introduction to isosceles triangles.Characteristicsof isosceles triangles are explained via definitions, diagrams, and conjectures.Thesite provides links to two Geometers Sketchpad demonstrations of the isoscelestriangle conjectures.
2.

Isoscelesand Equilateral Triangles

This website providesdefinitions for isosceles and equilateral triangles; gives some key pointsto remember when working with isosceles and equilateral triangles; andprovides example problems involving the two types of triangles.Thereis also a quiz available to test your knowledge of isosceles and equilateraltriangles.

3.

Constructions of Isosceles and EquilateralTriangles

This website providesa resource for teaching the geometry of Euclid in relation to isoscelesand equilateral triangles via guided constructions in Geometers Sketchpad.Thesite also offers activity extensions, as well as links to other resourcesfor teaching the ideas of Euclid.

4.

I.M.Peis East Building Solving Problems of Form and Function.

This site is anexcellent resource for teachers who want to answer the question, Whenam I ever going to use this isosceles triangle stuff?Thesite tells the story of an architect and one of his projects, whose unifyingelement is an isosceles triangle.Thisis an excellent real-world application of isosceles triangles.

5.

Isosceles Triangle

This website containsa step-by-step exploration of the area of an isosceles triangle, whichis great for introducing Geometry students to the concept.Thesite also provides an explanation of the relationship between the vertexangle of an isosceles triangle and its area, which is an excellent resourcefor students in Trigonometry or even Pre-Calculus.

6.

Nine Paper Models of Polyhedra Made ofIsosceles Triangles

This website isa wonderful resource for teachers of Geometry.Thesite provides reproducible models of polyhedra made mostly of isoscelestriangles.Teachers could use thepolyhedra to initiate classroom conversations as to what properties ofisosceles triangles make them so useful.

7.

Properties of Isosceles Triangles as DevelopedThrough Geometers Sketchpad

This website providesteachers with a wonderful hands-on activity relating to isosceles triangles.Studentsare actively engaged in discovering some properties of isosceles trianglesusing Geometers Sketchpad.Studentworksheets for the activity are provided on the website, as well.

8.

Isosceles Triangles

This site providesa hands-on, cooperative learning activity for Geometry students who arebeing introduced to isosceles triangles.Thesite encourages students to begin by studying definitions and a website,and to then use classroom materials to construct isosceles triangles.Thesite promotes the communication of math both verbally and in written form.

9.

Math Grade Ten Worksheets: Isosceles Triangles

This site providesteachers with free, reproducible worksheets that require students to applytheir knowledge about isosceles triangles.Theneat aspect of the site is that every time Create Worksheet Now is clicked,a new worksheet is created.Teacherscan get many ideas for problems involving isosceles triangles from thiswebsite.

10.

Dividing Triangles into Isosceles Triangles

This website containsan excellent example of a challenge activity for students who have beenstudying isosceles triangles.Studentsare to divide particular triangles into pairs of isosceles triangles basedon their knowledge of the properties of isosceles triangles.Copiesof student worksheets are provided on the site.

Geometric Transformationsand Tessellations (Holly Budzinski and Tilola Mitchell)

# Geometric Transformations (Holly Budzinski)

1.

This site hasa large table of contents with various topics from how transformationsare used in computer graphics to vector transformations.Both2-dimensial and 3-dimensial transformations are discusses.

2.

This site hasGSP files linked to the page. It has a nice discussion of symmetry as wellas basic geometric transformations.Alsohas links to tessellations and Escher drawings.

3.

This site haslinks to specific activities related to transformations, area, and volume.Thelessons are spelled out and seem to take on interesting problems.

4.

I like this sitebecause it shows all of the basic transformations but also includes shears.Thepage shows the derivation of each and goes into a demonstration of a matrixderivation.

5.

This site isa page off of Mr. Whiteleys homepage.Itis a nice summary of his grant that allows him to use dynamic softwareto teach geometric concepts.He alsohas links to many of the big-name sites such as Key Curriculum Press, MAA,and Math Forum.

6. www.ics.uci.edu/~eppstein/junkyard/

Thissite if really what it says a geometry junkyard.Ithas tons of great miscellaneous geometry stuff.Thereare lesson plans and great drawings.Itcovers virtually every geometry topic including tiling and symmetry.

1.  archives.math.utk.edu/visual.calculus/0/functions
Thissite looks at the connection with calculus and geometric transformations.Hasapplets and online quizzes.

Thissite shows simple pictures on a coordinate plane with a description ofeach transformation.Appears to bedone by a student which is nice for our students to see.
Thissite affords a good connection to the medical field.Itgets complicated quickly but still is nice to show application of whatwe teach.
Thisis a chapter from the BIPS users manual.Apparentlytransformations are quite common when conducting a medical screening. Thisis another useful application of geometric transformations that is usedin every day life.

Hieroglyphics,Transformations, and Tessellations (Tilola Mitchell)

Tessellation Tutorial are tutorialsand templates for making tessellations using ClarisWorks, the Geometer'sSketchpad, HyperCard, HyperStudio, and straightedge and compass, includingstep-by-step instructions for classroom activities.

Guardians Egypt is a web site that photographs provide a virtual tour of thisarchitectural wonder. Also find plans, diagrams and pictures of the hieroglyphicsfound inside.
http://www.guardians.net/egypt/gp1.htm

GreatScott-Hieroglyphs teaches the basics of the hieroglyphic language of ancientEgypt. Learn about pictographs, numerals, fractions, and scribes.

www.greatscott.com/hiero.htm

TotallyTessellated: Symmetry and Transformation is a website that is helpfulin the understanding of tessellations.Itis a simple introduction to tessellations.

http://library.thinkquest.org/16661/background/symmetry.1.html

Lesson: Geometry in Tessellations Abstract , This lesson allows students toexamine tessellations and their geometric properties. The activity anddiscussion may be used to develop students' understanding of lines, planes,angles, and polygons.

http://www.shodor.org/interactivate/lessons/tessgeom.html

GeometersSketchpad is a website that discusses the projects that can be done

usingGeometers Sketchpad .Also the sitegives samples of the projects.

http://www.keypress.com/sketchpad/projideas/projideas.html

TotallyTerrific Tessellations is an internet treasure hunt on tessellations.Itgives a brief introduction to tessellations , and quizzes you on your knowledge.

http://www.kn.pacbell.com/wired/fil/pages/hunttessellams.html

Hieroglyphs Introduces the language and decipherment of Hieroglyphs andoffers a learning section for kids. Find Egyptology links.
http://www.isidore-of-seville.com/hieroglyphs/index.html

EgyptFun Guide is a web site where you learn hieroglyphics or do the mummymaze. Find out about the Nile, the power of irrigation and the mysteryof the pyramids.
http://www.seaworld.org/Egypt/egypt.html

Egypt,Art, Architecture, and History-Hieroglyphics helps you gain an understandingof reading and using hieroglyphs; learn about its development, generalcharacteristics and form. It includes a translator, word processor, andfonts.
http://www.ragz-international.com/hieroglyphics.html

Egyptian Hieroglyphs is a site that helps you peruse a description ofthe major components of ancient Egyptian hieroglyphics, including ideogramsand phonograms.
http://www.torstar.com/rom/egypt/

Probability (Will Joyner)

1.ProbabilityCentral Main Page-Thiswebpage is great.It gives the studentan introduction to probability.Itincludes a probability calculator, and even a poker game to help demonstratethe probabilities of certain events happening.

2.Lessonson Probability From Math Goodies-Thispage contains several lessons on probability ranging from an introductionto conditional probability.It usesreal world applications to help explain each topic in probability.

3.Gamesof Chance-Thiswebsite has several java applets that demonstrate the probability of certainevents happening in certain games.Itis hard though to interpret these results.

4.IntroductionTo Probability Models-Thiswebsite shows the relationship between the possible outcomes of sums ofrolled dice and their frequency of occurrence.Whenrolling one dice, the each sum has an equal chance of occurring.Whensumming many dice rolled at once, we can see a bell curve starting to shape.Italso shows that it can take many events to see the relationship develop.

5.TheMathematics behind Magic The Gathering:Probability-Iwill not use this in class because most people do not play this card game.Thissite though does some calculations on drawing certain cards in an order.Ijust thought it was interesting looking at the probability a certain gamewill turn out.It also tells youthe probability of a certain color/style deck will win.

6.Introductionto Probability-Thiswebsite links to chapters of a probability book used in an introductoryprobability class in college.Iused this book to familiarize myself to probability (chapter 1).

7.Probabilityand chance-Thissite goes step by step in explaining different aspects of probability fromterminology to history to probability rules.Italso has some exercises at the end of the lesson to test your knowledge.

8.MnMActivity-Thisis a lesson plan to determine the probability of the different colors ofMnMs in a bag.I would use this asa sponge file resource for an Algebra I or lower level math class.Thestudents talk about probability without getting too involved, and it wouldbe something easy and fun to do on a day before a break or a day when theteacher is absent.

9.DiceProbabilities - The Wizard of Odds-Thiswebsite looks at the probabilities of rolling 2 dice to get a certain sum.Iused this type of activity on day two of my two-day lesson plan.

10.-Encarta Schoolhouse-Rock Paper Scissors-Thisis a lesson plan to help demonstrate the fairness of another game: Rock,Paper, Scissors.If you dont wantto have all the groups explore the dice experiments, you can use this oneas an alternative.

Conics and the Ellipse (Jackie Elliott and SherriGarrett)

1.TheMath Forum InternetMathematics Library: Conicscontains links to lessons, FAQs, and resources related to conic sections.Part of the Math Forum site hosted at Drexel University.

2.Conicsfrom Manipulative Math with Java (a Japanese Site) is a page of nine linksto interactive applets. These can be used to demonstrate some of the propertiesof conics and a few methods of constructing them.

3.ConicSectionsfrom ExplorMath,com has four interactive applets to explore vertical andhorizontal parabolas, hyperbolas and ellipses. Exploratory exercises areincluded. A nice feature is the copying of data or graphs to the clipboard.

4.MathematicEncyclopedia,Conic Sectionsis an excellent site for an overall review of definitions and propertiesof conics.It is one of the manymath resources from Platonic Realms.

5.Occurrenceof the Conicsis a great site for drawings and real-life uses of conics. Jill Britton,a mathematics instructor from Camosun College, maintains it.

6.PlaneConicsis one of Wilson Stothers'Geometry Pages. Itfeaturesan interactive applet on the focus-directrix definition of conics and additionalinformation including drawings, definitions and theorems.

7.JohannesKepler:The Laws of Plantary Motionprovides historical information about Kepler and his use of conic equationsto explain the orbit of the earth and other planets. It contains excellentdiagrams and explanations for ellipses.

8.PBSMathlinefeatures an interdisciplinary lesson on the ellipse, using the Blue Roomof the White House as a real world example of an ellipse. A student worksheetis provided, with answers.

9.TheConicSectionsas theLocus of PerpendicularBisectorsis an interactive use of java sketchpad from Key Curriculum Press. By manipulatingfocus and thus adjusting eccentricity, user can see different shaped conicsbeing formed. The directrix can also be shown and animated.

10.InstructionsUnit on ConicSectionsis provided from the University of Georgia as a supplementto a classroom textbook. It discusses the history, the geometric and algebraicdefinitions, and various types of equations used to represent conics. Thereis also a list of real-world applications at the bottom of this page.

11.ConicSectionsby Xa Lee, present a wealth of information on conics including history,formulas, and properties. Graphs and links to related web sites are alsoincluded.

ExuberantEllipse (Sherri Garrett)
1.http://www.ies.co.jp/math/java/conics/toy/toy.html

Hereis a java applet called the Ellipsograph!Studentsmay explore the locus definition of an ellipse with this dynamic activity.Studentsactually create an ellipse by moving sliders while making a connectionwith trigonometry.

2.http://www.geom.umn.edu/~fjw/calcIII/Lab15/area.html

Youcan take ellipses to an advanced level with this website.Here,calculus students can estimate the area bounded by domed stadiums usingellipses.This activity is greatfor showing the rationale for ellipses with the Metrodome.

3.http://www.geom.umn.edu/docs/reference/CRC-formulas/node29.html- SECTION01730000000000000000

WOW!Thissite introduced me to some really in-depth properties of ellipse.Ilearned about parametric representation of the ellipse, arc lengths, andarea of sectors.I would recommendthis site for a teacher to use as enrichment for advanced students.

4.http://chickscope.beckman.uiuc.edu/explore/eggmath/shape/pins.html

Chickscopeoffers an awesome, very practical teaching tip.Thispins and string technique really brings the locus definition of the ellipseto life for students, and it is easy to model in class with a few simpletools.

5.http://www.nas.com/~kunkel/ellipse/ellipse.htm

Weall know that making connections is key in teaching mathematics, and thissite will help you do just that.Thisresource shows how manipulating triangles creates an ellipse.ThisReuleaux Triangle application comes complete with GSP files and java appletsfor better understanding.This isa great opportunity for enrichment.

6.http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

Thislink offers lots of connections!Hereis the place to look for tips on tying the ellipse to astronomy, history,algebra II/ advanced math, and calculus.Thisis a great resource for demonstrating the importance of mathematics, specificallythe ellipse, in other realms.Thereis even a java applet that is great for that much needed hands-on activelearning.

7.http://go.hrw.com/ndNSAPI.nd/gohrw_rls1/pKeywordResults?MB1%20Ellipse

Ifyou want action and adventure, visit this locale.Youwill find an ellipse tracer, an internet assignment, a planetary orbitsimulator and an ellipse game.Studentscould learn a lot from these links while having fun.

8.http://online.redwoods.cc.ca.us/instruct/darnold/MultCalc/PolarConics/conics.htm

Mostof us did not learn the ellipses focus-directrix definition, but you canfind it here.The definition is accompaniedby great illustrations and a discussion of eccentricity.Thereis also an awesome Geometers Sketchpad script for constructing an ellipse,complete with calculations.

9.http://www.exploremath.com/activities/Activity_page.cfm?ActivityID=3

TheExploreMath activity offers students a look at the connection between theequation of an ellipse and its graph in a dynamic environment.Thissite would also be great for teachers to use for double-checking theirwork or for creating test items.

10.http://www.pbs.org/teachersource/mathline/concepts/president/activity3.shtm

ThisTeacherSource site sponsored by PBS provides practical, real life applicationsof the ellipse in our nations capitol.Itconnects the conic with architecture in a neat activity for students tostudy the Blue Room in the Capitol Building.Thissite even includes which standards are met!

Vectors (Cheryl Keeton)

1)Twenty-ninevector applets from the Manipula Math Applet collection.Goodfor quick explanation and demonstration of vector arithmetic and applications.

http://www.ies.co.jp/math/java/vector/index.html

2)Draggablecomponents of a vector on an interactive applet - Zona Land.

http://id.mind.net/~zona/mstm/physics/mechanics/vectors/componentAddition/componentAddition2.htm

3)AHigh School Physics Tutorial with explanation of momentum, forces, andprojectile motion.Complete withanimations.

http://www.glenbrook.k12.il.us/gbssci/phys/Class/vectors/vectoc.html

4)Mathforum:explanation of vectors and directions for Sketchpad exploration.

http://mathforum.org/~klotz/Vectors/vectors.intro.html

5)Exploratoriumsite shows how a baseball's trajectory is changed by the change in theangle and speed of the ball.Interactiveapplet allows the user to conduct experiments.

http://www.exploratorium.edu/baseball/scientificslugger.html

6)Gallery MathsOnlineThis site shows the differentcoordinsate planes and uses vectors to demonstrate ordered pairs.Doesnot emphasize vectors but would be a good connector between systems.

http://www.univie.ac.at/future.media/moe/galerie/zeich/zeich.html

7)Vector Componentsshows the relationship between right triangle trig and the way in whicha vector is described.Short animationin the right corner displays the horizontal and vertical components.

http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/Vectors/VectorComponents.html

8)Vectors definition and sections that show how to add and subtract.Notinteractive but the descriptions are colorful and concise.

http://home.nc.rr.com/enloephysics/enloephysics/VECTOR/Page_1x.html

9)TheNCTM Illuminations site E-Example.Absolutelythe best interactive website to explain vectors.Lotsof flexibility for student interaction and questioning.

http://illuminations.nctm.org/swr/review.asp?SWR=179

10)Vectorsin 3D beautiful colors and graphics.Inputfields allow for interaction and ability to change parameters and perspective.

http://home.a-city.de/walter.fendt/me/line3d.htm

PythagoreanTheorem (Kenneth Leary)
Allen,Don.(Feb. 6 1997).Pythagorasand the Pythagoreans.April 28,2002, from http://www.math.tamu.edu/~don.allen/history/pythag/pythag.html

This site tells about Pythagorass followers.Itdescribes his philosophies, his school, systems of primes, and the PythagoreanTheorem.

Bogomolny,Alexander.(n.d.).PythagoreanTheorem.January 22, 2002, fromhttp://www.cut-the-knot.com/pythagoras/index.html

This sitegives various ways to prove Pythagoreans Theorem.Itgives a multitude of ways for teachers to describe why a^2+b^2=c^2, tostudents who may not understand it one way.

Bogomolny,Alexander.(n.d.).PythagoreanTheorem.January 22, 2002, from http://www.cut-the-knot.com/pythagoras/pythTriple.html

This site gives direct insight as to how generatePythagorean Triples.It gives proofsto help you understand why a Pythagorean Triple, is a Pythagorean Triple.

Colarusso, Sherry.(n.d.).ThePythagorean Theorem.January21, 2002, from

http://www.arcytech.org/java/pythagoras/index.html

This sitegives you numerous of review tips to help you understand PythagoreansTheorem.It also gives many interestingtidbits and problems to further a persons interest in this concept.

Fairbanks,Arthur.(1898).Pythagorasand the Pythagoreans, Fragments and Commentary.April28, 2002, from http://history.hanover.edu/texts/presoc/pythagor.htm

This siteisnt really about Pythagorass methods.Thissite gives various philosophers analysis and commentary on his style andmethods.This is a good site to seewhat those people think of his work.

Iyer, Raghavan.(Nov.1977).PYTHAGORAS AND HIS SCHOOL.April28, 2002, from http://theosophy.org/tlodocs/PythagorasandHisSchool.htm

This siteis about the school Pythagoras opened up.Itgives valuable information as to the philosophies of Pythagoras and howand why he started the school.

Mathgym,Australia.(n.d.).PYTHAGORASofSAMOS:ACollection of Essays and Lessons for Junior and Senior High School.April28, 2002, from http://www.mathgym.com.au/history/pythagoras/pyth.htm

This site gives many explorations about essays andlessons.Students can use this siteto find out about Pythagoras and his methods.

Meyerson,Mark D. (Aug. 18, 1999).AnimatedProof of the Pythgorean Theorem.March25, 2002, from http://www.nadn.navy.mil/MathDept/mdm/pyth.html

This site gives a neat demonstration of the PythagoreanTheorem.It shows pieces translatingback and forth to show that the pieces equal the size of the square.

OConnor,J.J. and E.F.Robertso.(Jan. 1999).Pythagorasof Samos.April 28, 2002, from http://www-groups.dcs.stand.ac.uk/~history/Mathematicians/Pythagoras.html

This site gives a wealth of information about thePythagorean Theorem.It also givedetails of the man behind the Pythagorean Theorem and a lot of biographicalinformation.

Yoshioka-Maxwell,Seth.(n.d.).PythagorasTheorem.January 21, 2002, fromhttp://www.geocities.com/CapeCanaveral/Launchpad/3740/

This site shows a step-by-step of how the PythagoreanTheorem is developed.It gives adetailed explanation of how to construct the triangles and proves why a^2+b^2=c^2.

Guardians Egypt is a web site that photographs provide a virtual tour of thisarchitectural wonder. Also find plans, diagrams and pictures of the hieroglyphicsfound inside.

GreatScott-Hieroglyphs teaches the basics of the hieroglyphic language of ancientEgypt. Learn about pictographs, numerals, fractions, and scribes.

www.greatscott.com/hiero.htm

TotallyTessellated: Symmetry and Transformation is a website that is helpfulin the understanding of tessellations.Itis a simple introduction to tessellations.

Lesson: Geometry in Tessellations Abstract , This lesson allows students toexamine tessellations and their geometric properties. The activity anddiscussion may be used to develop students' understanding of lines, planes,angles, and polygons.

GeometersSketchpad is a website that discusses the projects that can be done

usingGeometers Sketchpad .Also the sitegives samples of the projects.

TotallyTerrific Tessellations is an internet treasure hunt on tessellations.Itgives a brief introduction to tessellations , and quizzes you on your knowledge.

Hieroglyphs Introduces the language and decipherment of Hieroglyphs andoffers a learning section for kids. Find Egyptology links.

EgyptFun Guide is a web site where you learn hieroglyphics or do the mummymaze. Find out about the Nile, the power of irrigation and the mysteryof the pyramids.

Egypt,Art, Architecture, and History-Hieroglyphics helps you gain an understandingof reading and using hieroglyphs; learn about its development, generalcharacteristics and form. It includes a translator, word processor, andfonts.

Egyptian Hieroglyphs is a site that helps you peruse a description ofthe major components of ancient Egyptian hieroglyphics, including ideogramsand phonograms.

Probability (Will Joyner)

1.ProbabilityCentral Main Page-Thiswebpage is great.It gives the studentan introduction to probability.Itincludes a probability calculator, and even a poker game to help demonstratethe probabilities of certain events happening.

2.Lessonson Probability From Math Goodies-Thispage contains several lessons on probability ranging from an introductionto conditional probability.It usesreal world applications to help explain each topic in probability.

3.Gamesof Chance-Thiswebsite has several java applets that demonstrate the probability of certainevents happening in certain games.Itis hard though to interpret these results.

4.IntroductionTo Probability Models-Thiswebsite shows the relationship between the possible outcomes of sums ofrolled dice and their frequency of occurrence.Whenrolling one dice, the each sum has an equal chance of occurring.Whensumming many dice rolled at once, we can see a bell curve starting to shape.Italso shows that it can take many events to see the relationship develop.

5.TheMathematics behind Magic The Gathering:Probability-Iwill not use this in class because most people do not play this card game.Thissite though does some calculations on drawing certain cards in an order.Ijust thought it was interesting looking at the probability a certain gamewill turn out.It also tells youthe probability of a certain color/style deck will win.

6.Introductionto Probability-Thiswebsite links to chapters of a probability book used in an introductoryprobability class in college.Iused this book to familiarize myself to probability (chapter 1).

7.Probabilityand chance-Thissite goes step by step in explaining different aspects of probability fromterminology to history to probability rules.Italso has some exercises at the end of the lesson to test your knowledge.

8.MnMActivity-Thisis a lesson plan to determine the probability of the different colors ofMnMs in a bag.I would use this asa sponge file resource for an Algebra I or lower level math class.Thestudents talk about probability without getting too involved, and it wouldbe something easy and fun to do on a day before a break or a day when theteacher is absent.

9.DiceProbabilities - The Wizard of Odds-Thiswebsite looks at the probabilities of rolling 2 dice to get a certain sum.Iused this type of activity on day two of my two-day lesson plan.

10.-Encarta Schoolhouse-Rock Paper Scissors-Thisis a lesson plan to help demonstrate the fairness of another game: Rock,Paper, Scissors.If you dont wantto have all the groups explore the dice experiments, you can use this oneas an alternative.

Conics and the Ellipse (Jackie Elliott and SherriGarrett)

1.TheMath Forum InternetMathematics Library: Conicscontains links to lessons, FAQs, and resources related to conic sections.Part of the Math Forum site hosted at Drexel University.

2.Conicsfrom Manipulative Math with Java (a Japanese Site) is a page of nine linksto interactive applets. These can be used to demonstrate some of the propertiesof conics and a few methods of constructing them.

3.ConicSectionsfrom ExplorMath,com has four interactive applets to explore vertical andhorizontal parabolas, hyperbolas and ellipses. Exploratory exercises areincluded. A nice feature is the copying of data or graphs to the clipboard.

4.MathematicEncyclopedia,Conic Sectionsis an excellent site for an overall review of definitions and propertiesof conics.It is one of the manymath resources from Platonic Realms.

5.Occurrenceof the Conicsis a great site for drawings and real-life uses of conics. Jill Britton,a mathematics instructor from Camosun College, maintains it.

6.PlaneConicsis one of Wilson Stothers'Geometry Pages. Itfeaturesan interactive applet on the focus-directrix definition of conics and additionalinformation including drawings, definitions and theorems.

7.JohannesKepler:The Laws of Plantary Motionprovides historical information about Kepler and his use of conic equationsto explain the orbit of the earth and other planets. It contains excellentdiagrams and explanations for ellipses.

8.PBSMathlinefeatures an interdisciplinary lesson on the ellipse, using the Blue Roomof the White House as a real world example of an ellipse. A student worksheetis provided, with answers.

9.TheConicSectionsas theLocus of PerpendicularBisectorsis an interactive use of java sketchpad from Key Curriculum Press. By manipulatingfocus and thus adjusting eccentricity, user can see different shaped conicsbeing formed. The directrix can also be shown and animated.

10.InstructionsUnit on ConicSectionsis provided from the University of Georgia as a supplementto a classroom textbook. It discusses the history, the geometric and algebraicdefinitions, and various types of equations used to represent conics. Thereis also a list of real-world applications at the bottom of this page.

11.ConicSectionsby Xa Lee, present a wealth of information on conics including history,formulas, and properties. Graphs and links to related web sites are alsoincluded.

ExuberantEllipse (Sherri Garrett)
1.

Hereis a java applet called the Ellipsograph!Studentsmay explore the locus definition of an ellipse with this dynamic activity.Studentsactually create an ellipse by moving sliders while making a connectionwith trigonometry.

2.

Youcan take ellipses to an advanced level with this website.Here,calculus students can estimate the area bounded by domed stadiums usingellipses.This activity is greatfor showing the rationale for ellipses with the Metrodome.

3.- SECTION01730000000000000000

WOW!Thissite introduced me to some really in-depth properties of ellipse.Ilearned about parametric representation of the ellipse, arc lengths, andarea of sectors.I would recommendthis site for a teacher to use as enrichment for advanced students.

4.

Chickscopeoffers an awesome, very practical teaching tip.Thispins and string technique really brings the locus definition of the ellipseto life for students, and it is easy to model in class with a few simpletools.

5.m

Weall know that making connections is key in teaching mathematics, and thissite will help you do just that.Thisresource shows how manipulating triangles creates an ellipse.ThisReuleaux Triangle application comes complete with GSP files and java appletsfor better understanding.This isa great opportunity for enrichment.

6.

Thislink offers lots of connections!Hereis the place to look for tips on tying the ellipse to astronomy, history,algebra II/ advanced math, and calculus.Thisis a great resource for demonstrating the importance of mathematics, specificallythe ellipse, in other realms.Thereis even a java applet that is great for that much needed hands-on activelearning.

7.

Ifyou want action and adventure, visit this locale.Youwill find an ellipse tracer, an internet assignment, a planetary orbitsimulator and an ellipse game.Studentscould learn a lot from these links while having fun.

8.

Mostof us did not learn the ellipses focus-directrix definition, but you canfind it here.The definition is accompaniedby great illustrations and a discussion of eccentricity.Thereis also an awesome Geometers Sketchpad script for constructing an ellipse,complete with calculations.

9.

TheExploreMath activity offers students a look at the connection between theequation of an ellipse and its graph in a dynamic environment.Thissite would also be great for teachers to use for double-checking theirwork or for creating test items.

10.

ThisTeacherSource site sponsored by PBS provides practical, real life applicationsof the ellipse in our nations capitol.Itconnects the conic with architecture in a neat activity for students tostudy the Blue Room in the Capitol Building.Thissite even includes which standards are met!

Vectors (Cheryl Keeton)

1)Twenty-ninevector applets from the Manipula Math Applet collection.Goodfor quick explanation and demonstration of vector arithmetic and applications.

2)Draggablecomponents of a vector on an interactive applet - Zona Land.

3)AHigh School Physics Tutorial with explanation of momentum, forces, andprojectile motion.Complete withanimations.

4)Mathforum:explanation of vectors and directions for Sketchpad exploration.

5)Exploratoriumsite shows how a baseball's trajectory is changed by the change in theangle and speed of the ball.Interactiveapplet allows the user to conduct experiments.

6)Gallery MathsOnlineThis site shows the differentcoordinsate planes and uses vectors to demonstrate ordered pairs.Doesnot emphasize vectors but would be a good connector between systems.

7)Vector Componentsshows the relationship between right triangle trig and the way in whicha vector is described.Short animationin the right corner displays the horizontal and vertical components.

8)Vectors definition and sections that show how to add and subtract.Notinteractive but the descriptions are colorful and concise.

9)TheNCTM Illuminations site E-Example.Absolutelythe best interactive website to explain vectors.Lotsof flexibility for student interaction and questioning.

10)Vectorsin 3D beautiful colors and graphics.Inputfields allow for interaction and ability to change parameters and perspective.

PythagoreanTheorem (Kenneth Leary)
Allen,Don.(Feb. 6 1997).Pythagorasand the Pythagoreans.April 28,2002, from

This site tells about Pythagorass followers.Itdescribes his philosophies, his school, systems of primes, and the PythagoreanTheorem.

Bogomolny,Alexander.(n.d.).PythagoreanTheorem.January 22, 2002, from

This sitegives various ways to prove Pythagoreans Theorem.Itgives a multitude of ways for teachers to describe why a^2+b^2=c^2, tostudents who may not understand it one way.

Bogomolny,Alexander.(n.d.).PythagoreanTheorem.January 22, 2002, from

This site gives direct insight as to how generatePythagorean Triples.It gives proofsto help you understand why a Pythagorean Triple, is a Pythagorean Triple.

Colarusso, Sherry.(n.d.).ThePythagorean Theorem.January21, 2002, from

This sitegives you numerous of review tips to help you understand PythagoreansTheorem.It also gives many interestingtidbits and problems to further a persons interest in this concept.

Fairbanks,Arthur.(1898).Pythagorasand the Pythagoreans, Fragments and Commentary.April28, 2002, from

This siteisnt really about Pythagorass methods.Thissite gives various philosophers analysis and commentary on his style andmethods.This is a good site to seewhat those people think of his work.

Iyer, Raghavan.(Nov.1977).PYTHAGORAS AND HIS SCHOOL.April28, 2002, from

This siteis about the school Pythagoras opened up.Itgives valuable information as to the philosophies of Pythagoras and howand why he started the school.

Mathgym,Australia.(n.d.).PYTHAGORASofSAMOS:ACollection of Essays and Lessons for Junior and Senior High School.April28, 2002, from

This site gives many explorations about essays andlessons.Students can use this siteto find out about Pythagoras and his methods.

Meyerson,Mark D. (Aug. 18, 1999).AnimatedProof of the Pythgorean Theorem.March25, 2002, from

This site gives a neat demonstration of the PythagoreanTheorem.It shows pieces translatingback and forth to show that the pieces equal the size of the square.

OConnor,J.J. and E.F.Robertso.(Jan. 1999).Pythagorasof Samos.April 28, 2002, from

This site gives a wealth of information about thePythagorean Theorem.It also givedetails of the man behind the Pythagorean Theorem and a lot of biographicalinformation.

Yoshioka-Maxwell,Seth.(n.d.).PythagorasTheorem.January 21, 2002, from

This site shows a step-by-step of how the PythagoreanTheorem is developed.It gives adetailed explanation of how to construct the triangles and proves why a^2+b^2=c^2.